Postulati della Relatività speciale (1905)
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“Se non riesci a spiegare una teoria di fisica con parole semplici vuol dire che non l’hai capita” |
C = velocità della luce. Dal latino: velocità = “Celeritas – celeritatis” (terza declinazione)
Gli scienziati che hanno cambiato la scienza e la storia del XX secolo.
Solvay conference, 1924. Fourth Solvay Conference, Bruxelles , 1924, the theme was the electrical conductivity of metals.
Albert Einstein (1879-1955), partiva da due postulati:
- Primo postulato (principio di relatività): tutte le leggi fisiche sono le stesse in tutti i sistemi di riferimento inerziali;
- Secondo postulato (invarianza della velocità della luce): la velocità della luce nel vuoto ha lo stesso valore in tutti i sistemi di riferimento inerziali, indipendentemente dalla velocità dell’osservatore o dalla velocità della sorgente di luce.
Il primo postulato è un’estensione di quello di Galilei. Il secondo postulato generalizza l’osservazione che tutte le oscillazioni meccaniche (onde acustiche, onde sull’acqua, onde su una corda) si propagano con una velocità che dipende solamente dalle caratteristiche del mezzo che le supporta e non dalla velocità con cui la sorgente dell’eccitazione si muove rispetto a tale mezzo. Questo non avviene per la luce in quanto lo spazio, rimosso l’etere inutile, è omogeneo e isotropo. Quindi non c’è bisogno di misurare la velocità della luce rispetto all’etere e non esiste un sistema assoluto.
A) Nulla può viaggiare a velocità superiori a quella della luce.
Due raggi di luce, emessi nello stesso istante di tempo dal Sole e dall’astronave Enterprise che si muove nello spazio a una certa velocità viaggiano alla velocità della luce (C=300.000 km/s). La velocità dell’astronave Entreprise e quella del fascio di luce non si sommano |
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Le velocità sono relative al sistema di riferimento in cui ci si trova. 1) Nell’immagine superiore Einstein è fermo e colpisce la palla da baseball che acquista una data velocità. 2) Sotto invece Einstein si muove su uno skateboard e colpisce la palla da baseball che acquista una velocità data dalla somma della velocità della mazza da baseball e dello skateboard. Le velocità si sommano. |
C = velocità della luce. Dal latino: velocità = “Celeritas – celeritatis” (terza declinazione)
Limite galileiano
Per velocità Vo molto piccole rispetto a quella della luce, le trasformazioni di Lorentz si riconducono a quelle di Galileo: le quali si ricavano facendo il limite delle trasformazioni di Lorentz per
c → ∞ , Vo / c→0.
Quindi per velocità piccole non si osservano più fenomeni come la perdita della contemporaneità, la dilatazione dei tempi e la contrazione delle lunghezze, il che spiega perché nella vita quotidiana noi non osserviamo nessuno di questi fenomeni.
Le velocità si sommano, viste dal sistema di riferimento fisso.
Hendrik Antoon Lorentz, Nobel per la fisica 1902
Hendrik Antoon Lorentz 1853-1928 – fisico olandese
Trasformazioni di Lorentz
x’ = (x – v t)/ √(1─ v^2/c^2)
y’ = y
z’ = z
t’ = [(t – ( v x /c^2)] / √(1─ v^2/c^2) .
le inverse diventano:
x = (x’ + v t’)/ √(1─ v 2/c2)
y = y’
z = z’
t = [(t’ + ( v x’ /c^2)] / √(1─ v2/c2) .
Conseguenze dei principi della relatività
Contrazione delle lunghezze di oggetti se visti in movimento da un sistema ritenuto fisso:
ΔL = ΔLo ·√(1─v2/c2) ;
DLo è la lunghezza propria misurata nello stesso tempo dall’osservatore solidale al sistema in cui si trova
Dilatazione dei tempi:
Δt =Δto/ √(1─v2/c2) ;
Δto è il tempo proprio nel sistema dove gli eventi avvengono nello stesso posto.
Esempio di applicazione:
Un razzo viaggia alla velocità di 0,6 c e passa accanto a una stazione spaziale nella quale un dispositivo elettronico rileva il suo passaggio. Appena la coda del razzo passa di fianco al dispositivo, questo emette un lampo di luce. La lunghezza del razzo, nel sistema di riferimento a esso solidale è Lo = 150 m.
– Dopo quanto tempo la luce raggiunge la prua del razzo, secondo un osservatore posto sul razzo?
– Dopo quanto tempo la luce raggiunge la prua del razzo, secondo un osservatore posto sulla stazione?
– A che distanza dalla stazione il raggio luminoso raggiunge la prua del razzo, nel sistema di riferimento della stazione?
Lunghezza propria misurata da chi è solidale al razzo:
Lo = 150 m;
velocità della luce c = 3 * 10^8 m/s.
- Delta to = 150 / c = 150 / (3 * 10^8) = 5 * 10^-7 s;
Per l’osservatore sulla stazione il razzo risulta contratto:
L = Lo * radice(1 – v^2/c^2)
L = 150 * radice[1 – (0,6c)^2/c^2 ] = 150 * radice(1 – 0,36);
L = 150 * radice(0,64) = 150 * 0,8 = 120 m;
radice(1 – v^2/c^2) = 1/gamma = 0,8.
trasformazioni di Lorentz:
t = (t’ + v * x’/c^2) / radice(1 – v^2/c^2)
Tempo misurato dalla stazione:
Delta t = [Delta to + v * Delta x’/c^2] / radice(1 – v^2/c^2);
Delta t = [5 * 10^-7 + 0,6 * c * 150 /c^2] / 0,8;
Delta t = [5 * 10^-7 + 0,6 * 150 / 3 * 10^8] / 0,8;
- Delta t = 8 * 10^-7 / 0,8 = 1 * 10^-6 s, (1 microsecondo).
Distanza dalla stazione della coda del razzo dopo t = 1 * 10^-6 s:
x = 0,6 * 3 * 10^8 * 1 * 10^-6 = 180 m;
La prua si trova a distanza x1 dalla stazione:
- x1 = x + L = 180 + 120 = 300 m = 3 * 10^2 m.
Composizione delle velocità :
In un sistema isolato la quantità di moto totale si conserva, ma in un sistema di riferimento in moto, sembra non conservarsi. La legge di composizione relativistica delle velocità non è quella galileiana:
u’ = u – vo
u = u’ + vo
( vo = velocità del sistema di riferimento in moto,
u = velocità vista dal sistema fisso,
u’ = velocità vista dal sistema in moto).
Relativisticamente la legge di composizione è:
u = (u’+ vo) /(1 + u’ * vo/c2) ;
la formula inversa è :
u’ = (u – vo) /(1 – u * vo/c2)
con questa formula la velocità della luce non si somma con altre velocità e non viene mai superata. Esempio: se u’ = c e vo = c, allora u vista dal sistema fisso, rimane c.
u = (c + c)/ (1+c2/c2) = 2c/2 = c
Esempio:
Tre fasci di particelle viaggiano uno dietro l’altro all’interno di un acceleratore di particelle. Il primo fascio ha velocità v1 = c/2 rispetto al secondo fascio, il quale ha velocità v2 = c/2 rispetto al terzo fascio; il terzo fascio ha velocità v3 = c/2 rispetto al sistema fisso del laboratorio.
Calcolare la velocità del primo fascio di particelle rispetto al laboratorio.
Secondo la composizione classica:
v = v’ + vo.
Il terzo fascio ha velocità v3 = c/2 rispetto al sistema fisso, quindi è la velocità vo;
il secondo fascio avrebbe velocità: v2 = c/2 + c/2 = c (impossibile).
il primo fascio avrebbe velocità: v1 = c/2 + c = 3/2 c (impossibile).
Bisogna fare la composizione relativistica di Einstein:
v = (v’ + vo) / (1 + v’ vo/c^2);
Per il secondo fascio:
v2 = (c/2 + c/2) / ( 1 + c^2/4 / c^2) = c / (1 + 1/4);
v2 = c / (5/4) = 4/5 * c; (velocità rispetto al laboratorio).
Per il primo fascio:
v1 = (v3 + v2) / (1 + v3 * v2) /c^2 );
v1 = (c/2 + (4/5 c) / ( 1 + c/2 * 4/5 c/c^2);
v1 = (13/10 * c) / (1 + 4/10 ) = 13/10 * c / 14/10;
v1 = 13/10 * 10/14 * c = 13 /14 * c; (velocità del primo fascio rispetto al laboratorio).
Le velocità sono sempre inferiori a c.
v1= 13/14 *c;
v2 = 4/5 * c;
v3 = 1/2 * c.
Orologio a luce
Due osservatori, uno nella stazione S e l’altro su un treno superveloce S’ che si muove a velocità v rispetto alle rotaie, vogliono misurare la durata di un fenomeno fisico (cioè la separazione temporale tra due eventi), naturalmente ognuno dal suo sistema di riferimento.
Essi utilizzano un orologio a luce, formato da due specchi piani posti parallelamente ad una distanza nota d; un raggio luminoso che si muove lungo l’asse degli specchi si riflette alternativamente su di essi ed il tempo occorrente per l’andata ed il ritorno della luce sullo stesso specchio costituisce il periodo dell’orologio.
Il periodo dell’orologio (misurato da un osservatore in quiete rispetto all’orologio) è
T0 = 2 d / c
L’intervallo di tempo T0 rappresenta la separazione temporale tra due eventi: l’evento partenza e l’evento arrivo del raggio luminoso sullo specchio inferiore.
Per un osservatore in quiete, i due eventi hanno separazione spaziale nulla.
La separazione temporale di due eventi con separazione spaziale nulla si dice tempo proprio.
Poiché sia nel riferimento S, sia nel riferimento S’ ci sono due orologi a luce identici, i due osservatori misurano lo stesso intervallo di tempo ognuno nel proprio riferimento.
Ma cosa avviene se l’osservatore nella stazione S prova a fare una misura di tempo mediante l’orologio a luce che si trova nel treno S’?
Per l’osservatore in S, l’orologio si muove con velocità v lungo le rotaie, quindi la luce percorre, tra andata e ritorno, una linea a zig-zag di lunghezza 2L maggiore di 2d. Poiché la luce ha sempre velocità c in qualsiasi riferimento inerziale, il periodo T’ dell’orologio in moto è allora (per S):
Il periodo T dell’orologio in moto è maggiore del tempo proprio T0: l’orologio in moto batte quindi un tempo più lento rispetto a quello in quiete. Si noti che ciò non è affatto vero per il passeggero sul treno che anzi può, per la stessa ragione, affermare che è l’orologio nella stazione a essere più lento!
In questa affermazione che può sembrare paradossale c’è tutto il significato del principio di relatività: le leggi della fisica sono eguali per tutti i riferimenti inerziali, nel senso che ognuno dei due osservatori afferma che l’orologio in moto rallenta.
BH^2 = AB^2 – AH^2
(C Δto)^2 = (C Δt)^2 – ( v Δt)^2
C^2 (Δto)^2 = C^2 (Δt)^2 – v^2 (Δt)^2
C^2 (Δto)^2 = C^2 (Δt)^2( 1 – v^2 /C^2)
(Δto)^2 = (Δt)^2 ( 1 – v^2 /C^2)
(Δt) = (Δto) / ( 1 – v^2 /C^2)
Δto è il tempo proprio all’interno del sistema con separazione spaziale nulla, dove gli eventi avvengono nello stesso luogo, mentre sono in moto rispetto ad un altro sistema ritenuto fisso e quindi avvengono in luoghi diversi. In questo sistema il tempo è Δt e risulta dilatato rispetto al tempo proprio Δto.
(Δt) > (Δto)
Le conseguenze fisiche di queste trasformazioni sono enormi e rivoluzionarie. Notiamo che spazio e tempo appaiono in un qualche modo “mescolati”
Contrazione delle lunghezze:
DL = DLo ·√(1─v2/c2)
ΔL è la distanza vista in movimento (contratta);
Dilatazione dei tempi:
Δt =Δto/ √(1─v2/c2) ;
Δto è il tempo proprio nel sistema dove gli eventi avvengono nello stesso posto.
Se la velocità v del sistema di riferimento è molto elevata il tempo si dilata (rallenta) e le distanze si contraggono per un osservatore esterno, fisso rispetto al sistema in moto con velocità v.
la velocità V è la stessa.
L = Lo * √(1 – v^2/c^2) ;
Lo/2 = Lo * √(1- v^2/c^2) ;
√(1- v^2/c^2) = 1/2
1 – v^2/c^2 = 1/4 ;
v^2/c^2 = 1 – 1/4
v^2/c^2 = 3/4
v^2 = 3/4* c^2;
v = radicequadrata(3/4 c^2) = 0,866 * c.
Il paradosso dei gemelli
L’esperimento ideale è questo. Ci sono due gemelli, A rimane “fermo” sulla Terra. L’altro, B, sale su una navicella che viaggia con una velocità prossima a quella della luce. Dopo un po’ di tempo B inverte la rotta e torna dal gemello A sulla Terra. La teoria di Einstein prevede che A sia più vecchio di B.
Questo è quello che la gente comune pensa sia il “paradosso dei gemelli”. Ma il paradosso non è questo. Il paradosso segue dal fatto che uno dei postulati della relatività ristretta di Einstein (così come nella relatività Galileiana) afferma che tutti i sistemi di riferimento sono equivalenti. Dunque il ragionamento fatto da A (B si muove poi ritorna) potrebbe essere fatto da B (A si muove e poi ritorna). In questo caso B sarebbe più vecchio di A: ecco il paradosso!
La soluzione del paradosso consiste nell’osservare che A e B non sono equivalenti perché B quando parte, quando inverte il moto e quando ritorna sulla Terra compie dei moti accelerati che A non compie. I conti provano che, per questo, B sarà più giovane di A e non viceversa.
Spiegazione intuitiva del rallentamento del tempo:
se sei di fronte a un orologio e questo si allontana da te, un raggio di luce proveniente dall’orologio arriverà a te più tardi.
Quindi se l’orologio si allontana con velocità prossime a quelle della luce, vedi l’orologio scorrere molto lentamente, e se si allontana esattamente alla velocità della luce vedi l’orologio fermo, perchè nessun raggio ti raggiungerà mai.
Esempio 1 : a quale velocità V devi viaggiare per raggiungere una stella che dista 50 anni luce dalla Terra, se quando la raggiungi sei più vecchio di 40 anni?
La distanza S è 50C; Dt è l’intervallo di tempo che scorre nel sistema fisso. Dto è l’intervallo di tempo proprio che scorre all’interno dell’astronave che viaggia verso la stella, pari a 40 anni.
Nel sistema fisso della Terra Dt = S /V = 50C / V
Dt = Dto / √(1─V2/C2) ; allora
50C / V = 40 / √(1─V2/C2) ;
50C = 40V /√(1─V2/C2) ;
(50C/40)2 = V2 / √(1─V2/C2) ;
25/16 C2(1─V2/C2) = V2
25/16 C2 – 25/16 V2 = V2
25C2 = 16 V2 + 25 V2
25 C2 = 41 V2
V = C√(25/41) = √(0,609) C = 0,78C
Esempio 2:
Una nave spaziale entra nel sistema solare muovendosi verso il sole a velocitàcostante rispetto ad esso. Secondo il suo orologio di bordo, il tempo trascorso tra l’istante in cui attraversa l’orbita di Giove e l’istante in cui attraversa quella di Marte è di 45 minuti. A quale velocità viaggia l’astronave verso il sole? Il raggio dell’orbita di Giove è 778 x 10^9 m e quello dell’orbita di Marte è 228 x 10^9 m.
S =(778 – 228) x 10^9 m = 550 x 10^9 m; Dto = 45 x 60 = 2700 s (tempo proprio)
Dt = Dto / √(1─V2/C2) : allora Dt = S / V ;
550 x 10^9 / V = 2700 / √(1─V2/C2)
550 x 10^9 x √(1─V2/C2) = 2700 x V
3,025 x 10^18 x ( 1 – V2/C2) = (2700 x V )^2
3,025 x 10^23 x C2 – 3,025 x 10^23 xV2 = 7,29 x 10^6 x C2V2
3,025 x 10^23 xV2 + 7,29 x 10^6 x C2V2 = 3,025 x 10^23 x C2
V2 = 3,025 x 10^23 x C2 /9,586 x 10^23 = 0,3155 C2
V = 0,56 C
Esercizio 3 : Un astronauta si propone di raggiungere una stella distante 5 anni-luce.
Calcolare:
– la velocità della navicella spaziale rispetto alla Terra in modo che la durata del viaggio, misurata dall’orologio dell’astronauta, sia di un anno;
-la durata del viaggio secondo un osservatore terrestre.
t = to / radquad(1 -V^2/C^2)
to = 1 anno; t = Spazio / Velocità(astronauta) ; Spazio = 5(anni luce) x C
t = 5C/ V
5C/V = 1 / radquad(1 -V^2/C^2)
V / 5C = radquad(1 – V^2/C^2)
V^2 / 25C^2 = 1 – V^2/C^2
V^2 /25C^2 + V^2/C^2 =1
V^2 + 25 V^2 = 25 C^2
V^2 (1 + 25) = 25 C^2
V^2 = 25 C^2/ (1 + 25)
V = 5 C / (radquad( 1 + 25) = 5C/5,099 = 0,98 C
t = S / V = 5 x C / 0,98 C = 5,102 anni.
Effetto Doppler Relativistico
z = redshift; la frequenza dell’onda elettromagnetica (f emessa) diminuisce se la sorgente si allontana con velocità v. L’osservatore percepisce una frequenza minore.
f’ = frequenza percepita; f = frequenza emessa dalla sorgente.
f percepita < f emessa; f percepita risulta spostata verso il rosso.
z = f / f’ – 1; (redshift);
z = [f emessa / f percepita] – 1;
se [f emessa / f percepita] = 1; allora z = 0; sorgente ferma.
[f emessa / f percepita] = z + 1;
(f percepita) = (f emessa) * radicequadrata[(1 – β) / (1 + β)];
β = v / c;
(f emessa) / (f percepita) = radicequadrata[(1 + β) / (1 – β)];
z + 1 = radicequadrata[(1 + β) / (1 – β)];
Esempio:
Tre oggetti celesti hanno redshift z pari a 1, 2 e 3 .
– Calcolare la velocità di allontanamento degli oggetti in funzione della velocità della luce.
1) z = 1; z + 1 = 2;
2^2 = (1 + β) / (1 – β);
4 * (1 – β) = (1 + β);
4 – 4β = 1 + β;
3 = 5 β;
β = 3/5;
v/c = 3/5;
v = 3c/5;
2)
z = 2; 2 +1 = 3;
3^2 = (1 + β) / (1 – β);
9 * (1 – β) = (1 + β);
9 – 9β = 1 + β;
8 = 10β;
β = 8/10;
v/c = 8/10 = 4/5;
v = 4c/5;
3) z = 3; z +1 = 4;
4^2 = (1 + β) / (1 – β);
16 * (1 – β) = (1 + β);
16 – 16β = 1 + β;
β = 15/17;
v/c = 15/17;
v = 15c/17.
