Undergrad Why isn't the Roemer type experiment a one way measure of c?

[Ibix]

Sorry, I thought we were discussing the physics of light propagation. What you propose is not a symmetry of nature nor anything having to do with the observable speed of light anisotropic or otherwise. The OP has to do with an experiment and its interpretation so I thought my comments might have relevance.

How he interprets it depends on his choice of coordinates, or equivalently his synchronisation convention. That's the whole point.

 

[pervect]

I was doing some reading, and for theories which respect the principle of relativity, we have two or three noteworth ones - two if one regards theories that are observationally equivalent as being the same theory, which is general practice, three if one does. The two that are observationally equivalent are special relativity and the Edwards frame that other posters mentioned. One can regard the Edward's theory as a simple coordinate change to coordinates that makes the speed of light look anisotropi in the chosen coordinates, but doesn't make any diffrent physical predictions than special relativity (SR).

The third theory (or second, if one regards the first two as equivalent) is the Mansouri-Sexyl test theory, which is observationally different from special relativity and usually used as a test theory - i.e. when analyzing results, people determine wither special relativity (SR) or the Mansouri-Sexyl (MS) theory fits the data better. So far it's always been SR that is the best fit.

Of course there are theories that are not compatible with the principle of relativity, for instance Newtonian mechanics as practiced before Einstein. This has been experimentally falsified for some time now, but here on PF we see many people trying to hold onto it. People who haven't formally studies SR are particularly likely to take the Newtonian mechanics they learned in high school, and attempt to apply it to relativistic problems not having learned what they need to do differently to do SR. SR is offbeat enough that the average person isn't likely to think of it themselves, meaning that one proprbably won't reach an understanding of the theory without specifically studying it.

 

[pervect]

So, the Earth is spinning and revolving around the sun and the galactic center and we're magically in an Edwards frame to the precision needed to replicate EM observations to current standards? sweet.

An Edwards frame is mathematically a coordinate transformation of a Lorentz frame from my reading. I don't have access to the primary source (Edward's original papers) but there's an interesting and quite readable arxiv paper that touches on the issue in passing.

https://arxiv.org/pdf/1111.4423.pdf

Edwards formulated a theory in which the one-way speed of light could be
anisotropic, with values that depended on direction [1]. The interpretation of
such theories is delicate, however, because the time parameter that appears in
the equation may not be directly related to the time experimentally measured by
clocks. This happens because experimentally, one needs to synchronize clocks at
different locations and the choice of synchronization method determines the re-
lation between measured time and the time that appears in the transformations.
It turns out that when this is done, Edwards’s theory is empirically equivalent
to standard special relativity [11, 12]

So, no more (and no less) magic is needed to put the Earth in a locally Edwards frame than a locally Lorentz frame. Edwards theory isn't actually any different than special relativity in its physical predictions, it just uses an oddball clock synchronization convention.

There is the issue here of how local the local Lorentz frame is, and whether one needs to use GR rather than SR to analyze the original problem. But I'd rather avoid that issue.

My main focus is communicating that clock synchronization is a convention. Unfortunately it seems that the message about why clock synchronization is considered to be a convention isn't getting through - though it's quite well known. (I don't have a specific reference handy - would that help?).

An additional concern of mine is that the message may be not being understood properly. Not following the usual conventions for clock synchronizations will affect certain relationships that some posters may be assumed as being always true, but actually are only true when one follows the synchronization conventions. Momentum = mass*velocity (or the relativistic equivalent with the gamma factor) is the relevant example.

Given any inertial frame of reference in the flat space-time of special relativity, the point is there is exactly one clock synchronization method that makes p=mv (or p=gamma m v) correct in that particular frame. This is the Einstein convention.

The second point I want to repeat is that according to special relativity, different inertial frames REQUIRE different clock synchroinzation schemes to make the above relationships (p=gamma m v) true. There isn't one universal method of synchronizing clocks in special relativity.

The third issue is - what theory are we really wanting to talk about? SR? GR? Newtonian theory? Mansouri-Sexyl theories (they are relevant if one is really interested in anisotorpy and has the necessary background). Something else? If we're all talking about different frameworks and/or at different levels, the discussion gets very muddled.

