Transitivity condition for Einstein synchronization and the one-way light speed

[matheinste]

Hello elisir,

How does this differ essentially from having a light source next to a clock and a mirror at a known distance. You don't synch clocks but all you measure is the average speed of light. Your more complex path can be broken down in many ways into components which have equal path lengths in opposite directions, the same as the mirror scenario.

I am a little short on time and so will take a closer look later but it looks a non starter to me.

Matheinste.

 

[elisir]

How does this differ essentially from having a light source next to a clock and a mirror at a known distance. You don't synch clocks but all you measure is the average speed of light. Your more complex path can be broken down in many ways into components which have equal path lengths in opposite directions, the same as the mirror scenario.

I am a little short on time and so will take a closer look later but it looks a non starter to me.

The geometry you describe, in the closed path you propose, the light speed in both direction exist. In triangular geometry, once you choose clockwise or anti-clockwise direction only one direction of the light speed exists. You can not break down let's say the clockwise direction on the triangular path into superposition of two-way round trip on straight lines.

 

[ghwellsjr]

Your pictures are the same ones from the link you provided in which you said that you only provided the link to answer DaleSpam's request for a mathematical demonstration of the Trimmer experiment. I didn't think you were promoting this new proposed experiment.

When I looked at the paper and saw the diagrams with the cars on the streets and read the explanation, it made absolutely no sense to me but I didn't ask for an explanation because you didn't indicate you were putting any confidence in this proposed new experiment but now it appears that you are. But, your explanation makes no sense. I have questions:

Why are there two lanes going one way but only one lane going the other way?
Why is there only one car shown in the top graphic but two cars shown in the bottom graphic?
Is there any significance to the fact that the two-lane direction is outside the one-lane direction in the triangle and therefore a longer distance?
Are these graphics applicable to the Trimmer experiment or only to the new proposed experiment?
Isn't it the case that in the Trimmer experiment and the new proposed experiment, the light traverses exactly the same path in the two directions?
Why doesn't the graphic show something equivalent to the piece of glass or other optical device that is present in the real experiments?

But to answer your million dollar question: of course, we super-beings looking down on this graphic could measure the one way speed of the cars because we have super clocks and super rulers that allow us to determine the real graphic distances and times. But graphic-beings can't "see" ahead to know when the car reaches the other end of the track.

That is our problem when we try to measure the one-way speed of light. Once the light leaves our source, we have no idea where it "really" is until something (a detector or mirror) a known distance away communicates back to us that it has arrived at that point and then it takes time to communicate that information back to us so unless we make some assumptions about how long it takes for the communication of that information back to us, we cannot determine absolutely when the light reached our detector or mirror.

How does your graphic (or the Trimmer experiment or the new proposed experiment) solve this problem?

 

[matheinste]

The geometry you describe, in the closed path you propose, the light speed in both direction exist. In triangular geometry, once you choose clockwise or anti-clockwise direction only one direction of the light speed exists. You can not break down let's say the clockwise direction on the triangular path into superposition of two-way round trip on straight lines.

My basic geometry may be a bit rusty but is it not the case that in a journey, starting from and returning to the same point, the total integrated displacement by all paths is zero, or better to say in this case, that in all directions, the components, referred to a set of coordinates, of a journey by any arbitrarily chosen path to any point, and the components of an arbitrarily chosen return path, referred to the same coordinate axes, sum to zero. They are all in principle analogous to a straighline path out and back. Of course such an "integration " of paths may not be true in a non conservative field or spacetime, but we are dealing with such advanced scenarios here, are we?.

Matheinste

 

[DrGreg]

It seems to me that describing this as a measurement of the one-way speed of light is misleading (and why everyone else in this thread has objected). It would be more reasonable to describe it as a measurement of the "three-way" speed of light (round a triangle in each direction).

Special relativity asserts that the three-way speed of light should be the same either way round an inertial triangle, but not for a rotating triangle. So this experiment is really to confirm that the Sagnac effect is zero when the angular velocity is zero. It says nothing at all about the one-way speed of light which is determined purely by your choice of coordinates (or synchronization convention) and can't be determined experimentally.

 

[elisir]

...

I discard your teasing questions.