Spazio di Minkowski : cono luce
X2 = C2t2 (intervallo luce)
Nello spazio-tempo galileiano, la distanza fra due oggetti nello spazio e fra due eventi nel tempo è una quantità assoluta, che non dipende dal sistema di riferimento inerziale in cui è posto l’osservatore. Nella relatività ristretta, entrambe queste quantità diventano invece relative. I cambiamenti di coordinate fra sistemi di riferimento sono infatti più complicati, descritti dalle trasformazioni di Lorentz. Vi è comunque una “distanza” che non dipende dal riferimento (cioè che non viene modificata da una trasformazione di Lorentz).
L’intervallo spazio-temporale d2 = X2 – C2t2
assume il medesimo valore qualunque sia il sistema di riferimento nel quale esso viene calcolato: è un invariante relativistico spazio-temporale.
(DX’)2 – C2(Dt’)2 = (DX)2 – C2(Dt)2
Il punto rosso nell’origine O sul piano è il presente.Tutto ciò che è fuori dal cono è il presente di O e non può essere influenzato da O, nè può influenzare O
Il doppio cono rappresenta il passato e il futuro del nostro presente.
x = ct ; x = – ct, sono le rette che separano il cono dal resto dello spazio di Minkowski.
(Ponendo c = 1, x = t , x = -t, sono le bisettrici del piano).
Per cono ci luce intendiamo il possibile passato e futuro di un dato evento. Per rappresentarlo su un foglio bidimensionale dobbiamo immaginare che lo spazio sia l’asse delle ascisse (una sola dimensione invece di tre) e che il tempo sia l’asse delle ordinate che può scorrere solo in un senso, verso l’alto, ossia verso il futuro. Il cono di luce è l’insieme di tutte le possibili posizioni che un certo evento (o se preferite, un certo oggetto) potrà assumere nel suo futuro e che avrebbe potuto assumere nel suo passato. Il vertice del cono rappresenta l’evento al tempo presente e nella posizione attuale. Ovviamente la sezione del cono con il piano del foglio dà luogo a due rette che si incrociano nel vertice e che si protendono verso l’infinito futuro e quello passato (attenzione: questo è uno dei punti limitativi del suddetto cono, la non quantificazione grafica dell’infinito).
I bordi del cono (ossia le due rette della figura) sono inclinate di 45° e rappresentano il limite invalicabile per un corpo in movimento, ossia le traiettorie descritte dalla luce. In altre parole, qualsiasi posizione futura (o passata) di un oggetto o di un evento non potrà andare al di là di tali linee, perché per poterlo fare dovrebbe superare la velocità della luce. Tutto ciò è rappresentato in Fig. 1.
Lo spazio euclideo tridimensionale è lo spazio della nostra esperienza quotidiana. Il suo nome deriva da Euclide che, attorno al 300 a.C., per primo ne studiò a fondo proprietà e caratteristiche e le tramandò
ai posteri in un trattato che costituisce il primo esempio conosciuto di teoria matematica impostata su basi logico-assiomatico-deduttive.
Nello spazio tridimensionale si possono “disegnare” figure a due dimensioni, ad una dimensione e a zero dimensioni.
Le figure a zero dimensioni sono i punti, quelle ad una dimensione sono le linee e quelle a due dimensioni
sono le superficie.
Le figure dello spazio euclideo soddisfano numerose proprietà che caratterizzano lo spazio stesso. Ne riportiamo
solo alcune di particolare importanza :
– 1 – da un punto esterno ad una retta data passa una ed una sola retta parallela ad essa
– 2 – per i triangoli rettangoli vale il teorema di Pitagora, ovvero il quadrato costruito sull’ipotenusa eguaglia
la somma dei quadrati costruiti sui cateti
– 3 – la somma degli angoli interni di un triangolo eguaglia un angolo piatto (180°)
Nello spazio euclideo tridimensionale possiamo costruire un sistema di riferimento cartesiano ortogonale nel modo abituale ed assegnare così ad ogni punto P dello spazio una terna ordinata di numeri, le sue coordinate
(x , y, z) :
Esempio 2: Un mesone si forma a dieci chilometri di quota in atmosfera. Viaggiando a velocità v = 0,99C arriva a terra e viene registrato.
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Quanto è lunga la traiettoria nel sistema di riferimento in cui il mesone è fermo, se questa traiettoria lunga 10 km rispetto alla Terra ( sistema solidale con la traiettoria), viene “vista” in movimento dal mesone?
( DLo è la lunghezza propria misurata in quiete rispetto al sistema terrestre = 10 000 m)
DL = DLo ·√(1─v2/c2)
DL = 10·√(1─(0,99 c)2/c2) allora
DL = 10 * 0,141 = 1,41 km ( 7 volte più corta) Il mesone “vede” la traiettoria lunga solo 1,41 km
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Quanto vale il tempo di vita del mesone che arriva a terra? Dt = S / V = 10000 / 0,99 C = 3,367 ·10^-5 s ( visto dal sistema terrestre, tempo dilatato).
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Quanto vale il tempo proprio Dt’ del mesone nel suo sistema di riferimento?( la sua traiettoria qui è lunga 1,41 km, quindi Dt’ = S / V = 1410/0,99C= 0,4747 ·10^-5 s )
Dt = Dt’ / √(1─V2/C2) ; allora verifichiamo: Dt = 4,747 ·10^-6 / √(1─(0,99 C)2/C2) =
= 4,747 ·10^-6/ √(1─0,98) = 3,367 ·10^-5 s (visto in moto, dalla terra, vive 7 volte di più).
Composizione delle velocità In un sistema isolato la quantità di moto totale si conserva, ma in un sistema di riferimento in moto, sembra non conservarsi. La legge di composizione relativistica delle velocità non è quella galileiana
u’ = u – Vo
u = u’ + Vo
( Vo = velocità del sistema di riferimento in moto,
u = velocità vista dal sistema fisso,
u’ = velocità vista dal sistema in moto).
Relativisticamente la legge di composizione è:
u = (u’+ Vo) /(1 + u’Vo/c2)
u’ = (u – Vo) /(1 – uVo/c2)
con questa formula la velocità della luce non si somma con altre velocità e non viene mai superata. Esempio: se u’ = c e Vo = c, allora u vista dal sistema fisso, rimane c.
u = (c + c)/ (1+c2/c2) = 2c/2 = c
Affinchè si conservi la quantità di moto P e non si superi mai la velocità c, occorre cambiare la concezione di massa costante in qualsiasi sistema, e introdurre il concetto che la massa dipende dal suo stato di moto, non è una costante, ma dipende dal sistema in cui viene eseguita la misura. Così la massa diventa:
m = mo / √(1- v2/c2)
questa espressione si può sviluppare in serie di potenze se v2/c2 <1, e si può esprimere così:
m = mo · (1 + 1/2 v2/c2). Moltiplicando per c2 otteniamo
mc2 = moc2 + 1/2 mov2.
E tot = mc2 energia totale di un corpo di massa mo (a riposo).
E tot = E (riposo) + E (cinetica).
La massa di un corpo in moto è maggiore della sua massa a riposo perchè aumenta l’energia cinetica e l’energia “pesa”. L’energia cinetica relativistica si calcola così:
E cin = mc2 ─ moc2 .
Ecin = mo x C^2 / radquad(1 – V^2/C^2) – mo x C^2
Ecin = mo x C^2 x ( 1/ radquad(1 – V^2/C^2) – 1)
Energia E e quantità di moto P diventano:
E = moc2 / √(1- v2/c2)
P = mov /√(1- v2/c2)
Relatività generale
La deviazione dei raggi luminosi da parte del Sole, confermata sperimentalmente durante l’eclisse totale del 29 maggio 1919, contribuì in maniera decisiva all’affermarsi della Teoria della relatività generale.
La stella Aldebaran del Toro non doveva vedersi perchè nascosta dal disco solare. Invece apparve in cielo quando la Luna oscurò il Sole. Fu la prova che lo spazio intorno al Sole è curvo a causa della massa che deforma lo spazio. Anche i raggi di luce seguono la curvatura dello spazio.
Una stella vicina al disco solare appare, per la deflessione gravitazionale della luce, in una posizione leggermente più esterna. |
La mattina del 7 novembre 1919 Albert Einstein si svegliò a Berlino, dove aveva preso sonno la sera prima come lo sconosciuto direttore quarantenne dell’Istituto di Fisica Kaiser Wilhelm, senza immaginare che da lì a poco sarebbe diventato un personaggio popolare. Il nome dello scienziato tedesco era circolato sino a quel momento tra gli addetti ai lavori nel campo della fisica teorica, soprattutto per le bizzarre conseguenze astrofisiche derivanti dalle sue teorie, ma era completamente sconosciuto al grande pubblico e totalmente ignorato dai mezzi d’informazione.
L’annuncio dato il giorno prima a Londra, nel corso della riunione congiunta di Royal Society e Royal Astronomical Society, riguardante la conferma sperimentale dell’effetto esercitato dal campo gravitazionale sulla direzione di propagazione della luce, fu amplificato dai giornali pubblicati sulle rive opposte dell’Oceano Atlantico che in tal modo consegnarono Einstein alla fama mondiale. Quella stessa mattina, infatti, il quotidiano The London Times intitolava “Rivoluzione nella scienza – Nuova teoria dell’universo” un articolo dedicato al convegno londinese e qualche giorno dopo il New York Times pubblicò sull’argomento uno scritto dal melodrammatico titolo “Luci distorte nel cielo”.
La grande e geniale idea di Einstein è quella di “sostituire” la forza di gravità con la geometria dello spaziotempo.
Una massa deforma lo spazio circostante e ne determina una curvatura. La curvatura dello spaziotempo determina quindi la traiettoria delle masse che passano nelle vicinanze della deformazione dello spazio.
La griglia rappresenta il “tessuto” spaziotemporale dove si muovono le masse. Al centro, la gravità del Sole determina una deformazione della geometria dello spazio attorno al quale possono esistere tre possibili traiettorie: “e” sta per traiettoria ellittica, “c” sta per traiettoria circolare ed “a” sta per traiettoria aperta.
Curvatura dei raggi di luce
Un raggio di luce proveniente dalla stella A viene curvato passando nelle vicinanze del campo gravitazionale del Sole. La stella viene osservata nella posizione apparente B data dalla proiezione del raggio di luce che arriva a Terra. I raggi di luce vengono curvati passando nelle vicinanze di un campo gravitazionale causato dalla presenza di una massa.
Spostamento del perielio di Mercurio
Uno degli effetti previsti dalla R.G. è lo spostamento del perielio di Mercurio, ossia del punto più vicino dell’orbita, nel campo gravitazionale del Sole. Nel caso di Mercurio, per il quale l’effetto è maggiore essendo il pianeta più vicino al Sole, l’effetto dell’avanzamento del perielio è di circa 43″ per secolo. Nel caso della Terra è di circa 4″ per secolo.
La Teoria della Relatività generale si fonda essenzialmente su due principi:
1) Le leggi della fisica devono essere formulate in modo da non dover dipendere dal luogo in cui vengono applicate e dal moto dell’osservatore. Ciò significa che i requisiti della relatività generale sono più ampi rispetto a quelli della Teoria ristretta, per la quale le leggi devono essere valide per osservatori che si spostano di moto rettilineo uniforme.
I corollari della Teoria speciale non valgono quando ci si avvicina a un forte campo gravitazionale, se si cambia la direzione del moto, oppure quando se ne modifica la velocità. In questi casi i risultati della Teoria speciale devono essere sostituiti da quelli della Teoria generale.
2) Principio di equivalenza: gravità e accelerazione sono equivalenti.
Ognuno di noi può verificarlo empiricamente: quando un ascensore inizia a salire avvertiamo un leggero aumento del nostro peso e un senso di vuoto allo stomaco; quando l’ascensore si ferma, la sensazione è di leggerezza. Ciò significa che un’accelerazione verso l’alto è in grado di aumentare la forza di gravità esercitata sui nostri corpi, mentre un’accelerazione verso il basso ne provoca la diminuzione.
Sono forze di tipo gravitazionale anche quelle che avvertiamo a bordo di un’automobile in rapida accelerazione: in questo caso la forza risultante ci schiaccia contro il sedile. Ne sanno qualcosa gli astronauti quando i loro veicoli spaziali sono in fase di accelerazione, e per imparare a sopportare questo tipo di forze vengono sottoposti a periodi di preparazione all’interno di una centrifuga atta a simulare proprio gli effetti della gravità.
Questi due principi fondamentali portano a svariate conclusioni di notevole importanza, la prima delle quali riguarda il moto delle particelle. Secondo la prima legge di Newton, una particella permane nel proprio stato di quiete o di moto rettilineo uniforme a meno che non le venga applicata una forza tendente a modificare uno di questi due stati iniziali. Ciò significa che la quiete o il moto rettilineo uniforme sono le condizioni normali delle particelle e che, se si trovano nell’uno o nell’altro stato, su di esse non agisce alcuna forza. Per ognuno dei due possibili stati la linea d’universo di una particella nello spazio-tempo sarebbe una retta.
In matematica la linea retta viene definita come la distanza più breve tra due punti. Ciò è vero se uniamo due punti su una superficie piana o nel consueto spazio tridimensionale. ma non è più vero se siamo obbligati a spostarci su una superficie curva o all’interno di una regione limitata dello spazio che presenta una curvatura.
Le barche e le navi che attraversano la superficie marina, una superficie curva, devono tener conto di tale conformazione al momento di stabilire la rotta. Un velivolo è obbligato a spostarsi nell’atmosfera terrestre, il cui spessore è minimo rispetto al raggio della Terra, quindi anche in questo caso per i tragitti particolarmente lunghi bisogna tener conto della curvatura dell’atmosfera. I piloti e gli ufficiali di rotta lo sanno molto bene; i marinai, quando devono viaggiare da un porto a un altro che dista migliaia di miglia, sanno di doversi spostare lungo quelli che sono chiamati archi dei cerchi massimi (un cerchio massimo divide la superficie della Terra esattamente a metà). Questo cerchio costituisce un caso particolare di una classe di linee matematiche chiamate geodetiche, che rappresentano il «cammino più breve» che unisce fra loro due punti su una superficie curva o in uno spazio «curvo».
Questo concetto può essere utile per discutere una delle conseguenze della Teoria generale. La Teoria generale considera «normale» il moto in presenza di gravità, il che implica che non bisogna cercare altre forze a meno che un corpo si muova in modo diverso dal suo «moto normale». Però la sua linea d’universo attraverso lo spazio e il tempo sarà retta solo se si trova lontana da qualsiasi oggetto dotato di massa.
Secondo questa teoria la «forma» dello spazio-tempo vicino a oggetti dotati di massa non è piatta ma curva, e pertanto, nella situazione di uno spazio-tempo «curvo», le particelle seguono speciali geodetiche curvilinee. La «curvatura» dello spazio-tempo è determinata dalla presenza e dalla distribuzione della materia e dalla distribuzione dell’energia.
Un raggio luminoso, lungo il quale l’informazione viaggia alla velocità della luce, sarà una geodetica speciale, denominata « geodetica di lunghezza nulla». Lontana da qualsiasi corpo provvisto di massa, questa geodetica di lunghezza nulla sarà una linea retta. Quindi, per le enormi distanze tra le stelle, possiamo trattare la luce come se si muovesse in linea retta, con un elevato grado di approssimazione. Ma questo non è più vero nelle vicinanze di corpi dotati di massa.
Accanto alla Terra, la cui massa è inferiore a quella del Sole, la curvatura di un raggio di luce è minima. E invece possibile rilevare questo effetto su un raggio di luce che sfiora la superficie del Sole, in determinate circostanze, come per esempio durante un’eclissi totale di Sole. Immaginiamo che in un determinato momento dell’anno una stella si trovi esattamente dietro il Sole, e che alcuni dei suoi raggi ne sfiorino la superficie per poi raggiungere la Terra. In questo caso saremmo in grado di vedere dietro al Sole. In una situazione normale la luminosità del Sole ci impedirebbe di osservare la stella ma, durante un’eclissi totale di Sole, la Luna si frappone tra noi e il Sole celandone i raggi e consentendoci di vedere la stella. La massa della Luna è notevolmente inferiore a quella del Sole, quindi il suo effetto è trascurabile. Questo esperimento è stato condotto per la prima volta nel 1919: le fotografie scattate durante l’eclissi fornirono una conferma convincente delle previsioni della Teoria della Relatività generale e, da un giorno all’altro, Albert Einstein divenne uno scienziato famoso in tutto il mondo.
Per la teoria della relatività generale un ascensore in caduta libera nel campo gravitazionale si comporta come un sistema di riferimento inerziale.
Poichè non esiste un sistema di riferimento assoluto, non è possibile distinguere chi sta accelerando rispetto a cosa. Gli effetti della gravità possono essere compensati da quelli prodotti dall’accelerazione.
Immaginiamo, a sinistra, Einstein all’interno di un ascensore in quiete. Qui è la forza di gravità che determina l’attrazione per cui non succede niente. Ma che succede invece se si spezza il cavo? L’ascensore va in caduta libera, Einstein si “sente” sollevato dal pavimento dell’ascensore e si ritrova come se galleggiasse nell’aria. Ad un certo istante, Einstein e l’ascensore subiscono la stessa accelerazione, mantenendo la stessa velocità. E’ come se fossero fermi l’uno rispetto all’altro. Gli effetti della gravità si sono sostituiti con quelli dell’accelerazione, essi sono della stessa natura perciò sono equivalenti.
Nella foto seguente: i più grandi scienziati del XX secolo. Notare l’unica donna in prima fila, la signora Marie Skłodowska Curie.
Bruxelles-1927 Solvay Conference on Quantum Mechanics
Terza fila : A. Piccard, E. Henriot, P. Ehrenfest, Ed. Herzen, Th. De Donder, E. Schrödinger, E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin,
Seconda fila : P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr,
Prima fila : I. Langmuir, M. Planck, M. Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch. E. Guye, C.T.R. Wilson, O.W. Richardson
Einstein e la meccanica quantistica
Einstein non accettava che esistesse un’indeterminazione sulle misure
quantistiche, ovvero che i risultati non fossero pienamente determinabili in anticipo: ciò, secondo Einstein, introduceva nella fisica l’influenza del “caso cieco”, per lui assolutamente inaccettabile. A questo proposito è rimasta
celebre la sua frase: “Dio non gioca a dadi con il mondo”. Meno famosa è la risposta di Bohr: “Non è compito degli scienziati dire a Dio come funziona il mondo, ma solo scoprirlo”.
Inoltre Einstein non credeva alla possibilità di caratteristiche fisiche “non-oggettive”, ma riteneva che i valori delle osservabili esistessero oggettivamente anche prima della misura, indipendentemente dal fatto che venissero misurati o meno. Insomma, secondo Einstein (come probabilmente secondo il lettore o qualsiasi persona che non abbia ancora accettato il nuovo messaggio implicito nella meccanica quantistica) l’universo deve esistere oggettivamente, sia che noi l’osserviamo o meno! Per questo egli considerava la meccanica quantistica “incompatibile con ogni concezione ragionevole e realistica dell’universo”.
