Isotropy of the speed of light

[andrew s 1905]

TL;DR Summary

Can diffraction demonstrate the speed of light is isotropic.

It has been put to me that a simple spectroscope could in theory demonstrate the isotropy of the speed of light . By using a frequency standard (laser comb or Th Lamp for example) with the spectroscope in various orientations the lack of shift of the spectral lines would prove its isotropic via the relation c = λf.

I see it would rest on other assumptions of isotropy but, it does seem to escape the issue of Einstein's clock synchronization protocol by using a single clock.

If there are any theoretical errors in this proposal please point them out.

I have reviewed the discussions here https://www.physicsforums.com/threads/measuring-possible-one-way-anistropy-of-light-speed.803992/

Regards Andrew

 

[hutchphd]

The Michelson interferometer will detect general anisotropy. The issue of one way anisotropy is different.

 

[mitochan]

Huygens Fresnel principle says, as the figure in https://en.wikipedia.org/wiki/Huygens–Fresnel_principle shows, spherical wave are generated from sources. If light speed had anisotropy, we would need not spherical but distorted shape generated waves to explain light diffraction phenomena.

 

[Dale]

I see it would rest on other assumptions of isotropy but, it does seem to escape the issue of Einstein's clock synchronization protocol by using a single clock.

There are many tests of the isotropy of the speed of light that do not depend on clock synchronization. The Michelson Morely experiment being the most famous.

Are you perhaps specifically talking about the isotropy of the one-way speed of light?

 

[andrew s 1905]

There are many tests of the isotropy of the speed of light that do not depend on clock synchronization. The Michelson Morely experiment being the most famous.

Are you perhaps specifically talking about the isotropy of the one-way speed of light?

Sorry my apologies, I was not sufficiently clear. Yes, the one way isotropy of the one way speed of light.

The spectroscope may be thought of as a simple transmission scope in which the light travels along the +ve x-axis apart from small deviations perpendicular to the x-axis due to diffraction. The whole apparatus is then rotated say 180 deg so the light now travels in the -ve x direction. The claim is that if the patterns match then the one way speed of light is isotropic along that axis. Obviously it could be rotated to arbitrary orientations to extend the proof.

My question is is this theoretically sound?

My assumption is it relies on the light frequency being isotropic.

Regards Andrew

 

[Dale]

My question is is this theoretically sound?

No, there is 100% unavoidably without reference to any experiment unambiguously without exception no possible way to measure the one-way speed of light without assuming a synchronization convention. It is not a matter of clever experimentation, it is a matter of definition. The one-way speed of light is DEFINED as the distance between a source and a detector divided by the difference in time between two synchronized clocks at the source and the detector. Regardless of HOW you are measuring it that is WHAT you are measuring if you are in fact measuring what is known as the one-way speed of light. There is no way to avoid the issue. It is intrinsic to the definition of the thing that is being measured.

 

[andrew s 1905]

No, there is 100% unavoidably without reference to any experiment unambiguously without exception no possible way to measure the one-way speed of light without assuming a synchronization convention. It is not a matter of clever experimentation, it is a matter of definition. The one-way speed of light is DEFINED as the distance between a source and a detector divided by the difference in time between two synchronized clocks at the source and the detector. Regardless of HOW you are measuring it that is WHAT you are measuring if you are in fact measuring what is known as the one-way speed of light. There is no way to avoid the issue. It is intrinsic to the definition of the thing that is being measured.

I am not arguing with your statement, I agree with it, but I am asking a different question (at least I think I am). The proposed arrangement does not attempt to measure the speed of light it seeks to show equivalence of the one way speed in two different directions.

It seek to show it is the same in both directions irrespective of it's particular value this seems to me to be a different issue to measuring its speed.

As examples one can show two objects have the same mass with a balance beam without knowing the actual mass involved or that two objects, initially practically coincident, have the same velocity if they do not diverge. As far as I can tell neither example rests on the definitions of how the kilogram, meter and second are defined.

