Special relativity and acceleration [Archive]

sylas

Jul16-09, 10:23 AM

Why can’t we separate the velocity contribution to time dilation and the acceleration contribution to time dilation? At a particular point in time there will be a given velocity and a given acceleration.

You can probably do that; but I would prefer to simply integrate proper time over the world line, without trying to decompose it. The point is that the case where there is a continually increasing relative velocity is not going to be a good match with a gravitational time dilation example.

Trying to work this one out, I keep getting more acceleration at the front (less at the rear). How did you work it out?

I wrote it from memory, which is not totally reliable. Here's how I rethought it to answer your question... consider a particle with constant proper acceleration a, using the parametric equations, with u as proper time, and x and t as co-ordinates in a suitably chosen inertial frame.
\begin{align*}
t &= \frac{c}{a} \sinh (ua/c) \\
x &= \frac{c^2}{a} \cosh (ua/c)
\end{align*}

Let this represent the front of the ship. Now imagine a photon sent backwards at a proper time u-d, and another received forward at time u+d. Their point of crossing defines a rear of the ship, which is a constant distance cd from the front. For a given u, let this rear be at (t', x') in the inertial frame.

Then
\begin{align*}
x'+t'c & = \frac{c^2}{a} (\cosh ((u-d)a/c) + \sinh ((u-d)a/c)) \\
&= \frac{c^2}{a} e^{(u-d)a/c} \\
x'-t'c & = \frac{c^2}{a} (\cosh ((u+d)a/c) - \sinh ((u+d)a/c)) \\
&= \frac{c^2}{a} e^{-(u+d)a/c} \\
x' &= \frac{c^2}{a} e^{-da/c} \cosh(ua/c) \\
t' &= \frac{c}{a} e^{-da/c} \sinh(ua/c)
\end{align*}

Hence, the rear of the ship, identified in this way, has an acceleration a', and a proper time u', so that
\begin{align*}
a' & = a e^{da/c} \\
u' &= u e^{-da/c}
\end{align*}

I'm taking d and a as positive, and so u' is running slow, just like a clock inside a gravitational well runs slow, and the acceleration at the rear is greater than at the front.

See also: Born Rigidity, Acceleration, and Inertia (http://www.mathpages.com/home/kmath422/kmath422.htm) at www.mathpages.com

Cheers -- sylas

Al68

Jul17-09, 12:13 AM

The reason that I ask the question is that Einstein’s equivalence principle says (basically) that one can’t differentiate between inertial and gravitational acceleration.
If this is the case then an inertial acceleration of g should also experience the same time dilation as a body at a particular gravitational potential where the acceleration due to gravity is g.The reverse of that argument is that according to the equivalence principle, since time dilation occurs for observers "stationary" in an accelerated reference frame (like a rocket) then time dilation should also occur for observers stationary in a gravitational field. This is exactly how gravitational time dilation was predicted by Einstein.

Austin0

Jul19-09, 07:26 AM

=sylas;2273802]You can probably do that; but I would prefer to simply integrate proper time over the world line, without trying to decompose it.

What do you think about the tests that seem to indicate that the curvilinear component of the integrated world line due to acceleration, doesn't have an actual ,real world, time dilation correspondence????

I'm taking d and a as positive, and so u' is running slow, just like a clock inside a gravitational well runs slow, and the acceleration at the rear is greater than at the front.

Do you think that an accelerated frame , after attaining a new inertial velocity, would then have to resynchronize its clocks to compensate for this asymetric dilation of the rear clocks??
Thanks

Austin0

Jul19-09, 07:33 AM

The reverse of that argument is that according to the equivalence principle, since time dilation occurs for observers "stationary" in an accelerated reference frame (like a rocket) then time dilation should also occur for observers stationary in a gravitational field. This is exactly how gravitational time dilation was predicted by Einstein.

I thought that this was not the case. That tests like Gravity Probe B , rotational acceleration tests and particle accelerator tests indicated that all observed dilation was due to the sum of instantaneous velocities with no actual dilation attributable to the acceleration itself. DO you have links to other findings??? Thanks

DrGreg

Jul19-09, 07:57 AM

I thought that this was not the case. That tests like Gravity Probe B , rotational acceleration tests and particle accelerator tests indicated that all observed dilation was due to the sum of instantaneous velocities with no actual dilation attributable to the acceleration itself. DO you have links to other findings??? ThanksWhat you say applies to the case when an inertial observer measures an accelerating object. In those conditions, dilation depends only on velocity and not on acceleration.

But it doesn't work the other way round, when an accelerating observer makes the measurement. In that case there is dilation depending on acceleration, even if the object being measured is a fixed distance from the observer in the observer's accelerating frame. The explanation for this is that a fixed distance in an accelerating frame becomes a Lorentz-contracting distance in an inertial frame, so there is movement and dilation.

sylas

Jul19-09, 12:19 PM

Do you think that an accelerated frame , after attaining a new inertial velocity, would then have to resynchronize its clocks to compensate for this asymetric dilation of the rear clocks??

In the context of the system I describe, there are two observers, one at the front and one at the rear of a spaceship. Both observers experience a constant acceleration, but the one at the front has a slightly smaller acceleration. The distance between the observers remains constant, as determined by either observer.

There can be no synchronization, and no re-synchronization. This is a steady state example which carries on indefinitely. As long as the acceleration remains constant and the distance remains fixed, the clock at the rear of the ship falls steadily behind the one at the front, because of the time dilation effect calculated.

This is a standard result, and can be calculated from special relativity. I gave a quick outline of the maths above. The conclusion has the status of a mathematical theorem. It's not just my guess about what goes on; it is the necessary implication of relativity for constant acceleration in a space ship.

