This puzzle is mainly for Jack, but others may play too.

In this puzzle, we're in a universe much like our own, except that in this universe there is a universal rest frame, in which light moves at c in vaccuum.
Length contraction and time dilation still apply. Moving rulers are contracted by a factor of gamma in their direction of motion. Moving clocks run slowly by a factor of gamma.

In this parallel Universe, on a parallel Earth, you're in a nice physics lab, with very precise timing devices, laser switches, precise rulers, and so on. You don't know which way your lab is facing, and your lab is shielded from the Earth's magnetic field.

Your task is to set up two clocks so that they are synchronized with each other at opposite ends of the lab.

How do you do it? Can it be done at all?

By sending a light pulse from one end of the lab to a mirror at the other end, and measuring the time it takes to come back, one can deduce the absolute velocity of the lab. The time dilation and length contraction will cancel each other so that one can forget about these effects when measuring velocity. So the velocity in one direction is c+u, and the other is c-u. From L/(c+u)+L/(c-u)=t we can find u. Then it is easy to synchronize the clocks, for example by sending a light signal from an appropriate point in the room.

Edit: On a second thought, it seems that the effects of time dilation and length contraction will actually amplify each other so that in the end we always have 2L=ct. So the above approach will not work.

How do you do it? Can it be done at all?


I can do it. You only need begin with the two clocks synchronized at the same corner of the lab and then slowly move one of them to the opposite end of the lab. The more slowly you move the moving clock, the more perfectly it will be synchronized with the clock on the other side of the lab.

<idea>Midpoint theorem</idea>
<hint>(delta t',delta s') = Lorentz(delta t,delta s) implies we don't need to know the lab frame's absolute motion to know what?</hint>

Shubert, it will then take an infinite amount of time for your clocks to be actually synchronized at opposite ends of the lab. That's not a useful answer.

From 2005:
http://www.physforum.com/index.php?showtopic=1099
http://www.physforum.com/index.php?showtopic=1317

This puzzle is mainly for Jack, but others may play too.

In this puzzle, we're in a universe much like our own, except that in this universe there is a universal rest frame, in which light moves at c in vaccuum.
Length contraction and time dilation still apply. Moving rulers are contracted by a factor of gamma in their direction of motion. Moving clocks run slowly by a factor of gamma.

In this parallel Universe, on a parallel Earth, you're in a nice physics lab, with very precise timing devices, laser switches, precise rulers, and so on. You don't know which way your lab is facing, and your lab is shielded from the Earth's magnetic field.

Your task is to set up two clocks so that they are synchronized with each other at opposite ends of the lab.

How do you do it? Can it be done at all?

Time dilation and length contraction are based on the relativity postulate.

Hence, these conditions cannot apply to this model.

That's not a useful answer.


The value of correct theory should never be underestimated. Here is a practical equivalent. Place the two clocks C1 and C2 at opposite ends of the lab. Measure the distance between them. Call that d. Let a photon pulse at C1 at time T1=0 be sent to a receiver at C2. When the photon pulse arrives at C2, set the time on C2 to be t=d/c. That's a practical definition of synchronization in a moving frame of reference. The fact that your universe has an absolute frame of reference will not affect this practical synchronization scheme in the moving frame.

Time dilation and length contraction are based on the relativity postulate.

Hence, these conditions cannot apply to this model.
Wrong again! But at least you are batting 100, Jack_. Consistency is a good thing or maybe not.

Pete's toy universe is essentially the Lorentz Ether Theory (LET) universe. Time dilation and length contraction can still apply -- and they do apply for the simple reason that Pete said so. This is his toy problem. If you want to debate that time dilation and length contraction you need to prove it.

The value of correct theory should never be underestimated. Here is a practical equivalent. Place the two clocks C1 and C2 at opposite ends of the lab. Measure the distance between them. Call that d. Let a photon pulse at C1 at time T1=0 be sent to a receiver at C2. When the photon pulse arrives at C2, set the time on C2 to be t=d/c. That's a practical definition of synchronization in a moving frame of reference. The fact that your universe has an absolute frame of reference will not affect this practical synchronization scheme in the moving frame.

If it is the case that c is absolute, as ST claims with saganc, then you only way you can claim r=d/c is if thee is no motion relative to the fixed absolute light.

Otherwise, you will detect a linear sagnac effect.

Wrong again! But at least you are batting 100, Jack_. Consistency is a good thing or maybe not.

Pete's toy universe is essentially the Lorentz Ether Theory (LET) universe. Time dilation and length contraction can still apply -- and they do apply for the simple reason that Pete said so. This is his toy problem. If you want to debate that time dilation and length contraction you need to prove it.

LOL, I suppose I might do this and know how. But, up front, you are wrong.

Assume, light proceeds at c period.

It does not keep up with the frame as in Ritz's theory and SR to measure c.

I mean think about it. You know the earth is moving right?

If you agree and light is always measure c, then it must be the case that the speed light is speed injected in the absolute direction of travel whatever that is.

This way a frame always measures c.

You do not know that the Earth is moving. That is you assumption, not Pete's.

If it is the case that c is absolute, as ST claims with saganc, then you only way you can claim r=d/c is if thee is no motion relative to the fixed absolute light.


No. I'm assuming that there is an absolute frame of reference. I'm claiming that clocks can easily be synchronized in moving frames by the method I've described so that the motion of a photon pulse in the moving frame can be described by the equation x=ct and that no contradictions, under simple conditions, will develop.

You do not know that the Earth is moving. That is you assumption, not Pete's.

If light is absolute, then it is the case you can find this.

This is obvious.

He said, light is but one speed in this "aether".

So, any object moves relative to the fixed aether and can detect their motion just like with sagnac.


Why does MMX refuse to detect any type of motion when GPS does?

No. I'm assuming that there is an absolute frame of reference. I'm claiming that clocks can easily be synchronized in moving frames so that the motion of a photon pulse can be described by the equation x=ct in moving frames and that no contradictions, under simple conditions, will develop.

So, what is you math for clock syncing with an absolute frame for light?

I wonder if there is an absolute frame for light since light cannot ever be speed injected beyond c, or so they say.

http://web.stcloudstate.edu/ruwang/PRL93.pdf

IOP, linear sagnac.