Regards Andrew

 

[hutchphd]

Have you carefully worked it out in detail? Draw up the two scenarios: incident beam comes in normal to grating and produces both a +1 and -1 diffraction max. The angular location of each will be the same even if the +x speed differs from the -x speed. This will be true because the overall diagonal speed of the diffracted beams +/-1 will also differ. This is a generic result as @Dale says

Check

 

[andrew s 1905]

Have you carefully worked it out in detail? Draw up the two scenarios: incident beam comes in normal to grating and produces both a +1 and -1 diffraction max. The angular location of each will be the same even if the +x speed differs from the -x speed. This will be true because the overall diagonal speed of the diffracted beams +/-1 will also differ. This is a generic result as @Dale says

Check

Thank you, this was the type of hint I was looking for. Regards Andrew

 

[Vanadium 50]

I have reviewed the discussions here

Indeed. And you did not find the argument that you have one more unknown than you have equations convincing? Why not?

 

[andrew s 1905]

Indeed. And you did not find the argument that you have one more unknown than you have equations convincing? Why not?

Thank you. I did not appreciate that. I was trying to find a weakness in a proposal put to me and had failed to do so hence the post. I assume you must be both infallible and psychic as I don't recall posting any equations.

I am not sure why some "staff" on PF feel the need to post such passive aggressive comments. Fortunately, @hutchphd was more considerate in his posting and actually posted something helpful.

 

[hutchphd]

I am glad that my suggestion helped you see what you needed to see. But I think @Vanadium 50 question is a valid one, and not intended as an attack. That explanation is equally good and you need to be able to see all angles.

 

[Vanadium 50]

I assume you must be both infallible and psychic as I don't recall posting any equations.

Do you really want to go down that path? It sounds a lot more like a crackpot posting his own cranky ideas than someone genuinely looking for help. Is that how you want to sound? Especially when someone tries to help you understand by asking what part of the argument you didn't find convincing.

If you have the speed of like equaling something, you have an equation. Whether you write it down or not. (And it would be wise to write these ideas in the form of an equation, as you did with c = λf. ) And the argument given in the other thread is both general and sound: no matter how many measurements you add, you are always one short.

 

[andrew s 1905]

I am not a crackpot (I have a PhD in Physics albeit some years ago now) and I was genuinely trying to understand a proposal put to me. As I tried to point out I was not trying to measure the one way speed of light which is why the points in the other thread were not directly relevant. I also acknowledged and I agreed you could not do so.

I tried to show by example that two thing can be shown to be the same was different from measuring them and was wondering if that may have made a difference in this case. You did not comment on acknowledged this.
I can check if you and I are the same height or different by standing us next to each other and looking for a difference. No clocks or measuring sticks no equations.

That is why I asked the question and not because of some crackpot idea.

If I miss read the tone of your post I apologise but you seemed to be scalding me for not recognising what to you was obvious. "Indeed" has a certain meaning when used in that way in the UK.

Regards Andrew

 

[Ibix]

As I tried to point out I was not trying to measure the one way speed of light which is why the points in the other thread were not directly relevant.

The problem with this line of thinking is that if I can measure the average round-trip speed (which I can) then an anisotropy measure would immediately give me a one-way speed measure, since I would have two equations in two unknowns. So a measure of anisotropy is just as impossible as a measure of one-way speed.

 

[Dale]

but I am asking a different question (at least I think I am). The proposed arrangement does not attempt to measure the speed of light it seeks to show equivalence of the one way speed in two different directions

It is not a relevant distinction for the key issue. The isotropy of the one way speed of light still requires one way speeds and one way speeds are still defined based on a simultaneity convention. You cannot make that go away from any discussion of the one way speed of light since it is part of the definition of the concept itself.

As examples one can show two objects have the same mass with a balance beam without knowing the actual mass involved or that two objects, initially practically coincident, have the same velocity if they do not diverge. As far as I can tell neither example rests on the definitions of how the kilogram, meter and second are defined.

No, but they do rest on how mass, length, and time are defined. For example, mass is a property of a physical system. So you cannot use a balance beam to compare the masses of non-physical things like trust and love. The physical system is part of the definition of mass and there is no way to avoid it regardless of if you are looking to measure mass or detect differences in mass.