 

[Paul Colby]

An Edwards frame is mathematically a coordinate transformation of a Lorentz frame from my reading. I don't have access to the primary source (Edward's original papers) but there's an interesting and quite readable arxiv paper that touches on the issue in passing.

Thanks for the reference. I'm still interested in how the capacitor example I raised fairs in the anisotropic case. It's difficult to see how all observable effects can be swept under the coordinate transformation rug while at the same time one may claim it is possible to measure an anisotropic space-time. If Maxwell's equation sprout non-standard anisotropic terms in the lab then these terms should effect electrical measurements. No doubt one will reply that all physical dimensions change as I slowly rotate the device under test and in such a way that the capacitor separation is $L$ when measured from the left and $L'$ from the right. The only sane reply to that would be there is nothing to measure and this is not physics as it is commonly understood.

 

[Ibix]

Paul - freedom to change coordinates is a gauge freedom. It's fundamentally no different from the notion that you can set the zero of potential anywhere you like. It can make the maths harder or easier, and it changes how you interpret things. But it doesn't ever change your measurements.

It must work out because the theory asserts that all direct observables are Lorentz scalars and invariant under coordinate transform. Unless there's something fundamentally wrong with the idea that physics should be coordinate independent.

 

[Paul Colby]

Paul - freedom to change coordinates is a gauge freedom. It's fundamentally no different from the notion that you can set the zero of potential anywhere you like. It can make the maths harder or easier, and it changes how you interpret things. But it doesn't ever change your measurements.

It must work out because the theory asserts that all direct observables are Lorentz scalars and invariant under coordinate transform. Unless there's something fundamentally wrong with the idea that physics should be coordinate independent.

After the morning shower I've adopted the view that the capacitor test is to this (Edwards) symmetry as MML is to Lorentz symmetry. The only difference is no one seriously expects an anisotropy of this type.

 

[Paul Colby]

It must work out because the theory asserts that all direct observables are Lorentz scalars and invariant under coordinate transform.

This is a statement about physics that can be experimentally verified. Nothing must "work out". That an observable is a Lorentz scalar is a highly non-trivial testable assertion.

 

[Bartolomeo]

I think that the "sound" theory, which is empirically equivalent to the SR is the Lorentz's theory. One way speed of light is isotropic only in "absolute frame". In moving frame it is anisotropic. It is well known, that dilation of moving clock and length contraction completely hide " proper" motion and anisotropy. Though expanations of relelativistic phenomena and "paradoxes" is plain and simple. For what reason you don't even mention it as alternative?

 

[PeterDonis]

For what reason you don't even mention it as alternative?

PF policy:

https://www.physicsforums.com/insights/pfs-policy-on-lorentz-ether-theory-and-block-universe/

 

[Ibix]

This is a statement about physics that can be experimentally verified. Nothing must "work out". That an observable is a Lorentz scalar is a highly non-trivial testable assertion.

All I'm doing is defining $t'$ implicitly as $t=t'-\alpha x$ then substituting for $t$ throughout the maths. If that doesn't work out then we seem to have broken algebra. Since I can write an expression for my sensor output in terms of $t$ and $x$, then simply substituting something for $t$ can't make the answer different. That's basically why I'm confident that any EM measurement will come out the same when analysed in any coordinate system.

Whether or not Lorentz scalars (or other geometric invariants if you can measure them directly) are truly invariants in nature is, of course, open to question. But only if you are trying to challenge special relativity, which I wasn't.

Dragging this back on topic, the one-way speed of light is not a direct observable. It can't be measured by one clock. It needs two. And although I can state confidently that all coordinate systems will agree the reading on one clock when the light pulse left and on the other when it arrived, whether or not the clocks were synchronised is a matter of convention. Hence the one-way speed of light is a matter of convention.

 

[Paul Colby]

Hence the one-way speed of light is a matter of convention.

So if one sits down and determines the form of Maxwell's equations by careful measurement one might choose a complex anisotropic form for them? No thanks.

 

[PAllen]

So if one sits down and determines the form of Maxwell's equations by careful measurement one might choose a complex anisotropic form for them? No thanks.

Of course. For all of physics, before SR as well as after, the physical content (IMO) of isotropy is:

1) assuming it leads to simpler expression of laws
2) any anisotropic formulation must be 'conspiratorial' in the sense that many different phenomena must be jointly anisotropic in a highly constrained way. This requirement for 'jointly constrained anisotropy', to me, is just disguised isotropy.