Let us see how prepared everyone is for the math of all this.

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#moving-source_tests

3.3 Tests of Light Speed from Moving Sources
If the light emitted from a source moving with velocity v toward the observer has a speed c+kv in the observer's frame, then these experiments place a limit on k. Many but not all of these experiments are subject to criticism due to Optical Extinction.

Experiments Using Cosmological Sources
Comstock, Phys. Rev. 10 (1910), pg 267. DeSitter, Koninklijke Akademie van Wetenschappen, vol 15, part 2, pg 1297–1298 (1913). DeSitter, Koninklijke Akademie van Wetenschappen, vol 16, part 1, pg 395–396 (1913). DeSitter, Physik. Zeitschr. 14, 429, (1913) http://www.datasync.com/~rsf1/desitter.htm. DeSitter, Physik. Zeitschr. 14, 1267, (1913) http://www.datasync.com/~rsf1/desitter.htm. Zurhellen, Astr. Nachr. 198 (1914), pg 1.
Observations of binary stars. k < 10−6. These are all subject to criticism due to Optical Extinction.

K. Brecher, “Is the Speed of Light Independent of the Velocity of the Source?”, Phys. Rev. Lett. 39 1051–1054, 1236(E) (1977).
Uses observations of binary pulsars to put a limit on the source-velocity dependence of the speed of light. k < 2×10−9. Optical Extinction is not a problem here, because the high-energy X-rays used have an extinction length considerably longer than the distance to the sources.

Heckmann, Ann. d. Astrophys. 23 (1960), pg 410.
Differential aberration, galaxies versus stars. This experiment is subject to criticism due to Optical Extinction.

Observations of Supernovae
A supernova explosion sends debris out in all directions with speeds of 10,000 km/s or more (known from Doppler broadening of spectral lines). If the speed of light depended on the source velocity, its arrival at Earth would be spread out in time due to the spread of source velocities. Such a time spread is not observed, and observations of distant supernovae give k < 5×10−9. These observations could be subject to criticism due to Optical Extinction, but some observations are for supernovas considerably closer than the extinction length of the X-ray wavelengths used.


Now, if a frame by luck happened to be at absolute rest, then these experiments confirm light cannot ever exceed one speed c under any conditions.

Thus, the light frame is absolute, or so these experiments suggest.

So, what is you math for clock syncing with an absolute frame for light?


Clock synchronization schemes are arbitrary, even in universes with an absolute frame of reference.

Clock synchronization schemes are arbitrary, even in universes with an absolute frame of reference.

Can you prove this?

Can you prove this?


Yes. See problem number 1 and 2 at the end of the page Generalized Lorentz Transformations (http://www.everythingimportant.org/relativity/generalized.htm). I invented those problems and I can solve them also.

Yes. See problem number 1 and 2 at the end of the page Generalized Lorentz Transformations (http://www.everythingimportant.org/relativity/generalized.htm). I invented those problems and I can solve them also.

How nice.

We are not talking about SR so your "views" are not relevent.

He said, light is but one speed in this "aether".

So, any object moves relative to the fixed aether and can detect their motion just like with sagnac.

How, Jack?
Design a simple experiment to do this.

Don't forget that clocks moving relative to the aether run slowly, and rulers moving relative to the aether are contracted in the direction of motion.

How, Jack?
Design a simple experiment to do this.

Don't forget that clocks moving relative to the aether run slowly, and rulers moving relative to the aether are contracted in the direction of motion.

Is that right?

Let me see the math like with Einstein's LT.

Is that right?

Let me see the math like with Einstein's LT.

What math? I'm describing the basic physics of a hypothetical universe. They're postulates, if you like.

What math? I'm describing the basic physics of a hypothetical universe. They're postulates, if you like.\

Yea, prove your case. Show your conclusions with math.

I haven't made a case, or attempted any conclusions.
I've posed a puzzle, which you seem to be ignoring.

I don't know what the answer to the puzzle is. I suspect it has no answer, but I don't know for sure.
I'm trying to learn something, and I'm inviting you to help.

Let me see the math like with Einstein's LT.
All the math you should need is that a clock in this hypothetical universe moving at velocity v relative to the aether runs slowly by a factor of gamma, and a ruler moving at velocity v relative to the aether is contracted by a factor of gamma.

gamma = \frac {1}{\sqrt{1-v^2/c^2}}

We are not talking about SR so your "views" are not relevent.


You are greatly mistaken. The mathematical trickery behind resetting clocks is very revealing and general. For example, let's suppose that you're not terrified by the freedom of synchronizing clocks in a moving frame of reference according to a simple symmetry and the speed of sound in the rest frame of the stationary medium in Galilean spacetime. With the new resetting of clocks, I can legitimately change the Galilean transformation equations to become:

x' = x-vt
t' = (Y(v)^2)(t - vx/c^2)

where c is the speed of sound (not the speed of light) and
Y(v) = 1/sqrt(1-v^2/c^2)

I can do it. You only need begin with the two clocks synchronized at the same corner of the lab and then slowly move one of them to the opposite end of the lab. The more slowly you move the moving clock, the more perfectly it will be synchronized with the clock on the other side of the lab.

Have you checked this mathematically?

Have you checked this mathematically?


Yes. I have checked it directly using the Tangherlini equations:

x' =Y(v)(x-vT)

T' = T/Y(v)

which are essentially the specifications given in the opening post.

The more slowly you move the moving clock, the more perfectly it will be synchronized with the clock on the other side of the lab.
I assume the lab will need to be made out of rigid material of some kind? in order to avoid the elastic coupling of the clock mechanisms (unless these don't couple somehow)? as you slowly move them apart, that is?

Yes. I have checked it directly using the Tangherlini equations:

x' =Y(v)(x-vT)

T' = T/Y(v)

which are essentially the specifications given in the opening post.

I don't know these Tangherlini equations. I'm not convinced they match our hypothetical universe.


I can do it. You only need begin with the two clocks synchronized at the same corner of the lab and then slowly move one of them to the opposite end of the lab. The more slowly you move the moving clock, the more perfectly it will be synchronized with the clock on the other side of the lab.

Working from first principles and plugging in some values, I find that as the transfer time increases to infinity, the synchronization error decreases to a non-zero value. My working is a bit ugly, but I'll try to tex it up later, including a proper evaluation of the limit.