But to answer your million dollar question: of course, we super-beings looking down on this graphic could measure the one way speed of the cars because we have super clocks and super rulers that allow us to determine the real graphic distances and times. But graphic-beings can't "see" ahead to know when the car reaches the other end of the track.

Perhaps this is another teasing. I have better method to tease. Look :P .. please discard the possibility that you are a super being and answer.

That is our problem when we try to measure the one-way speed of light. Once the light leaves our source, we have no idea where it "really" is until something (a detector or mirror) a known distance away communicates back to us that it has arrived at that point and then it takes time to communicate that information back to us so unless we make some assumptions about how long it takes for the communication of that information back to us, we cannot determine absolutely when the light reached our detector or mirror.

Have you ever heard of the detectors? Measure the time. Send a pulse to a mirror, have that pulse reflected back to another mirror, and from the second mirror to your detector near the place that you have emitted it from. As soon as you detect the pulse, measure the time. Reflect before you write.

How does your graphic (or the Trimmer experiment or the new proposed experiment) solve this problem?

Read the papers for detailed mathematical answer to your questions.

 

[elisir]

Special relativity asserts that the three-way speed of light should be the same either way round an inertial triangle, but not for a rotating triangle. So this experiment is really to confirm that the Sagnac effect is zero when the angular velocity is zero. It says nothing at all about the one-way speed of light which is determined purely by your choice of coordinates (or synchronization convention) and can't be determined experimentally.

First thank you. If we go to theories that include a generalisation of special relativity that allows for anisotropy of one-way light speed, such as SME, then the triangular geometry will measure the anisotropy of the one-way speed of light. This is similar to Sagnac effect but it is not that effect. It measures the one way light speed.

 

[elisir]

My basic geometry may be a bit rusty but is it not the case that in a journey, starting from and returning to the same point, the total integrated displacement by all paths is zero, or better to say in this case, that in all directions, the components, referred to a set of coordinates, of a journey by any arbitrarily chosen path to any point, and the components of an arbitrarily chosen return path, referred to the same coordinate axes, sum to zero. They are all in principle analogous to a straighline path out and back. Of course such an "integration " of paths may not be true in a non conservative field or spacetime, but we are dealing with such advanced scenarios here, are we?.
Matheinste

Dear Matheinste,

You are right that any-closed path can be broken to pieces. We then can integrate over the pieces. But on every piece of line, we have two bits of information: the light speed in both directions.

When you consider a straight line, you break the line, on every piece you have moved twice. You sum over the directions too. You sum over extra bits of information. At the end, you have only integral.

When you apply your breaking procedure on a triangle, you sum over pieces. But you do not sum over the extra bits of information that exists on each piece. You can define two integral over the pieces, one that includes the bit of clockwise direction and one that includes the bit of anti-clockwise direction.

 

[ghwellsjr]

I have better method to tease.

Yes, you do, goodbye.

 

[elisir]

Yes, you do, goodbye.

It was the thing that I did not know. Have good times.

 

[Dale]

Do not keep the system rotating. Rotate the triangle. stop rotating. Now every thing is in inertial system. Measure the beat frequency. Does the beat frequency depend on the configuration of the triangle? if yes, you have detected the one-way anisotropy of light.

Don't you see the problem in this? The way you determine whether or not the frame is inertial is by this measurement. When the beat frequency is non-zero the frame is non-inertial, therefore you can NEVER get a non-zero reading in an inertial frame by DEFINITION. It does not depend on the configuration of the triangle.

Could you please spare me why you expect to find what you have defined as intertial frame in nature?

Because more than 100 years of scientific evidence shows it: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

I totally disagree. ... I understand you, I expect you reflect and try to understand me.

I not only understand your idea, but I immediately recognized your proposed experiment as ring interferometer of the kind commonly used in inertial navigation systems to measure the Sagnac effect. The fact that you did not see this relationship to the Sagnac effect shows that you, in fact, do not fully understand the topic. That is not an insult, that is the whole purpose of this site: to educate about mainstream physics. You are in the right spot to learn.

You are wrong. There exist some ways.

Then please provide an example of some way to measure the one-way speed of light. A ring interferometer is not such a device.