 

[andrew s 1905]

Ok @Dale.

 

[Nugatory]

The problem with this line of thinking is that if I can measure the average round-trip speed (which I can) then an anisotropy measure would immediately give me a one-way speed measure,

To be precise, there would only be one simultaneity convention consistent with both the outbound and inbound measurements in a round trip. The difficulty here is, as @hutchphd shows in #8, proving isotropy without inadvertently including it in your initial assumptions.

 

[Vanadium 50]

Yes, the one way isotropy of the one way speed of light.

t I was not trying to measure the one way speed of light

Those are the same things. If you say "The speed of light in direction x is 10% faster than the two-way speed" you have measured the one-way speed of light.

If you have a PhD in physics, you can surely use equations. If you write down an expression for the one way speed of light, or any equivalent, you will see right away that it doesn't work out (or you have a hidden synchronization convention).

 

[andrew s 1905]

@Vanadium 50 I have repeatedly said I agree you can't measure the one way seep of light.

I was challenged to show that by the use of the diffraction experiment I described above that you could not show that the one way speeds were the same. This method did not attempt to measure the speed of light directly but used a null method based of the laws of diffraction. I was reluctant to describe it as I might be accused of expressing a personal theory. However, I will do so now.

The grating equation is

(Born & Wolf "Principles of Optics" 6th Edition page 403)
So for the transmission grating used with normal incidence the diffraction angle only depends on the order m grating spacing d and wavelength λ . In the experiment the the diffraction angle is found to be the same irrespective of the direction the light path takes along any given axis in an inertial frame. (He has done this with his simple spectroscope to about 1 in 10^-4 in testing its stability.)

If you use the equation c = λf. then it shows that c/f is constant. So if you assume that f is isotropic then so is c.

I have pointed this out to my challenger that his conclusion rest on the isotropy of the lights frequency but was trying to gain further insight on this.

@Dale , has contended that measuring the ratio of the speeds (or c/f) in this example is illegitimate as it would allow me to deduce the one way seep, but I am still struggling with this. To elaborate:

If I have two trains traveling on a parallel tracks passing an observer "A" simultaneously and then some time later pass an observer "B" simultaneously I would conclude they had the same velocity but I would not know what it was. So I believe I can compare two velocities to show they are the same without measuring them.

If that is acceptable, then I don't see how if "A" simultaneously emits two light pulses which are simultaneously detected by "B" I can't conclude they have the same velocity (same one way speed), not what it was but just that they were the same.

Repeating it can't be done is not helping me and I would prefer if someone could point out the logical error I am making in my elaboration or elsewhere in the above.

My aim is to convince my challenger his experiment can't show the seed of light is isotropic not justify it!

Regards Andrew

 

[Dale]

has contended that measuring the ratio of the speeds (or c/f) in this example is illegitimate

That is not what I said at all. I said that the one way speed of light includes a simultaneity convention in its definition. So by using the concept of a one way speed you are inherently, unavoidably, and intrinsically using a simultaneity convention.

My aim is to convince my challenger

We do not conduct debates by proxy. Our aim is to educate members.

Repeating it can't be done is not helping me and I would prefer if someone could point out the logical error I am making in my elaboration or elsewhere in the above.

That is not what is happening here. You have been told exactly what the logical error is two different ways: the definition of a one way speed includes a simultaneity convention and if you actually write the equations (with the simultaneity convention as an unknown) you get more unknowns than equations.

 

[andrew s 1905]

@Dale I apologies for wasting your time and miss-quoting you but I expressed the conclusion I drew from what you had said. I was genuinely trying to educate myself on this.

I will not trouble any of you further.

Regards Andrew

 

[meekerdb]

No, there is 100% unavoidably without reference to any experiment unambiguously without exception no possible way to measure the one-way speed of light without assuming a synchronization convention. It is not a matter of clever experimentation, it is a matter of definition. The one-way speed of light is DEFINED as the distance between a source and a detector divided by the difference in time between two synchronized clocks at the source and the detector. Regardless of HOW you are measuring it that is WHAT you are measuring if you are in fact measuring what is known as the one-way speed of light. There is no way to avoid the issue. It is intrinsic to the definition of the thing that is being measured.