Cheers -- sylas

Al68

Jul20-09, 05:06 AM

I thought that this was not the case. That tests like Gravity Probe B , rotational acceleration tests and particle accelerator tests indicated that all observed dilation was due to the sum of instantaneous velocities with no actual dilation attributable to the acceleration itself. DO you have links to other findings??? ThanksSure, time dilation for inertial observers is due to velocity, not directly due to acceleration. That's why I specified "observers "stationary" in an accelerated reference frame", since these accelerated observers will have relative velocity between them as measured in an inertial frame. The time dilation calculated from the inertial frame due to relative velocity will equal the "gravitational" time dilation measured by the accelerated observers due to their accelerated frame.

Another way to look at it is that gravitational time dilation is also solely attributable to relative velocity as measured in an inertial frame.

Austin0

Jul20-09, 09:26 AM

Originally Posted by Austin0
Do you think that an accelerated frame , after attaining a new inertial velocity, would then have to resynchronize its clocks to compensate for this asymetric dilation of the rear clocks??

.
There can be no synchronization, and no re-synchronization. This is a steady state example which carries on indefinitely. As long as the acceleration remains constant and the distance remains fixed, the clock at the rear of the ship falls steadily behind the one at the front, because of the time dilation effect calculated.

If you will check what I said you will see that I was specifically refering to after the period of acceleration [of whatever duration] , when the system was once again in inertial motion.
If one way light speed tests were conducted between the front of the system and the back,,, and the back to the front , do you think that

A --- The tests would result in c as usual???

B --- The tests would result in asymetric and incorrect results due to the desynchronization due to the greater dilation that had occured in the rear clock.
The clocks would have to be resynchronized with light???

This is a standard result, and can be calculated from special relativity. I gave a quick outline of the maths above. The conclusion has the status of a mathematical theorem. It's not just my guess about what goes on; it is the necessary implication of relativity for constant acceleration in a space ship.

I was not questioning either the math or your command of the math, both are beyond me. ANy reservations I have are regarding the physical assumptions behind and the implications deriving from the conclusion. Thanks Stephen

Austin0

Jul20-09, 09:55 AM

=Al68;2278116]Sure, time dilation for inertial observers is due to velocity, not directly due to acceleration.

That's why I specified "observers "stationary" in an accelerated reference frame", since these accelerated observers will have relative velocity between them as measured in an inertial frame.
Are you refering here to the infinitesimal difference in acceleration or instantaneous velocity due to length contraction???

The time dilation calculated from the inertial frame due to relative velocity will equal the "gravitational" time dilation measured by the accelerated observers due to their accelerated frame.
Measured how??? Does this mean you would choose B in the post above???

Another way to look at it is that gravitational time dilation is also solely attributable to relative velocity [I]as measured in an inertial frame.[/I
Intriguing concept I will have to give more thought to .

sylas

Jul20-09, 10:12 AM

Originally Posted by Austin0
Do you think that an accelerated frame , after attaining a new inertial velocity, would then have to resynchronize its clocks to compensate for this asymetric dilation of the rear clocks??

I was describing a continuous never ending constant acceleration. During this acceleration, the clocks run at different rates.

If acceleration stops, then the clocks will run at the same rate again, and so you can sychnronize them if you like. They'll certainly be out of sync after any period of acceleration, given that they were running at different speeds.

Of course, in most cases with which we are familiar, the spaceship is small or the acceleration is weak or the duration of acceleration is short, so that the dilation effect between front and back is very very small.

If one way light speed tests were conducted between the front of the system and the back,,, and the back to the front , do you think that

A --- The tests would result in c as usual???

The speed of light is measured as c, in all cases, by all observers, accelerating or not.

B --- The tests would result in asymetric and incorrect results due to the desynchronization due to the greater dilation that had occured in the rear clock.
The clocks would have to be resynchronized with light???

Each clock is assumed to be perfectly correct in measuring the passage of time, in all conditions. They move out of sync because they are correct; because time dilation is a real effect that can be measured by correct clocks.

In a state where acceleration has stopped and the entire ship is moving at one constant velocity, you can sychnronize the clocks because they'll be running at the same speed. You can synchronize them however you like.

I was not questioning either the math or your command of the math, both are beyond me. ANy reservations I have are regarding the physical assumptions behind and the implications deriving from the conclusion. Thanks Stephen

No problem. I understand that. I'm just explaining the nature of the assumptions I am making... namely, that relativity is correct. There's no other special assumption needed; the result is necessary consequence of the maths of relativity.

Technically, there's is an assumption of a "rigid" spaceship, which is a very natural assumption that you might not even think of. It means that the spaceship size remains always about the same for passengers on board. You don't have any continuous deformation or compression of the ship. You might not even think of this as an assumption, although it is needed in the derivations.

Cheers -- sylas

Austin0

Jul20-09, 10:35 AM

What you say applies to the case when an inertial observer measures an accelerating object. In those conditions, dilation depends only on velocity and not on acceleration.

But it doesn't work the other way round, when an accelerating observer makes the measurement. In that case there is dilation depending on acceleration, even if the object being measured is a fixed distance from the observer in the observer's accelerating frame. The explanation for this is that a fixed distance in an accelerating frame becomes a Lorentz-contracting distance in an inertial frame, so there is movement and dilation.

Given any kind of real world acceleration wouldn't the linear distance difference, in total path length between the front and back of the system over the full course of acceleration, be negligable in terms of relative velocity ???? Or relative acceleration???
If the cumulative overall difference is slight wouldnt the instantaneous or slight interval difference be vanishingly small??
I am assuming that real world acceleration would mean that as system length and mass increased, that time of acceleration/path length would increase also. That if you consider a very long system where the contraction difference would be greater it would also take longer to achieve comparable velocities. ??? Thanks

Austin0

Jul21-09, 10:00 AM

=sylas;2278316]
If acceleration stops, then the clocks will run at the same rate again, and so you can sychnronize them if you like. 1 They'll certainly be out of sync after any period of acceleration, given that they were running at different speeds.