L’elettrodinamica dei corpi in movimento
Zur Elektrodynamik bewegter Korper, Annalen der Physik 17, 891-921 (1905).
A. Einstein (1905)
E’ noto che l’elettrodinamica di Maxwell – come la si interpreta attualmente –
nella sua applicazione ai corpi in movimento porta a delle asimmetrie, che non
paiono essere inerenti ai fenomeni. Si pensi per esempio all’interazione elettromagnetica tra un magnete e un conduttore. I fenomeni osservabili in questo caso dipendono soltanto dal moto relativo del conduttore e del magnete, mentre secondo l’interpretazione consueta i due casi, a seconda che l’uno o l’altro di questi corpi sia quello in moto, vanno tenuti rigorosamente distinti. Se infatti il magnete `e in moto e il conduttore `e a riposo, nei dintorni del magnete esiste un campo elettrico con un certo valore dell’energia, che genera una corrente nei posti dove si trovano parti del conduttore. Ma se il magnete `e in quiete e si muove il conduttore, nei dintorni del magnete non esiste alcun campo elettrico, e si ha invece nel conduttore una forza elettromotrice, alla quale non corrisponde nessuna energia, ma che – a parità di moto relativo nei due casi considerati – dà luogo a correnti elettriche della stessa intensità e dello stesso andamento di quelle alle quali dà luogo nel primo caso la forza elettrica. Esempi di tipo analogo, come pure i tentativi andati a vuoto
di constatare un moto della terra relativamente al “mezzo luminoso” portano alla
supposizione che il concetto di quiete assoluta non solo in meccanica, ma anche in
elettrodinamica non corrisponda ad alcuna proprietà dell’esperienza, e che inoltre
per tutti i sistemi di coordinate per i quali valgono le equazioni meccaniche debbano valere anche le stesse leggi elettrodinamiche e ottiche, come già è dimostrato
per le quantità del prim’ordine. Assumeremo questa congettura (il contenuto della
quale nel seguito sarà chiamato “principio di relatività”) come postulato, e oltre
a questo introdurremo il postulato con questo solo apparentemente incompatibile,
che la luce nello spazio vuoto si propaghi sempre con una velocità determinata V ,
indipendente dallo stato di moto dei corpi emittenti. Questi due postulati bastano
a pervenire ad un’elettrodinamica dei corpi in movimento semplice ed esente da
contraddizioni, costruita sulla base della teoria di Maxwell per i corpi in quiete.
L’introduzione di un “etere luminoso” si dimostra fin qui come superflua, in quanto
secondo l’interpretazione sviluppata non si introduce uno “spazio assoluto in quiete” dotato di proprietà speciali, nè si associa un vettore velocità ad un punto dello spazio vuoto nel quale abbiano luogo processi elettromagnetici. La teoria da svilupparsi si fonda – come ogni altra elettrodinamica – sulla cinematica dei corpi rigidi, poiché le affermazioni di una tale teoria riguardano relazioni tra corpi rigidi (sistemi di coordinate), orologi e processi elettromagnetici. La non sufficiente considerazione di queste circostanze è la radice delle difficoltà, con le quali l’elettrodinamica dei corpi in movimento attualmente deve lottare.
http://fisicavolta.unipv.it/antoci/re/Einstein05.pdf
La Teoria della Relatività è un colossale edificio concettuale sorto in Germania all’inizio del ‘900. Questo straordinario modello della realtà è diventato imprescindibile per lo sviluppo della fisica teorica e ha introdotto nella scienza, e in parte nel comune sentire, concetti apparentemente assurdi, del tutto contrari all’intuizione e persino alla logica.
Secondo Einstein, l’ideatore della Teoria della Relatività, lo spazio ed il tempo si deformano in prossimità di corpi molto massicci (stelle, pianeti, etc.) oppure quando un corpo si muove a una velocità tanto elevata da essere comparabile a quella della luce. In tali situazioni lo spazio si “accorcia” ed il tempo “rallenta”. Questi singolari fenomeni di deformazione dello spazio e del tempo sono tanto più pronunciati quanto più è forte l’attrazione gravitazionale o elevata la velocità. Siccome le distorsioni di spazio e tempo sono legate tra loro, si preferisce considerare le due entità come un’unica realtà chiamata spaziotempo che possiamo dunque considerare come qualcosa di “elastico”. E’ importante sottolineare come ad accorgersi della deformazione dello spaziotempo non è l’osservatore che si trova nei pressi di un corpo massiccio o che si muove a forte velocità, ma soltanto chi osserva dall’esterno. Se viaggiassimo su un’astronave proiettata a velocità prossima a quella della luce, percepiremmo le dimensioni nostre e della navicella così come l’avanzare dei nostri orologi come assolutamente normali, ma chi ci osservasse dall’esterno vedrebbe la navicella accorciarsi e noi che la occupiamo muoversi al rallentatore. Il discorso è analogo per la gravità.
Per quale ragione gravità e velocità estreme hanno questo effetto? Lo spaziotempo si comporta come un telo elastico modificando la propria forma nei pressi di corpi molto massicci. Se la massa di un corpo supera una certa soglia, lo spaziotempo finisce col “chiudersi su se stesso”, diventando una trappola da cui neppure la luce può fuggire una volta che ci è caduta dentro: un buco nero. Gli effetti della relatività legati alla velocità di spostamento stabiliscono inoltre una specie di limite naturale di velocità. Più acceleriamo e più l’universo “ci rema contro” rallentando sempre più il nostro ritmo interno, fino a che, raggiunta la velocità della luce, il tempo si arresta completamente. Ciò rende quella velocità la massima raggiungibile in assoluto. Avvicinandoci a tale limite assisteremmo anche ad un altro strano fenomeno: la massa della navicella aumenterebbe sino a diventare infinita in corrispondenza della velocità della luce. Anche tale circostanza suggerisce che la velocità della luce sia un limite che non si può superare.
C’è un altro fatto rilevante riguardo la velocità della luce. Quando due paracadutisti si buttano insieme, ciascuno vede l’altro quasi fermo. Invece, per chi li sta guardando da terra, essi stanno cadendo a folle velocità. Insomma: un oggetto si muove a diverse velocità in base al punto di osservazione dal quale scelgo di guardarlo. Si tratta di un fatto ovvio, tutti ne abbiamo fatto esperienza e vale qualunque sia l’oggetto osservato. Ma non per la luce! Se, per raggiungere un raggio di luce e vederlo un po’ “rallentato”, provassimo a muoverci a una frazione della sua velocità, magari a bordo di una potente navicella spaziale, non otterremmo un bel niente. Come detto prima la natura “ci rema contro” compensando perfettamente la nostra velocità. In breve: più rapidamente corriamo e più intensamente gli effetti effetti relativistici (massa che cresce, tempo che rallenta, spazio che si contrae) ci fanno da zavorra. La luce si muove sempre alla stessa velocità a prescindere da quanto spedita sia la nostra andatura! Ecco perché si dice che con la Relatività di Einstein la velocità della luce viene elevata a costante universale: perché è la stessa per qualsiasi osservatore. Allo stesso tempo lo spazio ed il tempo sono state “declassate”, da entità assolute e immutabili a qualcosa di relativo. Dunque con la Relatività, la luce non è soltanto una semplice comparsa nell’immenso film dell’Universo, ma interpreta un ruolo unico e speciale.
Il ruolo eccezionale riservato alla velocità della luce emerge anche in un altro contesto: dicendo che, a grandi velocità, la massa aumenta non si intende certo dire che viene creata dal nulla. Ma allora da cosa è originata? Ad essere convertita in massa è semplicemente parte dell’enorme energia spesa dalla navicella spaziale per l’accelerazione. Einstein nella sua titanica opera di riformulazione dei concetti fondamentali della fisica scopre che massa ed energia, fino ad allora considerate del tutto indipendenti, sono in realtà convertibili una nell’altra (come accade per esempio nelle esplosioni nucleari) secondo la celebre legge E=mc2. In questa formula E è l’energia, m è la massa mentre c elevato al quadrato è il fattore di conversione tra le due. Ebbene c rappresenta esattamente la velocità della luce, che diventa cosi il “ponte” che mette in comunicazione massa ed energia.
Costellazione di Orione – Betelgeuse (la spalla del gigante) – dstanza: 600 a. l.
cavinimaurizio ha detto:
Nell’articolo si legge:
“se sei di fronte a un orologio e questo si allontana da te, un raggio di luce proveniente dall’orologio arriverà a te più tardi.
Quindi se l’orologio si allontana con velocità prossime a quelle della luce, vedi l’orologio scorrere molto lentamente, e se si allontana esattamente alla velocità della luce vedi l’orologio fermo, perché nessun raggio ti raggiungerà mai.”
Direi così: mentre l’orologio inizia ad allontanarsi lo vediamo andare più piano per l’effetto doppler. Quando la velocità supera un certo limite l’effetto doppler non basta più a spiegare ciò che vediamo e bisogna cominciare a considerare la dilatazione del tempo. Naturalmente nessun orologio può accelerare fino alla velocità della luce, ma se lo facesse le cose non sarebbero così semplici. Finché le velocità rimangono inferiori a quella della luce, ciò che vedono i due osservatori (quello fermo e quello in moto) è uguale e la relatività del moto è confermata. Ma qualora un orologio si allontanasse da noi alla velocità della luce noi vedremmo un orologio fermo (perché le sue immagini non dovrebbero raggiungerci? Se ad esempio avesse il quadrante trasparente e fosse illuminato da dietro da una fonte luminosa remota potremmo ancora vedere le sue lancette ferme), ma il nostro orologio continuerebbe ad avanzare, indicando che noi siamo ad una velocità inferiore. Questo metterebbe in crisi la relatività.
hiroji kurihara ha detto:
Speed of Light : Reexamination
Plane waves of light (wavelength is constant) are coming from just above. An observer is moving horizontally at different speed. Speed relative to the waves does not vary. But speed relative to photons or light ray will vary (both will be real existence). With the formula : light speed = f λ, speed of waves can be shown. However, speed of photon and light ray will not be shown. Because of large speed of light, this problem is not noticeable.
In outer space, plane waves of a star light are coming. An observer is at a standstill. Speed of light waves and photons (light ray) relative to the observer will not be the same (in general). By the way, speed of light waves and of photons (light ray) relative to the aether frame will be the same (as a physical constant : not c, maybe).
Sorry, I cannot receive E-mail. I do not have PC.
http://www.geocities.co.jp/Technopolis/2561/eng.html
ChastityBig ha detto:
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Hiroji kurihara ha detto:
Thank you Chastity Big,
Lorentz contraction
Plain waves of light (wavelength is constant) are coming from the upper right 45 degrees. Two bars of the same length are moving to the right and the left at the same speed. The number of waves hitting the bars is the same. Lorentz contraction is unthinkable. And also,time dilation will be denied.
Hiroji kurihara ha detto:
Time dilation
A light source is shinning (frequency is constant). Two observers are receding from the light source at the same speed (in the opposite direction). Two observers receive the same frequency. Where is the time dilation ?
Below is new URL of my web site. Yahoo’s service ends on Mar 2019.
http://lifeafterdeath.vip/eng.html
Hiroji kurihara ha detto:
An elevator in free fall
In it, action and reaction are working. The two are equal as a whole and at the selected infinite small area. By the way, in an elevator accelerated horizontally, the two are equal at every area.
Hiroji kurihara ha detto:
An elevator in free fall
Are the two indistinguishable? Vector of the two are opposite.
Hiroji kurihara ha detto:
Free fall
Vector of inertial force acting on a mass point follows principle. Vector of gravity acting on a mass point (usually as a resultant force) follows principle. And we can know these vector. There will be no reason to make free fall an exception.
Hiroji kurihara ha detto:
Bremsstrahlung
A website say, “A charged particle is decelerated. And energy of motion is emitted as electro magnetic waves”. But, difference between deceleration and acceleration seen from inertial frames will be relative. Or, phenomenon bremsstrahlung depends on the absolute rest frame?
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MM experiment
For over a hundred years, we are suffering from a picture of MM experiment. Now, imagine to replace light with beams of particles.(speed is constant). And it will be real behavior of light. Time and space will be absolute. All will be Galilean transformation.
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Free fall
Inertial force ma is said to be virtial. If so, mg in free fall will be the same. And normal force will be virtual.
Vector of gravity and vector of inertial force are ubiquitous around us. And resultant forces are the same. Why they make a big fuss on an elevator in free fall ? By
Hiroji Kurihara ha detto:
Lorentz contraction
In a moving passenger car, MM experiment is being done. Between two light pathes diverged by a half mirror, there is considerable difference in length. Lorentz contraction will not stand up.
Hiroji Kurihara ha detto:
Constancy of speed of light
They say, it stands up on an observer in every inertial frame. Yes, when the light source shines in that frame, it is true.
Some man mistook this fact natural for a great discovery. And it is believed widely.
Hiroji Kurihara ha detto:
Inertial force
From the roof of an accelerating passenger car, two bodies the same in appearance are hung by strings. Mass is m and 2m. Inertial force is not fictitious.
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Falling of non free
Imagine elevator cabins are falling in various density of air. Hydrodynamics tell motions of these complately. Equivalence principle is invalid.
Free fall
There are innumerable vectors of inertial force and gravity everywhere. On an elevator cabin, why they are making a big fuss ?
Hiroji kurihara ha detto:
Difference of motion
Difference of inertial motion and accelerated motion will be difference relative to aether frame. And accelerated motion and inertial force are the front and back of a fact. Inertial force is not fictitious.
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Horizontal Doppler effect
On a plane, pararell lines are drawn. On each line, light sources (frequency is the same) are moving in the opposite direction. Imagine light sources form japanese letter エ. Horizontal Doppler effect will not be.
Hiroji kurihara ha detto:
Equivalence principle ?
A passenger car is accelerating (to the right, at g). A body is hung from the roof by a string. Can the string distinguish mg caused by acceleration and gravity ? No, it is a joke. But, an elevator cabin seems to be a joke also.
Hiroji kurihara ha detto:
Time dilatation
A light source is shining (frequency is constant). Two observers are receding from the source in the opposite direction at the same speed. Two observers receive the same frequency. Where is the time dilation ?
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Accelerated motion
Accelerated motion will be the motion relative to aether frame. Vector causes the same vector of inertial force. Gravity has no connection.
From every inertial frame, accelerated motion is possible to know qualitatively and quantitatively.
Hiroji kurihara ha detto:
The emission theory
If there is no rest frame in space, light must follow the emission theory (but for a few seconds only).
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Space and time
Our motion will not affect on space and time. Our motion is various and space and time is one and only. Every relative speed will follow gallirean transformation. Including the light.
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A site on anti relativity
A web site written by member voluntees of Japan science council is now being published (in Japanese). Below is URL.
http://reriron.kage-tora.com
Hiroji kurihara ha detto:
Equivalence principle
An elevator cabin in free fall is explained fully by Newton. There is no room for Einstein.
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Caduta liberal (Free fall)
Any gravity is measurable. Any inertial force is measurable. In an elevator cabin in free fall, these are measurable.
Problem is limited to the infinite small area. It is not physics.
Gravity gradient and infinite small area ??
Gravity is gravity. Inertial force is inertial force. Resultant force is resultant force.
Hiroji kurihara ha detto:
Inertial force
Inertial force is depending on m. So, it is not fictitious.
Hiroji kurihara ha detto:
Constancy of speed of light
In an area where propagation of light follows the emission theory, it is constant relative to the light source. In an area where propagation of light follows aether, it is constant relative to aether. So, it cannot be constant relative to moving observers.
Hiroji kurihar ha detto:
Basis of special relativity
We seem to measure c by the light source situated on the same inertial frame. A web site says, reasonable basis of constancy of c cannot be found in web (with three words).
Hiroji kurihara ha detto:
Inertial force
On a slope (no friction), a body m is sliding down. Action of gravity is mg. Then, how about the reaction ? It is resolved to two vectors. Inertial force is not fictitious.
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Reexamination of propagation of light ( I say again)
In outer space, a mirror is reflecting a star light ray. Speed of reflected light relative to the mirror is constant. Speed of incident light relative to the mirror is not constant (the latter is constant relative to the aether).
Hiroji kurihara ha detto:
Inertial force is not fictitious
On a plane, there are two bodies. One is at a standstill, the other is accelerating. Acceleration (a) and inertial force (ma) both are not fictitious.
There are two disks. One is not rotating, the other is rotating. Acceleration and inertial force both are not fictitious.
Hiroji kurihara ha detto:
Acceleration
From nothing, “a” seems not to emerge. By acceleration of body relative to aether, “ma” will emerge. Qualitatively and quantitatively.
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Light is propagated in two ways
Propagation follows the emission theory is propagated in vaccum space and propagation follows aether is propagated in aether space. A mirror in outer space that is reflecting star light ray shows above.
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Acceleration (I say again)
On a plane, two bodies are receding. One is at a standstill, the other is accelerated uniformly. On the one, inertial force is emerging but not on the other. All is shown by a and ma.
But what distinguishes acceleration and nonacceleration ? In above picture, uniform isotropic aether will be hidden. This picture is not picture of geometry.
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Space is rest frame
Into space, let us draw plural vectors of acceleration a. Space will be rest frame absolute.
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About space
Every motion is possible to show as a motion relative to luminiferous aether. This
rest frame can not be emerged by means of of dynamics. But space will be uniform isotropic field also to dynamics.
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Demon fires
Are there still berievers of relativity ? Demon fires. It is not a thing of this world.
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No one realizes
In air, all the effect of aether is excluded. No one seems to realize this simple picture. Like Michelson.
Whether the result of Fizeau measurement (on the ight speed : with gear) varies in the direction of the optical axis relative to the celestial sphere ? And how about when it is done in vaccum ?
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Equivalence principle (I say again)
Vector of inertial force is shown as an arrow. Vector of gravity cannot be shown as an arrow generally. The two are different as facts of physics.
Hiroji kurihara ha detto:
Aether
Speed of light relarive to mediums is constant. Speed of light relative to aether (physical substance) will be constant also. Aberrations show this.
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About inertial force (I say again)
On a plane, there are two passenger cars. One is accelerating and the other is at a standstill. Difference of the two is not relative but absolute .
On a plane, a passenger car is accelerating. On the floor (no friction), a body is put. This body is not accelerated (to everyone). From physics of 20th century, nonsenses overflow.
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Accelerated motion of a light source
Light emitted from an accelerated source will follow instantaneous speed of the source. In short, light will scceed the motion of vector of instantaneous speed of the source. The emission theory imply the above.
I say again, the emission theory will be valid for a few seconds only after the emission. After this, light follows aether.
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Propagation of light (I say again)
Light is propagated in three ways (as follows)
1 In mediums, speed of light is c/n. MM experiment (done in air) is nonsense.
2 In outer space, a star light is reflected by a mirror. Speed of incident light is constant relative to aether.
3. In outer space, a star light is reflected by a mirror. Speed of reflected light is constant relative to the mirror.
In three pictures above each, speed of light to a moving observer follows Galilean transformation.