Only by virtue of peculiarities in the history of SR has the fact that you can't rule out conspiratorial anisotropy been prominent. Note, that many modern approaches to SR start by assuming isotropy, and homogeneity, and the POR, arriving at SR as one of only two possibilities, with no assumptions about light at all. With such an approach, the question of one way speed of light as distinct from two way, cannot even be asked.

IMO, physically significant anisotropy would be a universe where assuming isotropy forced complications, e.g. the need to add a special field that was wholly undetectable except for its hiding isotropy from being directly observed.

 

[Paul Colby]

Yeah, I don't know. If a phenomena can't as a matter of principle be measured, I'm not willing to concede that it's part of physics. Suppose I have two beam splitters separated by a distance L. They are angled so that when a short light pulse entering from the left a fraction of the pulse is directed to a sensor a distance 1000L from the pair along a line perpendicular to the line between the two splitters. When a pulse enters from the left the sensor will detect two pulses L/c+ apart in time. The splitters are then angled so a pulse entering from the right will yield two pulses L/c- apart in time. Why isn't this a one way measurement?

 

[PAllen]

Yeah, I don't know. If a phenomena can't as a matter of principle be measured, I'm not willing to concede that it's part of physics. Suppose I have two beam splitters separated by a distance L. They are angled so that when a short light pulse entering from the left a fraction of the pulse is directed to a sensor a distance 1000L from the pair along a line perpendicular to the line between the two splitters. When a pulse enters from the left the sensor will detect two pulses L/c+ apart in time. The splitters are then angled so a pulse entering from the right will yield two pulses L/c- apart in time. Why isn't this a one way measurement?

Well, playing devil's advocate for conspiratorial anisotropy, that one is easy. The two almost perpendicular paths are ... almost perpendicular. Deviation about 1 part in a thousand. Then, the small difference in light speed along the so called perpendicular legs, accumulated over a very long path length, compensates for the difference in light speed each way between the beam splitters, such that the signal reception difference and the receiver is the same as under the assumption of isotropy.

 

[Paul Colby]

Well, playing devil's advocate for conspiratorial anisotropy, that one is easy. The two almost perpendicular paths are ... almost perpendicular. Deviation about 1 part in a thousand. Then, the small difference in light speed along the so called perpendicular legs, accumulated over a very long path length, compensates for the difference in light speed each way between the beam splitters, such that the signal reception difference and the receiver is the same as under the assumption of isotropy.

You should check again. Those errors are identical for both left and right going measurements and therefore cancel identically.

[edit] whatever.

 

[PAllen]

You should check again. Those errors are identical for both left and right going measurements and therefore cancel identically.

[edit] whatever.

No they don't, for the fast direction, they increase the signal delay, for the slow direction they decrease it, such that the observed deltas match. Perhaps 'whatever' means you worked this out.

 

[Paul Colby]

No they don't, for the fast direction, they increase the signal delay, for the slow direction they decrease it, such that the observed deltas match. Perhaps 'whatever' means you worked this out.

Yes and no. If I assume a physically reasonable anisotropy of the form $c(\hat{n}) = c_o + \alpha \hat{n}\cdot \hat{v}$ for propagation along $\hat{n}$ and where $\hat{v}$ is some fixed direction in space, then all I need do is place the sensor's 1000L in the plane $\hat{v}\cdot\hat{n}=0$ and the beam splitters along $\hat{v}$. In this case the errors cancel as I claim because both long arms are retarded or advanced by the same amount and the anisotropy on the short leg is maximum. So this form of anisotropy is detectable. I assume the anisotropy in this discussion isn't physically reasonable .

Oh well. This isn't my night.

I would still need to accept terms in Maxwell's equations that are unneeded. Ain't going to happen.

 

[Dale]

If a phenomena can't as a matter of principle be measured, I'm not willing to concede that it's part of physics.

So then the one way speed of light is not part of physics.

 

[PAllen]

Yes and no. If I assume a physically reasonable anisotropy of the form $c(\hat{n}) = c_o + \alpha \hat{n}\cdot \hat{v}$ for propagation along $\hat{n}$ and where $\hat{v}$ is some fixed direction in space, then all I need do is place the sensor's 1000L in the plane $\hat{v}\cdot\hat{n}=0$ and the beam splitters along $\hat{v}$. In this case the errors cancel as I claim because both long arms are retarded or advanced by the same amount and the anisotropy on the short leg is maximum. So this form of anisotropy is detectable. I assume the anisotropy in this discussion isn't physically reasonable .