2 The speed of light is measured as c, in all cases, by all observers, accelerating or not .3

Each clock is assumed to be perfectly correct in measuring the passage of time, in all conditions. 3 a [ B]They move out of sync [i]because they are correct[/i[/B]]; because time dilation is a real effect that can be measured by correct clocks.

Would you agree that, by definition and convention, any set of clocks that measures the speed of light as c in both directions is synchronized ???

Would you agree that any set of clocks that are not synchronized within the terms of that convention, could not possibly measure the speed of light as c in both directions????

SO if you believe #2 above [which is what I believe] how do you justify #1 above.

In what sense can they be determined or even considered as out of synch if they return correct results for light tests???

In what possible way could the assumed dilation be empirically confirmed ,you think it is not perceived by outside observers in inertial frames and does not effect the functioning of clocks in some observable way within the system itself????

#3a What do you mean by correct in this context????

I have no question that time dilation is a real effect on real world clocks. But there is also no question that there is uncertainty and lack of concensus regarding the :

A physics involved. Is there physics involved?? Is it just a coordinate effect, a purely relative perception without any physical implications?? We see the same effect due to gravitational potential in which case we do assume an underlying physicality to the phenomenon.

B relationship to acceleration. The twins question. While it doesnt seem to actually produce dilation , it in some way is considered to turn relative[reciprocal] dilation, due to velocity, into a nonreciprocal phenomenon .
Kind of a catalytic effect. Whether or not this is correct it is certainly without explanation or reason to be found within the conceptual or mathematical structure of SR.

QUOTE] I'm just explaining the nature of the assumptions I am making... namely, that relativity is correct. There's no other special assumption needed; the result is necessary consequence of the maths of relativity.[/QUOTE]

I am certainly not questioning the assumption that SR is correct. But where in the Lorentz maths does it become inevitable that acceleration causes time dilation???

Without additional assumptions regarding the physics of acceleration.

Without the assumption that the perceived contraction relative to some inertial frame has actual physical meaning and implications. [which may be true but are not known or understood at this time]

Without the assumption of relativistic differentials of velocity between the front and the back.

This whole question seems to assume a conception of acceleration that is divorced from its basic meaning of a change of velocity over time. To disregard the D in D/t.
It seems to say that over the course of an acceleration, the total distance traveled by the rear [ R] dx relative to the total distance traveled by the front - [F] dx could be a relativistic velocity Fdx - Rdx/ t = [relativistically significant] v where Rdx = Fdx +gamma (length of system)
Does this seem realistic to you????
Thanks Stephen

sylas

Jul21-09, 10:43 AM

Would you agree that, by definition and convention, any set of clocks that measures the speed of light as c in both directions is synchronized ???

No. As I have said, all clocks measure the speed of light as c. This applies for ALL clocks, whether they are synchronized or not.

Would you agree that any set of clocks that are not synchronized within the terms of that convention, could not possibly measure the speed of light as c in both directions????

No. All clocks measure the speed of light as c.

SO if you believe #2 above [which is what I believe] how do you justify #1 above.

Both statements are false. This is fundamental.

In what sense can they be determined or even considered as out of synch if they return correct results for light tests???

In the sense that they run at different rates. Note that measurement of time AND length depends on the frame. Hence there is no contradiction with different observers measuring the same speed for light, even though they measure times and distances with different values. It is light speed that is the same for all frames; but not times or distances.

In what possible way could the assumed dilation be empirically confirmed ,you think it is not perceived by outside observers in inertial frames and does not effect the functioning of clocks in some observable way within the system itself????

Time dilation is measured directly using clocks. There are many experiments doing this. My favourite is the family that measured a gravitational time dilation by carrying a small van with three atomic clocks up Mt Rainer for a holiday weekend. Dad took the kinds for an exciting and educational holiday, while Mum stayed home watching over atomic clocks left in the kitchen. It's described in msg #10 of thread "Gravitational Time Dilation - Confused".

#3a What do you mean by correct in this context????

A clock is correct if it lets you measure the passage of time.

I have no question that time dilation is a real effect on real world clocks. But there is also no question that there is uncertainty and lack of concensus regarding the :

A physics involved. Is there physics involved?? Is it just a coordinate effect, a purely relative perception without any physical implications?? We see the same effect due to gravitational potential in which case we do assume an underlying physicality to the phenomenon.

B relationship to acceleration. The twins question. While it doesnt seem to actually produce dilation , it in some way is considered to turn relative[reciprocal] dilation, due to velocity, into a nonreciprocal phenomenon .
Kind of a catalytic effect. Whether or not this is correct it is certainly without explanation or reason to be found within the conceptual or mathematical structure of SR.

There is only uncertainty and lack of consensus with students who don't actually know enough physics yet. The physics is completely unambiguous and any student who can pass an introductory course in relativity should get precisely the same answers. If they don't, then they they are wrong. Relativity is a consistent theory that is thoroughly tested and gives only one possible answer to these questions.

You've come to the right place to learn more about it... but make no mistake... you do need to learn more about it.

I'm just explaining the nature of the assumptions I am making... namely, that relativity is correct. There's no other special assumption needed; the result is necessary consequence of the maths of relativity.

I am certainly not questioning the assumption that SR is correct. But where in the Lorentz maths does it become inevitable that acceleration causes time dilation???

I gave the maths before. You can't simply use a Lorentz transformation; that only applies for mapping between non-accelerating frames. But with a bit of calculus applied as well, the result falls out.

This is a bit more advanced than just using the Lorentz transformation itself, but from your initial questions in this post, I think you are best to get thoroughly familiar with inertial frames, and measurement of light speed for inertial observers, before worrying about the accelerating case.

