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Science Forum Index » Physics - Relativity Forum » The correct addition of velocities falsifies relativity
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| Albertito |
 Posted: Thu May 01, 2008 2:47 am |
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This the correct addition of velocities
w = u + v,
and this is the correct Doppler formula for all moving
bodies,
f' = Exp(-v/c) f
From these two equations we can prove time dilation and
length contraction are nonsensical artifacts of Einstein's
relativity.
Consider three inertial observers, A , B and C, moving in
a straight line, with velocities
v_ba (velocity of B with respect to A),
v_cb (velocity of C with respect to B),
v_ca (velocity of C with respect to A),
Observer B sends a ray of light towards A with frequency f_ba,
so it is observed by A with a frequency f_ba'.
Observer C sends a ray of light towards B with frequency f_cb,
so it is observed by B with a frequency f_cb'.
Observer C sends a ray of light towards A with frequency f_ca=f_cb,
so it is observed by A with a frequency f_ca'.
We have two Doopler effects as input
f_ba' = Exp(-v_ba/c) f_ba
f_cb' = Exp(-v_cb/c) f_cb
and the addition of velocities
v_ca = v_ba + v_cb
So, the frequency f_ca = f_cb sent by C towards A is
observed by A as
f_ca' = Exp(-v_ca/c) f_cb
This means
f_ca' = Exp(-(v_ba + v_cb)/c) f_cb,
f_ca' = Exp(-v_ba/c) Exp(- v_cb/c) f_cb,
f_ca' = f_ba f_cb Exp(-v_ba/c) Exp(- v_cb/c) f_cb /(f_ba f_cb),
f_ca' = f_ba' f_cb' f_cb /(f_ba f_cb),
f_ca' = f_ba' f_cb' / f_ba.
We can easily see that f_ca' is the frequency that SR can predict
to second order of v_ca = v_ba + v_cb.
Let's see. Consider the result
f_ca' = Exp(-(v_ba + v_cb)/c) f_cb,
and the relativistic formula
f_ca'' = sqrt((1 - s/c)/(1 + s/c) f_cb,
where s = (v_ba + v_cb)/(1 + v_ba v_cb/c^2)
is Einstein's addition, which can also be expressed
as s = c tanh( arctanh(v_ba/c) + arctanh(v_cb/c) ).
Let c=1, and
x = arctanh(v_ba/c) + arctanh(v_cb/c).
then
f_ca'' = sqrt(cosh(2x) -sinh(2x)) f_cb,
(f_ca'' / f_cb)^2 = cosh(2x) - sinh(2x),
we know that
cosh(2x) = (Exp(2x) + Exp(-2x))/2
sinh(2x) = (Exp(2x) - Exp(-2x))/2
so, it is
(f_ca'' / f_cb)^2 = Exp( - 2x)
then
f_ca'' = Exp( - x) f_c
and
f_ca' = Exp(- (v_ba + v_cb) ) f_cb
Now, we can clearly see where those equations disagree.
The question is, to what order?
f_ca'' / f_ca' = Exp( - x + v_ba + v_cb ),
- x + v_ba + v_cb = ln( f_ca'' / f_ca' ),
x = arctanh(v_ba) + arctanh(v_cb),
So we can define a test parameter A, as
A = v_ba + v_cb - arctanh(v_ba) - arctanh(v_cb) =
= ln( f_ca'' / f_ca' ),
Perform an experimental test to evaluate that A.
For a given level of confidence, to what order is
still A within the error bars? |
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| Dono |
| Posted: Thu May 01, 2008 3:19 am |
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| Albertito |
| Posted: Thu May 01, 2008 10:59 am |
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On May 1, 7:39 pm, "Paul B. Andersen"
<paul.b.ander...@guesswhatuia.no> wrote:
Quote: Albertito skrev:
This the correct addition of velocities
w = u + v,
and this is the correct Doppler formula for all moving
bodies,
f' = Exp(-v/c) f
From these two equations we can prove time dilation and
length contraction are nonsensical artifacts of Einstein's
relativity.
Please explain how 'we' by writing two equations can falsify
a theory of physics.
--
Paul
http://home.c2i.net/pb_andersen/
You are right, 'we' can't. 'We' need one equation.
this one: f' = Exp(-v/c) f, plus one experimental test. |
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| Eric Gisse |
| Posted: Thu May 01, 2008 11:25 am |
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On May 1, 4:47 am, Albertito <albertito1...@gmail.com> wrote:
Quote: This the correct addition of velocities
w = u + v,
Nope.
[snip rest, unread] |
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| Paul B. Andersen |
| Posted: Thu May 01, 2008 1:39 pm |
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Guest
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Albertito skrev:
Quote: This the correct addition of velocities
w = u + v,
and this is the correct Doppler formula for all moving
bodies,
f' = Exp(-v/c) f
From these two equations we can prove time dilation and
length contraction are nonsensical artifacts of Einstein's
relativity.
Please explain how 'we' by writing two equations can falsify
a theory of physics.
--
Paul
http://home.c2i.net/pb_andersen/ |
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