Relativistic Problems for the 21st Century: Concise refutation of SR
Albert Zotkin
c dt = t dv, [1]
t = t_0 Exp(v/c),
1/t = (1/t_0) Exp(-v/c),
f = f_0 Exp(-v/c).
Under SR it is:
c dt = t dv / (1 - v^2/c^2), [2]
ln(t/t_0) = arctanh(v/c),
ln(t/t_0) = (1/2)ln[ (1+v/c)/(1-v/c) ],
t = t_0 sqrt[ (1+v/c)/(1-v/c) ],
1/t = (1/t_0) sqrt[ (1-v/c)/(1+v/c) ],
f = f_0 sqrt[ (1-v/c)/(1+v/c) ].
The factor 1/(1 - v^2/c^2) in eq.[2] comes from the
absurdity of the 2nd postulate of SR. Actually, that
factor (which is equal to gamma^2) works fine for
accelerating charged particles in electric/magnetic
fields, because it tells us that a charged particle
can't be accelerated by the field beyond c. But, for
neutral particles/bodies, that factor is a false constraint,
and eq.[1] should be applied instead.
PS: Cosmological connection of the correct Doppler
equation f = f_0 Exp(-v/c). For distant receding galaxies,
v is often interpreted as a recessional speed, so the
observed frequency redshift z of a distant galaxy is
z + 1 = Exp(-v/c).
Regards
Eric Gisse
> The correct derivation of Doppler effect is:
>
> c dt = t dv, [1]
> t = t_0 Exp(v/c),
> 1/t = (1/t_0) Exp(-v/c),
> f = f_0 Exp(-v/c).
Does not agree with second order Doppler measurements.
You went away. Stay away.
[snip]
Albert Zotkin
What second order Doppler measurements?
Your moronic, laconic reply is clueless, as usual.
I'll give you a hint: if those Doppler measurements
are performed on charged particles being accelerated
by electric/magnetic fields, then the factor
1/(1 - v^2/c^2) works fine and SR would be a good
approach for describing that Doppler effect on relativistic
speeds. But, if we talk about neutral particles, that
factor is quite unnecessary, and if you include it,
then your second order measurements would not agree
with the expected predictions. Isn't that the reason
why SR can't account for recessional speeds of distant
galaxies (that, in average, are neutral bodies), and a
FRW metric must be applied instead?
Eric Gisse
> On 15 oct, 12:47, Eric Gisse <jowr...@gmail.com> wrote:
>
> > On Oct 15, 1:37 am, Albert Zotkin <albertito1...@gmail.com> wrote:
>
> > > The correct derivation of Doppler effect is:
>
> > > c dt = t dv, [1]
> > > t = t_0 Exp(v/c),
> > > 1/t = (1/t_0) Exp(-v/c),
> > > f = f_0 Exp(-v/c).
>
> > Does not agree with second order Doppler measurements.
>
> > You went away. Stay away.
>
> > [snip]
>
> What second order Doppler measurements?
> Your moronic, laconic reply is clueless, as usual.
> I'll give you a hint: if those Doppler measurements
> are performed on charged particles being accelerated
> by electric/magnetic fields, then the factor
> 1/(1 - v^2/c^2) works fine and SR would be a good
> approach for describing that Doppler effect on relativistic
> speeds. But, if we talk about neutral particles, that
> factor is quite unnecessary, and if you include it,
> then your second order measurements would not agree
> with the expected predictions.
The factor is required regardless of charge.
>Isn't that the reason
> why SR can't account for recessional speeds of distant
> galaxies (that, in average, are neutral bodies), and a
> FRW metric must be applied instead?
No, as SR does not handle gravitation.
The TimeLord
<albert...@gmail.com> in
c8280428-c721-47bc...@k36g2000pri.googlegroups.com:
> The correct derivation of Doppler effect is:
>
> c dt = t dv, [1]
This doesn't even make sense. Using some algebra we get
dv/dt = c/t
Since c is constant, you're claiming that all acceleration can only
decay with time. How come this is not observed in real life? How do
accelerating rockets and automobiles work?
[...]
Nonsense equations.
>
> Under SR it is:
>
> c dt = t dv / (1 - v^2/c^2), [2]
[...]
> 1/t = (1/t_0) sqrt[ (1-v/c)/(1+v/c) ], f = f_0 sqrt[ (1-v/c)/(1+v/c)
> ].
Incorrect. Under SR it is as follows:
The 4-vector of an EM wave is
k0:=[2*pi/lambda0, 2*pi/lambda0_x, 2*pi/lambda0_y, 2*pi/lambda0_z]
The boost is
L:=matrix([gamma,-v/c*gamma,0,0],[-v/c*gamma, gamma, 0,0],
[0,0,1,0],[0,0,0,1])
gamma:=sqrt(1-v^2/c^2)
Now let the 4-vector in any frame moving at speed v is
k:=2*pi/lambda*[1,cos(theta),sin(theta),0]
Since the components of k and k0 must correspond along the EM wave's world-
line we get
k=L.k0
and after some algebra
1/lambda0 = (1/lambda)*(gamma-gamma*v/c*cos(theta))
After setting theta=0 and using f*lambda=c and some more algebra we get
the result you quote in the last line of [2].
>
> The factor 1/(1 - v^2/c^2) in eq.[2] comes from the absurdity of the 2nd
> postulate of SR. Actually, that factor (which is equal to gamma^2) works
So you think that the assumption that natural laws should be consistent
for all observers is an absurdity? Prove it. By the way, the first equation
in [2] is nonsense and has nothing to do with SR.
[...]
> PS: Cosmological connection of the correct Doppler equation f = f_0
> Exp(-v/c). For distant receding galaxies, v is often interpreted as a
> recessional speed, so the observed frequency redshift z of a distant
> galaxy is
>
> z + 1 = Exp(-v/c).
Actually, its v=H*d with z+1=sqrt((c+v)/(c-v)).
Hint: Before criticizing something, you should make an attempt to
understand it first.
--
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!
Spaceman
> Am Wed, 15 Oct 2008 02:37:09 -0700 schrieb Albert Zotkin
> <albert...@gmail.com> in
> c8280428-c721-47bc...@k36g2000pri.googlegroups.com:
>
>> The correct derivation of Doppler effect is:
>>
>> c dt = t dv, [1]
>
> This doesn't even make sense. Using some algebra we get
>
> dv/dt = c/t
>
> Since c is constant, you're claiming that all acceleration can only
> decay with time. How come this is not observed in real life?
c is not constant to all
Doppler effect with light even proves such.
Dr. Henri Wilson
Hey Spaceman, get it right or the EPG will pounce.
'c' actually does appear to be a universal constant. It also appears that light
initially move at c wrt its source. Generally however, as you say, relative
light speed is c+v.
Henri Wilson. ASTC,BSc,DSc(T)