Cheers -- sylas

Al68

Jul21-09, 05:34 PM

That's why I specified "observers "stationary" in an accelerated reference frame", since these accelerated observers will have relative velocity between them as measured in an inertial frame.Are you refering here to the infinitesimal difference in acceleration or instantaneous velocity due to length contraction???The latter.
The time dilation calculated from the inertial frame due to relative velocity will equal the "gravitational" time dilation measured by the accelerated observers due to their accelerated frame.Measured how??? Does this mean you would choose B in the post above???No, of course not. The way I read that post, there is no proper acceleration when the measurement is taken.

Another way to look at it is that gravitational time dilation is also solely attributable to relative velocity as measured in an inertial frame.
Intriguing concept I will have to give more thought to .The concept isn't new, this was the basis for Einstein's prediction of gravitational time dilation to begin with. I just worded it in a weird way for this thread.

Obviously, we can predict the elapsed time on each of two accelerated clocks between two defined events by using SR time dilation due to velocity relative to an inertial frame. We can then derive equations that can in turn be used in the accelerated frame to predict the same thing for the same clocks. Then we call it gravitational time dilation in the accelerated frame. That's essentially what Einstein did around 1908? Maybe there is a link to the paper online I could find.

Austin0

Jul22-09, 08:55 AM

Original Austin0
If one way light speed tests were conducted between the front of the system and the back,,, and the back to the front , after stopping acceleration ,,do you think that

A --- The tests would result in c as usual???

B --- The tests would result in asymetric and incorrect results due to the desynchronization due to the greater dilation that had occured in the rear clock.
The clocks would have to be resynchronized with light???

Originally Posted by Al68
The time dilation calculated from the inertial frame due to relative velocity will equal the "gravitational" time dilation measured by the accelerated observers due to their accelerated frame.

Measured how??? Does this mean you would choose B in the post above???

=Al68;2280052] The way I read that post, there is no proper acceleration when the measurement is taken.

You were quite right ,the question was regarding after the cessation of acceleration.
But I would still definitely like to know what your answer would be.
Also I am unclear what means you are talking about when you say measured by the accelerated observers. DO you mean moving one of the clocks and making a direct comparison?
Finding an actual discrepancy in synchronization between the front and back??
Or with light tests revealing loss of synch??

There was a thread in the past, wherein I mentioned the possiblity of quasi gravitational time dilation, I was pointed to most of the actual tests I mentioned above, by someone in this forum, with the admonition that the EP didnt work this way. I thought I got it then but apparently I need to take another look.
Thanks

Austin0

Jul22-09, 10:02 AM

=sylas;2279626]No. As I have said, all clocks measure the speed of light as c. This applies for ALL clocks, whether they are synchronized or not.

By this do you mean; if you are aware of the desynchronization and know the degree of error you can make adjustments in calulation and testing to correctly get the value of c.
If you mean something else could you explain.

sylas;2278316]
If acceleration stops, then the clocks will run at the same rate again, and so you can sychnronize them if you like.
#1 They'll certainly be out of sync after any period of acceleration, given that they were running at different speeds.

#2 The speed of light is measured as c, in all cases, by all observers, accelerating or not .

austin0--SO if you believe #2 above [which is what I believe] how do you justify #1 above.

= sylas Both statements are false. This is fundamental.

I think there is a little miscommunication here as both statements refered to here [#1 and #2]
were made by you . I just quoted.

In the sense that they run at different rates. Note that measurement of time AND length depends on the frame. Hence there is no contradiction with different observers measuring the same speed for light, even though they measure times and distances with different values. It is light speed that is the same for all frames; but not times or distances.
That is not what I am trying to address here. I am familiar with how relative inertial frames all measure the same value for light speed. Through length contraction, dilation and dsynchronization. In this case we are talking about how can two different clocks within the same frame measure the same value for that speed in both directions if they are not synchronized.

Time dilation is measured directly using clocks. There are many experiments doing this.
This is my question. How the observers in an accelerated frame measure the time dilation and detect the relative dilation between the front and the back.
I am also aware of the gravitational tests and there is no question regarding gravitational dilation.

There is only uncertainty and lack of consensus with students who don't actually know enough physics yet.
What I was refering to here was based on my reading here in this forum as well as other sources. I also wasnt refering to the fundamentals of SR or its application but to certain areas and questions growing out of the basics. If you read that paper on Born rigidity you linked in this thread, it touches on some of these. The possibility that inertia may in part be a matter of temporal resistance and other ideas. I have read any number of treatments of the Bell ship problem. They certainly didnt all agree on either the physical assumptions or conclusions. One actually applied two different assumptions regarding the way to calculate acceleration ,giving two different conclusions. The line snapped in one and not in the other case.
I have read many twins threads , where very knowledgable people in this forum have presented quite different ideas of the problem. Some say it is resolved on the basis of acceleration. Others have said "no" , acceleration has no direct dilation effect but it is resolvable purely through simultaneity ,contraction and normal dilation.And others. These are not students I am talking about.
And then there are all the questions that nobody even pretends to know the answer to , which in fact may not be answerable, but still should be explored. The how behind the effects. A physical model that would explain length contraction etc etc. The question of whether or not that question has any meaning.

You've come to the right place to learn more about it... but make no mistake... you do need to learn more about it.

No argument there. On both counts Thanks

sylas

Jul22-09, 11:01 AM

By this do you mean; if you are aware of the desynchronization and know the degree of error you can make adjustments in calulation and testing to correctly get the value of c.
If you mean something else could you explain.

No, I mean that the speed of light really is c for all observers. There are no corrections or adjustments needed; anyone equipped with a clock and a ruler will measure the speed of light, directly, with the same value. No adjustments. It doesn't matter how fast they are moving, or how strong their local gravitational field, or how they are accelerating. Speed of light is still c.

austin0--SO if you believe #2 above [which is what I believe] how do you justify #1 above.

Because it is not only time that is dilated. Distance measurements change also.

