Velocity of light in acceleration frame.

[fxdung]

Velocity of light in uniform motion frame is the same.But does velocity of light change in acceleration frame? Does the Cagnac effect(the shift of diffraction pattern in rotation frame) result of this change of velocity in the acceleration frame?If velocity of light in acceleration still is c why we have Cagnac effect because the rotation tranformation is only mathematical tranformation,it only ''rearrange'' the variables of space and time,but not physically change the time which affect the diffraction pattern.

 

[A.T.]

But does velocity of light change in acceleration frame?

Yes, it can.

 

[Orodruin]

You will have to define what you mean by speed of light if you go to an arbitrary frame. Unlike galilean relativity, there is also no unique notion of what an "accelerated frame" is.

 

[fxdung]

I mean the acceleration frame versus inertial frame.Do you mean the space-time is locally flat so that there is no unique notion of acceleration frame?

 

[Orodruin]

I mean the acceleration frame versus inertial frame.

As I said, there is not anything like "the" acceleration frame that exists in Galilean relativity. You will also have to be more specific with what you refer to when you say "speed of light".

 

[vanhees71]

Perhaps for a first study, that's a good source (I haven't looked at it in detail, but usually McDonald's lecture notes are simply brilliant)

http://physics.princeton.edu/~mcdonald/examples/rotatingEM.pdf

It's however for slowly rotating reference frames only. Another paper I found via Google Scholar is

Fugmann, W. & Kretzschmar, M. Nuov Cim B (1991) 106: 351.
http://dx.doi.org/10.1007/BF02725687

 

[Vanadium 50]

It might be a good idea to back up a bit. If a baseball has a constant velocity in an inertial frame, what is its velocity in an accelerated frame?

 

[Nugatory]

Do you mean the space-time is locally flat so that there is no unique notion of acceleration frame?

As far as this thread is concerned, it makes no difference whether the space time is curved or flat. Curvature is present only when gravity is present, but of course you can have acceleration even when there is no gravity.

 

[Kevin McHugh]

In Minkowski space, there are no accelerated frames, correct? And in GR, there are no global reference frames, correct? There is only the relative acceleration between geodesics. Other than that the freely falling reference frame is local. Is that correct?

 

[vanhees71]

Why shouldn't there be no accelerated frames in SR? You can choose any frame you like, but maybe it's unwise to change an accelerated frame of reference in SR, because it complicates things. In non-relativistic physics we consider the rotating Earth to deal with the free fall (east and south drift) and the Foucault pendulum (i.e., the "Coriolis force"). I've never tought about this in the relativistic context, but in principle you can do so, and it's way more complicated than in the non-relativistic case. What's often discussed are Rindler coordinates, i.e., a reference frame for an observer under constant proper acceleration:

https://en.wikipedia.org/wiki/Rindler_coordinates

Note that this is, however, not covering the entire Minkowski space and thus is, as correctly said in the Wikipedia, only a chart covering a part of it.

 

[GeorgeDishman]

Understanding the effect of an accelerated frame in SR can be useful when considering Bell's Spaceship Paradox.

 

[Nugatory]

In Minkowski space, there are no accelerated frames, correct?

Not correct. That's a common misconception that perpetuates itself because most introductory textbooks and exercises only consider inertial frames just because the math is easier. But when you never see accelerated frames being used to solve a problem in SR, it's easy to incorrectly assume that it's because it can't be done.

Google for "Rindler coordinates" to see one of the better easy examples of how it is done.

 

[Orodruin]

Accelerated coordinates, or more generally, arbitrary coordinate systems in Minkwoski space is the special relativity analogue of using curvilinear coordinates in a Euclidean space. You will usually learn about Cartesian coordinates before you learn the general framework for curvilinear coordinates, just as you learn about inertial frames before using curvilinear coordinates on Minkowski space. Of course, this does not mean you cannot use curvilinear coordinates, just that it is simpler not to in many cases.

 

[pervect]

Velocity of light in uniform motion frame is the same.But does velocity of light change in acceleration frame? Does the Cagnac effect(the shift of diffraction pattern in rotation frame) result of this change of velocity in the acceleration frame?If velocity of light in acceleration still is c why we have Cagnac effect because the rotation tranformation is only mathematical tranformation,it only ''rearrange'' the variables of space and time,but not physically change the time which affect the diffraction pattern.

I believe it's spelt "Sagnac effect".

Due to the mathematical complexities of correctly treating accelerated frames in special relativity, I'd suggest trying to understand the Sagnac effect without using them. There is a principal of physics called covariance, which, loosely stated, says that the choice of frame of reference is a human choice, therefore it can't affect the answer to any computation.

