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?

On May 1, 5:47 am, Albert****o wrote:
http://newmedia.funnyjunk.com/pictur...en-costume.jpg

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/

On May 1, 7:39 pm, "Paul B. Andersen"
wrote:
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.

On May 1, 4:47*am, Albertito wrote:
This the correct addition of velocities

* * * * *w = u + v,


Nope.

[snip rest, unread]

Albertito wrote:
On May 1, 7:39 pm, "Paul B. Andersen"
wrote:
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.

"Pluss one experimental test".
I see.
It is "one experimental test" that falsifies SR.
So this "one experimental test" proves the SR prediction
for Doppler f' = sqrt ((c+v)/c-v)) f to be wrong.
Which experimental test are you referring to?

And if this "one experimental test" really falsifies SR,
what is then the significance of the equation
f' = Exp(-v/c) f?


--
Paul

http://home.c2i.net/pb_andersen/

On May 2, 9:16 am, "Paul B. Andersen"
wrote:
Albertito wrote:
On May 1, 7:39 pm, "Paul B. Andersen"
wrote:
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.

"Pluss one experimental test".
I see.
It is "one experimental test" that falsifies SR.
So this "one experimental test" proves the SR prediction
for Doppler f' = sqrt ((c+v)/c-v)) f to be wrong.
Which experimental test are you referring to?

Any experimental test that could measure the observed
frequency f' with enough accuracy, given that the
original frequency f and speed v are assumed to be known.

And if this "one experimental test" really falsifies SR,
what is then the significance of the equation
f' = Exp(-v/c) f?


The significance of f' = Exp(-v/c) f, is that bodies can move
relatively without any upper bound for their relative speeds.
Thus, velocities will add as euclidean vectors, w = u + v. There
is no need for time dilation and length contraction, because there
is a relative anisotropy for the propagation of light. That relative
anisotropy is expressed as

c' = c Exp(-v/c)

Suppose a source emits electromagnetic pulses towards you
(observer), with a width between adjacent pulses of t seconds,
it is saying with a frequency of f =1/t . That source is travelling
at
a relative speed v wrt you. Question: what time t' between
adjacent pulses will you measure, or what frequency f' =1/t'?

If you apply the standard solution, f' = f (1 - v/c), then you will
need
some artifact, as time dilation, in order to agree with your
observation.
If you look deeper at the factor (1 - v/c), you will see it is the
first
order approximation of the Doppler effect.

If you apply the relativistic solution, f' = gamma f (1 - v/c), you
will
see it includes a second order approximation (1 - v/c + v^2/2c^2).
But, there are other higher order terms involved. Actually,

gamma (1 - v/c) = sqrt(1 - v/c)/(1 + v/c)) =
1 - v/c + v^2/2c^2 - v^3/2c^3 + v^4/8c^4 - ...

This higher order terms impose a severe constraint in any
experimental
test of SR . Are you suggesting that SR has been tested with success,
for
its relativistic Doppler, beyond the second order approximation
(1 - v/c + v^2/2c^2)? Are you suggesting it has been tested with
success even for (1 - v/c + v^2/2c^2 - v^3/2c^3 )?

Well, the Doppler factor, Exp(-v/c), I propose, also includes the
same second order approximation (1 - v/c + v^2/2c^2). Actually,
it is

Exp(-v/c) = 1 - v/c + v^2/2c^2 - v^3/6c^3 + v^4/24c^4 - ...

So, it suffices to perform an experimenatl test for the third-order
approximation A= (1 - v/c + v^2/2c^2 - v^3/6c^3) in my model,
and for B= (1 - v/c + v^2/2c^2 - v^3/2c^3 ) in SR, and see which
one can predict better the observation. Their respective third-order
terms only differ in the ratio (v^3/6c^3) / (v^3/2c^3) = 1/3.

