This is my version of a paradox described by Waldron.


S |---L--| A B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L, the length of the interferometer. He can calculate the
wavelength as L/n so
frequency Fo = cn/L ---------------- [1]

He signals the value n to B

Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

The frequency will be Doppler shifted and he will find the frequency as
f' = Fo x Sqr(1 - vv/cc) / (1 + v/c)

He can therefore calculate the
speed of light c' = f' x L'/n
c' = Fo x [Sqr(1 - vv/cc) / (1 + v/c)] x L x sqr(1-vv/cc) /n
c' = Fo x (1 - vv/cc) / (1 + v/c) x L/n
From [1] L/n = c/Fo
c' = Fo x (1 - vv/cc) / (1 + v/c) x c/Fo
c' = (1 - vv/cc) / (1 + v/c) x c
c' = (1 - v/c) x c
c' = c - v

-----------------------------------------------------------------------

Now relativists will claim that the formula for wavelength L'/n is wrong
and claim that you should 'assume' that the speed of light is c and
calculate the wavelength from F'. - Even if that is what you believe
that in no way explains why the above - based as it is on what is
measured - is incorrect.

------------------------------------------------------------------------
OK so let us devise another experiment. Before Setting out B, together
with A, sets up the interferometer to have exactly n wavelengths in
length L. Let us assume that the output is by way of a dark fringe and
this is fed into a light detector and comparator. The threshold of the
comparator is set such that a small increase in brightness will give an
output and the output is fed to a detonator attached to a pile of
explosives.

B sets off. Based on the assumption that the speed of light in B's FoR
is c the calculations are trivial but essentially in B's FoR the length
of the interferometer gets shorter and, due to Doppler shift, the
wavelength gets longer. Longer wavelength in shorter interferometer
means in B's FoR n wavelengths no longer fit, therefore the output is no
longer a dark fringe so in B's FoR the explosives go *BANG*. Of course
in A's FoR nothing has changed so no bang! That is of course impossible.
The explosives cannot both go bang, and not go bang and one has to
conclude that the fate of the explosives cannot be affected by anything
B might do. One concludes therefore that independent of the motion of B
the number of wavelengths occupying the length of the interferometer
will remain n in all FoR. This means the original calculation is valid
which gives the speed of light relative to B as c-v.
--
John Kennaugh

John Kennaugh wrote in message

This is my version of a paradox described by Waldron.


S |---L--| A B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L, the length of the interferometer. He can calculate the
wavelength as L/n so
frequency Fo = cn/L ---------------- [1]

He signals the value n to B

Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)

No, certainly not.
Let's imagine for example events of zero electric field to define
wavelenght.
A sees two such simultaneous events where the field is zero.
As you should be able to verify from the transformation equations,
Dx' = g ( Dx - v Dt )
Dt' = g ( Dt - v Dx/c^2 )
Dx = g ( Dx' + v Dt' )
Dt = g ( Dt' + v Dx'/c^2 )
this so-called time dilation equation is valid for events that are
simultaneous in the B-frame (Dt' = 0 and see the third equation).
This is not the case in your setup. You have two such events
that are simultaneous in the A-frame (Dt = 0), so they define
the wavelength in *that* frame - they cannot be taken to define
wavelenght in the B-frame.
You are *heavily* cheating.


He calculates the wavelength as L'/n

The frequency will be Doppler shifted and he will find the frequency as
f' = Fo x Sqr(1 - vv/cc) / (1 + v/c)

He can therefore calculate the
speed of light c' = f' x L'/n
c' = Fo x [Sqr(1 - vv/cc) / (1 + v/c)] x L x sqr(1-vv/cc) /n
c' = Fo x (1 - vv/cc) / (1 + v/c) x L/n
From [1] L/n = c/Fo
c' = Fo x (1 - vv/cc) / (1 + v/c) x c/Fo
c' = (1 - vv/cc) / (1 + v/c) x c
c' = (1 - v/c) x c
c' = c - v

Of course, that is because the ruler along which the min/max
are seen, is itself moving with speed v w.r.t. B. You have calculated
the closing speed between the signal and the endpoint of the moving
ruler. That is indeed c - v. So you immediately see from this that
the speed of the signal is c.
QED. Sheesh.



-----------------------------------------------------------------------

Now relativists will claim that the formula for wavelength L'/n is wrong
and claim that you should 'assume' that the speed of light is c and
calculate the wavelength from F'. - Even if that is what you believe
that in no way explains why the above - based as it is on what is
measured - is incorrect.

------------------------------------------------------------------------
OK so let us devise another experiment.

Not before you understand the first experiment and/or aknowledge that
you have been cheating.

Dirk Vdm

On Mar 3, 6:14 am, John Kennaugh
wrote:
This is my version of a paradox described by Waldron.