Should I start to insult back? ... This is hypocrisy, ... Please don't employ hypocrisy.

elisir, you need to take a breath and calm down. If you feel that stating that you don't understand something is an insult then you probably don't have the temperament for this site. I find it interesting that you consider my assertion that you didn't understand the topic (a minor deficit in education) to be an inappropriate insult, but you consider your assertion that I am a hypocrite (a major deficit in character) to be appropriate. It doesn't bother me either way; I have been called much worse. But I find the juxtaposition rather amusing. You need to develop a little bit of a "thick skin" and not be so sensitive in this medium.

 

[elisir]

Don't you see the problem in this? The way you determine whether or not the frame is inertial is by this measurement. When the beat frequency is non-zero the frame is non-inertial, therefore you can NEVER get a non-zero reading in an inertial frame by DEFINITION. It does not depend on the configuration of the triangle.

A rotating frame leads to a specific beat frequency. That is the beat frequency is a functional of the parameters determining the configuration of the triangle and the circular velocity of the inertial frame. Measure the beat frequency, if that frequency profile coincides to the profile you expected you will conclude that you are in a rotating frame. Your measured quantity may deviate from this profile.

Because more than 100 years of scientific evidence shows it: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Even I started from the original paper of Einstein. Special relativity is moot to the possibility of anisotropy of the one-way light speed. Please note that anisotropy in the one-way light speed contradicts the assumption of Einstein that his synchronisation is an equivalence relation. Once the light speed is anisotropic, his assumption on page three of the English translation of his paper breaks. Please do not use the outcome of an argument when the assumption is broken.

I not only understand your idea, but I immediately recognized your proposed experiment as ring interferometer of the kind commonly used in inertial navigation systems to measure the Sagnac effect. The fact that you did not see this relationship to the Sagnac effect shows that you, in fact, do not fully understand the topic.

I do agree that ring experiment is not capable of measuring one-way light speed. Consider an inertial ring or a rectangle. In this path, for each direction present in the path, light speed in both direction exists. Let me illustrate it more:
Consider a rectangle ABCD:
Consider a pulse of light moving on the rectangle from A to B, B to C and C to D, and finally back to A.
The light speed in direction of AB, and BA; and BC to CB equally contribute to the time for the travel of pulse. Only two-ways of light speed contributes to ring or rectangle.

This is the reason that I disagree with you. You know Sagnac experiment and you are saying the Sagnac experiment does not measure one-way light speed. I agree with you on this fact.

However, once you consider a triangle path, you see that you can measure the anisotropy of the one-way light speed.

That is not an insult, that is the whole purpose of this site: to educate about mainstream physics. You are in the right spot to learn.

Thanks. I try to correct myself.

Then please provide an example of some way to measure the one-way speed of light. A ring interferometer is not such a device.

I am over-repeating myself. Triangular path enables us to measure one-way light speed. While ring or rectangular does not make us enable to measure the anisotropy of the one-way light. Please refer to
Phys.Rev.D8:3321-3326,1973, Erratum-ibid.D9:2489-2489,1974
and read this paper carefully. This is an established example. After reading this paper, you may wonder why the community has forgotten this method. I wonder for this too.

elisir, .. You need to develop a little bit of a "thick skin" and not be so sensitive in this medium.

Thanks for your advice, I shall try my best to consider it.

 

[Dale]

Measure the beat frequency, if that frequency profile coincides to the profile you expected you will conclude that you are in a rotating frame. Your measured quantity may deviate from this profile.

It doesn't matter what frequency you measure. If you measure one beat frequency you will determine that you are rotating at some specific angular velocity. If you measure a beat frequency 2x greater then you determine that you are rotating at twice the angular velocity. There simply is no data left over to additionally measure any anisotropy. Any frequency can be accounted for by rotation.

Please do not use the outcome of an argument when the assumption is broken.

The point is that if the assumptions were broken then the resulting theory would not accurately predict the results of experiments. Since the results of experiments agree to very high precision with the predictions of the theory we can conclude that any violations of the assumptions are very small.