Hiroji kurihara ha detto:
Equivalence principle
Difference between acceleration and nonacceleration seems to be more basic. If so, equivalence principle is invalid.
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All of light speed
All of light speed is shown by aberrations. One is that in outer space, speed of light is constant relative to aether. Every motion of light source is cancelled. The other is that light speed is not constant relative to the moving earth.
Hiroji kurihara ha detto:
Acceleration and nonacceleration
A passenger car is accelerating (uniformly). A body is hung from the roof, a body is placed on the floor (no friction) and a station building. Physics seems not to distinguish the three.
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Time dilation
Ahead of us, a light source is shining. On the left space, two space ships are passing each other (horizontally : at the same speed). How is difference of frequency of light observed by two space ships explained ?
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Time dilation
In outer space ahead, two space ships are receding to the right and the left (at the same speed : aether is invalid). On the outside of each ship, the same light source is shining and this light is observed by facing ship. Time dilation (twin paradox also) will be impossible.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Mercury revolving is divided in two (hemisphere A facing the sun and the other B). Inertial force is A<B and gravity is A>B (center of gravity is not on the orbit).
Hiroji kurihara ha detto:
Perihelion shift is of Mercury
Yesterday’s post must be the most natural explanation of perihelion shift of Mercury. Because the value of perigee movement of the moon is remarkable ( around 8.85 years). On the other hand, value of asteroids will not be found. Common explanation is not acceptable.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Perihelion shift moves forward constantly. It cannot be explained by gravity of other planets.
On asteroids, no perihelion shift will be observed. Some size will be needed.
Cause of perigee movement of the moon is written to be the sun. Not consistent. Because it will be the same phenomenon to perihelion shift of planets.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
The value of perihelion shift of planets is constant. It will not be three body problem or many body problem. And it will be the same to binary star.
Hiroji kurihara ha detto:
Time dilation
Two passenger cars are passing each other. At the front of side wall of each car, the same light source (frequency is the same also) is settled and light ray is emitted backward at 45 degrees. Each ray is reflected by mirror sticked on the side wall wholely and is coming back. Time dilation is impossible.T
Hiroji kurihara ha detto:
MM experiment
How about MM experiment done in still water ?
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Eddington experiment (on solar eclipce : 1919)
Eddington experiment is said to find the bending of star light by gravity of the sun. But the additional exam seems not to be done. Surface gravity of the sun is 28.02g and that of Jupiter is 2.53g. Gravity of position apart from each surface (at each radius) is a quater of surface gravity each. Experiment of Jupiter will be possible.
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Equivalence principle (I say again)
An elevator cabin is accelerating horizontally (no friction : at 2g). At every mass point (at every infinite small area), acceleration is 2g.
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Perihelion shift of Mercury (I say again)
In an binary system (formed by main star and companion star), periapis is shifted also. Motion of companion star (apsidal shift) will be depending considerably on its size (mass is supposed to be the same). Common view (says main cause is pertubation of other planets) will be invalid.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Main cause of perihelion shift of Mercury is said to be gravity of the other planets. But position of other planets move (also position of perihelion of Mercury moves). If so, values 5.75 secarc/year is unthinkable. Main cause
will be in Mercury itself. And also it will be the same on values of perihelion shift of the other planets.
Perihelion shift of Mercury is said to be 5.75 secarc. Sometimes it is shown as 575 arcsec/100 years. Only on Mercury ? Because the value is unreliable ? For evasion ?
Hiroji kurihara ha detto:
Perihelion shift of Mercury
What are the causes of perihelion shift of planets ? Speed of revolution ? Speed of rotation ? Slope of rotation ?Mass of planet and its distribution ? Mass of satellites and these distribution ? Gravity of the other planets will perhaps be weak and position is not stationary.
Imagine that long radius of Mercury separates the space of the solar system in half. Probability of the existence of the other planets in the left and right is the same. Perihelion shift at constant speed will be impossible (common view is wrong).
Hiroji kurihara ha detto:
Gravity lense
Gravity lenses are said to be a positive evidence of GR. However if gravity of gravitational source can be estimated, which is real GR or Newton’s theory will be clarified.
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Is light speed constant!?
To the upper right at 45 degrees in still water, plane waves of light is propagated. Above the water surface is vacuum. Value of inclination of waves in vacuum can be determined. And also speed of light waves relative to moving observer who moves in vacuum horizontally or vertically can be determined.
How about when there is air above the water surface ? When air is stationary relative to the water, apparent difference in looks will not be found.
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Perihelion shift of Mercury
“It can be safely said that gravity of other planets has no effect on the perihelion shift of Mercury”. It’s in a website.
Imagine that with long radius of orbit of Mercury, the space of the solar system is divided into left and right. The probability that other planets exist on the two is equal. There will be no shift of perihelion in one direction at constant speed (common view is wrong).
But main cause of perihelion shift of Jupiter and Saturn will be mutual effect of gravity. Each perihelion is shifted every moment.
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Perihelion shift of Mercury
There is a model of Mercury. A long lod penetrates a true sphere and at the both ends of the lod, weights are set. This model is rotating horizontally and is moving on the orbit of Mercury (two planes fall on). Main forces acting on the weights are gravity of the sun and inertial force (centrifugal force). And each force acting on the outside weight and inside weight is different.
Inertial force pulls the orbit to the outside. But actual orbit of Mercury is pulled to the inside. Gravity of the sun acting on the two weights is inversely proportional to the square of the distance (not come out even. not plus minus zero). In Mercury, the action of gravity will be superior.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
A model of Mercury is shown previously. Now, there are plural models. Length of lods and mass of weight each is different. These are revoleved around separately on the real orbit of Mercury. Maybe, all will be explained by Newton’s theory (including 575 arcsec).
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Perihelion shift of Mercury
Value 5.75 arcsec/year seems to be an observed value. In a website, contribution of other planets to this value is shown. These are added simply !! And value 5.75 arcsec (and contributions) seems to be constant every year !!
I say again, other planets will not be main cause of this value 5.75 arcsec.
Hiroji kurihara ha detto:
Absolute rest frame (Aether)
What distinguishes acceleration from non-acceleration ? Only inertial force can. And it is based on aether. Yes, aether exists. Evidently, aberration shows it.
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Perihelion shift of Mercury
The perihelion shift of the earth is 11.45 arcsec / year. Main cause will be its size (size of sphere). It is the same to Mercury. In addition, the earth has a moon as a satellite that Mercury does not have. The inertial force of the moon and gravity of the sun acting on the moon are also considerable. And like Mercury, effect of other planets must be slight and unstable.
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DrPerihelion Shift of Mercury (unfamiliar figure)
I found a figure unfamiliar on web. About two Mercury’s orbits are shown. New orbit is outside the previous orbit twice and inside the previous orbit twice during one round.
Note) This site is in Japanese. image page. big red sun. 水星の近日点移動
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Perihelion shift of Mercury
This is the top of tall tower. Two rods of equal mass and different length are arranged vertically (heigth of center of gravity is the same). Now, two rods start to fall at the same time. The fall of center of gravity will not be the same. Because the strength of gravity is inversely proportional to the square of the distance. This will be the main cause for perihelion shift of Mercury.
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Perihelion shift of Mercury (I say again)
Imagine that two Mercuries are revolving on an orbit. One is located at the perihelion and the other is at the aphelion. Gravity of the sun acting on the two is different because distance is different. In addition, there will be difference corresponding to the size of sphere (hemisphere inside > hemisphere outside). The strength of gravity is inversely proportional to the square of the distance. This will be main cause for perihelion shift of Mercury. The effect of other planets must be slight and unstable.
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Hiroji kurihara ha detto:
Perihelion shift of Mercury
Mercury has an own size as a sphere. Therefore, the sun’s gravity will have a different effect on Mercury than it does on the center of gravity. Actual orbit will be different from that the center of gravity must follow. On Mercury, it will be the main cause of the perihelion shift.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Let’s reconsider the main cause of perihelion shift again. On Mercury or Venus, main cause will be the size of sphere. On Earth or Mars, effect of satellite is added. On asteroids each, effects of size is negligible. On Jupiter or Saturn each, the powerful and unstable effect of the other will act. On Uranus or Neptune each, slight and unstable effect of the other all planets will act. Anyway, common view on Mercury is wrong.
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Perihelion shift of Mercury
In Mercury, the non-uniformity of the Sun’s gravity (in the size of Mercury) will be the main cause of perihelion shift. Even in artificial satellites, the effects of non-uniformity of the Earth’s gravity (the position of the center of mass and the center of gravity are different) are also mentioned.
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Perihelion shift of Mercury (rewritten)
Mercury is moving on the revolution orbit. The sun’s gravity is equal to the centrifugal force. Because the two are action and reaction. Following are some explanations. Centrifugal force follows Mercury’s mass. But in addition, gravity is affected by the size of Mercury (and acting position of gravity is different). These are caused by the non-uniformity of gravity (in the space occupied by Mercury). And after perihelion passage, orbit will be pulled inward (from its original orbit).
High tide level twice a day is the same. Gravity and centrifugal force caused by the moon will be action and reaction. Centrifugal force is not fictitious.
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Moon and earth (an essay)
In an illustration, the moon and the earth are drawn side by side. Because of the lunar attractive force, seawater is bulged in the left and right edges of the round earth. The bulge is symmetrical. Two resultant forces are acting at two edges (to the opposite direction). Two resultant forces each are composed of the lunar attractive force and the centrifugal force caused by earth’s orbital motion (moves around the common center of gravity with the moon). Two resultant forces will be equal strength. This will explain that the level of high tides twice a day are generally the same.
Also, the lunar attractive force acting on the earth’s center of gravity (not the center of mass) and the centrifugal force resulting from its orbital motion (mentioned above) will be action-reaction and will be equal.
P.S. Is action-reaction in the sky exactly equal ?
Hiroji kurihara ha detto:
Moon and Earth (additional)
Suppose the moon and the earth is two-body problem. And imagine, the earth is revolving (not rotating) around the common center of gravity with the moon. The orbit is a perfect circle. If lunar attractive force acting on the center of gravity of the earth is action, the centrifugal force of the earth is a reaction. And the strength of the two will be equal. This will be also true for the earth as a whole.
In an illustration, the earth is drawn next to moon. Imagine two points on the surface of the earth closest to the moon and farthest from the moon. The difference between lunar attractive force and the centrifugal force of the earth at above two points will be almost equal and therefore the resultant force will also be almost equal. This will explain that the level of high tides twice a day are almost equal.
Note: Is the law of action and reaction valid for celestial bodies on elliptical orbits ?
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Moon and earth (rewritten again)
Allow me to rewrite again.
Moon and earth are supposed to be two-body problem. Also it is supposed that the common center of gravity of moon and earth is situated outside the earth. And the orbit of earth is a perfect circle, and earth is a perfect sphere. In the illustration, the surface of earth closest to moon is A and the surface farthest from moon is B. At the two points A and B, the strength of resultant forces of moon’s gravity and centrifugal force (of earth) will be the same (act to opposite directions). Otherwise, earth cannot stay on orbit of perfect circle. This will explain that the level of high tide twice a day are the same.
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Moon and earth (an essay)
As moon passes overhead, high tide (one of two tides a day) will come after a short delay. But why ? Why is seawater with a low specific gravity bulged ? Newton imagined that moon will continue falling. Earth will continue falling also. And seawater will cotinue falling too. So, it doesn’t matter how specific gravity is.
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Pelihelion shift of Mercury (an essay)
Some wide binaries are separated by one light years. And many wide binaries are at most (as much as) by 1000 au. These motion will be treated as mass points (a point). On the other hand, many close binaries are found out also. What are physicists who repeat nonsense on perihelion shift of Mercury ?
Hiroji kurihara ha detto:
Moon and earth (an essay)
Moon and earth are supposed to be two-body problem. In the illustration, the surface of earth closest to moon is A and the surface farthest from moon is B. At the two points A and B, the strength of resultant forces of moon’s gravity and centrifugal force (of earth) will be the same (act to opposite directions). It will be proved by the sameness of high tides.
Also it will be proved by stability of orbits of each body.
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Moon and earth
Attractive force (centripetal force) of sun is acting on an asteroid (supposition : mass point and orbit is perfect circle). Attractive force and centrifugal force is equal (action and reaction). Like asteroid, planets are on orbits around sun. If planets are rigid or not broken, the above two forces are equal in total (supposition : orbit is perfect circle).
In moon and earth, tidal force will be internal force. The level of high tides twice a day is the same.
Hiroji kurihara ha detto:
Moon and earth (an essay)
Moon and earth are supposed to be two-body problem. Also supposed that common center of gravity of the two is outside of earth : the orbit of earth is perfect circle : and earth is a perfefct sphere. The strength of moon’s attractive force acting on earth and centrifugal force due to revolution of earth are equal in total (as action reaction : as centrifugal force and centrepital force).
The points on the surface of earth closest to moon is A and the surface farthest from moon is B. It will mean that the forces acting on the two points AB must be offset. It will explaine that level of high tides twice a day is the same.
Hiroji kurihara ha detto:
Perihelion shift of Mercury (an essay)
A celestial body called Vulcan is revolving on orbit of Mercury. It has the same mass and revolution cycle as Mercury. And diameter is twohold (the both stars are uniform in density). Since the sun’s gravitational field is non-uniform, the sun’s gravity acting on both stars will be slightly larger in Vulcan and smaller in Mercury. The value of perihelion shift also likely will be similar. In short, the size of the celestial body (close to the gravitational source like Mercury) will be the main reason for the perihelion shift.
Imagine a cone with evenly spaced concentric circles on its surface. The non-uniformity of gravity will be exponential non-uniformity.
Hiroji kurihara ha detto:
Perihelion shift of Mercury (an essay)
On planets, it is said that centrifugal force caused by orbital motion is balanced with attractive force of sun (and the action and reaction are equal). On Mercury, it will stand up also. But exactly ? Solar wind or some other solar-derived substances seem to go down slightly speed of orbital motion of Mercury (one of perturbation ?). If so, centrifugal force will be reduced accordingly. On the other hand, attractive force of sun will not be affected at all. This may be the main reason for the perihelion movement of Mercury.
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Propagation of gravity
The propagation of gravity will be done in an instant. For this, here are two reasons. One reason is that two-body problem, many-body problem are true for celestial bodies. The other reason is that the whole solar system is in an uniform linear motion and planets are in elliptical revolution on their revolution planes.
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Inertial force, centrifugal force, centripetal force (an essay)
Between accelerated motion and non-accelerated motion (uniform linear motion), there is an immovable distinction. And accelerated motion is always accompanied by an inertial force (corresponding to the vector of motion). These are based on the existence of absolute rest frame.
A motion of a disk rotating is an acceleration motion. And the disk is accompanied by an inertial force called centrifugal force. It is said that centrifugal force depends on the situation of observer. But the physical phenomenon (centrifugal force) cannot be influenced by observers. Centrifugal force will show the same value to everyone.
The wiki defines centripetal force as “the force that moves an object in a curved motion”. But is that the correct definition? Is mere external force centripetal force also? Isn’t tension, tensile stress, gravity, etc. all the same? Is there any commonalities (grouped together)?
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Centrifugal force : reconsidering
Two mass points a and b (with large difference of mass) are in motion of two-body problem (a large, b small). One picture is in outer space, and the knot of a,b is gravity (b is in a circular motion). The other picture is on a plane (no friction), and the knot is tension of a string (the mass of the string is zero). In the two pictures, the centrifugal force of b is a vector that is on the extension line of a,b. The reaction is gravity in one picture and tension of the string in the other picture. Where and how is the centripetal force?
Tension of the string between a and b is constant. Gravity is not constant.
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Inertial force is not fictitious
Three passenger cars are moving in different accelerated motions. These are shown with the formula, F = ma, 2F = m2a, 3F = m3a. Inertial force will not be fictitious (even for those in the passenger car).
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All about inertial forces
A body is hung by a string from the roof the passenger car accelerating to the right. The string is leaning to the lower left. The leaning of the string depends on the equilibrium of forces. The string is under tension. The leaning of the string is the same for one outside the car and for the other inside the car. Inertial force is not fictitious to them.
Hiroji kurihara ha detto:
About inertial force
Inertial force seen from the accelerated frame is said to be fictitious. Who brought it (for the first time) and when? This my doubt is still suspending. This is brought after advent of general relativity ? They seem to say that inertial frame in an elevator in free fall is the same to accelerating passenger cars (also to acceleration in general). Also they seem to say that this problem is within the framework of Newtonian mechanics.
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Local inertial frame
An elevator is falling in free fall. On a horizontal plane, multiple observers are moving in uniform linear motions. For these observers, the elevator draws parabola and is in an accelerated frame. This is, the accelerated frame and the non-accelerated frame all are white and black. This means that there is no inertial frame in the accelerated frame. Even it be local.
Hiroji kurihara ha detto:
About free fall
Is there a unified explanation for free fall and similar form of fallings ? Is there a unified explanation for the local inertial frame and the adjacent spots ? Probably not.
Hiroji kurihara ha detto:
About free fall
Is there a unified explanation for free fall and similar form of fallings ? Is there a unified explanation for the local inertial frame and the adjacent spots ? Probably not.9
Hiroji kurihara ha detto:
About inertial force
A body is placed on a plane (no friction). The body has two strings (zero mass), the left string is tied to a wall and the right string is pulled by the force ma to the right.
Then the left string is removed. The body begins accelerating by force ma to the right. There is no change in the tension of the right string. According to the action-reaction law, inertial forces cannot be fictitious.
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The emission theory
By Evenson et al, in 1973., a measurement of speed of light was done. With modifying of this measurement, the emission theory will be proved to be true. Firstly, by motion of light source, it will be possible to detect effects (if it be) of the few air molecules remaining in vacuum. Then, with motion of light source , with motion of measurement device, the refutations will be closed. There may be other ways, but the above will be enough for the validity of the emission theory.
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Acceleration and non-acceleration (inference)
A passenger car is accelerating to the right. In rear of the car, there is a light source and in front, an observer. The number of waves existing in the passenger car during acceleration will be larger than before acceleration. The difference between acceleration and non-acceleration will not be relative but be absolute. PS : Inside of the passenger car is vacuum.
Hiroji kurihara ha detto:
About emission theory
The speed of light inside glass is c / n. And it is said that in the space between molecules in glass, light moves at c. If so, the speed of light going out of the glass (to vacuum) will also be c. The emission theory will be true.
Hiroji kurihara ha detto:
Local inertial frame
An elevator is falling in free fall. Imagine many mass points regularly arranged in space inside the elevator. The direction and magnitude of vectors of the inertial force acting on the mass points are all the same. There will be no local inertial frame.
Inertial force and gravity are acting on each mass point in the falling elevator. Is the action-reaction law valid for these two forces ? However, it is not problem of relativity.
Hiroji kurihara ha detto:
Local inertia frame
On a plane (no friction), two elevators are separating horizontally. One is in accelerated motion, the other is in non-accelerated motion. With an accelerometer, it is possible to determine which one is accelerating. And there is no local inertial frame in an accelerating elevator.