I assume the lab will need to be made out of rigid material of some kind? in order to avoid the elastic coupling of the clock mechanisms (unless these don't couple somehow)? as you slowly move them apart, that is?
They don't have to couple. Two separate clocks. One on a trolley so you can move it away.

I assume the lab will need to be made out of rigid material of some kind? in order to avoid the elastic coupling of the clock mechanisms (unless these don't couple somehow)? as you slowly move them apart, that is?


One always assumes in special relativity theory that time is being measured with ideal clocks that are unaffected by their surroundings or ordinary forces like acceleration.

The existence of the lab and its material composition has nothing to do with selecting a useful clock-synchronizing scheme.

I hope this makes sense. I'm not the best at presenting readable equations. I've left out all the working, but there's nothing unusual involved.


I can do it. You only need begin with the two clocks synchronized at the same corner of the lab and then slowly move one of them to the opposite end of the lab. The more slowly you move the moving clock, the more perfectly it will be synchronized with the clock on the other side of the lab.
Working from first principles and plugging in some values, I find that as the transfer time increases to infinity, the synchronization error decreases to a non-zero value. My working is a bit ugly, but I'll try to tex it up later, including a proper evaluation of the limit.
I find that if:
- two clocks are synchronized at one end of our lab, moving at speed v1 along the x-axis
- one clock then moves at speed v2 (>v1) along the x-axis until the distance between the clocks is d, measured by lab rulers (ie true distance = d/gamma_1),

then the time difference between the clocks will be:

\Delta t = d\frac {\frac{1}{\gamma_1} - \frac{1}{\gamma_2}}{(v_2 -v_1)\gamma_1}

If the clocks are separated more and more slowly, a limit is reached (evaluated using L'Hopital's rule):

\displaystyle\lim_{v_1 \leftarrow v_2} \Delta t = \frac{v_1d}{c^2}

I don't know these Tangherlini equations. I'm not convinced they match our hypothetical universe.
They look like the coordinate transformation that would result if the lab frame had length contracted rulers, time dilated clocks, and the same notion of simultaneity as the ether frame (since T' doesn't depend on position). They only make sense if you already have a way of synchronising clocks in the lab frame, so it looks like Schubert is effectively presupposing what he's trying to demonstrate in the first place.

They only make sense if you already have a way of synchronising clocks in the lab frame, so it looks like Schubert is effectively presupposing what he's trying to demonstrate in the first place.


Your suspicion that the Tangherlini equations imply a clock synchronization scheme for the moving frame is correct. Furthermore, you should be able to prove that this follows from the requirement that T' = T/Y(v), which is the simplest possible interpretation to the words of the opening post.

As I've testified already, I know how to unnecessarily complicate transformation equations to reflect a wide variety of extremely bizarre clock synchronization schemes but what would be the point?

One always assumes in special relativity theory that time is being measured with ideal clocks that are unaffected by their surroundings or ordinary forces like acceleration.

The existence of the lab and its material composition has nothing to do with selecting a useful clock-synchronizing scheme. Ok, just checking. You know how it is..

Your suspicion that the Tangherlini equations imply a clock synchronization scheme for the moving frame is correct.
No, they're the result of already having established a clock synchronisation scheme. If you've established a way of synchronising clocks in the lab frame, then their times will be independent of the x coordinate and you can write the coordinate transformation as t^{\prime} = \frac{t}{\gamma(v)}. Otherwise, your transformation is an equation that doesn't necessarily have anything to do with anything.


Furthermore, you should be able to prove that this follows from the requirement that T' = T/Y(v), which is the simplest possible interpretation to the words of the opening post.
You're not being asked to find the simplest transformation equation consistent with the OP. You're being asked to find a clock synchronisation procedure that results in the coordinate transformation you've posted. It should be your end result, not your starting point. And as Pete's just shown a few posts up, the sync'ing procedure you suggested doesn't accomplish this.

Hmm. Is the task here to synchronise two clocks then move them apart, or move them apart and synchronise them?
I think there is an important difference. In OEMB Einstein glosses over the construction of (arbitrarily) accurate clocks (he states that he could check the hands of a watch against those of a clock at a railway station, for instance), and appears to assume that clocks can be synchronised.

However, I believe that whatever the 'process', synchronisation can't be independent of some kind of coupling mechanism... in the case of eyeballing a watch or a clock, the coupling is an obervers vision, plus the mechanism of 'adjustment' of, presumably, the wristwatch, following the observation. Thus in the case of 'line-of-sight' synchronisation the accuracy is down to a human's reaction time to the 'clock signal'...

Tempus fugit, sic...

Hmm. Is the task here to synchronise two clocks then move them apart, or move them apart and synchronise them?
The task is to have two clocks that are apart and synchronized. Synchronizing them, then moving them apart doesn't seem to work, because they become desynchronized.


I think there is an important difference. In OEMB Einstein glosses over the construction of (arbitrarily) accurate clocks (he states that he could check the hands of a watch against those of a clock at a railway station, for instance), and appears to assume that clocks can be synchronised.
It's safe to assume that clocks can be synchronized when they are very close to each other.


However, I believe that whatever the 'process', synchronisation can't be independent of some kind of coupling mechanism... in the case of eyeballing a watch or a clock, the coupling is an obervers vision, plus the mechanism of 'adjustment' of, presumably, the wristwatch, following the observation. Thus in the case of 'line-of-sight' synchronisation the accuracy is down to a human's reaction time to the 'clock signal'...
You can assume that you have devices capable of instantaneous reactions, but they can't react instantly to events at a distance - they can only react to a local stimulus (eg a transmitted signal).

The task is to have two clocks that are apart and synchronized. Synchronizing them, then moving them apart doesn't seem to work, because they become desynchronized.


Moving the clocks apart is not a problem, because you already know the moving one becomes dilated by a factor of gamma. Once the moving clock stops moving, you simply re-calibrate for the difference.

Moving the clocks apart is not a problem, because you already know the moving one becomes dilated by a factor of gamma. Once the moving clock stops moving, you simply re-calibrate for the difference.
Well, in this hypothetical universe, I only know what the time dilation factor is relative to the universal rest frame. I don't know what it would be relative to the lab.