S |---L--| A B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L, the length of the interferometer. He can calculate the
wavelength as L/n so
frequency Fo = cn/L ---------------- [1]

He signals the value n to B

Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

The frequency will be Doppler shifted and he will find the frequency as
f' = Fo x Sqr(1 - vv/cc) / (1 + v/c)

He can therefore calculate the
speed of light c' = f' x L'/n
c' = Fo x [Sqr(1 - vv/cc) / (1 + v/c)] x L x sqr(1-vv/cc) /n
c' = Fo x (1 - vv/cc) / (1 + v/c) x L/n
From [1] L/n = c/Fo
c' = Fo x (1 - vv/cc) / (1 + v/c) x c/Fo
c' = (1 - vv/cc) / (1 + v/c) x c
c' = (1 - v/c) x c
c' = c - v

-----------------------------------------------------------------------

Now relativists will claim that the formula for wavelength L'/n is wrong
and claim that you should 'assume' that the speed of light is c and
calculate the wavelength from F'. - Even if that is what you believe
that in no way explains why the above - based as it is on what is
measured - is incorrect.

Congratulations. You have discovered an internal inconsistency in both
Maxwell's equations and special relativity, and by extension all of
real analysis. You have brought down all of modern mathematics.

Or you made an error.


------------------------------------------------------------------------
OK so let us devise another experiment. Before Setting out B, together
with A, sets up the interferometer to have exactly n wavelengths in
length L. Let us assume that the output is by way of a dark fringe and
this is fed into a light detector and comparator. The threshold of the
comparator is set such that a small increase in brightness will give an
output and the output is fed to a detonator attached to a pile of
explosives.

B sets off. Based on the assumption that the speed of light in B's FoR
is c the calculations are trivial but essentially in B's FoR the length
of the interferometer gets shorter and, due to Doppler shift, the
wavelength gets longer. Longer wavelength in shorter interferometer
means in B's FoR n wavelengths no longer fit, therefore the output is no
longer a dark fringe so in B's FoR the explosives go *BANG*. Of course
in A's FoR nothing has changed so no bang! That is of course impossible.
The explosives cannot both go bang, and not go bang and one has to
conclude that the fate of the explosives cannot be affected by anything
B might do. One concludes therefore that independent of the motion of B
the number of wavelengths occupying the length of the interferometer
will remain n in all FoR. This means the original calculation is valid
which gives the speed of light relative to B as c-v.
--
John Kennaugh

John Kennaugh skrev:
This is my version of a paradox described by Waldron.


S |---L--| A B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L, the length of the interferometer. He can calculate the
wavelength as L/n so
frequency Fo = cn/L ---------------- [1]

He signals the value n to B

Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

Then 'he' doesn't know how to use the LT.
Wavelength doesn't transform like the length of a rod!

The light wave can be written like this:
E(x,t) = Eo.sin(2pi(ft-x/L))
L is the wavelength, f is the frequency in the unprimed frame.
The speed of the wave is Lf = c.

Now, let's transform this wave to the primed frame.
x = g(x' + vt')
t = g(t' + x'v/c^2)
g = 1/sqrt(1 - v^2/c^2)

E(x',t') = Eo.sin(2pi(f(g(t' + x'v/c^2))-(g(x' + vt'))/L))
E(x',t') = Eo.sin(2pi[g(f-v/L)t' - g(1/L - fv/c^2)x'])
comparing this to:
E(x',t') = Eo.sin(2pi(f't'-x'/L'))
where f' is the frequency and L' is the wavelength in the primed frame
yields:
f' = g(f-v/L) inserting L = c/f:
f' = f.sqrt((1-v/c)/(1+v/c))
-----------------------------
1/L' = g(1/L - fv/c^2) inserting f = c/L
1/L' = (1/L)sqrt((1-v/c)/(1+v/c))
L' = L.sqrt((1+v/c)/(1-v/c))
---------------------------
c' = L'f' = Lf = c
------------------

[..]

Yet another 'falsification of SR by doing a very elementary error'.

--
Paul

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

On Mar 3, 10:14*am, John Kennaugh
wrote:
This is my version of a paradox described by Waldron.

* * * * *S * * * * *|---L--| A * * * * * * * * B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L, the length of the interferometer. He can calculate the
wavelength as L/n so
frequency Fo = cn/L ---------------- [1]

He signals the value n to B

Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

The frequency will be Doppler shifted and he will find the frequency as
f' = Fo x Sqr(1 - vv/cc) / (1 + v/c)

He can therefore calculate the
speed of light c' = f' x L'/n
* * * c' * = Fo x [Sqr(1 - vv/cc) / (1 + v/c)] x L x sqr(1-vv/cc) /n
* * * c' * = Fo x (1 - vv/cc) / (1 + v/c) x L/n
*From [1] L/n = c/Fo
* * * c' * *= Fo x (1 - vv/cc) / (1 + v/c) x c/Fo
* * * c' * *= (1 - vv/cc) / (1 + v/c) x c
* * * c' * *= *(1 - v/c) x c
* * * c' * *= * c - v

-----------------------------------------------------------------------

Now relativists will claim that the formula for wavelength L'/n is wrong
and claim that you should 'assume' that the speed of light is c and
calculate the wavelength from F'. - Even if that is what you believe
that in no way explains why the above - based as it is on what is
measured - is incorrect.