I do agree that ring experiment is not capable of measuring one-way light speed. Consider an inertial ring or a rectangle. In this path, for each direction present in the path, light speed in both direction exists. Let me illustrate it more:
Consider a rectangle ABCD:
Consider a pulse of light moving on the rectangle from A to B, B to C and C to D, and finally back to A.
The light speed in direction of AB, and BA; and BC to CB equally contribute to the time for the travel of pulse. Only two-ways of light speed contributes to ring or rectangle.

This is the reason that I disagree with you. You know Sagnac experiment and you are saying the Sagnac experiment does not measure one-way light speed. I agree with you on this fact.

However, once you consider a triangle path, you see that you can measure the anisotropy of the one-way light speed.

The shape of the path does not matter for the Sagnac effect, it depends only on the area of the loop and the angular velocity. The triangular ring interferometers are well understood and behave the same as a square or circular interferometer of the same area. In fact, many commercially available laser ring gyroscopes (interferometers) are triangular shaped:
http://www.airpower.au.af.mil/airchronicles/aureview/1985/may-jun/siuru.html
http://www.google.com/images?q=lase...itle&resnum=3&ved=0CEEQsAQwAg&biw=996&bih=970

With this many devices on the market if triangular shaped gyros were sensitive to some additional effect that could degrade their performance in detecting rotation then they would universally be avoided due to competitive pressures.

 

[elisir]

The shape of the path does not matter for the Sagnac effect, it depends only on the area of the loop and the angular velocity.

There exists no angular velocity in Trimmer method. The triangle is not rotating, the angular velocity is vanishing. So what you measure is not Sagnac effect. The Trimmer paper is about five pages:
http://prd.aps.org/abstract/PRD/v8/i10/p3321_1
Please take a glimpse on this paper.

 

[Dale]

There exists no angular velocity in Trimmer method. The triangle is not rotating.

How do you know that it is not rotating?

 

[elisir]

How do you know that it is not rotating?

A quick reply:
I do not rotate it myself. My laboratory might be rotating. I measure the phase difference of lights moving clock-wise and anti-clockwise on the perimeter of various triangles. If the phase difference is a functional of the area of the triangle (as you suggest that the Sagnac effect is), then it is Sagnac effect. I find that my laboratory is rotating. I find the angular velocity.

If the phase difference is a functional of the perimeter of the triangle, than rotation can not describe what I see. It is due to anisotropy of the one-way light speed.

 

[Dale]

That is fair enough, now you have two measurements so you could in principle tease out two effects.

There are different-sized triangular laser ring gyros available commercially. To my knowledge none of the designers have reported any effect of the perimeter, which would easily have been uncovered during routine testing.

 

[elisir]

There are different-sized triangular laser ring gyros available commercially. To my knowledge none of the designers have reported any effect of the perimeter, which would easily have been uncovered during routine testing.

True. This null result, however, should lead to a bound on the anisotropy of the one-way light speed. The one-way light speed is isotropic with the precision of these commercial gyros. I am quite sure that this null result has not been translated to the anisotropy of one-way light speed. Such a translation sounds very nice to me.

 

[Dale]

True. This null result, however, should lead to a bound on the anisotropy of the one-way light speed. The one-way light speed is isotropic with the precision of these commercial gyros. I am quite sure that this null result has not been translated to the anisotropy of one-way light speed. Such a translation sounds very nice to me.

So go ahead and do so. You consider yourself to be highly motivated and knowledgeable on the subject, do you not?

 

[elisir]

So go ahead and do so. You consider yourself to be highly motivated and knowledgeable on the subject, do you not?

In so doing, one uses the commercial equipments to extracts scientific data from. I gauss that this can not reach the precision of 0.1 nm/s on the anisotropy of the one-way light speed in mSME inferred from the absence of Cerenkov radiation for the ultra-high-energy-cosmic radiation, or 1 nm/s of the proposed cavity resonators. It would reach the precision of about or around cm/s, which is the precision of the Trimmer experiment in 1973, or about of the Tobar et al. experiment in 2009. It would be nice, but its outcome shall not improve the best current bounds.

 

[Dale]

So then why are you proposing this as your test?

Btw, the journal you linked to above is not free access, so can you rigorously derive the dependence of the beat frequency on the anisotropy of the one-way speed of light and the perimeter of the ring interferometer?