It would certainly be interesting to figure out what the result would be of doing what you describe. Note that you would first have to specify how you measure the speed of the moving clock relative to the lab.

You're being asked to find a clock synchronisation procedure


I did that on page 1. Recall post #6.


And as Pete's just shown a few posts up, the sync'ing procedure you suggested doesn't accomplish this.


Are you confident that Pete knows how to interpret and correctly manipulate the Tangherlini equations? If you do a little research, you'll find that the Tangherlini equations are just the Lorentz transformation equations in disguise. Clocks have been merely synchronized in an unusual way in the moving frame to confound the naïve and unsuspecting.

This puzzle is mainly for Jack, but others may play too.

In this puzzle, we're in a universe much like our own, except that in this universe there is a universal rest frame, in which light moves at c in vaccuum.
Length contraction and time dilation still apply. Moving rulers are contracted by a factor of gamma in their direction of motion. Moving clocks run slowly by a factor of gamma.

In this parallel Universe, on a parallel Earth, you're in a nice physics lab, with very precise timing devices, laser switches, precise rulers, and so on. You don't know which way your lab is facing, and your lab is shielded from the Earth's magnetic field. Under these assumptions, the absolute motion of the lab is (v_x \, , \, v_y \, , \, v_z ) and V^2 = v_x^2 + v_y^2 + v_z^2 and \gamma = \frac{1}{\sqrt{1 - \frac{V^2}{c^2}}} and the relationship between any pair of events in the Lab frame (primed coordinates) and the absolute rest frame (unprimed coordinates) is given by a general Lorentz transform.
\begin{bmatrix}c\,\Delta t' \\ \Delta x' \\ \Delta y' \\ \Delta z' \end{bmatrix}
= \begin{bmatrix}
1+\frac{(\gamma-1) c^2}{c^2}&-\frac{\gamma v_x}{c}&-\frac{\gamma v_y}{c}&-\frac{\gamma v_z}{c}\\
-\frac{\gamma v_x}{c} & 1+\frac{(\gamma-1) v_x^2}{V^2}&\frac{(\gamma-1) v_x v_y}{V^2}&\frac{(\gamma-1) v_x v_z}{V^2}\\
-\frac{\gamma v_y}{c}&\frac{(\gamma-1) v_x v_y}{V^2}&1+\frac{(\gamma-1) v_y^2}{V^2}&\frac{(\gamma-1) v_y v_z}{V^2}\\
-\frac{\gamma v_z}{c}&\frac{(\gamma-1) v_x v_z}{V^2}&\frac{(\gamma-1) v_y v_z}{V^2}&1+\frac{(\gamma-1) v_z^2}{V^2} \end{bmatrix}
\begin{bmatrix} c\,\Delta t \\ \Delta x \\ \Delta y \\ \Delta z \end{bmatrix}
= \begin{bmatrix} c\,\Delta t \\ \Delta x \\ \Delta y \\ \Delta z \end{bmatrix}
+ \begin{bmatrix} \gamma - 1 \\ -\frac{\gamma v_x}{c} \\ -\frac{\gamma v_y}{c} \\ -\frac{\gamma v_z}{c} \end{bmatrix} c\,\Delta t
+ \begin{bmatrix} -\frac{\gamma}{c} \\ \frac{(\gamma-1) v_x}{V^2} \\ \frac{(\gamma-1) v_y}{V^2} \\ \frac{(\gamma-1) v_z}{V^2} \end{bmatrix} ( v_x \, , \, v_y \, , \, v_z ) \cdot ( \Delta x \, , \, \Delta y \, , \, \Delta z )


Then, as demonstrated before (http://sciforums.com/showpost.php?p=2595020&postcount=4),
(c\,\Delta t')^2 - (\Delta x')^2 - (\Delta y')^2 - (\Delta z')^2 = (c\,\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2 which implies the speed of light is isotropically measured to be c in the lab frame.


Your task is to set up two clocks so that they are synchronized with each other at opposite ends of the lab.

How do you do it? Can it be done at all?
In the lab frame, you can consistently measure the speed of light to be the same, and your clocks will be equidistant from a certain midpoint, from which you can send synchronizing pulses of light. So you can certainly synchronize clocks in the lab frame. But if the dot-product between the lab's absolute motion and the physical separation of the clocks is not zero, then c\,\Delta t' between events at the two clocks will not be simply proportional to c\,\Delta t.

So while you may synchronize clocks in this lab frame, they are unlikely to be synchronized in the absolute frame unless the direction in which they are separated is orthogonal to the labs' absolute movement.

And unless the laws of physics are sensitive to this absolute motion, you will have no way of determining the lab's absolute velocity, and no way to synchronize absolutely.

I did that on page 1. Recall post #6.

Are you confident that Pete knows how to interpret and correctly manipulate the Tangherlini equations?
I didn't try. I worked from first principles to show that no matter how slowly you move that clock, you will still get a minimum synchronization error of vd/c^2 (where v is the speed of the lab, and d is the distance you move the clock).

See post #33.


If you do a little research, you'll find that the Tangherlini equations are just the Lorentz transformation equations in disguise. Clocks have been merely synchronized in an unusual way in the moving frame to confound the naïve and unsuspecting.
But clocks have not yet been synchronized at all. That's the whole point of this thread - to investigate whether it can be done.

But clocks have not yet been synchronized at all. That's the whole point of this thread - to investigate whether it can be done.


And I repeat. I did synchronize the clocks in the lab frame on page 1 in post #6.

Thanks rpenner,

Under these assumptions, the absolute motion of the lab is (v_x \, , \, v_y \, , \, v_z ) and V^2 = v_x^2 + v_y^2 + v_z^2 and \gamma = \frac{1}{\sqrt{1 - \frac{V^2}{c^2}}} and the relationship between any pair of events in the Lab frame (primed coordinates) and the absolute rest frame (unprimed coordinates) is given by a general Lorentz transform.
I think you need an extra assumption to reach that conclusion. Why can't \Delta t'=\Delta t/\gamma, as Eugene suggests? That would also seem to be consistent with the given assumptions.


In the lab frame, you can consistently measure the speed of light to be the same
Only if you have synchronized clocks, or if you only measure round-trip speed, right?