To measure the speed of light, you time how long it takes to get from one point to another, and also see how far apart the two points are.

Different observers may obtain different times for light to get from one point to another, because of time dilation. But they ALSO obtain different distances from one point to the other, and by the same factor. The speed is what remains unchanged.

I think there is a little miscommunication here as both statements refered to here [#1 and #2]
were made by you . I just quoted.

The statements you quote HERE are from me, and they are correct.

The statements I commented upon in the previous post were NOT by me, and they were incorrect.

That is not what I am trying to address here. I am familiar with how relative inertial frames all measure the same value for light speed. Through length contraction, dilation and dsynchronization. In this case we are talking about how can two different clocks within the same frame measure the same value for that speed in both directions if they are not synchronized.

"Same frame"? What do you mean by "same frame"?

Clocks that are inside an accelerating spaceship, but at different locations in the ship, are not in the same frame, and they run at different speeds, due to a time dilation effect analogous to gravitational time dilation.

I think your use of the word "synchronized" is a bit odd here. The usual meaning is to make sure the clocks have the same reading at a given point in space and time. After that, the clocks may diverge from each other again, if they are not in the same frame.

This is my question. How the observers in an accelerated frame measure the time dilation and detect the relative dilation between the front and the back.
I am also aware of the gravitational tests and there is no question regarding gravitational dilation.

Whatever method you choose for measuring gravitation dilation will also measure dilation within an accelerating spaceship. It's the same effect, after all.

However, the different ends of the accelerating spaceship are not the same frame, in the same way that the top and bottom of a tower are not the same frame.

What I was refering to here was based on my reading here in this forum as well as other sources. I also wasnt refering to the fundamentals of SR or its application but to certain areas and questions growing out of the basics. If you read that paper on Born rigidity you linked in this thread, it touches on some of these. The possibility that inertia may in part be a matter of temporal resistance and other ideas. I have read any number of treatments of the Bell ship problem. They certainly didnt all agree on either the physical assumptions or conclusions. One actually applied two different assumptions regarding the way to calculate acceleration ,giving two different conclusions. The line snapped in one and not in the other case.

You can get the same result with different methods. That's normal in maths, or physics.

In a situation that is impossible (like an infinitely rigid rod, or something like that) different people may propose different ways in which the situation "breaks down". Technically, that means they are looking at slightly different situations.

I have read many twins threads , where very knowledgable people in this forum have presented quite different ideas of the problem. Some say it is resolved on the basis of acceleration. Others have said "no" , acceleration has no direct dilation effect but it is resolvable purely through simultaneity ,contraction and normal dilation.And others. These are not students I am talking about.

There are differences in the way this is put, and some people do actually get it wrong; even people that appear to be expert. I've made mistakes myself as well. We all make errors from time to time.

It's not a good idea, in my view, to try and calculate results using simultaneity, contraction, dilation etc. You can, but it's really easy to go wrong. You are best to calculate using Lorentz transformations (when working with inertial frames) or integrating proper time over world lines (which working with more general motions), and take the differences in simultaneity, time dilation, length contraction, etc, as consequences you can show from the basic calculation.

In my view, it is misleading to think of acceleration causing dilation. Acceleration is just a way of changing the motions; at every instant the time dilation for a clock in SR is always obtained by considering its relative velocity to your reference observer.

Cheers -- sylas

Al68

Jul23-09, 07:33 AM

Does this mean you would choose B in the post above???No, A is correct. The speed of light would be measured as c.
Also I am unclear what means you are talking about when you say measured by the accelerated observers. DO you mean moving one of the clocks and making a direct comparison?
Finding an actual discrepancy in synchronization between the front and back??
Or with light tests revealing loss of synch??Any of the above. Like I mentioned above, the predicted difference in clock rates for between two accelerated clocks for an observer at rest with the clocks will be the same whether the prediction is made from an inertial frame (velocity based time dilation) or in the accelerated frame (gravitational time dilation). They're not really two different effects.

There was a thread in the past, wherein I mentioned the possiblity of quasi gravitational time dilation, I was pointed to most of the actual tests I mentioned above, by someone in this forum, with the admonition that the EP didnt work this way. I thought I got it then but apparently I need to take another look.
ThanksI'm not sure what you mean by "quasi gravitational time dilation", but gravitational time dilation for clocks at rest in a gravitational field was predicted by applying the EP to the predicted time dilation for clocks in an accelerated frame (like a rocket).

Al68

Jul23-09, 07:46 AM

"Same frame"? What do you mean by "same frame"?.............

.........However, the different ends of the accelerating spaceship are not the same frame, in the same way that the top and bottom of a tower are not the same frame.I think he was referring to the accelerated frame defined as the spaceship being "stationary", or in which earth's surface is stationary, not an inertial frame.

sylas

Jul23-09, 08:07 AM

I think he was referring to the accelerated frame defined as the spaceship being "stationary", or in which earth's surface is stationary, not an inertial frame.

I don't think that is a "frame" in the proper sense of the word. There's an accelerated frame for the front of the ship, and another accelerated frame for the back of the ship, but since the actual acceleration is different at the front and at the back, you can't have a single "frame" for the entire ship. But I am not entirely sure of what the word "frame" encompasses.

It's analogous to the case of a tower in a gravitational field, with a clocks at the top and at the bottom of the tower running at different rates. The difference is simply that you can calculate the effect in the accelerating space ship without using general relativity, but (by the equivalence principle) the net effect for clocks and rulers is the same.