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Hiroji kurihara ha detto:
Action-reaction law (reposting)
The original text of Newton’s third law starts with action and reaction (F=-F). But many texts in books and websites start with two bodies (objects). Why? To prevent people from realizing that the inertial force is not fictitious force, but true force.
Hiroji kurihara ha detto:
Speed of light can vary (restating)
For an observer, speed of sound waves and water surface waves can vary. It is the same for light waves propagating through aether. It is the same also for light waves that follow the emission theory. Goodby relativity.
Hiroji kurihara ha detto:
Speed of light
In the value of speed of light measured by Evenson et al (in 1972), error is ± 1.1 m / s. If the measurement device is moved at a higher speed, a different value will be read. Also, if light source is moved, a different value will be read.
Hiroji kurihara ha detto:
Accelerated frame and non-accelerated frame
A passenger car is accelerating to the right. Light is emitted from light sources (frequency is constant) settled on rear and front walls in the car, and interference fringes are observed at the center of the car. Varying of interference fringes will reflect varying of acceleration. Sagnac effect will also occur on acceleration in a straight line.
Hiroji kurihara ha detto:
Acceleration and non-acceleration
A laser beam is emitted from the light source on the right wall inside a passenger car (vacuum) and is reflected by a mirror on the rear wall. Then, standing waves are formed. Now, this passenger car begiThereacceleration to the right. Standing waves will lose their form and disappear. Also, the speed of light can be said that it is not constant.
Hiroji kurihara ha detto:
Allow me to rewrite the above !
Acceleration and non-acceleration
A laser beam is emitted from the light source on the right wall inside a passenger car (vacuum) and is reflected by a mirror on the left wall. Then, standing waves are formed. Now, this passenger car begins acceleration to the right. Standing waves will lose their form and disappear. Also, the speed of light can be said that it is not constant.
Hiroji kurihara ha detto:
About speed of light
Snails, TGV trains, sound waves (in air), sound waves (in railroad rails), earthquake waves, light waves (follow emission theory : valid for a few seconds only : in vacuum), light waves (follow aether frame), light waves (in air : in various pressures), light waves (in media other than air). All follows Galilean transformations.
Hiroji kurihara ha detto:
Emission theory (rewritten)
In the speed of light measurement by Evenson et al.(in 1972), error was ± 1.2m / sec. This value seems to be unrelated to directivity of the light path on the celestial sphere. This will support the emission theory.
As written formerly, in outer space, light is propagated in two ways. Imagine a mirror that is reflecting star light waves.
Hiroji kurihara ha detto:
Lorentz transformation
In a web-site titled “Why is the Light Speed constant ?” (In Japanese), there is a writing as follows. “I googled ‘Einstein, constancy of speed of light, evidence’. But I couldn’t find any evidences for it in literatures. Regardless of this, Lorentz transformation seems to be active ?
bevitorimgrazia ha detto:
Lorentz transformations are valid. The speed of light in vacuum is a constant of the universe. There is evidence. Buon Natale!
Hiroji kurihara ha detto:
Difference of color
The color is said to be due to the difference in the wavelength of light. It must not be. It must be due to the difference in the frequency. The color of the light varies as an observer move closer to or further from the light source. The wavelength of light coming in this situation cannot vary. The relativity twists the facts.
Light rays (monochromatic laser) are emitted from one light source into water and air. The frequency in both media are the same, but the wavelengths are different. What is the color development of the color film exposed in both media?
Hiroji kurihara ha detto:
Speed of light will be variable
Speed of light (for an observer) will be variable. One thought experiment that shows this consists of a moving mirror in outer space and incident and reflected light (of a certain star). In this thought experiment, light is propagated in two ways (propagation on aether and propagation follows the emission theory for a few seconds only). However, the following thought experiment will be possible also.
A space probe loading a frequency measuring device is moving along the light path of a certain star in outer space. Wavelength of incoming star light is not affected by the motion of the space probe. That is, the speed of light varies in the formula : light speed = frequency X wavelength.m
bevitorimgrazia ha detto:
The speed of light is always constant.
Hiroji kurihara ha detto:
Speed of light is variable
A book says that a photon (even a single one) has attribute of wavelength. Yes, wavelength is in the equation that shows energy and momentum of a photon (even a single one). And the motion of an observer has no effect on the wavelength of a photon of light coming from outer space. The equation light speed = wavelength X frequency shows that light speed is variable.
Hiroji kurihara ha detto:
Laser light is coherent
Laser light is coherent. So, interference fringes will be visible when lasers of two light sources (the same frequency) separated in space are overlapped. Experiments using this phenomenon in air and vacuum will be a follow-up to the MM experiment.
Hiroji kurihara ha detto:
Laser light is coherent (P.S.)
Laser sources are placed at both ends of the long horizontal supporting arm, and interferometer is placed off the midpoint between the two. Supporting arm rotates gently (on the ground surface) as in the MM experiment. This experiment will be sufficient on an easy chair.
Hiroji kurihara ha detto:
Bending of light
A passenger car is moving in a uniform accelerated motion to the right. In the car, a ray of light emitted downward from the roof will be bent to the left (from viewpoint of the car). This is not a phenomenon caused by gravity.
Hiroji kurihara ha detto:
Speed of light variable
In outer space, toward a star, an observer is moving in a uniform accelerated motion. The value frequency is increasing. Therefore, in the equation light speed = frequency X wavelength, one of the two : wavelength or light speed must vary. It must be the speed of light that vary.
Hiroji kurihara ha detto:
Gravitational redshift
Laser beam is emitted from the ground, reflected by the mirror at the top of the high tower, and returned to the ground (close to the emitted point). Frequency at these three points are the same. As shown before (Dec. 20, 2020), the difference in color is due to the difference in frequency, not wavelength. Therefore, there will be no gravitational shift (red or blue) in the returned light. The same will be true for the light coming back from geostationary satellites.
Translated with http://www.DeepL.com/Translator (free version)
Hiroji kurihara ha detto:
Gravitational redshift (reference)
A passenger car is moving in a uniform accelerated motion to the right. The light emitted from the light source on the right inner wall (frequency is constant) is measured on the left inner wall. The wavelength is measured longer than when the passenxger car is not accelerating. The frequencies are the same. As shown before (Dec 20, 2020), difference in color is caused by difference in frequency, not by difference in wavelength. No redshift will be observed.
Hiroji kurihara ha detto:
Sagnac effect and medium
A pillar of glass laying horizontally is accelerating to the right. Light is emitted from light sources (frequency is the same and constant) settled on rear and front ends of the pillar, and interference fringes are observed at the center of the pillar. Varying of interference fringes will reflect varying of acceleration. Sagnac effect will also occur on acceleration in a straight line.
Hiroji kurihara ha detto:
About contancy of speed of light
Is light speed constant or not ? It will depend on experiment. In an experiment, it is constant (invariable).In an experiment, it is not constant (variable).
Hiroji kurihara ha detto:
Is equivalence principle true?
A disk is rotating. Tilt of axis of rotation is 45 degrees. Centrifugal force (inertial force) and gravity will be non-interfering and independent. In addition, gravity of the moon is also acting.
Hiroji kurihara ha detto:
About constancy of speed of light
In outer space, light is propagated on aether. On it, there is no doubt because proper motion of every star (including planets) is ignored. Therefore, constancy of light speed is unthinkable for an observer moving relative to aether.
Hiroji kurihara ha detto:
About aether
A star is shining in outer space. From the light (spherical waves) emitted from this star, effect of proper motion of the star is eliminated (cancelled) by aether. Therefore, light of two adjacent stars on the celestial sphere always arrive at the earth at the same speed (the same aberration).
Light of stars on the celestial sphere shows the position of light source only. It is caused by aether.
Motion of the star in the line-of-sight direction (relative to aether) will vary f and λ of light. Also it will vary bright lines of spectrum.
Hiroji kurihara ha detto:
Speed of light (a thought experiment)
Descartes said like this, “divide the difficulties”. The formula for
sound Doppler effect is simplified as follows.
In vacuum, an observer is moving (at different speed) relative to a
light source stationary. Formula c = fλ is valid for light source
and observer each. The two formulas show the reality as it is. In
the observer’s formula, c is variable.
Hiroji kurihara ha detto:
Aether is real
There are words : solar apex and solar antapex. Following is a related thought experiment. In outer space, there is a space probe. Outwardy, it looks like sea urchin on beach. Main body is sphere and many long tubes are attached. These tubes are pointed on the celestial sphere at equal intervals. Light sensor at bottom of each tube detects light that reaches bottom of tube.
Recall illustration of aberration. If space probe were in a uniform linear motion, all tubes will not detect light. As a result, uniform linear motion of space probe relative to celestial sphere and aether will be revealed quantitatively.
Hiroji kurihara ha detto:
Apology
It seems that my previous post (February 28) was not valid thought experiment. Sorry for that. But, how about if uniform linear motion of space probe is assumed to be uniformly accelerated motion in a straight line? No, it would still not be an impactful thought experiment.
Hiroji kurihara ha detto:
About aberration
◎ If observer is stationary relative to aether, no aberration will occur. Aberration occurs due to observer’s motion relative to aether.
◎ Aberration is not a phenomenon of each star, but a phenomenon of distortion of celestial sphere or aether frame.
Hiroji kurihara ha detto:
Secular aberration and aether : an essay (part 1)
In my mind, an illustration of planetary aberration of Mars (I saw in a textbook) is even now attractive. Like that, is it possible to illustrate secular aberration of Mars ? The following is a prototype. Orbits of Mars and Earth are assumed to be parallel lines (as equal sign=). Mars is located right above Earth, and two stars are moving to the left at 30 km/sec. Geometric center of spherical waves of Mars does not move in the frame of aether. Therefore, light of Mars comes to Earth from slightly behind. On the other hand, aberration observed in hollow tube (located in outside the atmosphere) displaces the apparent position of Mars slightly forward.
Hiroji kurihara ha detto:
Secular aberration and aether : an essay (part 2)
Two phenomena will cancel each other out and Mars will be visible at right above. This total cancellation will be actual (regardless of direction and distance. imagine letter F and also distorted F). In other words, in the appearance of objects of solar system, positional shift due to secular aberration will be cancelled out.
Note : Ratio of horizontal lines to vertical line of letter F is the same in the sky and in a tube. It will be the same also in distorted F. ct: vt = ct’: vt’.
Hiroji kurihara ha detto:
Constancy of speed of light
Light of a star arriving in space is being reflected by a mirror. Speed of reflected light relative to the mirror is c. Speed of incident light relative to the mirror is also c? Since f of the two lights is the same, λ is also the same?
Hiroji kurihara ha detto:
Constancy of speed of light
Basic problem seems to be left in speed measurement (also in wavelength measurement) of light. A thought experiment below will be free from the problem.
Remind Fizeau measurement of light with one gear. This thought experiment done on moon’s surface is with two gears. A device telescope-like is pointed at a star, and star light is visible through two gears (the two are placed on front and rear of the device). When two gears start rotation (rotation speed of the two is the same), and speed increases, starlight will disappear.
Note: By measurements of plural stars, existence of aether will emerge.
Hiroji kurihara ha detto:
Constancy of speed of light (in vacuum)
If light source and measuring device are in an inertial frame (A), speed of light is c. On the other hand, if light is coming from different inertial frame (B), speed will not be c. And if light is coming from that inertial frame (B), and is transmitted or reflected by glass or mirror located on this inertial frame (A), speed will be c.
Note: Above all is in the area where the emissions theory is valid.
Hiroji kurihara ha detto:
About emission theory
For a few seconds only after emission, light will follow the emission theory. After that, light will follow aether frame. In the light emitted from Earth, Moon is in the area where the emission theory will be valid.
Reference: Matzo 18, 2020
Hiroji kurihara ha detto:
Space and time will be absolute (a supposition)
Perhaps, space and time each will be absolute. Each will not be affected by any phenomenon or situation (at all). If so, relativity is impossible.
bevitorimgrazia ha detto:
Space and time are not absolute. Ciao!
Hiroji kurihara ha detto:
Constancy of speed of light will be impossible
Plane waves of light coming from the upper left are reflected to the upper right by an upward-facing mirror (in outer space). Generally, speed of the two lights is different, and angle of incidence and reflection is different. By the way, the other mirror is moving vertically. Constancy of speed of light will be impossible.
Hiroji kurihara ha detto:
Constancy of speed of light will be impossible
Plane waves of light come from the upper left (in outer space) and is incident on two glass cubes A and B. A is stationary and B is moving upward at a constant speed. Wavelength of light in cubes is A > B. Since speed of coming light relative to the cubes is different, the wavelength in the cubes is also different.
Hiroji kurihara ha detto:
Constancy of speed of light (Reexamination)
Constancy of speed of light is not possible always. No, it will be possible limitedly in the following two events only. Btw, speed of light in mediums is not subject of this reexamination.
1) A geometric point and a light source are in the same inertial frame. Distance between the two is supposed to be within a few light seconds.
2) A geometric point is stationary in aether frame. Light propagated in aether comes to this point. Distance from the light source is supposed to be more than a few light seconds.
Translated with http://www.DeepL.com/Translator (free version)
Hiroji kurihara ha detto:
It will be impossible
Constancy of light speed will be impossible. It will be clear if the formula c = f λ is looked at.
Equivalence principle will be impossible. It will be clear if the formula F = m a is looked at.
Hiroji kurihara ha detto:
Allow me to rewrite my post (25.April).
Constancy of speed of light (Reexamination)
Constancy of speed of light is not possible always. No, it will be
possible limitedly in the following two events only. Btw, speed of
light in mediums is not subject of this reexamination.
1) A measurement point and a light source are stationary in the same
inertial frame. Distance between the two is within a few light
seconds. Speed of light is c.
2) A measurement point is stationary in aether frame. Light
propagated in aether is coming to this point. Distance from the
light source is more than a few light sveconds. Speed of light will
not be c.
Translated with http://www.DeepL.com/Translator (free version)
Hiroji kurihara ha detto:
Supplement to my post (July 10)
1) In space far from light source, propagation of light follows aether frame. See again various aberrations.
2) In space close to light source, propagation of light follows the emission theory. See again various facts.
3) In outer space, a mirror is moving at a uniform speed. Plane waves of light of a star are reflected by this mirror. 1) and 2) must be seen as facts.
Hiroji kurihara ha detto:
Aether
Existence of aether (uniform isotropic) is precondition for Newton’s first and second laws of motion. There can be no other explanation.
Hiroji kurihara ha detto:
Aberration (reexamination)
Aberration is caused by various motions of Earth relative to stationary aether (uniform isotropic). Light that enters upper air of Earth (from aether) is bent in the direction of motion of Earth. As a phenomenon, aberration is completed in the upper air. The same as refraction.
Therefore, illustration of raindrops and an umbrella is NG. Result of Airy’s experiment with a water-filled telescope is only natural. It is said that apparent displacement of stars is displaced in the direction of Earth’s motion, but in fact, it will be the opposite. You can check this by drawing light bending (in upper air) on a paper.
Hiroji kurihara ha detto:
Free fall (reexamination)
Problem of free fall in an elevator will be problem of resultant force of inertial force and gravity (nothing else). In any local area, it will be so also.
Note: Inertial forces acting on every local area of the cabin (supposition: mass of every local area is m) is the same ma.
Note: External force (gravity) and inertial force acting on entire cabin are equal (Newton’s second law and third law of motion). How about in local area ? To image will not be difficult.
bevitorimgrazia ha detto:
A body in free fall is equivalent to a body not subjected to forces. A system accelerated in one direction (upwards) is equivalent to a system in which gravity acts in the opposite direction (downwards). Ciao.
Hiroji kurihara ha detto:
Supplement to my post (sep 4 2021)
Even in a resultant force, inertial force is inertial force, and gravity is gravity. Vector follows own law each and is inviolable.
Cabin is made by a 3D printer. Material is uniform.
On a plane (no fliction), elevator cabin is moving in a uniformly accelerated linear motion (to the right). Inertial force acting on every local area (mass is m) of the cabin is the same ma (vector is the same also).
Hiroji kurihara ha detto:
Free fall (an essay)
An elevator cabin is falling in free fall. Cabin is made up of n mass points (with the same mass of m). Free fall is supposed to be a uniform acceleration.
Inertial force acting on each mass point is the same ma. No exceptions. On the other hand, magnitude of gravity acting on each mass point is not the same slightly. Difference depends on the position of the mass point.
P.S. For the entire cabin, magnitude of inertial force and gravity is equal.
Hiroji kurihara ha detto:
Mass (supposition)
Two bodieds (mass m each), tied (up and down) by a string (zero mass), are in free falling. As they fall, tension of the string increases. This increase will follow Newton’s law. Inertial mass and gravitational mass should simply be mass.
Hiroji kurihara ha detto:
Is Einstein’s theory of relativity a lie ?
Propagation of light follows the aether frame, the emission theory, and the air (mediums) frame. In any case, the speed of light varies for a moving observer.
Hiroji kurihara ha detto:
Light propagates through aether frame (reconfirmation)
Various aberrations show the existence of aether. Various motions of the Earth in the uniform isotropic frame of aether result in various aberrations. Light propagates at a constant speed in aether frame.
That is, Propagation of light in aether is the same as the propagation of sound in air. Therefore, Doppler effect is the same. Doppler effect for a moving observer is also the same. Neither speed of light nor speed of sound can be constant.
Hiroji kurihara ha detto:
Lorentz contraction
Plane waves of starlight (wavelength is constant) is arriving from upper left 45 degrees. Two spacecrafts are sailing in the right and left directions. Number of waves hitting the front and rear ends (A and B) of each spacecraft is the same. Therefore, number of waves existing between A and B is invariant (for both spacecrafts, regardless of lateral motion). Lorentz contractions will be impossible.
Relativity of simultaneity will be impossible also.
Hiroji kurihara ha detto:
Free fall (an essay)
Rewriting of my past post (Sett 7 2021)
An elevator cabin is falling in free fall. Cabin is made up of n mass points (with the same mass of m). Imagine a single moment of falling.
Inertial force acting on each mass point is the same ma. No exceptions. On the other hand, magnitude of gravity acting on each mass point is not the same slightly. Difference depends on the position of the mass point.
P.S. For the entire cabin, magnitude of inertial force and gravity is equal.
Hiroji kurihara ha detto:
About light (re-post)
◎ How does light propagate ?
1) Emission theory (for a few seconds only)
2) On aether (after the above)
◎ How is light sources visible ?
1) Light sources beyond a few light-years are stationary on the celestial sphere (aether). Effect of emission theory is too small to be found (e.g. binary stars). Also various aberrations.
2) Moon is by emission theory.
3) Celestial bodies in solar system (excluding moon) are depending on planetary aberrations. Also, depending on other aberrations (but, is secular aberration offset ?).
◎ Motion of light seen by observers
Same as bodies. Follows Galilean transformation. Constancy of speed of light cannot be hypothesized. By the way, light waves (c = fλ) and photons (rays) are basically different. Especially in outer space.0
Hiroji kurihara ha detto:
Gravitational time dilation
Laser beam (frequency is constant) emitted from the ground is reflected by the mirror at the top of the high tower, and returned to the ground. Frequency at these three points is the same. There is no time dilation.