And I repeat. I did synchronize the clocks in the lab frame on page 1 in post #6.

Eugene, I investigated your suggestion (see post #33) and I really don't think it works. You're welcome to disagree, of course, but simply repeating yourself isn't awfully productive.
Can you explain your reasoning more fully?
Would you mind glancing at my calculations and see if I made a mistake?

Can you explain your reasoning more fully?
Would you mind glancing at my calculations and see if I made a mistake?


It's not necessary to answer your opening post. To answer that first question, just start with the Lorentz transformation equations. Let the unprimed x refer to the spatial coordinate in your universal rest frame and let t be the clock time for a clock at that coordinate point. Then let x' refer to the spatial coordinate in your moving frame and let t' denote the clock time for a clock at that point in the moving frame.

You have stated that light moves at c in vacuum in the universal rest frame. That law specifies how clocks are synchronized in the rest frame. The system of Lorentz transformation equations is a choice of clock synchronization in the moving frame. That's what you wanted. That's what I've given you in post #6. In essence, you have a non-problem.

The idea of the exercise was to find a way to investigate if the clocks could be synchronized in the absolute rest frame. I'm sorry that wasn't made clearer.

But I am now a little confused as to what your intention was. You seemed to imply earlier that your method provided synchronization in the primed coordinates given by a Tangherlini transform from the absolute rest frame, yet now you imply that it provides synchronization in the primed coordinates given by a Lorentz transform from the absolute rest frame?

I did that on page 1. Recall post #6.
That doesn't work either.


Are you confident that Pete knows how to interpret and correctly manipulate the Tangherlini equations?
He doesn't need the Tangherlini equations. I don't know why you keep bringing them up. Whatever point you're trying to make, it looks to me like it has little to do with the topic of this thread.


Would you mind glancing at my calculations and see if I made a mistake?
You didn't make a mistake. I could just make one really minor point and say that you don't even need to bother with bringing up L'Hopital's rule. I don't know if you noticed, but if you rewrite v_{1} = v and v_{2} = v + \Delta v, then your limit

\lim_{\Delta v \rightarrow 0} \, \frac{1}{\Delta v} \, \Bigl[ \frac{1}{\gamma(v+\Delta v)} \,-\, \frac{1}{\gamma(v)} \Bigr]
is just the definition of the derivative of \gamma(v)^{-1}.

You didn't make a mistake. I could just make one really minor point and say that you don't even need to bother with bringing up L'Hopital's rule. I don't know if you noticed, but if you rewrite v_{1} = v and v_{2} = v + \Delta v, then your limit

\lim_{\Delta v \rightarrow 0} \, \frac{1}{\Delta v} \, \Bigl[ \frac{1}{\gamma(v+\Delta v)} \,-\, \frac{1}{\gamma(v)} \Bigr]
is just the definition of the derivative of \gamma(v)^{-1}.
Thanks! That's strikes me as really interesting.
So, the derivative of the gamma function gives the relative difference in synchronization per unit distance, or something... Something I might have fun thinking about.

The idea of the exercise was to find a way to investigate if the clocks could be synchronized in the absolute rest frame.


In post #1 you said that, in the universe under consideration, there is a universal rest frame in which light moves at c in vacuum. That means that you have two clocks C1 and C2 separated by a distance d. Furthermore, it means that if a photon pulse is sent from C1 when that clock reads time T1 and the pulse travels in a straight line directly to clock C2, then the time at C2 when that pulse arrives will be T1 + d/c. That's the meaning of standard clock synchronization.


But I am now a little confused as to what your intention was. You seemed to imply earlier that your method provided synchronization in the primed coordinates given by a Tangherlini transform from the absolute rest frame, yet now you imply that it provides synchronization in the primed coordinates given by a Lorentz transform from the absolute rest frame?


It is well known that the only significant difference between the Tangherlini transform and the Lorentz transform is how clocks are synchronized in the moving frame.

In post #1 you said that, in the universe under consideration, there is a universal rest frame in which light moves at c in vacuum.
Right.

That means that you have two clocks C1 and C2 separated by a distance d. Furthermore, it means that if a photon pulse is sent from C1 when that clock reads time T1 and the pulse travels in a straight line directly to clock C2, then the time at C2 when that pulse arrives will be T1 + d/c. That's the meaning of standard clock synchronization.
If C1 and C2 are at absolute rest, yes.
But, we don't have access to anything at absolute rest. All we have is the lab, which has unknown motion.


It is well known that the only significant difference between the Tangherlini transform and the Lorentz transform is how clocks are synchronized in the moving frame.
Right.
When you move one clock slowly across the lab, the clocks will remain synchronized in the moving frame under a Lorentz transform, and not synchronized under a Tangherlini transform.
Either way, they will not remain synchronized in the absolute rest frame.

Well, in this hypothetical universe, I only know what the time dilation factor is relative to the universal rest frame. I don't know what it would be relative to the lab.


Hmmm, you're right. The moved clock might slow down, or it might speed up, depending on which direction it's moved. Unless the lab happens to be at rest in the universal rest frame, in which case the moved clock always slows down, regardless of direction.


It would certainly be interesting to figure out what the result would be of doing what you describe. Note that you would first have to specify how you measure the speed of the moving clock relative to the lab.


Measure the length of the lab with a tape measure, and then use the stationary lab-clock to time how long it takes for the moving lab-clock to get from one side of the lab to the other. Then the relative speed of clock-to-lab is just the length divided by the time.

In order to find the absolute speed of the lab, you can try a Michelson-Morley experiment. However, I'm not quite sure that you wouldn't get a null result, in this hypothetical universe.

I haven't made a case, or attempted any conclusions.
I've posed a puzzle, which you seem to be ignoring.

I don't know what the answer to the puzzle is. I suspect it has no answer, but I don't know for sure.
I'm trying to learn something, and I'm inviting you to help.

Here is the correct proof for your puzzle.

www.proofofabsolutemotion.com/pete2.pdf

Any equation put forth that involves γ, automatically confesses multiple light emission points as does SR.

In other words. for SR to be consistent, light must have divergent light emission points in the coordinates of any frame ie one light pulse must be emitted from an infinte number of points in the coordinates of one frame.

Under absolute motion, there exists one unique light emission point for all frames. Does this seem more reasonable in reality?