Cheers -- sylas

Austin0

Jul26-09, 09:49 AM

Gentlemen it seems like there is a great deal of confusion and miscommunication here. I basically caused this when I entered a discussion about an accelerating system = S (a) ,,and started talking about after it stopped accelerating and was then an inertial system. = S ( i )
So I have been asking questions within the context of and regarding frame S ( i) and getting responces that related to system S ( a ) ,leaving me frustrated because I wasn’t getting answers to the actual questions I asked and you with the impression I was relativitively retarded..
I find the topic very interesting and appreciate the opportunity to get your input so I hope you will bear with me if I try to clear things up a bit
Here's the collated set of relevant posts

_____ POST 1_________________________________________________ ______
=sylas;2278316]
If acceleration stops, then the clocks will run at the same rate again, and so you can sychnronize them if you like.

1 They'll certainly be out of sync after any period of acceleration, given that they were running at different speeds.
2 The speed of light is measured as c, in all cases, by all observers, accelerating or not . .

C Would you agree that, by definition and convention, any set of clocks that measures the speed of light as c in both directions is synchronized ???

D --Would you agree that any set of clocks that are not synchronized within the terms of that convention, could not possibly measure the speed of light as c in both directions????

SO if you believe #2 above [which is what I believe] how do you justify #1 above

POST 2_________________________________________________ ________________________
= sylas Both statements are false. This is fundamental.

POST 3
__________________________________________________ _________________________
I think there is a little miscommunication here as both statements refered to here [#1 and #2]
were made by you . I just quoted.
POST 4
__________________________________________________ __________________________
Sylas
The statements you quote HERE are from me, and they are correct.

The statements I commented upon in the previous post were NOT by me, and they were incorrect.________________________________________ ____________________________________

DOes this mean then that you think that the statements above C ,D are wrong??

C ---- By definition and convention, any set of clocks that measures the speed of light as c in both directions is synchronized ???

D----Would you agree that any set of clocks that are not synchronized within the terms of that convention, could not possibly measure the speed of light as c in both directions????

Sylas I think your use of the word "synchronized" is a bit odd here. The usual meaning is to make sure the clocks have the same reading at a given point in space and time. After that, the clocks may diverge from each other again, if they are not in the same frame.

Of course that is the fundamental definition. But Einstein and SR also provide a means of achieving and testing synchronization with clocks that are spatially separated . Initially through two way reflected light transmissions/2 and also through one way transmissions with an agreed upon transmission time. The end result is exactly the same. This is also part of the SR convention regarding synchronization.

SO do you think wrt statement C above; that clocks that passed this test could possibly be unsynchronized??? By what definition??
Do you think that clocks that were not synchronized , ie: didnt read the same time while collocated or had different readings at different locations could possibly measure light at c???

To measure the speed of light, you time how long it takes to get from one point to another, and also see how far apart the two points are.

Self evidently,,, but it also assumes that since the clocks are apart they must be synchronized. SO they must either be synched while collocated and moved apart or synched by the light method.

In the accelerating ship it is assumed they started out synched while collocated but went out of synch while they were separated. SO to observe any desynch would neccessitate either moving them together or being able to detect it by light tests while separated.
SO do you think that in this circumstance you could move the clocks together and detect different time readings but then move them back apart and get correct readings for c??? If you consider them to be in two different frames how could they correctly measure c in any case. SR says that any two synched clocks in any single frame will always measure c in both directions.
Do you think it says that light measurements between a single clock in one frame and a single clock in a second frame would, that they could be in synch?

"Same frame"? What do you mean by "same frame"?

Sorry I was simply using the word frame when I should have said system.

I hope the questions are becoming clearer Thanks Stephen

Austin0

Jul26-09, 10:16 AM

If one way light speed tests were conducted between the front of the system and the back,,, and the back to the front , do you think that

A --- The tests would result in c as usual???

B --- The tests would result in asymetric and incorrect results due to the desynchronization due to the greater dilation that had occured in the rear clock.
The clocks would have to be resynchronized with light???

The time dilation calculated from the inertial frame due to relative velocity will equal the "gravitational" time dilation measured by the accelerated observers due to their accelerated frame.
Measured how??? Does this mean you would choose B in the post above???

=Al68;2282124]No, A is correct. The speed of light would be measured as c

Also I am unclear what means you are talking about when you say measured by the accelerated observers. DO you mean moving one of the clocks and making a direct comparison?
Finding an actual discrepancy in synchronization between the front and back??
Or with light tests revealing loss of synch??

Any of the above.

It seems like you are choosing both A and B
In case there is confusion between the accelerating system S (accl) and the inertial system S ( inrt) after acceleration.
So : S (accl) A or B ?
S ( inrt) A or B ?

Thanks for your patience Stephen

sylas

Jul26-09, 10:23 AM

I cannot tell whether you are just quoting old material, or whether you are asking the same questions again. But the answers are unchanged.

You seem to be asking, again, "Would you agree that, by definition and convention, any set of clocks that measures the speed of light as c in both directions is synchronized".

The answer is still an easy NO. Definitely and unambiguously not.

ALL observers ALWAYS measure the speed of light as "c". That means that clocks which are NOT synchronized... whatever you mean by that... will STILL measure the speed of light as c in both directions.

There are two possible ways you can mean synchronized. One is that clocks are synchronized if they are set to read the same value at a single point in space and time. It doesn't matter if they are moving relative to each other; as long as they pass right next to one another then you can ensure both read the same value in that shared instant.

The other is that clocks which are in the same frame (and hence are not dilated with respect to each other) can be synchronized to read the same value at the same time. You can do this because they share the same frame, and hence share the same notion of what is simultaneous.

But you can't synchronize clocks that are moving with respect to each other and are also separated from each other... because those two clocks don't have a common concept of "simultaneous". You can't make them read the same value at the same time because they don't agree as to what "at the same time" implies.

None of this makes any difference for measuring the speed of light. ALL observers always measure the speed of light, in any direction, as c. Whether they are synchronized or not.

Cheers -- sylas

DrGreg

Jul26-09, 04:27 PM

There's a misunderstanding here between Austin0 and sylas; you are talking about different things without realising it.