If you do want to deal with accelerated frames in SR correctly, the only references that come to mind use tensors. I don't know your background, but I strongly suspect that this would be too advanced.

Therefore, if your main motivation is to better understand the Sagnac effect, it would be easier and generally more productive to understand the effect without using an accelerated frame of reference.

 

[Orodruin]

So,in ''locally accelerated frame'' the speed of light is c,but in '' global accelerated frame'' the speed of light is change.Is that correct?

No, you still have not defined what you refer to with "accelerated frame" or "speed of light". You implicitly assume that these things have unique generalisations from galilean to special relativity. They don't.

In general, SR in curvilinear coordinates goes quite far beyond B level, as noted by pervect in #14.

 

[fxdung]

Which books say about SR in curvilinear cordinates?

 

[pervect]

Which books say about SR in curvilinear cordinates?

Most GR books will discuss the tensor math you need in one form or other. Rindler's book "Relativity, special and general" comes to mind - not because it's such a fantastic book, but because it's a bit less advanced than some of the full-blown GR treatments. But this would be overkill for your problem, if you just want to understand the Sagnac effect. You don't need curvilinear coordinates or tensors for that.

The first thing to realize is that in order to measure velocities fairly, most particularly when you're measuring the speed of light, you need some concept of how to synchronize clocks. To take an example, suppose you're trying to find the speed of an airpline flying from Chicago to Los Angeles and back again, and you use daylight savings time to time the flights. You find the flight takes half an hour or so in one direction, and six hours in the other. So if you weren't careful, you might claim that the speed of the plane was much faster going from Chicago to LA than it was going back. Unfortunately, this would basically be wrong-headed. I hope this is obvious, but I suppose we could talk about it more if it isn't.

The particular issues with light are that it travels very fast, so a small synchronization error shows up as a large "velocity error" in the calculation. The other issue is that you might twig to the clock synchronization issue with the planes by carrying a clock onboard the plane and measuring your trip-time, but you can't pull that particular trick with light.

Thee question then becomes up - how do you synchronize clocks on a rotating platform. You might not think about this issue, and just assume that "surely, there's some way of doing this", and assume that's that's part of some hypothetical "rotating frame of reference" that does this for you. Unfortunately, this turns out to be a bad assumption. If you're careful to synchronize your clocks fairly using the Einstein convention, you find that all clocks on a rotating platform can not be synchronized. If you label 6 clocks around the periprhery, say A, B, C, D, E, F, you can syncnronize A with B, B with C, C with D, D with E, E with F, but when you do this, F is right next to A, as you've goon around the loop, but F is NOT synchyronized properly with A.

This is what the Sagnac effect is all about - it's really got very little to do with velocities, and a lot more to do with clock synchronization, something that people tend not to think about much if they are not familiar with SR - and sometimes even when they are.

 

[vanhees71]

https://en.wikipedia.org/wiki/Sagnac_effect#Reference_frames

 

[Ben Niehoff]

The local speed of light is always c, in any frame, including accelerated frames. By "local speed of light", I mean the speed of a photon as it passes by your position. I can't think of any other definition of the "speed of light" that makes any sense in GR.

 

[Kevin McHugh]

Not correct. That's a common misconception that perpetuates itself because most introductory textbooks and exercises only consider inertial frames just because the math is easier. But when you never see accelerated frames being used to solve a problem in SR, it's easy to incorrectly assume that it's because it can't be done.

Google for "Rindler coordinates" to see one of the better easy examples of how it is done.

IIRC, I've read statements to the effect that in SR, the velocityof the reference frames is constant, and the acceleration is zero. I believe I got this from Schutze, maybe WTW as well. Unless it is a boost where the frame is accelerated from V1 to V2?

 

[vanhees71]

This is a definition of speed of light that doesn't make sense or better said, it's not a definition at all, or how do you define "speed of a photon as it passes by your position"? The speed of light is rather the phase velocity of electromagnetic waves according to Maxwell's equations. As ist turns out (with overwhelming accuracty), that it is the same speed that occurs as the limiting speed in relativity.

 

[Nugatory]

IIRC, I've read statements to the effect that in SR, the velocityof the reference frames is constant, and the acceleration is zero.

When you see a statement like that, the author is expecting you to understand from the context that "reference frame" is intended to mean "inertial reference frame". In many introductory textbooks, the author isn't going to discuss non-inertial frames so avoids introducing the distinction in the first place.

It is true that the Lorentz transformations of SR only work between inertial frames, but that doesn't mean that those are the only coordinate transforms you're allowed to use in SR. The transformation to Rindler coordinates is an example.

 

[fxdung]

If we attach a coordinate frame into Earth and a coordinate frame into very distant Galaxy.Then is speed of a pulse of light in the two frame the same?