------------------------------------------------------------------------
OK so let us devise another experiment. Before Setting out B, together
with A, sets up the interferometer to have exactly n wavelengths in
length L. Let us assume that the output is by way of a dark fringe and
this is fed into a light detector and comparator. The threshold of the
comparator is set such that a small increase in brightness will give an
output and the output is fed to a detonator attached to a pile of
explosives.

B sets off. Based on the assumption that the speed of light in B's FoR
is c the calculations are trivial but essentially in B's FoR the length
of the interferometer gets shorter and, due to Doppler shift, the
wavelength gets longer. Longer wavelength in shorter interferometer
means in B's FoR n wavelengths no longer fit, therefore the output is no
longer a dark fringe so in B's FoR the explosives go *BANG*. Of course
in A's FoR nothing has changed so no bang! That is of course impossible.
The explosives cannot both go bang, and not go bang and one has to
conclude that the fate of the explosives cannot be affected by anything
B might do. One concludes therefore that independent of the motion of B
the number of wavelengths occupying the length of the interferometer
will remain n in all FoR. This means the original calculation is valid
which gives the speed of light relative to B as c-v.
--
John Kennaugh

xxein: I think I'll agree in principle (I've done a lot of work
here), but it seems as though others will insist HUP will have eaten
Schroedinger's cat and supress a burp.

Can't you make a better 'reality' example? Whoa! What was I
thinking? They can't understand a 'reality'.

Paul B. Andersen wrote in message

John Kennaugh skrev:
This is my version of a paradox described by Waldron.


S |---L--| A B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L, the length of the interferometer. He can calculate the
wavelength as L/n so
frequency Fo = cn/L ---------------- [1]

He signals the value n to B

Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

Then 'he' doesn't know how to use the LT.
Wavelength doesn't transform like the length of a rod!

The light wave can be written like this:
E(x,t) = Eo.sin(2pi(ft-x/L))
L is the wavelength, f is the frequency in the unprimed frame.
The speed of the wave is Lf = c.

Now, let's transform this wave to the primed frame.
x = g(x' + vt')
t = g(t' + x'v/c^2)
g = 1/sqrt(1 - v^2/c^2)

E(x',t') = Eo.sin(2pi(f(g(t' + x'v/c^2))-(g(x' + vt'))/L))
E(x',t') = Eo.sin(2pi[g(f-v/L)t' - g(1/L - fv/c^2)x'])
comparing this to:
E(x',t') = Eo.sin(2pi(f't'-x'/L'))
where f' is the frequency and L' is the wavelength in the primed frame
yields:
f' = g(f-v/L) inserting L = c/f:
f' = f.sqrt((1-v/c)/(1+v/c))
-----------------------------
1/L' = g(1/L - fv/c^2) inserting f = c/L
1/L' = (1/L)sqrt((1-v/c)/(1+v/c))
L' = L.sqrt((1+v/c)/(1-v/c))
---------------------------
c' = L'f' = Lf = c
------------------

Nice :-)

Dirk Vdm

"John Kennaugh" wrote in message
.uk...
This is my version of a paradox described by Waldron.

Now that others have tackled the paradox, just one question remains:
Who is (or was) Waldron?

Harald

Paul B. Andersen wrote:
John Kennaugh skrev:
This is my version of a paradox described by Waldron.
S |---L--| A B--v
Source S. Observer A stationary w.r.t S Observer B moving at v away
from S. A has an interferometer and shows that exactly n wavelengths
occupy a distance L, the length of the interferometer. He can
calculate the wavelength as L/n so
frequency Fo = cn/L ---------------- [1]
He signals the value n to B
Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

Then 'he' doesn't know how to use the LT.
Wavelength doesn't transform like the length of a rod!

The length of the interferometer *does* transform 'like the length of a
rod'. If there are a fixed number n of wavelengths occupying that
interferometer that 'fixed number' n transforms as a 'fixed number' n so
the wavelengths then also transform 'like the length of a rod' as a
wavelength is 1/nth of the length of the interferometer.