When Austin0 talks of "a set of clocks measuring the speed of light" he means you send light from clock A to clock B, measure the time of emission on clock A, measure the time of reception on clock B, and subtract the two times to give the time of transit. That method works when both A and B are stationary relative to the same inertial frame and the clocks have previously been synchronised in the standard way. It won't work when A and B are both stationary relative to the same accelerated frame, because, as has already been established, the clocks cannot stay in synchronisation.

On the other hand, sylas has in mind that each clock makes its own measurement of the local speed of light, independent of any other clocks. What does that mean? How do accelerating observers measure speed? The technical answer is that an accelerating observer asks an inertial oberver who happens to be momentarily travelling at the same speed (a "co-moving inertial observer") to make the measurement instead. In practice you can acheive the same end by using two clocks that are only a small distance apart (so the desynchronisation is negligible), or better still, consider the mathematical limit as the distance between the two clocks tends to zero. When an accelerating observer uses this method, they always measure the speed of light as c. That's what sylas meant.

Hopefully you will each realise what the other was talkiing about and can now continue this thread in less confusion!

sylas

Jul27-09, 12:24 AM

There's a misunderstanding here between Austin0 and sylas; you are talking about different things without realising it.

Ah. Thanks!

When Austin0 talks of "a set of clocks measuring the speed of light" he means you send light from clock A to clock B, measure the time of emission on clock A, measure the time of reception on clock B, and subtract the two times to give the time of transit. That method works when both A and B are stationary relative to the same inertial frame and the clocks have previously been synchronised in the standard way. It won't work when A and B are both stationary relative to the same accelerated frame, because, as has already been established, the clocks cannot stay in synchronisation.

Yes. You cannot have two synchronized clocks in the same accelerated frame but separated in space. Measuring the speed of light over a non-negligible distance within an accelerated frame (like my hypothetical accelerating spaceship of a non-negligible length) is (I think?) ambiguous, because it is not a Euclidean space, and will depend on how you assign co-ordinates.

On the other hand, sylas has in mind that each clock makes its own measurement of the local speed of light, independent of any other clocks. What does that mean? How do accelerating observers measure speed? The technical answer is that an accelerating observer asks an inertial oberver who happens to be momentarily travelling at the same speed (a "co-moving inertial observer") to make the measurement instead. In practice you can acheive the same end by using two clocks that are only a small distance apart (so the desynchronisation is negligible), or better still, consider the mathematical limit as the distance between the two clocks tends to zero. When an accelerating observer uses this method, they always measure the speed of light as c. That's what sylas meant.

Confirmed. That is precisely what I meant by having a clock that measures the speed of light, and indeed I thought of a set of clocks as all making their own independent measurements.

Hopefully you will each realise what the other was talkiing about and can now continue this thread in less confusion!

Thanks very much for your help there!

Cheers -- sylas

Added in edit: Stephen, let me attempt to answer your questions again more usefully!
If one way light speed tests were conducted between the front of the system and the back,,, and the back to the front , do you think that

A --- The tests would result in c as usual???

B --- The tests would result in asymetric and incorrect results due to the desynchronization due to the greater dilation that had occured in the rear clock.
The clocks would have to be resynchronized with light???

Measured how??? Does this mean you would choose B in the post above???

The measurements I had in mind for measuring time dilation was a repeat of the measurement of gravitational time dilation in the Harvard tower experiment. One clock sends messages to the other with a known frequency, and the other measures a frequency. If they measure different frequencies, they are measuring a different time between messages, and hence measuring time dilation.

The clocks must be a fixed spatial separation, which can be established by reflecting the messages back to the source and having them received at the same frequency as transmitted.

But measurement of the speed of light as it goes from one clock to the other will be ambiguous, because it depends on how you decide to define space. An obvious "radar" space distance will mean all the clocks continue to measure the speed of light as c, but they will differ on how far light travels from one clock to the other. A distance defined by having a local measurement with a light clock at all points on the ship will mean that the clock in the rear will see light moving slower at the front, and a clock at the front will see light moving faster at the rear... I think.

Also I am unclear what means you are talking about when you say measured by the accelerated observers. DO you mean moving one of the clocks and making a direct comparison?
Finding an actual discrepancy in synchronization between the front and back??
Or with light tests revealing loss of synch??

I'm assuming measurements made locally by observers at the front and the back of the accelerating spaceship.

Cheers -- sylas

Austin0

Jul27-09, 09:53 AM

=DrGreg;2286000]There's a misunderstanding here between Austin0 and sylas; you are talking about different things without realising it.
Hi Dr Greg and thanks. You have got the above right, in spades.
I suspect that there would be no real fundamental differences on the priciples and practices of SR between us if it werent for the semantic and situational confusion.

When Austin0 talks of "a set of clocks measuring the speed of light" he means you send light from clock A to clock B, measure the time of emission on clock A, measure the time of reception on clock B, and subtract the two times to give the time of transit.

Exactly, with the additional requirement of a known distance dx
ANd this is not only a method of testing the synch of spatially separated clocks but also works to synch [set] clocks that are out of synch . Say, stopped for a period.
With a transmitted T (at source)from a synched system clock and a known dx/c= t
gives T + t = correct T (at receiver) which compared to the observed t of reception shows the interval of desynchronization for adjustment. Is there any problem with this?? I assumed it was standard SR convention.

That method works when both A and B are stationary relative to the same inertial frame and the clocks have previously been synchronised in the standard way. It won't work when A and B are both stationary relative to the same accelerated frame, because, as has already been established, the clocks cannot stay in synchronisation.

It sounds like you are saying here that the answer to my question was that they would not be able to correctly measure light at c if they are spatially separated by a non-vanishingly small distance [at the opposite ends of the system]. Is this correct???