Hiroji kurihara ha detto:
Inertial force is not fictitious
On a plane (without friction), a body is pulled to the left by two strings and to the right by one string. The tension of each string is the same F. That is, the body is accelerating to the left. Inertial force is not fictitious (the third law of Newton’s motion holds at the left end of the body).
Hiroji kurihara ha detto:
34 notices on anti-relativity
Shown below (mine, selected) will be simple, certain and acceptable (sorry, in Japanese : 1-36 excluding 11&36).
http://www.asyura.com/0306/idletalk2/msg/1242.html
Hiroji kurihara ha detto:
Selected notices in English
28 selected notices (anti relativity) in English are added in a site below. Yes, these are selected.
http://www.asyura.com/0306/idletalk2/msg/1242.html
Hiroji kurihara ha detto:
Aberration on the moon
Many of widely accepted explanations for aberration will be right if these are on the moon. Illustration of raindrops and an umbrella will be OK. But as already mentioned, aberration on the earth is completed in the upper atmosphere. The explanation for aberration of earth must be rewritten.
Aberration (both on the moon and on the earth) is incompatible with constançy of the speed of light, and existence of aether is a prerequisite.
Hiroji kurihara ha detto:
Bending of light (by gravity)
Light will not be bent by gravity. Because…
1) At the center of Milky Way galaxy (where we live), it’s said that a black hole exists. Around it, several stars are revolving. These orbits seem to be natural.
2) How about a star, before it is occulted by the moon or Jupiter ?
Hiroji kurihara ha detto:
Perihelion shift of Mercury (an essay)
Perihelion shift of Mercury is about 574 arcsec per century, and main cause is said to be perturbations due to the gravity of other planets (Venus is about 280 arcsec, Jupiter is about 150 arcsec).
There is a question. At the left end and the right end of the orbit of Mercury (a view from above), force that accelerates and decelerates Mercury by perturbation by other planets will be equal (in probability). Especially in the span of the century. Main cause will not be gravity of other planets.
P.S. Perturbations of other planets will be caused only by the position of these on the orbits (and speed of gravity will be infinite).
Hiroji kurihara ha detto:
Accelerated motion & light
On the moon’s surface, a passenger car is accelerating to the right. A starlight (horizontal) is passing through a hole A in the front wall, and reaches B in the rear wall of the passenger car. Frequencies of A and B will be the same. Therefore, number of waves existing between A and B will be constant (even at different accelerations). Above is not only for uniform acceleration but also for non-uniform acceleration.
On the moon’s surface, a passenger car is accelerating to the right. A light emitted from light source A’ in the front wall reaches B in the rear wall. What is frequency of A’B ? How many waves exist between A’B ?
Hiroji kurihara ha detto:
Stationary aether
In outer space, an observer (in an inertial frame) is measuring light of stars. The number of stars being measured is reasonable and there is no clumping of stars on celestial sphere. What is measured is frequency and wavelength of each star’s light, i.e., speed of light. The results will reveal the existence of stationary aether.
Note: Existence of stationary aether is not in doubt due to aberration.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
In Wikipedia (in Japanese version : “Apsidal precession” 近点移動), there is
a table named “Perihelion shirt of planets of solar system”. These seem to
varies greatly depending on the distance from the sun and the
presence or absence of satellites. Newcomb’s table and explanation
of relativity would be NG.
A planet called Vulcan is revolving the orbit of Mercury. Assume
that mass is the same and diameter is half to Mercury. The
gravitational force of the Sun and the centrifugal force due to the
orbital motion each would be Mercury > Vulcan > mass point.
Newcomb’s table (of perturbation values of the planets acting on Mercury) should be nonsense.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Mercury is perihelion shift and binary star is periastron shift. Two shifts are smooth and in one direction. Two must be considered to be a two body problem.
See again that table (in 近点移動). Values are observed values. And these each will be two body problem.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Recurring orbits seem to show that this is a two body problem.
Hiroji kurihara ha detto:
Perihelion shift of Mercury (an essay)
Scaled models of Mercury and Vulcan (of my post, April 7) are falling in free fall. Magnitude of acceleration is probably Mercury > Vulcan > mass point. At the beginning of falling, centers of gravity of three models are at the same horizontal level.
A web-site says, periastron shift are many in close binaries. This will be a two body problem.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
5.75, 2.04, 11.45. These are observed value of perihelion shift of Mercury, Venus, and Earth (in a table of a website. Value are in arcsec/year. Table covers to Neptune). The decrease in Venus will be due to distance from the Sun, and the increase in Earth will be due to the Moon.
Hiroji kurihara ha detto:
Perihelion shift of Mercury
Here is a close binary. A companion star approaches the main star and is passing the periastron on orbit. Actual orbit of companion star is different from orbit of mass point of it. Difference will be due mainly to size of companion star (mass distribution).
Hiroji kurihara ha detto:
Perihelion shift of Mercury
In a close binary, gravity of main star is acting on companion star. Magnitude of gravity is inversely proportional to square of distance. Therefore, if size of companion star is large, gravity that acting is somewhat larger (even if mass is the same).
Note: Here is a horizontal line. From the right, gravity of main star is acting. On the line, we see three masses. Mass of right and left is m/2 and middle is m (interval is the same). Magnitude of gravity acting will be m<m/2+m/2.q
Hiroji kurihara ha detto:
Free fall (rewrited)
A body is falling in free fall. On a horizontal plane, an observer is moving in a uniform linear motion. To the observer, the falling body draws a parabola. Every point of the body is accelerating.
An elevator is falling in free fall. Assume, that there are two sources of gravity and there is a considerable distance between the two (even when viewed from elevator). How does equivalence principle explain ?
Hiroji kurihara ha detto:
Reviewing the Heliocentric Theory
Motion of earth is various, such as rotation, revolution, uniform linear motion of solar system, and others. And there is aberration to each. These are reflection of motions relative to uniform isotropic aether. Qualitative and quantitative.
Hiroji kurihara ha detto:
Newton’s Third Law of Motion
As an action and reaction, there are two examples about gravity. One is normal force. The other is Inertial force in free fall. The two should be accepted qualitatively and quantitatively.
Hiroji kurihara ha detto:
Newton’s Third Law of Motion
Does gravity always act as action? Is inertial force always reaction? It is a problem statement. As an example, there is an elevator cabin in free fall (mass is m).
Hiroji kurihara ha detto:
Galaxy Rotation Curve
Allow me to post an idea about the above. It is contraction of the size of galaxies. But in Wikipedia (in English), there seems to be no mention.
Hiroji kurihara ha detto:
Galaxy Rotatin Curve
Is it because gravitational sources (that revolve galaxy) also extend over the disk of galaxy ? Is it because the state of inverse square law of gravity is different from that of solar system ?
Hiroji kurihara ha detto:
Speed of light
In Wikipedia’s “Dispersion (optics)”, there is a video of dispersion. By a prism, white light is spectrally dispersed. The speed of light is different between red and violet light after dispersion (spectroscopy). It is obvious at a glance.
Hiroji kurihara ha detto:
Apology, Adjacent my post “Speed of light” (on prism) was wrong. Sorry.
To admin, i thank you always for accepting of my posts (I appreciate if you erace this and that two posts).
Hiroji kurihara ha detto:
Perihelion Shift of Mercury (repost)
Size of Sun relative to Mercury will be main cause of this problem (however, will be incompatible with Newton’s spherical shell theorem).
There are two drawings in which Mercury and gravity source (considered as a point) are drawn. In one drawing, gravity source is Sun and its mass is m. Distance from Mercury is 100. In the other drawing, there are two alternative gravity sources to the sun, Mass is m / 2 each. Distance from Mercury is 99 and 101(aligned on a straight line extending from Mercury). Magnitude of the gravity acting on Mercury is the latter > the former. It can be ignored on Neptune.
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Perihelion Shift of Mercury (repost)
In a drawing, a fixed star F homogeneous true sphere and a planet P orbiting nearby are drawn. F acts gravity on P. Is magnitude of gravity on P dpending solely on mass m of F and distance r between FP ? No, the size of F may also have a slight effect. This will be main reason for the perihelion shift (secondary reasons are omitted). Newton’s spherical shell theorem may not be perfect.
Square of 99 is 9801. Square of 101 is 10201. See above my post.
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Perihelion Shift of Mercury (Gleanings)
It is said that magnitude of Sun’s gravity acting on orbiting Mercury depends only Sun’s mass m and distance r between the two. But in reality, in addition, there will be an effect of Sun’s size. Gravity will be slightly greater. Therefore, Mercury’s orbit that has left aphelion will be slightly inward (and r will also be shorter), and then, perihelion will be shifted.
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Perihelion Shift of Mercury (correction)
Sorry, I ask to delete my post (giugno 9) and replace it with following.
It is said that magnitude of Sun’s gravity acting on Mercury depends on Sun’s mass m and distance r between the two. However, in reality, Sun’s size will have effect. Noticeably on Mercury, which is close to Sun. Gravity will be greater slightly. Let’s focus on orbit just after Mercury passes perihelion. Orbit will be slightly inward (r will be shorter also). This means that size of Sun shifts position of perihelion in the next around.
P.S. Orbit to be compared is orbit when Sun is a point.
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Perihelion Shift of Mercury (an essay)
Increase in gravity due to size of Sun will depend on distance r between Sun and Mercury. This increase in gravity will be larger at perihelion and smaller at aphelion. Is this the reason for perihelion shift of Mercury ? Sorry for my repetitive posts.
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Perihelion Shift of Mercury (an essay)
This is a thought experiment on close binary stars (imagine on a plane no friction). Imagine the same homogeneous true sphere with mass m. Main star is three spheres and companion star is two spheres (these are attached as a single unit). These are on a straight line. Gravity exerted and affected by and to each will depend on size of true spheres (of here and there). Forget the spherical shell theorem. Two-body problem is also complicated.
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Perihelion Shift of Mercury (an essay)
This is a guess. Because of size of Mercury (in its elliptical orbit), centrifugal force will be increased. And, as Sun is near, effect of size will be larger (other planets are more like point).
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Perihelion Shift of Mercury (essay)
Mercury is revolving in orbit. Size of Mercury increases centrifugal force acting on revolving Mercury. This will be reason for perihelion shift of Mercury. The angle is about 5.75 arc-sec in a year.
Size of Mercury will also increase gravity of Sun (which acts on Mercury). But it will not affect direction of long axis of elliptical orbit (after a round: that is, it will be unrelated to perihelion problem).
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Allow me to revise my yesterday’s post.
At each of Mercury’s mass points, centrifugal force and Sun’s gravity are canceled out. Like an elevator in free-falling. In formula of centrifugal force, “r” (distance between the two) is as it is. But, in formula of gravity, it is inversely proportional to square of distance of ” r”. Therefore, Mercury’s size will increase effect of centrifugal force. Sorry, only I can is qualitative saying (and these are guess).
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Perihelion Shift of Mercury (an essay)
This is an idea. In this problem, planets seem to be treated as a point. Now, planet is divided into two hemispheres. One is closer to Sun and the other is far from Sun (back to back). If the planet is far from Sun, centrifugal force and gravity each acting on two hemispheres will be the same(1/2). But, how about Mercury? We must imagine a spherical surface that centers on Sun, and this spherical surface coincides with center of Mercury ? And then, in whole Mercury, centrifugal force will be larger and gravity will be smaller. It is compared to Mercury as a point.
Sorry, please ignore my two posts immediately preceding this one.
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Perihelion shift of Mercury (an essay)
Another inference. Half mentioned already at end of May. Mentioned was problem posing about a single gravitational source and gravitational sources separated into two. Let’s call this effect as the 99-101 effect. The 99-101 effect is equal to the two of binary stars. The 99-101 effect is a candidate for explanation of perihelion shift of Mercury. However, it is incompatible with attempt to explain by Sun’s spherical surface. I don’t know which one is hopeful.
If gravity source is close, size of gravitational source will increase gravity slightly. Then, Newton’s sphericl shell theorem must be reviewed.
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Perihelion Shift of Mercury (an essay)
Centrifugal force is inertial force and cannot be the first cause of perihelion shift. The 99-101 effect mentioned above (tentative naming: contrary to Newton’s spherical shell theorem) will be caused by size of Mercury, size of Sun, and distance between Mercury and Sun. On Mercury, these have effect on gravity and it will be the first cause. And then, direction of elliptical orbit may be shifted. At perihelion, this effect will be greatest.
Magnitude of perihelion shift of planets with satellite is far superior. This is probably because gravity of Sun acting on satellite in half orbit close to Sun is far superior.
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Perihelion Shift of Mercury (an essay)
Shift is smooth, like a hand of clock. Mainly, it will be two-body problem.
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Equivalence Principle
On a mass point, two forces of equal magnitude are acting from the left and right. Two forces are tension, gravity, and inertial force. Wnen, left and right are not distinguished, there are five possible combinations (there is no combination of inertia force and inertia force). Is the equivalence principle still insisted upon ?
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Accelerated Motion is not Fictitious
A horizontally long container is filled with fluid. This container is being accelerated to the right. In the container, pressure of the fluid will be high on the left and low on the right (effect of gravity is separated question). Accelerated motion is not fictitious.
But is this worth writing down ?
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Inertial Force is not Fictitious
The same five bodies (mass m) are lined up sideways on a horizontal plane. Five bodies are tied with strings. Assume that horizontal plane is zero friction, and mass of strings is zero. On right most body, force of 5ma is acting and five bodies start a uniform linear accelerating motion toward the right. Tension acting on four strings are, from right to left, 4ma, 3ma, 2ma, and 1ma. For any observer.
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Inertial Force is not Fictitious
In addition to acceleration, there are jerk, snap, etc. And accordingly, inertial force must be varied. Inertial force cannot be fictitious.
There must be absolute rest frame, so there are acceleration, jerk, snap, etc. In wikipedia (Japanese), in “Acceleration”, there is a table titled “Comparison of magnitude of acceleration”. Many examples of acceleration are shown in 18 division by magnitude.
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Equivalence Principle
Starting is to accept inertial forces as inertial forces. In a free-fall elevator, inertial force and gravity acting on the entire cabin is equal. As Newton’s third law of motion shows. Magnitudes of inertial force and gravity acting on each mass point (assume fluid) in elevator are as shown by Newton. That’s all.
Eh, the equivalence principle? Will be worthless at all.
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Equivalence Principle ?
A body is suspended by a string from roof of a passengercar. The same two passengercars started at the same jerk at the same time. Tension of string is increasing, and string broke at about the same time (for both person in the car and on on the ground). Inertial force and gravity will not be equivalent.
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Moon and Sun (Hypothesis: Restated)
Assume that sun’s light follows emission theory for a few seconds only. Matter of those on few seconds will be indistinguishable from earth. That is, sun is being in aether. So, light-time correction. And, light-time correction will be offset by secular aberration.
Assume that moon’s light follows emission theory for a few seconds only. So, visible position of moon is exactly where it is. Just like sun. But the mechanism will be different.
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About Light
In outer space, frequency and wavelength of two star lights (coming from the opposite direction) are measured (at the same time). Sum of the speed of two lights will be constant. It is 2c or close to 2c.
Above shows that in outer space, light is propagated relative to aether. And, speed of light relative to an observer is not constant.
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Michelson-Morley Experiment
In a book Theory of Relativity by Pauli, W 1958, it’s written as follows (quoted from English version ; in 1-6). “Rather should one say that for an observer moving with medium, light is propagated as usual with velocity c/n in all directions”. It seems to be the “very and true explanation” for M-M experiment (done in air) !!
There is Einstein’s saying the same as above Pauli’s. Therefore, probably, he said that he didn’t know M-M experiment (and he mutters, “M-M experiment (done in air) is nonsense and I have no obligation to talk about it”).
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Secular aberration
This is what comes into my mind. Three aberrations; daily, annual, and secular seem to form a closed necklace drawn in one stroke. Pearl are 365 (assuming star is visible even during day time).
The star change its position at all times. Trajectory drawn on celestial sphere in one year will not be a ellipse but be an extended necklace with pearls.
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Does Aether Exist?
Two spacecrafts are sailing from left to right in outer space. It is as far apart as Mars. Speeds are v and 2v. Two spacecraft flash at the same and long time interval. What is interval between the position of flashes on the celestial sphere as seen from the Earth ?
WDoes Aether Exist?
Two spacecrafts are sailing from left to right in outer space. It is as far apart as Mars. Speeds are v and 2v. Two spacecraft flash at the same and long time interval. What is interval between the position of flashes on the celestial sphere as seen from the Earth ?
Does Aether Exist?
Two spacecrafts are sailing from left to right in outer space. It is as far apart as Mars. Speeds are v and 2v. Two spacecraft flash at the same and long time interval. What is interval between the position of flashes on the celestial sphere as seen from the Earth ?
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Does Aether Exist ?
Two spacecrafts are sailing from left to right in outer space. It is as far apart as Mars. Speeds are v and 2v. Two spacecraft flash at the same and long time interval. What is interval between the position of flashes on the celestial sphere as seen from the Earth ?
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Local Inertial Frame (repost)
Inertial frame or non-accelerating frame, is a frame that is non-accelerating with respect to aether. So, in free-falling elevator, there is no inertial frame, even locally. Term “local inertial frame” will be nonsense.
In the elevator, equal acceleration due to falling is acting on every mass point. There are no exceptions. Even locally.
There can be composition or partial composition of inertial force and gravity. But the two are inviolable to each other. Inviolable, qualitatively and quantitatively.
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Aether (repost)
All kinds of aberration are caused by motion of Earth. Qualitatively, quantitatively. For example, cycle of annual aberration is 365 days. It is reflection of motion of Earth. On the other hand, any motion of star’s side has no influence. Only position on the celestial sphere is valid. These facts will be explainable only by aether.
For an observer stationary with respect to the aether frame, there will be no aberration.
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Elevator Cabin and Inertial Frame
On a plane (no friction), an elevator cabin is accelerated horizontally by tension of a rope. Tension of rope is controlled so that horizontal acceleration is the same as free fall. Not only at infinite small area (local area), but also on whole area of this elevator cabin is inertial frame ?
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Equivalence Principle
An elevator cabin is slowly falling due to gravity of an asteroid below. In addition, a rope is extending below the elevator cabin, and the rope is under artificial tension. Let us assume that acceleration g due to gravity (uniform acceleration) is equal to acceleration a due to tension. The equivalence principle should be forgotten.
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Gravitational Acceleration
Gravitational acceleration is a compound word. But is it worth it? About acceleration, what is special ? Nothing, will be.
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Relativity of Simultaneity
On the moon’s surface, a passenger car is moving to the right. From the point at the center of ceiling, light rays are emitted at 45 degrees downward to the left and right. So, on the floor, there are two points of light. Position of two points are symmetrical for an observer in the car and stands on the moon’s surface. This drawing should be understood by the emission theory.