The objective is to find it.

Well, in this hypothetical universe, I only know what the time dilation factor is relative to the universal rest frame. I don't know what it would be relative to the lab.

It would certainly be interesting to figure out what the result would be of doing what you describe. Note that you would first have to specify how you measure the speed of the moving clock relative to the lab.

Time dilation is a consequence of the admission of multiple light emission points in one coordinate system.

Your model does not admit this logic.

Time dilation is a consequence of the admission of multiple light emission points in one coordinate system.
Time dilation is a fundamental fact of this hypothetical universe, in which space is absolutely defined relative to the aether. So no, there are no "multiple light emission points" to worry about here, whatever that means. And yes, moving clocks do indeed run slowly here.


Assume the inertial frame's absolute motion was detected according to the absolute motion finite proof.
Please describe how you would detect the lab's absolute motion.

Time dilation is a fundamental fact of this hypothetical universe, in which space is absolutely defined relative to the aether. So no, there are no "multiple light emission points" to worry about here, whatever that means. And yes, moving clocks do indeed run slowly here.


Please describe how you would detect the lab's absolute motion.

First, you must understand how we arrive at time dilation.

Do you understand why?

It is because we accept multiple light emission points in the context of one frame.

We allow the moving frame to have its own special light emission point different from the rest frame.

In order to proceed, you must realize this fact.

Your model does not admit multiple light emission points.

You must stay within your model.

Measure the length of the lab with a tape measure, and then use the stationary lab-clock to time how long it takes for the moving lab-clock to get from one side of the lab to the other.
How do we know, on this end of the lab, when to stop the 'stationary' clock so that it stops at the same time as the 'moving' clock reaches the other end?


However, I'm not quite sure that you wouldn't get a null result, in this hypothetical universe.
Length contraction alone is enough to ensure a null result for the Michelson Morley experiment. Length contraction was originally suggested to explain exactly that.

First, you must understand how we arrive at time dilation.

Do you understand why?

It is because we accept multiple light emission points in the context of one frame.
No, Jack, you're confusing my hypothetical universe with someone else's.

In my hypothetical universe, it's a simple fact of nature that any process that occurs while moving against the aether occurs more slowly. The faster the motion against the aether, the slower things happen.

Don't be confused by your "multiple emission points" stuff. That's not relevant here at all.


So how are you going to measure the lab's motion against the aether? I'm not sure if it can be done or not.

I've already addressed absolute motion in my "A Train, Three Clocks, and an Observer" thread. It is fact! In order for an observer to see two clocks as synchronized from a midpoint position in a frame of reference, the frame must be at an absolute zero velocity. BTW, the midpoint observer can not ever read his clock as the same as the two other clocks if separated by a distance. Impossible. The two separated clocks can be seen as the same (synchronized) but never that and reading the same as his midpoint clock. The midpoint clock will always read ahead of the other two clocks, even though they remain in sync.

The only way for two end balls on a train to travel towards each other towards a midpoint of the train at the same velocity, is for the train to have a zero velocity, for if not at a zero velocity, one ball is decelerated and one ball is accelerated.

No, Jack, you're confusing my hypothetical universe with someone else's.

In my hypothetical universe, it's a simple fact of nature that any process that occurs while moving against the aether occurs more slowly. The faster the motion against the aether, the slower things happen.

Don't be confused by your "multiple emission points" stuff. That's not relevant here at all.


So how are you going to measure the lab's motion against the aether? I'm not sure if it can be done or not.

First, you need to understand your model.

http://www.youtube.com/watch?v=KHjpBjgIMVk

Time dilation of a consequence of two light emission points of the two frames.

If you cannot understand why time dilation is not in your model, then there is no point in me proceeding.

You cannot just will it.

So, indicate why time dilation is consistent with an absolute light speed model.

If i am wrong, then you will show me and I will admit it.

I've already addressed absolute motion in my "A Train, Three Clocks, and an Observer" thread. It is fact! In order for an observer to see two clocks as synchronized from a midpoint position in a frame of reference, the frame must be at an absolute zero velocity. BTW, the midpoint observer can not ever read his clock as the same as the two other clocks if separated by a distance. Impossible. The two separated clocks can be seen as the same (synchronized) but never that and reading the same as his midpoint clock. The midpoint clock will always read ahead of the other two clocks, even though they remain in sync.

The only way for two end balls on a train to travel towards each other towards a midpoint of the train at the same velocity, is for the train to have a zero velocity, for if not at a zero velocity, one ball is decelerated and one ball is accelerated.

You claimed the midpoint is a known fixed point in space.

That is how you draw your conclusions.

Your argument is therefore circular.

First, you need to understand your model.
No, Jack, this is my construct. If you don't understand it, feel free to ask questions, but you don't make the rules.


So, indicate why time dilation is consistent with an absolute light speed model.
What do you mean by an "absolute light speed" model?
In this hypothetical universe, all we know about light speed is that light moves at c in our absolute reference frame.
So, we know that if we measured light speed using resting (undilated) clocks, and resting (uncontracted) rulers, we would measure a speed of c.
I haven't said anything about what we'd measure using moving, contracted rulers and/or moving, dilated clocks, so there's no inconsistency.

First, you need to understand your model.

http://www.youtube.com/watch?v=KHjpBjgIMVk

Time dilation of a consequence of two light emission points of the two frames.

If you cannot understand why time dilation is not in your model, then there is no point in me proceeding.

You cannot just will it.

So, indicate why time dilation is consistent with an absolute light speed model.

If i am wrong, then you will show me and I will admit it.


[EDIT]

http://en.wikipedia.org/wiki/Time_dilation

This provides the math for the reasoning of time dilation.

Now, this is completely stupid because I can construct a model in which there is no time dilation using this mathematical approach.

If I set x = vtγ /(1+γ) and x' = -x = -vtγ /(1+γ), then light reaches them when they are co-located.

In addition, Δt' = Δt and hence no time dilation.

Anyway, time dilation is not consistent with an absolute fixed speed of light model.

No, Jack, this is my construct. If you don't understand it, feel free to ask questions, but you don't make the rules.