OTOH

If Wavelength 'doesn't transform like the length of a rod' then the
number of wavelengths occupying the interferometer length must vary
depending on what FoR you are viewing from. As I point out you can set
up an experiment which indicates (with an explosion) whether in the FoR
of B the number of wavelengths has in fact changed. If it showed that it
did you would have the absurd idea that an explosion both 'takes place'
and doesn't.

Basically
"Wavelength doesn't transform like the length of a rod"
and
"the number of wavelengths occupying the interferometer is fixed"
are mutually exclusive.

The problem is not one of mathematics hence I have snipped your maths.

The bit you snipped said:
"Based on the assumption that the speed of light in B's FoR is c the
calculations are trivial but essentially in B's FoR the length of the
interferometer gets shorter and, due to Doppler shift, the wavelength
gets longer."

Your maths start with the LTs which are derived from the assumption that
the speed of light for B is c and derive the fact that the speed of
light for B is c. Which is just a rather convoluted way of doing the
maths I described as trivial. It does not address the problem either
way.


--
John Kennaugh

John Kennaugh wrote in message

Paul B. Andersen wrote:
John Kennaugh skrev:
This is my version of a paradox described by Waldron.
S |---L--| A B--v
Source S. Observer A stationary w.r.t S Observer B moving at v away
from S. A has an interferometer and shows that exactly n wavelengths
occupy a distance L, the length of the interferometer. He can
calculate the wavelength as L/n so
frequency Fo = cn/L ---------------- [1]
He signals the value n to B
Now in B's FoR length L becomes L' = L x sqr(1-vv/cc)
He calculates the wavelength as L'/n

Then 'he' doesn't know how to use the LT.
Wavelength doesn't transform like the length of a rod!

The length of the interferometer *does* transform 'like the length of a
rod'.

And wavelenght is defined with non-movng interferomers. Period.
You are cheating - and you know it.

Dirk Vdm

John Kennaugh skrev:
This is my version of a paradox described by Waldron.


S |---L--| A B--v

Source S. Observer A stationary w.r.t S Observer B moving at v away from
S. A has an interferometer and shows that exactly n wavelengths occupy a
distance L

------------------------------------------------------------------------
OK so let us devise another experiment. Before Setting out B, together
with A, sets up the interferometer to have exactly n wavelengths in
length L. Let us assume that the output is by way of a dark fringe and
this is fed into a light detector and comparator. The threshold of the
comparator is set such that a small increase in brightness will give an
output and the output is fed to a detonator attached to a pile of
explosives.

A 'one way interferometer'? There is no such thing.
An interferometer is when to rays interfere.
So there must be two rays going along separate paths.
Let's make a simple one, as equal to yours as possible.

***** |--------|
-*-*-*|--------|
| |
half sivered mirror
mirror
HSM M

***** incident ray, half reflected, half transmitted
----- transmitted ray, reflected at right mirror
-*-*- interference ray

We can determine the phase difference between the reflected ray
and the incident ray at the half silvered mirror by counting
the _instant_ number of wavelengths in the ray.
See:
http://home.c2i.net/pb_andersen/pdf/sagnac_ring.pdf
http://home.c2i.net/pb_andersen/pdf/...ror_sagnac.pdf
http://home.c2i.net/pb_andersen/pdf/...optic_gyro.pdf

This can be done in any frame of reference, so let's choose B's rest frame.
The interferometer is moving at the speed v to the left in this frame.
All primed entities are referred to B's rest frame.

N' = Nf' + Nb'
N' number of wavelengths in the ray from HSM-M-HSM
Nf' number of wavelengths in the ray from HSM-M
Nb' number of wavelengths in the ray from M-HSM

Nf' = L'/l_f'
Nb' = L'/l_b'
L' length of interferometer
l_f' wavelength of right going ray
l_b' wavelength of left going ray

L' = L.sqrt(1-v^2/c^2)
l_f' = l.sqrt((1+v/c)/(1-v/c))
l_b' = l.sqrt((1-v/c)/(1+v/c))
L proper length of interferometer
l wavelength of ray in interferometer-frame

Nf' = L.sqrt(1-v^2/c^2)/(l.sqrt((1+v/c)/(1-v/c))) = (L/l)(1-v/c)
Nb' = L.sqrt(1-v^2/c^2)/(l.sqrt((1-v/c)/(1+v/c))) = (L/l)(1+v/c)
N' = (L/l)(1-v/c)+(L/l)(1+v/c) = 2L/l

So the phase difference at the half silvered mirror doesn't depend
on the speed of the interferometer in the (arbitrary) chosen frame.

This will be the case for all interferometers. Obviously.

The phase difference between the HSM and M will however
depend on the speed. But this phase difference depend
on the definition of simultaneity at the two mirrors,
and it has no physical significance.
(Different observers will have different ideas of what is simultaneous
at the mirrors, and thus of what the phase difference is.)
There is no way an interferometer can compare these phases.

--
Paul

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