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Absolute Rest Frame (proposal)
Accelerated motion, non-accelerated motion (uniform linear motion) and combined motions of a body all will be motions relative to absolute rest frame.
1) Uniform linear motion of a body is through.
2) Accelerated motion of a body will have corresponding inertial force.
Absolute rest frame can be easily measured (as aether drift) using light.
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Absolute Rest Frame
Newton’s Bucket” is a thought experiment that assumes the existence of absolute rest frame because of the rotational motion accompanied by inertial forces. Let’s take the thought experiment one step further. Inertial force must occur by “all motions except uniform linear motion” of a body with respect to absolute rest frame. Without exception. And inertial force is real existence in physics.
Note: Uniform linear motion and other motions can be superposed. And, superposition is very universal.
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Absolute Rest Frame & Aether Frame
It would be easy to reveal the aether frame by optical means. By measuring aether drift. On the other hand, non-accelerated motion, accelerated motion (uniform linear motion and all other motions) of bodies are distinguished. And accelerating bodies show inertial forces. This is probably due to absolute rest frame. Aether frame and absolute rest frame each will probably be one and only, homogeneous, isotropic. And perhaps the two are the same frame. One thing two functions. Surprising.
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A Light clock
A light clock is working in a moving passenger car. Light path of light clock is illustrated vertically (in drawings). But this light clock leans somewhat to the right (or to left). So, to an observer stands on the ground, zigzag of light path (saw-tooth like) warps. Two kinds of dilation ? And if two clocks work, and these lean differs ?
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An Intermittent Ray of Light
Imagine that an incoming star light is intermittent (on and off: by human work). An observer is observing this ray of light. It will be certain that observer’s motion (in the light ray direction) does not affect anything of coming ray (intermittency, wavelength, amplitude, waveform, etc). So, in the equation c = f λ, it is f and c that vary for the moving observer.
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Murmur, Again
Starlight is coming from outer space. When an observer moves in the direction of the light path, frequency of the starlight varies. For light, there is a formula c = f λ. Which one, c or λ, varies with the above frequency varying ?
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Binary Star & Aether
Speed of light coming from approaching and receding stars of binary star is the same. This will be one of evidence of the existence of aether.
Note: However, as for evidence, aberrations (caused by motions of Earth relative to aether) will be more definite.
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Light is Propagated in Two Ways
In outer space, a starlight is reflected by a mirror. There is a formula c = f λ. Now, the mirror is stationary. In comparing of incident light and reflected light, f is the same. And usually, c & λ are different.
Now, the mirror moves in the direction of the light path of incident light. In the formula on incident light, λ is constant. And c & f will be variables. And in the formula on reflected light, c is constant. And f & λ will be variables.
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Light is Propagated in Two Ways (supplement to the 15th post)
◎ Statings on the formula: c = f λ are from the view point of the mirror (stationery or in uniform linear motion).
◎ Light will follow the emission theory for a few seconds only, after leaving light source. And then light follows aether.
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Gleaning (wavenumber, invariant)
In outer space, a starlight is coming. When an observer moves in the direction of light path, frequency varies. But, according to this, in the formula c = f λ, does wavelength λ vary ? Unbelievable !
There is a word “wavenumber”. It is the number of waves in a unit length (1 cm or 1 m) and is called Kayser. Like 25,000 K (visible red). This wavenumber and wavelength are reciprocals of each other. Therefore, since the wavenumber is an invariant, the wavelength will also be an invariant. That is, the wavelength cannot be varied with the motion of an observer. It is the speed of light that varies.
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Inertial Force is not Fictitious Force
Inertial force is not fictitious force. See, Newton’s third law of motion (law of action and reaction). Also see, formula F = ma in the second law of motion. This is a big problem.
P.S. There are two types of motion: uniform linear motion and all other motions. In the latter, inertial forces appear during the motion, and corresponding to the motion.
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Equivalence Principle
In free-falling elevator cabin, and at the especial local area, gravity and inertial force are equal in magnitude. This seems to be the reason for the equivalence principle. However, at many local area, gravity and inertial force are not equal in magnitude. Is it possible that the principle is based on this one especial local area ?
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Equivalence Principle
When a mass point is accelerated, inertial force appears. Its vector can be at our will. On the other hand, gravity acting on a mass point is unrelated to the accelerated motion of this mass point. And, the vector is not at our will. In summary, inertial force and gravity are two different things, like water and oil (even if the vector of the two acting on a mass point happen to cancel each other out).
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Inertial Force
◎ Inertial force is reaction of Newton’s law of action-reaction (the third law of motion). It is not a fictitious force.
◎ In the entire elevator cabin in free-falling, gravity and inertial force are action and reaction. And the two are equal. So, it is not surprising that in this cabin, there is a local area where the magnitude of gravity and inertial force are equal. In this local area, magnitude of inertial force is not zero. That is, this local area is not an inertial frame.
◎ There are two points that are not in relative motion. It is impossible to say for one to be an inertial frame and for the other an accelerated frame. There can be no such thing as a local inertial frame.
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About the speed of light
As for speed of light, constancy of speed of light, and the formula c = f λ seem to be all. But is it so simple ?
A ray of light is propagating through aether. An observer is moving in a uniform linear motion lerative to this ray at various angle. The speed of the observer relative to aether is also varies. And, the observer’s motion can be accelerated motion, jerk (on a straight line), or can be curvilinear motion. Besides, there will be areas where the propagation of light follows emission theory.
In short, there will be no reason to treat light specially. It’s so simple.
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About the Speed of Light
For light that is propagated in aether, speed of light waves and ray (photons) relative to an observer will be different (usually). And, for light that is propagated according to emission theory, above will be the same (different also, usually).
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About the speed of light (supplement to the above)
Plane waves and rays (photons) of light from the first-magnitude star, Sirius are propagating through outer space. An observer is moving in various motions. Speed of plane waves and light rays (photons) to the observer will be different (usually).
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Gravity and Time Dilation
There are two mirrors. One is on the ground, one is 22.6m above. These are facing each other. A laser beam is emitted downward from the left end of the upper mirror, forming letter W, and is coming to the upper right (beam is in vacuum). Frequency at five points will be the same. There will be no time dilation due to difference of gravity.
Note) A few translated books say that (outline), when the distance between two points on the light path remains the same, the frequency of two points are the same (assuming frequency of the light source is constant).
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Aberration on the Moon
Major aberrations observable on the moon’s surface are four. Two are corresponding to daily, annual aberrations of earth. Two are annual, secular aberrations of earth themselves (in common). These four aberrations show that aberration are caused by the motion of the telescope on the moon’s surface relative to aether. Qualitatively, quantitatively. Motion of telescope is motion relative to aether.
On the moon’s surface, a water-filled telescope will show what Airy imaged (but if light receiving surface is glass, it will follow the refractive index of the glass). Also on the moon’s surface, picture of tilted umbrella and rain drops (raindrops are photons) will be valid (invalid on earth).
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Local Inertial Frame (Monologue)
In all areas of a free-falling elevator, formula F ≒ ma ≠ 0, or F = ma ≠ 0 will consist. So, there will be no inertial frame, even locally.
In a free-falling elevator (assumed to be a rigid body), coexistence of inertial frame and accelerated frame will be impossible, even locally.
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Motions Relative to Aether (monologue)
1) Rotary motion: Two same disks are rotating. If the rotary speed is the same, the same inertial force will appear. Regardless of the direction of plane of rotation. It must be because of aether (homogeneous and isotropic).
2) Curvilinear motion: Two same spheres move in curvilinear motion. Two curves are the same in size and shape. If two spheres move at the same uniform speed (from the same starting point), the same inertial force will appear. Regardless of the direction of curve. It must be because of aether (homogeneous and isotropic).
3) Accelerated motion on straight lines: Two same spheres move on two straight lines. If motions are the same accelerated motion, the same inertial force will appear. Regardless of the direction of the straight line. It must be because of aether (homogeneous and isotropic).
4) Uniform linear motion: Two same spheres move in uniform linear motion. Inertial forces do not appear. Regardless of the direction of straight line. It must be because of aether (homogeneous and isotropic).
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Inertial Force is not Fictitious (partially reposted)
Gravity acts on everything equally. And if there is action, there is reaction. As stated by Newton’s third law of motion. Below are some examples.
F = mg (free fall)
F = normal reaction
F = air resistance (falling at terminal speed)
F = air resistance + inertial force (falling before terminal speed)
Is F in F = mg fictitious ? The claim of fictitious will not hold.
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Newton’s Third Law of Motion
A body of mass m is suspended from ceiling by a string. From below, this body is pulled by another string. Tension of this string is 2 mg. So, the tension of upper string is 3 mg. That is, action-reaction of upper string is both 3 mg. Mass of the body is basically irrelevant.
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Inertial force is not fictitious (monologue)
On a plane (no friction), there is a body mass 3m. It is pulled by a string from the left and is accelerated. Tension of the string F is 3ma. Now, suppose there is another body to the right of this body. Two bodies are tied with a string. Also suppose the mass of the left body be 2m and the mass of the right body be m. The force F that pulls the left string is the same. So, tension on the left string will be 3ma and tension on the right string will be ma.
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Inertial force is not fictitious (is something wrong ?)
Formula, F = ma, is well-known formula. Now, dividing both sides by m. It gives F/m = a. F on the left side is the force (external force) in “Newton”. Both F and m are physical quantities. Both will not be fictitious. Therefore, a and inertial force ma will not be fictitious also. Is there anything wrong with the above ?
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Inertial Force is not Fictitious (Continued)
In previous post, both sides of formula F = ma are divided by m. Now, alternatively, F = ma are divided by a. Then, formula F/a = m is given. This will also show that a and ma will not be fictitious.
Also, two formulas F = ma and F = mg may not be compatible with the assertion of gravitational mass and inertial mass (“Both are completely different phenomena” on Wikipedia “mass” in Japanese. Also, not be compatible with existence of two idioms).
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Inertial Resistance is not Fictitious (again).
Let’s review formulas, F = ma and F = mg.
Dividing both sides by m gives a = F/m and g = F/m. Therefore, a = g.
Thus, mass acting as gravity and mass acting as inertial force are (assumed to be) the same. Also, quantitatively as m. This is also guaranteed by Newton’s third law of motion.
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EInertial Resistance is not Fictitious (again)
Not a few explanations of law of action and reaction begins with two bodies. Misleading explanation. This law is the law at point of action of force. And, it is the law that action and reaction are equal, and direction of force is opposite.
A body is pulled by a string. At every point on the string, tension is the same. That is, action and reaction have the same magnitude and opposite directions. This is the same when the body is uniformly accelerated by the string. Both forces are true forces. It is Impossible that one (inertial resistance) is fictitious.
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Free Fall (Monologue)
A large number of particles are floating in vacuum space. To our eyes, these are visible as a cube or an elevator cabin. Suddenly, a gravity source appears below and the elevator-like thing starts free-falling. As time passes, the elevator-like thing gradually changes its shape.
The above can be explained by Newtonian mechanics.
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Local Inertial Frame ? (again)
A homogenous disk is rotating vertically. Gravity from below. Therefore, inertial force (centrifugal force) and gravity act on each mass point of the disk. When the rotation speed of the disk exceeds a certain magnitude, a mass point appears where vector of inertial force and gravity are canceled (as total). But it is only natural. It seems to not be note worthy.
In free falling elevator, mass point where vector of inertial force and gravity are canceled (as total) appears also. Physically, it would be the same phenomenon as a rotating disk.
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Free Fall
A body is in free fall. Assume that this body is a homogeneous rectangular. Inertial force is acting on every local area. Therefore, there can be no local inertial frame for this body.
Inertial force and gravity are canceled each other partially and sometimes totally. But canceled is action not existence.
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Equivalence principle (again)
For gravity and inertial force in free-falling elevator, acceptable explanation will be Newton’s law of action and reaction. Equivalence principle should be forgotten.
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Inertial Force is not Fictitious (again)
The same five bodies (mass m) are lined up sideways on a horizontal plane. Five bodies are tied with four strings. Assume that horizontal plane is zero friction, and mass of strings is zero. On right most body, force of 5ma is acting to the right and five bodies start a uniform linear accelerating motion toward the right. Tension acting on four strings are, from right to left, 4ma, 3ma, 2ma, and 1ma.
Tension in the string above will be the same to an observer of any frame of motion. Inertial force (accelerated motion) is not fictitious.
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Selected Posts on Anti-Relativity
◎ Michelson-Morley Experiment
It (done in air) is nonsense. In air, light is propagated at c/n. So, the result of M-M experiment (done in air) is only natural.
In a book “Theory of Relativity” by Pauli, W 1958, it’s written as follows (quoted from English version ; in 1-6). “Rather should one say that for an observer moving with medium, light is propagated as usual with velocity c/n in all directions”.
◎ Speed of Light
The defined value of speed of light is based on measurements (with wavelength and frequency) done by Evenson et al. in 1973. Error is 1.1 m / s in pramai. Now measuring instrument is separated into a measuring part and a light source part. When one of them is moved at a constant speed higher than above error (in the direction of light path), different value will be obtained.
◎ Propagation of Light
In outer space, a starlight is reflected by a mirror. There is a formula c = f λ. Now, the mirror is stationary. In comparing of incident light and reflected light, f is the same. And usually, c & λ are different.
Now, the mirror moves in the direction of the light path of incident light. In the formula on incident light, λ is constant. And c & f will be variables. And in the formula on reflected light, c is constant. And f & λ will be variables.
1. In outer space, a star light is reflected by a mirror. Speed of incident light is constant relative to aether.
2. In outer space, a star light is reflected by a mirror. Speed of reflected light is constant relative to the mirror (the emission theory).
In two pictures sbove each, speed of light to a moving observer follows Galilean transformation.
◎ Aether
All kinds of aberration are caused by motion of Earth. Qualitatively, quantitatively. For example, cycle of annual aberration is 365 days. It is reflection of motion of Earth. On the other hand, any motion of star’s side has no influence. Only position on the celestial sphere is valid. These facts will be explainable only by aether.
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Selected Posts on Anti-Relativity (2)
◎ Lorentz Contraction
Plane waves of starlight (wavelength is constant) is arriving from upper left 45 degrees. Two spacecrafts are sailing in the right and left directions. Number of waves hitting the front and rear ends (A and B) of each spacecraft is the same. Therefore, number of waves existing between A and B is invariant (for both spacecrafts, regardless of lateral motion). Lorentz contractions will be impossible.
Relativity of simultaneity will be impossible also.
◎ Aberration
Aberration is caused by various motions of Earth relative to stationary aether (uniform isotropic). Light that enters upper air of Earth (from aether) is bent in the direction of motion of Earth. As a phenomenon, aberration is completed in the upper air. The same as refraction.
Therefore, illustration of raindrops and an umbrella is NG. Result of Airy’s experiment with a water-filled telescope is only natural. It is said that apparent displacement of stars is displaced in the direction of Earth’s motion, but in fact, it will be the opposite. You can check this by drawing light bending (in upper air) on a paper.
◎ Inertial Force is not Fictitious.
The same five bodies (mass m) are lined up sideways on a horizontal plane. Five bodies are tied with four strings. Assume that horizontal plane is zero friction, and mass of strings is zero. On right most body, force of 5ma is acting to the right and five bodies start a uniform linear accelerating motion toward the right. Tension acting on four strings are, from right to left, 4ma, 3ma, 2ma, and 1ma.
Tension in the string above will be the same to an observer of any frame of motion. Inertial force (accelerated motion) is not fictitious.
◎ Equivalence Principle
For gravity and inertial force in free-falling elevator, acceptable explanation will be Newton’s law of action and reaction. Equivalence principle should be forgotten.
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Selected Posts on Anti-Relativity (3)
◎ Light Clock
A light clock is working in a moving passenger car. In books or in other illustrations, light travels back and forth vertically, but this light clock slightly leans to the right or left. So, the zigzag (sawtooth) of light path seen by an observer on the ground warps. Two kinds of dilations ? And how about if two light clocks with different lean work ?
◎ Time Dilation
In outer space, a spaceship is sailing horizontally. Plane wave of light (wavelength is constant) of the first-magnitude star Sirius is coming from directly above. Phenomenon of time dilation can not be valid.
◎ Relativity of Simultaneity
On the Moon’s surface, a passenger car is moving to the right. From the center of the ceiling of the car, light rays are emitted to directly below and diagonally downward to left and right at 45 degrees. And three points of light are reflected on the floor. Three points are symmetrical to observer on the Moon’s surface also. Relativity of simultaneity will be invalid.
◎ Perihelion Shift of Mercury
The perihelion shift moves in one direction and its speed seems to be almost constant. Like the hands of a clock. Main cause of the shift seems not to be gravity of other planets. Main cause will be two-body problem of Mercury and Sun. Not as points, but as spheres.
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Selected Posts on Anti-Relatiyity (4)
◎ Speed of Light
For speed of light, the constant speed, and the formula c = fλ seem to be all. But is it really that simple?
A beam of light is propagating through aether. An observer is in uniform linear motion at various angles relative to this beam. The speed of the observer relative to aether also varies. Observer’s motion can be accelerated motion, jerk motion, or curvilinear motion. Also, speed of light wave and light ray (photon) will generally be different.
No, to light, special treatment must not be given. Then, all must be simple.
◎ Aether
In outer space, frequency and wavelength of two stars light are being measured. Two stars are in opposite directions (antipodal point) on the celestial sphere, and the measurements are done simultaneously. The sum of the two values will be 2c or a constant close to 2c.
The above will show the motion of the observer relative to aether.
◎ Accelerated Motion and Aether
Accelerated motion will be absolute motion against aether. Accelerated motion and inertial force are two sides of the same coin. Gravity is not involved and is irrelevant.
That is, we are surrounded by aether.
◎ Acceleration and Non-Acceleration777
The passenger car is accelerating uniformly to the right. In this car, a ray of light (frequency is constant) is emitted from the rear to the front. The number of light waves existing inside the car will be higher than when the car is stationary. That is, there will be apparent difference between non-acceleration and acceleration.
Ray of light is emitted from the ceiling of the passenger car downward. If the passenger car is accelerating, the ray draw a parabola. That is, there will be apparent difference between non-acceleration and acceleration.
◎ Local Inertial Frame
An elevator-like but homogeneous rectangular body is in free falling. Suppose this body consists of many local area of mass m. So, inertial force acting on each local area is mg. That is, local inertial frame will be impossible.
Gravity and inertial force are cancelled out partially or sometimes totally. But, it is action that cancelled out, not existence.
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Selected Posts on Anti-Relativity (5)
◎ Doppler Effect of Light
Frequency of incoming light varies with the motion of an observer. In the formula c = fλ, it is clear that the speed of light (for the observer) cannot be constant.
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Perihelion Shift of Mercury (again)
Shift of perihelion is in the direction of Mercury’s own revolution, and speed of shift is constant. Like hands of clock. Main reason will be two-body problem.
How is Sun’s gravity acting on Mercury calculated ? Will be by Newton’s spherical shell theorem. But is this theorem right ? Has anyone raised any objection ?