Oh well. This isn't my night.

I would still need to accept terms in Maxwell's equations that are unneeded. Ain't going to happen.

I disagree. For light traveling in the fast direction, the signal from the first beam splitter arrives a little early compared to average c, while signal from the second beam splitter arrives a little late. The result is to augment the detection interval compared to the implicit reduced travel time between the splitters. For light in the slow direction, the signal from the first splitter hit arrives late, while from the second arrives early, which reduces the detection interval compared to the implicit augmented travel time.

For made up numbers, e.g.

10 + 1 + 2 - (10 - 1) = 4

vs.

10 - 1 + 6 - (10 + 1) = 4

 

[Paul Colby]

I disagree. For light traveling in the fast direction, the signal from the first beam splitter arrives a little early compared to average c, while signal from the second beam splitter arrives a little late. The result is to augment the detection interval compared to the implicit reduced travel time between the splitters. For light in the slow direction, the signal from the first splitter hit arrives late, while from the second arrives early, which reduces the detection interval compared to the implicit augmented travel time.

For made up numbers, e.g.

10 + 1 + 2 - (10 - 1) = 4

vs.

10 - 1 + 6 - (10 + 1) = 4

For the record I concur. As it's been pointed out several times this "phenomena" is merely a coordinated change and therefore moot. An anisotropy in light speed would do violence to Maxwell's equations. However, any self respecting experimentalist (played by myself) would never discover this in the underlying physics because we deal with observables which this is not.

 

[Dale]

However, any self respecting experimentalist (played by myself) would never discover this in the underlying physics because we deal with observables which this is not.

Same with the one way speed of light.

The way out of this dilemma is simply to recognize that the one way speed of light and the synchronization are two parts of the same convention. It makes no physical difference what convention you pick, so pick an easy (isotropic) convention. Since it is merely convention you are automatically justified in doing so, and you recognize that people who want to make extra work for themselves are also entitled to pick a silly convention.

 

[vanhees71]

Hm, is it really pure convention? I doubt it. Using SR as a spacetime model, which includes the assumption of isotropy and homogeneity of space for any inertial observer, of course implies the consistency of the standard Einstein-synchronization convention, but as soon as you take gravitation, and thus GR effects into account, you'll find deviations (like the gravitational deflection of light running close to the sun, as was one of the classical confirmations of GR, making Einstein the first superstar of science when this effect has been observed by the Eddington collaboration in 1919). So the deviation of spacetime from homogeneity (due to the presence of a "heavy body" like the sun) is objectively observable and cannot be cured by pure conventions. Of course you can, according to the (weak) equivalence principle, always find a locally inertial (and thus isotropic and homogeneous) frame of reference but, at presence of non-negligible gravity, never a global one!

 

[Dale]

Of course you can, according to the (weak) equivalence principle, always find a locally inertial (and thus isotropic and homogeneous)

Of more interest to the present discussion, you can also choose a locally anisotropic Edwards frame if you are a bit of a mathematical masochistic.

 

[vanhees71]

But, I didn't understand, why I should do that. Of course, you can in principle choose any kinds of coordinates, but how does it help to understand the determination of the speed of light a la Roemer?

 

[PAllen]

But, I didn't understand, why I should do that. Of course, you can in principle choose any kinds of coordinates, but how does it help to understand the determination of the speed of light a la Roemer?

It shows that using a model in which light speed is anisotropic, that the Roemer measurement would measure the two way light speed. That is, it would not exclude the ability to consider light speed highly anisotropic.

 

[Dale]

But, I didn't understand, why I should do that. Of course, you can in principle choose any kinds of coordinates, but how does it help to understand the determination of the speed of light a la Roemer?

It helps you understand that even a measurement like Roemer’s is not a measurement of the one way speed of light without a synchronization convention.

 

[Vanadium 50]

I'm glad we're getting back to the original question. One of the messages that the OP didn't have time to read points out that if you want to know two things - the one-way speed of light and the synchronization convention - you need to measure two things. Since there's only one measurement, I can pick a synchronization convention and get any one-way speed I like.