Is c invariant in Accelerating frames?

[Austin0]

ORIGINAL

Sylas The other way is to move your clock all over the ship, and use it as a "light ruler" at every point, and mark off distances that way. This will give you different distances from the "radar" method. It will also mean that the speed of light varies in different parts of the ship, from the perspective of an observer with a clock seeing how long it takes light to get from one point to another remote point.

ORIGINAL Responce ----- austin0______________________________________________________________________
The second ,the "light ruler" ,moving a clock around as a measure, is not valid in either inertial or accelerating frames for determining distance or ,testing and establishing synchronicity unless
the fundamental principle that moving a clock [ ie:at a relative velocity]
neccessarily causes time dilation and loss of synchronicity with the system is not valid.
Would you agree with this or not?

=sylas;2303547]No, I do not agree; but mainly because we are talking at cross purposes

austin0 interjectionI think it not neccessarily so much at cross purposes but is a question of crossed questions and answers. I asked a question and you are answering a different question.

The rulers are not moving with respect to each other. Rather, you have each point equipped with a clock and a ruler, and all the rulers are stationary with respect to each other... determined by the fact that the distances obtained between two rulers remains unchanged.

AS you can see above I was referring to the moving of the clocks and the effects of that movement and how that negated their reliability as gauges of distance or synchronicity.
In this context I would still very much like to get your responce.

You seem to have taken me as saying that the rulers are actually moving with respect to each other when they make the measurement. That's not the definition used. The rulers remain at unchanging distances from each other to make the measurement.

AS above, that is not what I took you as saying but now that you mention it, it brings up a relevant question; In the inertial reference frame that was the basis for the assumption of anisotropic dilation, it was determined that the front and the back of the system were actually moving wrt each other. Now in the context of the accelerating frame you want to assume the actuality of the dilation but toss out the assumption of relative motion.

Isn't this a little selective?

That is precisely the method I proposed; except rather than cut lengths, I use a light ruler as the common reference. It's the same thing. You move the rulers (transport them) all over the ship, and then when they are all at rest with respect to each other (fixed distances) you have your co-ordinates defined by those rulers.

Note that in your method also, having the rulers moving past any point brings in a Lorentz contraction. That's why we require the rulers to be at rest -- at fixed separation.

Agreed. That it exactly why I scratched it as a serious consideration. Because according to the conditions of the Dilation theorem and many of the posts in this thread the concept of a fixed separation in this situation is inherently invalid and arbitrary.

Now... how do you propose to define time? I have been supposing that we have a single reference clock, and give the time at any other point as given by that clock. You can define "simultaneous" with the reference clock as being the midpoint of the interval for light to get from the reference clock to an event and then back.

If c is not invariant under the elementary conditions I outlined in the beginning of this question then I have no definitive proposal for a method to define or determine time. This is something I have in fact, spent considerable time thinking about prior to this thread without coming up with any viable ideas. So i am openly considering all the ideas presented by these posts and have already examined many of them. If I raise objections it is not out of contrarity or because I have some fixed simplistic idea of my own but because I do recognize the inate complexity and difficulty of establishing any method or reliable reference.
SR provides logically consistent and definitive answers to all questions regarding physics in inertial frames. No other assumptions or definitions of coordinates , etc. required. But SR came about, not as a purely theoretical deduction but as an empirical induction. The fact that physics operates identically in all inertial frames is not a contrived fact through deduced convention but is a simple intrinsic aspect of reality, recognized by Einstein and Galileo before him. But any consideration of accelerating frames, must of neccessity be purely theoretical deductions, because we ,at this point, lack the technological capability to achieve significant accelerations or velocities.
So I certainly do not presume to know which is correct of the various possible assumptions , I am just trying to learn what they all are.
Thanks


Cheers -- sylas[/QUOTE]

 

[Klockan3]

Accelerating frames are covered fully in GR, and the conclusion is that yes, C is invariant in accelerating frames as long as you use proper coordinate systems. SR can't handle this problem since the metric tensor needs to be constant, but with a position dependent metric it is no problem.

So, what happens? Well, you as an observer can observe the time dilation of every point since you are in fact in the same curved coordinate system, time runs slower backwards from you and faster forwards from you in the acceleration direction which leads to a curved metric tensor. Now, considering that you calculate with this curved tensor instead of any flat tensor you will get the exact speed of C, and you can't get this result from SR and any discussion involving just things from SR is totally pointless since SR is not meant to treat accelerating systems.

 

[Ich]

Accelerating frames are covered fully in GR, and the conclusion is that yes, C is invariant in accelerating frames as long as you use proper coordinate systems.

And what are those "proper coordinate systems"?

 

[Austin0]

Accelerating frames are covered fully in GR, and the conclusion is that yes, C is invariant in accelerating frames as long as you use proper coordinate systems. SR can't handle this problem since the metric tensor needs to be constant, but with a position dependent metric it is no problem.