Gravity of Sun acting on Mercury depends on square of the distance between them. On the other hand, centrifugal force due to orbital motion of Mercury depends on distance between them. Therefore, the size of Mercury and Sun will also play a role. But it is contrary to the spherical shell theorem
If the above is right, because the two bodies are close, size of Mercury and Sun will increase the magnitude of gravity. And orbital motion of Mercury will be accelerated.
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Spherical Shell Theorem (クリ)
A homogeneous sphere, the source of gravity, and a line of action of gravity extending horizontally through the center of the sphere are drawn. At a fixed point, on left side of the line of action, not far apart, magnitude of gravity is calculated. Now, let the gravity source be the left and right hemispheres, and the gravity originating from the two hemispheres is calculated. Magnitude of gravity depends on the square of the distance. Therefore, sum of the gravity originating from the two hemispheres will differ from the magnitude calculated by the spherical shell theorem.
The above is on the Sun’s gravity only.
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Spherical Shell Theorem (Continued)
In figure A, let distance from the center of sphere to fixed point be 50. And in figure B, let distance between the center of sphere and center of gravity of two hemispheres be 1. In figure B, in the formula of gravity, denominators are square of 49 and 51. These are 2401 and 2601. Contrary to expectations, size of the sphere seems to reduce the magnitude of gravity.
Therefore, gravity seems not to be the cause of perihelion shift of Mercury. Size of Mercury will increase centrifugal force.
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Perihelion Shift of Mercury (again)
There is a figure of Mercury. Mercury is drawn as a circle. Plus, the center of it and an arc are drawn. This arc passes through the center and is extending symmetrically upward and downward. This arc is part of circle centered at the center of Sun that is located on the right of this figure. Therefore, the area of Mercury divided by the arc is left > right. Thus, actual magnitude of centrifugal force of Mercury due to its orbital motion will exceed the magnitude calculated as a point. Probably, this will be the main reason for perihelion shift of Mercury.
Note : For planets with satellites, perihelion shif seems to be larger. This will be due to centrifugal force.
Note : There must be more unknowns in perihelion shift.
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Spherical Shell Theorem
Let me revise my 03-12 post as follows.
There are two figures A and B that draw Sun and Mercury. A shows Mercury on the line of action of gravity of Sun extending from the left. Distance between two stars is 50. In B, Mercury is divided into two hemispheres, left and right. The distance between center of sphere (of A) and the center of gravity of two hemispheres each is 1. In B, denominators of formula for magnitude of gravity are 49 and 51. And squared are 2401 and 2601.
Magnitude of gravity is 2500 in A and 2501 in B. Size of sphere seems to be related to magnitude of gravity. Spherical shell theorem will not be valid. Main reason for perihelion shift of Mercury will be its size.
Note) In this post, only gravity of Sun is under consideration.
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Perihelion Shift of Mercury (Supplement)
Story will be started from aphelion. Starting is addition of centrifugal force (because of the size of Mercury), which causes orbit to be outside the original orbit. Then, very slight rotation of long axis and short axis, i.e., the elliptical orbit (centered on the forcal point where Sun is located) will continue.
Note: It is said that Moon is receding from Earth at a rate of a few centimeters per year. Perhaps, size of Moon will add centrifugal force on Moon’s orbital motion.
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Perihelion Shift of Mercury (problem posing)
I said earlier that this story should start from aphelion, not perihelion. Yes, size of Mercury will increase centrifugal force and will rotate the orbit of Mercury in the direction of revolution. It will also increase size of orbit and increase momentum of Mercury.
Moon is said to be receding away from Earth. Although it is on order of a few centimeters per year. There are not a few sites on web. Many of them say that reason is slowing down of rotation of Earth. And total angular momentum of Earth and Moon must be conserved. But is relationship between Earth and Moon still the same today ? I guess what I said in the first half of this post applies to Moon as well.
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Perihelion Shift of Mercury (Labyrinth)
This problem could be discribed as a problem in which Mercury’s elliptical orbit rotates slightly in the direction of Mercury’s orbital motion. Like hands of a clock. Reason for rotation may be due to the fact that Mercury is not a point but a sphere that has a size (mass distribution). But beyond that, it is a labyrinth for me.
Is the reason for rotation lies in perihelion or in aphelion ? Or is it in neither ? And, if the reason lies in aphelion, is it due to addition of centrifugal force ? Or is it due to weakening of gravitational pull of Sun ?
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Perihelion Shift of Mercury (reconfirmation)
As posted before, the size of Mercury as a sphere would be the core to this problem. Allow me to reconfirm.
Divide Mercury into two the same spheres (two are contacted). Two centers of sphere lie on the line of action of Sun’s gravity. Distance between Sun and centers of two spheres are 49 and 51. Magnitude of Sun’s gravity is F=GM/r^2. Therefore, the denominators of magnitude of Sun’s gravity acting on the two spheres are 2401 and 2601.
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Perihelion Shift of Mercury (Summary?)
Two laps of elliptical orbit of Mercury is drawn. Ellipse B after perihelion must be drawn outside previous ellipse A. However, in many figures such as web, it is inside. Ellipse is rotating around Sun. Many figures must be wrong.
In other words, state of ellipse nearby perihelion must be the same as that of nearby aphelion (the same qualitatively). Nearby these two points, Mercury will be affected by excessive acceleration due to its size. Acceleration will be caused by centrifugal force or gravity or by both.
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Perihelion Shift of Mercury (again)
In many figures, Mercury’s orbit is outside the previous orbit for some extent after aphelion, and inside for some extent after perihelion. Unacceptable.
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Perihelion Shift of Mercury (long axis)
Long axis of Mercury’s orbit is slowly rotating. That is, Mercury will follow an orbit outside its previous orbit after passing either perihelion or aphelion (for some extent). This is not so for perihelion in many figures.
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Equivalence principle (as an impression)
In laboratory experiment, inertial force is something that we can control. In a laboratory called thought experiment, we can control falling of an elevator cabin also. On the other hand, it seems that gravity is beyond our reach. In other words, inertial force and gravity will be different things.
Even outside laboratory (whether within our reach or not), inertial force and gravity may be different thing.
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Equivalence Principle
Two bodies of the same mass m tied by a fairly long string are in free fall to Jupiter. Two bodeies are back and forth, and increasing tension of the string is informed to Earth. Inertial force and gravity are different things.
Comet Shoemaker-Levy, which fell to Jupiter in 1994. It was broken into at least 21 pieces in falling.
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Mars & Aether
Annual aberration of Mars is based on its revolution period of 1.881 years and average orbital speed of 28.07 km/sec. That is, aberration is mainly caused by motion of observer relative to the aether. Qualitatively and quantitatively. Needless to explain.
Other aberrations of Mars are also.
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Aether
In outer space, three pinhole cameras are pointed in X, Y and Z directions (these are in uniform linear motion, the same as Sun). Cameras are pretty large. In the camera, on the inner wall, on the opposite side of the pinhole, disks rotate once and receiving position of star lights are recorded.
Recorded position of star lights on three disks will not be true circle. These may indicate motion of the pinhole cameras relative to aether. by
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Apology and Cancellation
My recent post Aprile 29 seem to be invalid. Sorry.
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Pinhole Camera
In outer space, a starlight is coming from the right. This ray enters the pinhole of a pinhole camera and is reflected upward by a mirror set at 45 degrees upwards in the camera.
When the camera moves to the right or left (at a uniform speed), the position where reflected light hits the upper inner wall of the camera will move. Incident light is propagated in aether, and reflected light follows emission theory.
Note: Speed of lincident light and rleflected light relative to the mirror are generally different. So, angle of the two are also. λ are also).
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Gravity (gravitational field) and Time
There is optical path of triangle ABC with top A of tall tower and mirror BC placed on the ground (as vertices). Laser light emitted from light source set at A (frequency is constant) is reflected by BC and returns to A. Frequencies of laser light at ABC will be the same. Time dilation due to gravity will be impossible.
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Speed of Light Varies
On the Moon’s surface, plane waves of Sunlight are arriving horizontally from above to two passenger cars. There is a small pinhole at the center of ceiling of two passenger cars, and on the floor, there is a spot of light that passed through pinhole.
Two passenger cars are moving on the Moon’s surface at different speeds (in x direction). For an observer inside the passenger car, position of light spot on the floor will be different. This difference in position will be the same for an observer stands on the Moon’s surface.
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Two Formulas for Speed of Light (in vacuum)
First formula, v=fλ: It is speed of light relative to aether, and v is constant. Area is where light follows aether frame. That is, more than a few light seconds away from light source.
Second formula, c=fλ; It is speed of light relative to light source, and c is constant. Area is where light follows emission theory. That is, within a few light seconds from light source.
Note) First formula is the same as formula for the speed of sound in air (depending on f and λ).
Note) In outer space, a starlight is passing through a tube. In the center of the tube, a plate of glass is placed. In front of the glass, the starlight follows aether frame, and in back of it, starlight follows emission theory.
Note) A starlight is moving in aether. It is possible that v and c move at the same speed. Usually, v will be below c.
Note) For a moving observer, speed of light must be reconsidered (starting with the Doppler effect).
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Local Inertial Frame (again)
Every mass point is either in an inertial (unaccelerated) frame or accelerated frame. If a rigid homogeneous cuboid is in free-falling, every mass point is in accelerated frame. In this cuboid, there can be no inertial frame, even locally.
P.S. This difference is not fictitious but absolute.
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Correction (on post Maggio 16 : on the third note)
A starlight > A light source
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Inertial Force and Gravity are Different Things
1) For inertial force, space is homogeneous isotropic. Gravity is not (gravitational field exsists).
2) For inertial force, every position in space is the same. Gravity is not (gravitational field exsists).
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Local Inertial Frame (rewritten)
An elevator cabin is in free falling. Let’s assume that every local frame of this cabin is the same (mass m). There can be no local inertial frame.
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Local Inertial Frame (additional)
A homogeneous cuboid made of atomic silver (atomic weight 107.9) is in free falling. Magnitude of inertial force acting on every silver atom is the same. There can be no local inertial frame.
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Inertial Force and Gravity are Different Things (rewritten)
◎ Inertia Force
1) Between inertial force and motion of a mass point in space, there will be direct connection.
2) Position in space has no meaning. Space is homogeneous isotropic.
3) Absolute space is required.
◎ Gravity
1) Between gravity and motion of a mass point in space, there will be no direct connection.
2) Position in space has meaning. As a gravitational field. Space is not homogeneous isotropic.
3) Absolute space is not required.
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Inertial Force and Gravity are Different Things (additional)
It is argued that inertial force and gravity are equivalent. However, in light of the followings, the two will not be equivalent. Even if vectors as action cancel each other out, vectors as existence do not disappear. Qualitatively, quantitatively. These are composing and decomposing of forces.
◎ Inertial force corresponds to accelerated motion of a mass point in homogeneous isotropic space.
◎ Gravity corresponds to position of a mass potint in space modified by gravitational fields.
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Inertial Force and Gravity are Different Things (additional)
In light of the followings, inertial force and gravity will not be equivalent.
◎ Inertial force: It is emerged in an accelerated motion (of a mass point) in space.
◎ Gravity: It does not emerge in an accelerated motion (of a mass point) in space.
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Inertial Force is not Fictitious
Gravity acts on a body as a vector. At a local area in free falling elevator, vector of gravity and vector of inertial force (vector of action, not of existence) will cancel each other. In that case, inertial force will not be fictitious.
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Centrifugal Force is not Fictitious
The same four spheres, connected to the ends of two rods are rotating on a plane (no friction). Asuume the bar as a cross and the whole as a disk. At any point on the rod, magnitudes of the centrifugal force and centripetal force are equal, as shown by Newton’s third law of motion. That is, centrifugal force (and centripetal also) is not fictitious to an observer in any frame.
P.S. Original text of the third law is said, it is not on two bodies, but on every point of action of force.
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Inertial Resistance/Inertial Force (rewritten)
Every mass point is placed in aether frame. When it is forced to move other than uniform linear motion (including zero speed) relative to aether frame, it shows resistance called inertial resistance. Inertial resistance is commonly said to be inertial force. Inertial force will correspond to the motion of mass in aether frame, qualitatively, quantitatively.
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Centrifugal Force is not Fictitious
Allow me to alter some of previous post. Previous setting was four spheres and two rods. Now, on two spheres and one rod (in X direction only), mass is two times (without deflection). Then, at close to the center, magnitude of centrifugal force and centripetal force will be about two times. Also, magnitude of centrifugal force and centripetal force will correspond to rotational speed.
Centrifugal Force is not Fictitious
Allow me to alter some of previous post. Previous setting was four spheres and two rods. Now, on two spheres and one rod (in X direction only), mass is two times (without deflection). Then, at close to the center, magnitude of centrifugal force and centripetal force will be about two times. Also, magnitude of centrifugal force and centripetal force will correspond to rotational speed.
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Centrifugal Force is not Fictitious
About centrifugal force, allow me to post one more. A disk and the same ten spheres (evenly spaced around the disk) are rotating on a plane (no friction). Spheres and outer edge of the disk are connected with strings of the same length. Each string will show the same tension. Tension will be a sign that centrifugal force is not fictitious.
Note) Centrifugal force and centripetal force will work on the string (on every point) as Newton’s third law of motion.
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Speed of Gravity Propagation (クリ)
Speed of gravity propagation is said to be the same to speed of light. But is it true ? Something can’t be found in thought experiments ? How about Sun and Mercury ? Solar system is said to move in the direction called sun facing point (on the celestial sphere). So position from which gravitational force of Sun acting Mercury will be the position some back in time. If so, this effect will slightly acuumlate (like free falling).
In Encyclopaedia Britannica 1969, there is a passage as follows (in item “Gravitation” ; original text). “If the action of gravitation were not absolutely instantaneous”(omission)”All experiments and observations were, however, consistent with the law, from the short distances employed in laboratory experiments to the long ranges used in interplanetary calculations”. It says, action will be instantaneous.
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Speed of Light
This is supplement to the former post .(20 Feb 2023). Half of measurement results of speed of light waves will exceed c.
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Newton’s Three Laws of Motion
Uniform linear motion (aether can be emerged in an optical way), uniform circular motion, inertial force, action and reaction are all existence graspable qualitatively and quantitatively. These are not fictitious.
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Newton’s Spherical Shell Theorem (correction)
In my previous post (2022-06-05), Mercury is divided into two spheres. But this thought experiment doesn’t seem to hold. Surprising ! It does not disprove Newton’s spherical shell theorem ! So, my hope is shifted in another thought experiment on centrifugal force.
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3Newton’s Spherical Shell Theorem (correction)
In my yesterday’s post, I made a mistake. To admin, please replace yesterday’s post to the following.
In my previous post (2023-03-20), Mercury is divided into two spheres. But this thought experiment doesn’t seem to explain perihelion shift of Mercury. Because, a/49^2 + a/51^2 = 2a/50^2. Surprising ! And also, it does not disprove Newton’s spherical shell theorem ! So, my hope is shifted in another thought experiment on centrifugal force (2023-03-15).
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Perihelion Shift of Mercury (rewritten)
In a figure, Mercury is drown as a circle. In addition, in the figure, center of the circle and an arc extending vertically through the center are drown. Arc is a part of orbit. The arc divides Mercury into left and right, and the area is left > right (Sun is in the right). This figure shows that actual magnitude of the centrifugal force exceeds magnitude calculated for Mercury as a point (see formula of centrifugal force, ignore rotation). Perihelion shift of Mercury may be due to Mercury’s size.
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Perihelion Shift of Mercury (rewritten)
In a figure, Mercury is drown as a circle. In addition, in the figure, center of the circle and an arc extending vertically through the center are drown. Arc is a part of orbit. The arc divides Mercury into left and right, and the area is left > right (Sun is in the right). This figure shows that actual magnitude of the centrifugal force exceeds magnitude calculated for Mercury as a point (see formula of centrifugal force, ignore rotation). Perihelion shift of Mercury may be due to Mercury’s size.
In a figure, Mercury is drown as a circle. In addition, in the figure, center of the circle and an arc extending vertically through the center are drown. Arc is a part of orbit. The arc divides Mercury into left and right, and the area is left > right (Sun is in the right). This figure shows that actual magnitude of the centrifugal force exceeds magnitude calculated for Mercury as a point (see formula of centrifugal force, ignore rotation). Perihelion shift of Mercury may be due to Mercury’s size.
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Decelerated Motion
From a passenger car moving to the right, a rope is extending to left, and on it, constant tension is acting. Then, the passenger car is decelerating. And, when the ground speed of passenger car falls in zero, tension of the rope is still constant. So passenger car starts accelerating to the left. But, there will be no difference in situation in before and after in the passenger car. There will not be much meaning in the ground speed of passenger car.
As written above, everything is accelerated motion and decelerated motion does not exist. But “counter-jerk motion” where degree of accelerated motion withdrawing may be possible.
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Moon’s Retreat
Moon is said to be moving away from Earth by several centimeters per year. As proposed formally (posted on Agosto 5. by me), size of Moon will increase its centrifugal force (compared to calculated as a point). This additional amount will be divided in rotation of long axis and in extension of long axis of orbit of Moon. Is Mercury moving away from Sun too ? Retreat
Moon is said to be moving away from Earth by several centimeters per year. As proposed formally (posted on Agosto 5. by me), size of Moon will increase its centrifugal force (compared to calculated as a point). This additional amount will be divided in rotation of long axis and in extension of long axis of orbit of Moon. Is Mercury moving away from Sun too ?
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Perihelion Shift of Mercury
Size of Mercury will increase gravity and increase centrifugal force quolitatively also. Of the two, gravity is probably the main factor. Because, increase in gravity shift aphelion in the direction of revolution. On the other hand, increase in centrifugal force shift aphelion in the opposite direction of revolution.
The formula for gravity F = mM/r^2 probably shows that magnitude of gravity is related to the size of Mercury (but surprisingly small).
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Perihelion Shift of Mercury
Size of Mercury will increase gravity and increase centrifugal force quolitatively also. Of the two, gravity is probably the main factor. Because, increase in gravity shift aphelion in the direction of revolution. On the other hand, increase in centrifugal force shift aphelion in the opposite direction of revolution.
The formula for gravity F = mM/r^2 probably shows that magnitude of gravity is related to the size of Mercury (but surprisingly small).
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Perihelion Shift of Mercury
[Size of Mercury increases gravity during orbital motion]
Mm/r^2 is formula for gravity. There are models for Mercury and Sun. When, 2Mm is 100 and r is 50, gravity is 0.04. Next, two spheres (with half of mass of Mercury each) are lined up on the line of action of Sun’s gravity. Mm is 50, r is 49 and 51. Then, gravity is 0.0400479.
[Size of Mercury increases centrifugal force during orbital motion]
See my post posted on March 15, 2023 (or around).
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Perihelion Shift of Mercury
There is one more problem. Size of Mercury send out surplus force. But where does this surplus force go ?
In figure of perihelion shift of Mercury, its destination seems not to be found. Ah, perhaps the same phenomenon as Moon’s retreat (Moon’s orbit is expanding) will be destination. This surplus force probably turns and expands Mercury’s elliptical orbit each time.