How does that apply to Bradley's measure of the speed of light by stellar aberration?

 

[Ibix]

How does that apply to Bradley's measure of the speed of light by stellar aberration?

He assumes the Einstein synchronisation convention. If you assume anything else you get a different value for how far the Earth moved "while the light was in the telescope tube" (because your clock synchronisation is different you have a different definition of when the light entered) and hence a different speed of light.

 

[meekerdb]

Why isn't it the assumption that the length of the tube is constant over the small change in angle.

 

[Ibix]

Why isn't it the assumption that the length of the tube is constant over the small change in angle.

I'm not sure what you mean.

Do be aware that a non-isotropic speed of light implies a non-orthogonal coordinate system on spacetime, with all the nasty cross-talk between your notions of space and time that is entailed in that. You can't interpret the measured angle the same way with a non-isotropic speed as you can with an isotropic speed.

 

[Dale]

How does that apply to Bradley's measure of the speed of light by stellar aberration?

None of the details of any experiment matter

 

[meekerdb]

None of the details of any experiment matter

All that Bradley had to measure was the speed of the Earth and the angle alpha.

 

[Dale]

All that Bradley had to measure was the speed of the Earth and the angle alpha.

And as I said that doesn’t matter. It cannot be used to measure the one way speed of light without assuming a simultaneity convention. (Think about how $\alpha$ is determined and what assumptions are needed)

 

[meekerdb]

Then you'll pardon me if I don't take your word for it.

 

[Dale]

Then you'll pardon me if I don't take your word for it.

Instead of asking me to pardon you or instead of taking my word for it, why don’t YOU work it out. Just apply Reichenbach’s simultaneity convention and work out the prediction mathematically for varying speed of light anisotropies.

 

[PeterDonis]

All that Bradley had to measure was the speed of the Earth

There is no such thing as "the speed of the Earth" in any absolute sense. Speed is relative. The "speed" Bradley measured was the speed of the Earth in a particular reference frame. And that particular reference frame also has a particular simultaneity convention. So Bradley's measurement depended on a particular simultaneity convention, one in which the speed of light is defined to be isotropic.

 

[Sagittarius A-Star]

All that Bradley had to measure was the speed of the Earth and the angle alpha.

Bradley's $\tan \alpha$ is a ratio between certain distances in the rest frame of the sun. For concluding, that this ratio is equal to the ratio between certain one-way-velocities, you need a simlutaneity convention.

 

[PAllen]

The fundamental issue with Bradley’s derivation was that he assumed light was a particle following Galilean relativity, the aberration being the same as raindrops observed in different frames. His derivation required that therefore the speed of light was frame dependent, not invariant. It remained an unexplained mystery why light always moved at nearly the same speed. (which led to many concerns about his derivation after source motion light speed independence was established by numerous astronomical observations; the complication of optical extinction would be irrelevant, since if that were taken into account in Galilean relativity there would be no aberration).

In other words, Bradley derived the speed of light in one frame, for one source, if and only if, it was sensitive to both source and target motion, as bullets are.

Einstein’s derivation of aberration was the first one ever consistent with the then well established effective source motion independence light speed. This was actually unique in Einstein’s first SR paper - none of the prior work by others (Lorentz, Poincare, Fitzgerald, etc.) treated the question and significance of aberration. Einstein’s derivation showed that within SR, aberration is not a measure of speed at all, but only a measure of how null directions transform between frames. This, in contrast to Bradley, which measures a speed, if and only if it is affected by both source and target motion.

 

[PAllen]

Bradley's $\tan \alpha$ is a ratio between certain distances in the rest frame of the sun. For concluding, that this ratio is equal to the ratio between certain one-way-velocities, you need a simlutaneity convention.

Bradley’s derivation was based on Galilean relativity, for which simultaneity is absolute. Its real issue for light speed determination is described in my prior post.