What do you mean by an "absolute light speed" model?
In this hypothetical universe, all we know about light speed is that light moves at c in our absolute reference frame.
So, we know that if we measured light speed using resting (undilated) clocks, and resting (uncontracted) rulers, we would measure a speed of c.

I don't know what we'd measure using moving, contracted rulers and/or moving, dilated clocks.

Perhaps you can teach me.

How are you going to make time dilation consistent with your model?

You cannot just will it.

We are conducting math.

Jack, have another squiz at post #1:

...in this universe there is a universal rest frame, in which light moves at c in vaccuum.
Length contraction and time dilation still apply. Moving rulers are contracted by a factor of gamma in their direction of motion. Moving clocks run slowly by a factor of gamma.

Did this slide on by ya?

Jack, have another squiz at post #1:


Did this slide on by ya?

No it did not.

It is simply inconsistent wtih an absolute fixed light speed model.

In other words, it is a comic book model.

I guess you are OK with this under the concept of science.

It is simply inconsistent wtih an absolute fixed light speed model.
Oh?
How is it inconsistent, can you explain the problem?

Have you formed any opinion of the posts that other contributors have made in this thread? Do you think synchronising clocks is possible in a universe with an absolute frame of rest (think "Feyman diagram")...

Oh?
How is it inconsistent, can you explain the problem?

Have you formed any opinion of the posts that other contributors have made in this thread? Do you think synchronising clocks is possible in a universe with an absolute frame of rest (think "Feyman diagram")...

Well, I provided a proof on how to sync clocks in this model. I am surprised you missed it with your "opinions".

So, you are now left to refute it.

How long will this take?

Perhaps you can teach me.

How are you going to make time dilation consistent with your model?

You cannot just will it.

We are conducting math.
I don't know if one of us is being dense or argumentative, Jack, but I really don't know why you think there is any inconsistency here.

In this hypothetical universe, if you measure the speed of a light beam using clocks and rulers at rest in the aether, you'll measure c.

If you measure it with moving clocks, maybe you'll measure something different, because moving clocks run slowly.

Where's the inconsistency?

How long will this take? Longer than my lifetime...?

Oh?
How is it inconsistent, can you explain the problem?

Have you formed any opinion of the posts that other contributors have made in this thread? Do you think synchronising clocks is possible in a universe with an absolute frame of rest (think "Feyman diagram")...

did you miss this??? do you read???? do you need help understanding the facts????


http://en.wikipedia.org/wiki/Time_dilation

This provides the math for the reasoning of time dilation.

Now, this is completely stupid because I can construct a model in which there is no time dilation using this mathematical approach.

If I set x = vtγ /(1+γ) and x' = -x = -vtγ /(1+γ), then light reaches them when they are co-located.

In addition, Δt' = Δt and hence no time dilation.

Anyway, time dilation is not consistent with an absolute fixed speed of light model.

Jack_, I understand the model being proposed. In this model, clocks run more slowly when they are in motion, and rigid rulers contract when they're in motion.

What's the inconsistency? Can you explain why you claim: "..time dilation is not consistent with an absolute fixed speed of light model" ??

I don't know if one of us is being dense or argumentative, Jack, but I really don't know why you think there is any inconsistency here.

In this hypothetical universe, if you measure the speed of a light beam using clocks and rulers at rest in the aether, you'll measure c.

If you measure it with moving clocks, maybe you'll measure something different, because moving clocks run slowly.

Where's the inconsistency?


In this hypothetical universe, if you measure the speed of a light beam using clocks and rulers at rest in the aether, you'll measure c.

This statement is correct.


If you measure it with moving clocks, maybe you'll measure something different, because moving clocks run slowly.

This statement is false.

This is pushed on folks by SR and is not part of this model.

The reason clocks move slow for the moving frame is because of the logic that SR agrees there is a light emission point in the rest frame and one in the moving frame, botj are assumed valid and this reconciles this stupidity.

Check the links I posted. Look at the math and understand why time dilation exists.

It did not exist in the 1800's.

So, see for yourself why it exists under SR. You should already know this.

Jack_, I understand the model being proposed. In this model, clocks run more slowly when they are in motion, and rigid rulers contract when they're in motion.

What's the inconsistency? Can you explain why you claim: "..time dilation is not consistent with an absolute fixed speed of light model" ??

Prove time dilation in a model where the speed of light is c in all directions only in an absolute rest frame.

You just assume it.

Prove it is consistent.

I don't need to "prove it" FFS.
Just assume it's a real condition of the model.

Jeez.

If you measure it with moving clocks, maybe you'll measure something different, because moving clocks run slowly.

This statement is false.

This is pushed on folks by SR and is not part of this model.
Jack, this model has nothing to do with SR.
This model is examining what would happen if time dilation and length contraction were fundamental laws.


Prove time dilation in a model where the speed of light is c in all directions only in an absolute rest frame.

You just assume it.

Prove it is consistent.
What's to prove? They're independent of each other.
The reading on a moving clock clearly has no effect on any measurement made using a stationary clock.

I don't need to "prove it" FFS.
Just assume it's a real condition of the model.

Jeez.

Here is a theory.

x + 2 = y.
x = y.

Is this theory consistent? No.

So, I only entertain theories that are consistent.

I see you are different. Any ole thing works for you and you get on board without further thought.

And so, you apply your usual "bait and switch" tactic, in a transparent effort to deflect from your inability to respond meaningfully.

Way to go, Jack_

Oh well, I guess he didn't want to play. Never mind, I'm sure he'll just carry on his crusade of ignorance somewhere else.
Now I can get some real work done.

Moderator note: Jack_ has been permanently banned from sciforums for trolling.

I have a question which may or not be related to the task.

In what sense are two photons from opposite edges of the sun (that is, in our line of sight) entangled?

Apologies. I realised that
You don't know which way your lab is facing, and your lab is shielded from the Earth's magnetic field. means you can't introduce the diameter of the sun, except for the idea of two spatially separated clocks.

That is, photons from opposite edges of a star are an 'encoding' of the diameter, so this represents the idea of a frame of reference (assuming the star maintains a steady-state).
Then, the idea of separating clocks (they might be moving apart, or together) is related to entangling them, in some "informational" sense. Thus there is an entropy of information in the "handshaking" or protocol.