Regards

On May 2, 2:47 am, Albert****o wrote:


So, it suffices to perform an experimenatl test for the third-order
approximation A= (1 - v/c + v^2/2c^2 - v^3/6c^3) in my model,
and for B= (1 - v/c + v^2/2c^2 - v^3/2c^3 ) in SR, and see which
one can predict better the observation. Their respective third-order
terms only differ in the ratio (v^3/6c^3) / (v^3/2c^3) = 1/3.


Albert****o

What in the "MMX,KT and IS experiments show zero terms in (v/c)^2 in
the RMS framework" didn't you understand?

Albertito skrev:
On May 2, 9:16 am, "Paul B. Andersen"
wrote:
Albertito wrote:
On May 1, 7:39 pm, "Paul B. Andersen"
wrote:
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.
"Pluss one experimental test".
I see.
It is "one experimental test" that falsifies SR.
So this "one experimental test" proves the SR prediction
for Doppler f' = sqrt ((c+v)/c-v)) f to be wrong.
Which experimental test are you referring to?

Any experimental test that could measure the observed
frequency f' with enough accuracy, given that the
original frequency f and speed v are assumed to be known.

Am I to read this as "I, Albertito, am convinced that
any test where the observed frequency f' is measured with
enough accuracy would prove the equation f' = sqrt ((c+v)/c-v)) f
wrong, but no such experiment is ever actually performed."?

In other words, you are not referring any "one experimental test"
that falsifies SR, because you don't know about any such test.


And if this "one experimental test" really falsifies SR,
what is then the significance of the equation
f' = Exp(-v/c) f?


The significance of f' = Exp(-v/c) f, is that bodies can move
relatively without any upper bound for their relative speeds.

The only equations that can prove SR wrong are obviously
the equations of SR which are used when calculating
the predictions of SR. Any other equations you might devise
are utterly irrelevant when it comes to falsify SR.

It is very simple.
As long as no measurement is done which prove a prediction of SR
wrong, SR isn't falsified.

[..]

"
| 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.
"

No, from these two equations we can't prove SR wrong.
What a crazy idea? :-)

--
Paul

http://home.c2i.net/pb_andersen/

On May 4, 8:41 pm, "Paul B. Andersen"
wrote:
Albertito skrev:



On May 2, 9:16 am, "Paul B. Andersen"
wrote:
Albertito wrote:
On May 1, 7:39 pm, "Paul B. Andersen"
wrote:
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.
"Pluss one experimental test".
I see.
It is "one experimental test" that falsifies SR.
So this "one experimental test" proves the SR prediction
for Doppler f' = sqrt ((c+v)/c-v)) f to be wrong.
Which experimental test are you referring to?

Any experimental test that could measure the observed
frequency f' with enough accuracy, given that the
original frequency f and speed v are assumed to be known.

Am I to read this as "I, Albertito, am convinced that
any test where the observed frequency f' is measured with
enough accuracy would prove the equation f' = sqrt ((c+v)/c-v)) f
wrong, but no such experiment is ever actually performed."?

In other words, you are not referring any "one experimental test"
that falsifies SR, because you don't know about any such test.

And if this "one experimental test" really falsifies SR,
what is then the significance of the equation
f' = Exp(-v/c) f?

The significance of f' = Exp(-v/c) f, is that bodies can move
relatively without any upper bound for their relative speeds.

The only equations that can prove SR wrong are obviously
the equations of SR which are used when calculating
the predictions of SR. Any other equations you might devise
are utterly irrelevant when it comes to falsify SR.

It is very simple.
As long as no measurement is done which prove a prediction of SR
wrong, SR isn't falsified.

[..]

"
| 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.
"

No, from these two equations we can't prove SR wrong.
What a crazy idea? :-)

--
Paul

http://home.c2i.net/pb_andersen/

"Your theory is crazy, but it's not crazy enough
to be true" [Niels Bohr, to a young physicist]

There is a better way to falsify SR. Find a theory
that can do the same predictions that SR. A theory
that could even predict phenomena SR can't. Test
that theory with success, proving that it can predict
the same observable phenomena SR can, but with
better accuracy.

OTOH, if your experimental tests only intend to falsify
SR, then if SR is actually falsified, what theory is ready
to replace it?