Definition of an Inertial Frame

[JustinLevy]

What kind of coordinate system is this?


Imagine a rocket is moving with constant velocity, across the field of vision of an observer. The observer films the rocket but rather than keeping the camera stationary he pans with the rocket so that when the film is played back the rocket appears to be stationary.

In the playback, the "stationary" rocket is length contracted. Light signals going from the back of the rocket to the front take longer than the reflected signal takes to return giving an apparent anisotropic speed of light in the playback. (Light signals going from the back of the rocket to the front take longer than light signals going in the opposite direction in the played back movie.). The time taken for the light signal to travel from the back of the rocket to front and back again is 2L/c seconds according to an observer onboard the rocket and (2L/c)y seconds as seen on the "movie" due to time dilation. The two way speed of light inside the rocket as seen on the in the played back film is c/y^2.

Assume that the film is processed by a computer to correct for light travel times from the rocket to the camera to remove visual artifacts such as Terrell rotation. It might even be better to imagine a network of automated clocks and cameras that record events of the rocket moving relative to the network, and presents the measurements in real time to the observer in a form a computer graphic that keeps the rocket centered on the screen.

Is there a formal coordinate system that corresponds to the one I have just described?

Since you are using the same time, length, and simultaneity definitions from the original frame it sounds like you are looking for the coordinate system defined by a galilean transformation from the original frame.

x' = x - vt
t' = t

This gives a round trip average speed of light as:

\Delta t' = \frac{L}{c-v}+\frac{L}{c+v} = \frac{2L}{c(1-v^2/c^2)}

So, as you said, the two way average speed of light is c/y^2 for this coordinate system.

 

[1effect]

You completely misunderstand the point here. The point is that:
1) the coordinate system meets your definition of an inertial frame
2) the speed of light is not constant in that coordinate system
3) special relativity postulates that the speed of light is constant in inertial frames
4) therefore either your definition is wrong OR relativity is wrong by definition

All this shows is that the average speed of light for a round trip according to this coordinate system is a constant. Are you saying that you wish to consider the second postulate of relativity to refer to the average speed of light for a round trip instead?

No, it shows a lot more than what you are willing to admit : it shows that the Selleri theory is experimentally indistinguishable from SR, its prediction of light speed anisotropy is not detectable experimentally (as explained in the FAQ).
More importantly ,it shows that , despite the prediction of anisotropy, the set of transforms result into a null prediction for MMX, exactly like SR.
This means that your counterexample is invalid. I suggest that you go thru the exercise of using the transforms that you provided to convince yourself that the prediction for the other two experiments is identical to the one made by SR. Have you tried the exercise? What results did you get?

 

[1effect]

Hello all.

At the risk of appearing ignorant, what have all these various coordinate systems got to do with the definition of inertial frames. I thought that coordinates were just a set of labels assigned to a frame and did not affect how the laws physics are.

Correct.

To quote from Rindler's Special Relativity """ An Inertial Frame is one in which spatial relations are determined by rigid scales at rest in the frame, are Euclidean and in which there exists a universal time in terms of which free particles remain at rest or continue to move with constant speed along straight lines ( Newton' first law )------""""

Correct again.

My preferred definition is that in which an inertial frame in SR is one in which an accelerometer registers zero force.

Correct again.

So as a genuine question, what is wrong with defining a frame as inertial if an accelerometer registers zero and the frame includes all objects at rest relative to the accelerometer with a Euclidean coordinate system attached ie. with an origin at a certain point in that frame.

...and again :-)

 

[JustinLevy]

You completely misunderstand the point here. The point is that:
1) the coordinate system meets your definition of an inertial frame
2) the speed of light is not constant in that coordinate system
3) special relativity postulates that the speed of light is constant in inertial frames
4) therefore either your definition is wrong OR relativity is wrong by definition

All this shows is that the average speed of light for a round trip according to this coordinate system is a constant. Are you saying that you wish to consider the second postulate of relativity to refer to the average speed of light for a round trip instead?

No, it shows a lot more than what you are willing to admit : it shows that the Selleri theory is experimentally indistinguishable from SR, its prediction of light speed anisotropy is not detectable experimentally (as explained in the FAQ).
More importantly ,it shows that , despite the prediction of anisotropy, the set of transforms result into a null prediction for MMX, exactly like SR.
This means that your counterexample is invalid.

Here is a direct question:
Do you agree with statements 1-3 I gave there?

You continue to ignore all the content, and questions, and maintain contradictory statements... at this point it is difficult to resist writing you off as either a crackpot or a troll. I truly hope you will prove those worries baseless by having a logical discussion here.



May I remind you that the book you recommended did not support your opinion:

We emphasize again that the key point for constructing an inertial frame is the clock synchronization.

I am NOT saying that your definition of an inertial frame is a priori incorrect. After all it is just a definition. What I am saying is that your definition makes one of the postulates of special relativity incorrect by definition. Your definition is incompatible with special relativity.

Showing that calculations performing in another coordinate system agree with the calculations of SR in an inertial coordinate system in no way invalidate this point. The second postulate of SR isn't that the Michelson-Morley, Kennedy-Thorndike, or Ives-Stilwell experiments give particular results... those would be derived experimental predictions. The postulate is that the speed of light is a constant in inertial frames. Your definition contradicts this postulate. You can't have it both ways.

 

[1effect]

Here is a direct question:
Do you agree with statements 1-3 I gave there?

You continue to ignore all the content, and questions, and maintain contradictory statements... at this point it is difficult to resist writing you off as either a crackpot or a troll. I truly hope you will prove those worries baseless by having a logical discussion here.



May I remind you that the books you recommend, do not support your opinion:





I am NOT saying that your definition of an inertial frame is a priori incorrect. After all it is just a definition. What I am saying is that your definition makes one of the postulates of special relativity incorrect by definition. Your definition is incompatible with special relativity.

Showing that calculations performing in another coordinate system agree with the calculations of SR in an inertial coordinate system in no way invalidate this point. The second postulate of SR isn't that the Michelson-Morley, Kennedy-Thorndike, or Ives-Stilwell experiments give particular results... that would be derived experimental predictions. The postulate is that the speed of light is a constant in inertial frames. Your definition contradicts this postulate. You can't have it both ways.

This is the fourth time you have contradicted the FAQ in this thread. There is no point in continuing this discussion.

 

[ZapperZ]

Then this is a good time to close this thread.

Please note: if you think someone posted something that is crackpottery, or someone is being a troll, use the REPORT post button. If you continue to respond, then you are feeding the trolls and crackpots.

Zz.