Edit: extending the model, where the sun, plus say, the rotation of the earth are the protocol, synchronisation is an effective 'halt' of the rotation so that during a sunrise or sunset, for instance, a diameter is seen in both cases (this doesn't need to be a full diameter, it depends on how you interpret the protocol). In the case of the lab, the separated clocks are an unknown distance apart.

Edit again: for the public, the fixed, stable diameter of the sun as a reference is the material analogy of the Einsteinian rigid body (rod), with clocks at either end. The chain of logic here is: entanglement (entropy) -> synchronisation of separated clocks -> spatial encoding.

In case you are thinking: "this guy shouldn't have inhaled", google hanbury brown twiss.

The connection that occured to me is that synchronising clocks in the model (in which there is no external view, only the lab in an unknown state of motion) is related to determining the angular diameter of distant stars. Note that the actual astronomy doesn't depend on distance as such, only on the entangled information. The surprise is that this information is preserved over such distances.

Ain't the universe weird?

In case you are thinking: "this guy shouldn't have inhaled", google hanbury brown twiss.

The connection that occured to me is that synchronising clocks in the model (in which there is no external view, only the lab in an unknown state of motion) is related to determining the angular diameter of distant stars. Note that the actual astronomy doesn't depend on distance as such, only on the entangled information. The surprise is that this information is preserved over such distances.

Ain't the universe weird?

Time has nothing to do with the stars, or the angular diameter of such objects. Time is a duration, of which we have already chose a standard unit of measure.

Ok. Does measuring the diameter have to do with time, though?

Suppose you don't know anything about stars, except they are like holes in a big black "curtain" of some kind, through which coherent patterns of light appear, when you "analyse" it. Assume you have an interferometric method at your disposal.

The two clocks in this model are just two identical, or maybe not, oscillating systems of some kind. You want to know about how coherent a signal you can measure from either of these clocks, so you can "synchronise" them.

Ok. Does measuring the diameter have to do with time, though?

No, it can take you 10 seconds to measure the diameter or it can take you 10 years to measure the diameter.

If it takes 10 seconds to measure do you say, "The diameter is 1,000 ft/10 sec, or if it takes you 10 years do you say 1,000 ft/10 yrs? NO, you say, the diameter is 1,000 ft. The measure of distance is timeless. There is no unit of time to distance.

Suppose you don't know anything about stars, except they are like holes in a big black "curtain" of some kind, through which coherent patterns of light appear, when you "analyse" it. Assume you have an interferometric method at your disposal.

The two clocks in this model are just two identical, or maybe not, oscillating systems of some kind. You want to know about how coherent a signal you can measure from either of these clocks, so you can "synchronise" them.

You are not synchronizing the rate at which they tick, you are synchronizing the "starting lines and the ending lines," in such a fashion that when you stand at a midpoint between them you see the same on both at any point in time. Note that light takes time to travel, so if the light is timestamped at departure and when it arrives at your midpoint position, the two timestamps must be different, regardless of the rate of travel. It is impossible for them to read the same as a midpoint clock because of distance and time. You can't break causality by traveling faster (than the speed of light)!

You can't break causality by traveling faster (than the speed of light)! Who said anything about breaking something?
Apart from that, your post is saying pretty much what I said.

...but, how do you timestamp light? And how do you know how to stand at a midpoint between two clocks, how do you measure it?
All I've done is introduce a way to calculate distance, not to a star but across one, and what the implications are.

How do we know, on this end of the lab, when to stop the 'stationary' clock so that it stops at the same time as the 'moving' clock reaches the other end?


In your hypothetical universe, I can send the 'moving' clock across the lab at very close to v=c. I also have the option of sending the 'moving' clock across the lab at very close to v=0 (slow clock-transport method). Thus, I can measure time dilation effects along different vectors.


Length contraction alone is enough to ensure a null result for the Michelson Morley experiment. Length contraction was originally suggested to explain exactly that.


Yes, length contraction alone explains the null MMX. But that experiment took place in the real universe, not your hypothetical universe. Considering that I can do the aforementioned experiments in your hypothetical universe, I wonder if perhaps the MMX would have a different result in that universe.

Gee-whiz stuff:

Light from stars is incoherent. The coherence radius of the pattern seen in a stellar intensity interferometer (q.v.) suggests that incoherent starlight can self-interact over large distances, and "synchronise itself".

Is light affected by gravity? (well, yeah) Light from a star is affected by the size of the "hole" that the light comes from, in much the same (exactly the same?) way light passing through a pinhole forms a coherent pattern on a screen.

So that intensity interferometry in fact gauges the effect of the "size" of a star, its gravity, on radiation. Strangely, this also indicates that light affects itself, transforming from an incohererent non-synchronised state to a coherent state, over time (and of course distance).

But all of this depends on how the radiation is measured. Synchronisation and entanglement appear to be much the same thing, at some step, or you could say that adjusting a wristwatch against a clock reference is equivalent to entangling the two mechanisms.

Therefore, Einstein's rigid rod with clocks at either end is a synchronisation / entanglement of 'clock-states'...

Pucker up those biological neurons, baby:

Of course, a mechanical clock will only record time with a certain accuracy, and two of them will eventually desynchronise. Even atomic clocks will only stay synchronised if they are at the same gravitational potential.

Pete's model universe is the equivalent of (one of) Einstein's. Clearly, the rigid rod made of unknown material can also have unknown length, and in the model length of rigid rods is a function of velocity.

The time-rate of change of velocity and length determines the rate that time can be recorded (i.e. "watched") because in the accelerated frame, clocks slow down, and it takes longer to synchronise them. It will take less time to adjust a clock on a mountain than at sea-level, because adjustement "takes" time--this is "discarded" or "lost time".

The work done adjusting a clock mechanism is "forgotten" or "lost" to the environment.
The work required to entangle two clock states has an entropy, since either you have a record of the time required to adjust one of the clocks, the information entropy, or, that the energy required to synchronise the states isn't "used" thermodynamically by the clocks.

In intensity interferometry, the "work" done synchronising incoherent light is also lost, but the interferometer records the time it took to do this, in the coherence pattern. The energy that synchronises the light (into a spatially coherent signal)--the adjustment mechanism--must come from somewhere.

http://faculty.virginia.edu/austen/HanburyBrownTwiss.pdf