So, what happens? Well, you as an observer can observe the time dilation of every point since you are in fact in the same curved coordinate system, time runs slower backwards from you and faster forwards from you in the acceleration direction which leads to a curved metric tensor. Now, considering that you calculate with this curved tensor instead of any flat tensor you will get the exact speed of C, and you can't get this result from SR and any discussion involving just things from SR is totally pointless since SR is not meant to treat accelerating systems.

Thanks for your response. I got a general idea of the concepts you were describing
but it would help considerably to put it in a simple context.

A hypothetical empirical situation. Two observers at opposite ends of a ship test and synch their clocks and then the system accelerates and they simply repeat the procedure.

Would they derive different measurements depending on the direction [back to front vs front to back] that in both cases were not exactly c given the explicit distances.
These measurements being subject to reinterpretation within the parameters of GR coordinates to indirectly derive c ?

Or would they directly ,as observations of their clocks, get invariant and isotropic measurements ?

Thanks for your help
Oh a related question. I assume that by this time light speed has been measured in all possible circumstances and directions. Do you know the results of actual tests up and down differing altitudes and potentials?

 

[Klockan3]

^^
In accelerating frames the tricks used to derive the SR formulas doesn't work, SR can't handle negative time dilations and such. Sure it looks like C changes if you do not consider the metrics time dilation at different points. Like with a light clock experiment, both observers would observe the same distance traveled by the light (The distance between all the observers and the clock is constant) as long as you make a new photon per bounce so it doesn't deviate from its course. The difference is that it would take longer time for it to happen for one observer than then other.

The correct observation then is that time flows with different rates at different parts in the accelerating frame, if you consider this then C is constant. And yes, they have made experiments and shown that time dilation due to gravitation exists, don't know about acceleration but it would be really strange if it wasn't the same.

WIKI
Experimental confirmation
Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks that traveled aboard the airplanes upon return were slightly fast with respect to clocks on the ground. The effect is significant enough that the Global Positioning System needs to correct for its effect on clocks aboard artificial satellites, providing a further experimental confirmation of the effect.[2]
Gravitational time dilation has also been confirmed by the Pound-Rebka experiment, observations of the spectra of the white dwarf Sirius B and experiments with time signals sent to and from Viking 1 Mars lander.

And what are those "proper coordinate systems"?

http://en.wikipedia.org/wiki/Metric_tensor_(general_relativity)
Coordinate systems are described by their metric tensors.

 

[Austin0]

=Klockan3;2307655]^^
.

The correct observation then is that time flows with different rates at different parts in the accelerating frame, if you consider this then C is constant. And yes, they have made experiments and shown that time dilation due to gravitation exists, don't know about acceleration but it would be really strange if it wasn't the same.

I think you misread my question:
austin0
Oh a related question. I assume that by this time light speed has been measured in all possible circumstances and directions. Do you know the results of actual tests up and down differing altitudes and potentials?

I am aware of the tests for dilation. And yes tests of accelerating clocks have confirmed dilation there to. I was wondering if tests with precision clocks had been made for light speed with and against the potential gradient or, to and from satellites to
earth etc.

As regards the original question. Can I interpret your answer as meaning that light would NOT be isotropic and invariant as directly observed as clock readings at the ends of the frame?
Thanks

 

[Klockan3]

As regards the original question. Can I interpret your answer as meaning that light would NOT be isotropic and invariant as directly observed as clock readings at the ends of the frame?
Thanks

Yes, things wouldn't make sense otherwise.

1: There is time dilation in this system.
2: Both observers agree of the distance of a light clock positioned at one of them directed orthogonally to the distance between them.
3: The distance between the observers is constant so they would both observe the same bouncing in the light clock.

If we sum these together then one observer will observe a different speed of light relative to their own time than the other, which is due to the time dilation, but if you consider proper time C is constant. This only occurs in GR and never in SR. SR only works between inertial frames, this is a single accelerating frame and you can't study it trying to break it down into inertial frames.

 

[Ich]

Sorry, I didn't make myself clear.
I'm a bit irritated about you jumping in an already confused thread, claiming strange things.
Therefore I asked you to specify the coordinate system you're speaking of. If you fail to do so -what I, I admit, expect- it would hopefully show you and the OP that your claims are unfounded. If you can write down these coordinates and their relation to Rindler coordinates, I'll have to explain why they don't pertain to the OP's question.

 

[Al68]

And yes, they have made experiments and shown that time dilation due to gravitation exists, don't know about acceleration but it would be really strange if it wasn't the same.

It would be very strange, since the only reason time dilation exists due to gravity is due to the equivalence principle equating being "at rest" in a gravitational field to an accelerated reference frame, in which time dilation is expected between different positions in the frame.