How do accelerating observers measure speed? The technical answer is that an accelerating observer asks an inertial oberver who happens to be momentarily travelling at the same speed (a "co-moving inertial observer") to make the measurement instead.
That is another interesting question. One that invoking ICMO's doesnt really solve does it?? Because to measure speed generally requires two observers . So you have two different instantaneously co-moving inertial frames instead of one accelerating frame that might possibly have a degree of desynch in its clocks. We know for sure that the two ICMIF's have different distances and times so I dont see a real difference.
In any case in this situation I was interested in the hypothetical method assumed for observers actually in the system to be able to observe [detect] dilation if it was present .

Thank you very much for your timely assistance and in put. Very ap[preciated. Stephen

Austin0

Jul27-09, 10:29 AM

Hi Sylas

The measurements I had in mind for measuring time dilation was a repeat of the measurement of gravitational time dilation in the Harvard tower experiment. One clock sends messages to the other with a known frequency, and the other measures a frequency. If they measure different frequencies, they are measuring a different time between messages, and hence measuring time dilation.
If you are talking about what I think , it was a measure of electron emmissions and receptions of a particular frequency range. The reception statistics were reduced because of blue doppler shift of the photons or electron reception resonance frequency due to time dilation . Is this the experiment you mean? They accelerated the emmission source away from the receiver creating a comparable red shift in the photons and the absorbtion stats went right up.
If it is, I found it very interesting but the test parameters seemed too complex , with too many variables that are not yet completely sure themselves. I have read differing views on the action of gravity on light. That it does not effect the velocity but does doppler shift it.
That it does neither.
If clocks are dilated how would it be detected if it did increase in speed infintesimally.
Other GR explanations which seemed to say that it does go faster but not really????Too complex for me to follow.

But measurement of the speed of light as it goes from one clock to the other will be ambiguous, because it depends on how you decide to define space. An obvious "radar" space distance will mean all the clocks continue to measure the speed of light as c, but they will differ on how far light travels from one clock to the other. A distance defined by having a local measurement with a light clock at all points on the ship will mean that the clock in the rear will see light moving slower at the front, and a clock at the front will see light moving faster at the rear... I think.
Well thats certainly ambiguous. Kidding

Thanks for your input Stephen

sylas

Jul27-09, 11:24 AM

If you are talking about what I think , it was a measure of electron emmissions and receptions of a particular frequency range. The reception statistics were reduced because of blue doppler shift of the photons or electron reception resonance frequency due to time dilation . Is this the experiment you mean? They accelerated the emmission source away from the receiver creating a comparable red shift in the photons and the absorbtion stats went right up.

Yes; it is the Pound and Rebka experiment, at Harvard, performed in 1959.

If it is, I found it very interesting but the test parameters seemed too complex , with too many variables that are not yet completely sure themselves. I have read differing views on the action of gravity on light. That it does not effect the velocity but does doppler shift it.

Shrug. I disagree; the experiment used clever techniques to detect tiny frequency changes, but there's nothing overly complex about it. More to the point, the experimental details don't matter. We're dealing with a hypothetical case of an accelerating spaceship; I am refering to the time dilation between front and back, and describing in principle how it can be measured. You can look at messages from one clock sent to the other with a known frequency. Time dilation will mean a change in the received frequency. I don't care how it is measured... the effect is real.

Clocks at the front and the back of an accelerating space ship run at different rates, in precisely the same way that clocks at the top and bottom of the Harvard tower, or any other tower.

Another more direct experiment was done by a family with a physicist Dad. Dad took the kids up Mt Rainer for a weekend, along with three atomic clocks. Mum stayed home and worked, watching over atomic clocks left in the kitchen. The time difference showed up directly on the readings of the clocks. See msg #10 in thread "Gravitational Time Dilation - Confused" for pics and a description.

Basically, I am simply describing what happens to clocks in an accelerating spaceship. It is the same things as clocks separated from each other in a gravitational field. I don't really mind how you measure it. There are two methods given here for measuring the same time. Use messages sent at a known frequency. Or carry a clock slowly from one end to the other, leave it a while, and bring it back. Either way, you get a direct measure of the time dilation between clocks at the two locations.

That it does neither.
If clocks are dilated how would it be detected if it did increase in speed infintesimally.
Other GR explanations which seemed to say that it does go faster but not really????Too complex for me to follow.

I don't understand your question here. In principle, the speed of light is measured using a "ruler" and a "clock". The speed of light measured locally by any observer is always c. This applies regardless of velocities, accelerations or gravity.

I've explained how you detect time dilation at a remote clock, using two methods, both of which work as long as the remote clock remains at a fixed distance.

But measuring the speed of light over a long light path, moving beyond the local region of the observer, can run into issues if the spacetime geometry is curved somehow; as it is in an accelerating spaceship or in a gravitational field. In this case, the notion of speed over the whole path depends on co-ordinates chosen.

Cheers -- sylas

Austin0

Jul31-09, 05:43 AM

Hi I think I need to make it clear that I consider both the invariance of c and gravitational time dilation as empirically verified phenomena, there has never been any question there.
Time dilation due to acceleration is a theoretically validated phenomenon.
I am not rejecting it as a phenomenon or a theorem nor am I arguing against it.
I dont know enough about it yet to even have a strong opinion let alone question its actuality.
I dont accept it for exactly the same reasons.
I am just trying to learn about it. The principles and assumptions foundational to the theorem?. The parameters and postulated magnitude of the effect?. What different interpretations and ideas do different people have regarding it.?
I am working with the premise that it is actual and taking it for a spin to see the implications , detection methods , how it fits with other effects of acceleration , the measurement of light and on and on.
Of course I am being critical ,,to the limit of my powers of logical analysis.
I have no problem with the phenomenon itself, it is no stranger than a whole lot of other things, even strange,r that I now take for granted, I do have a problem with the idea of two clocks in different frames , desynchronized , that can still measure c accurately.
Unless the magnitude of the effect is so small as to be negligable. In any case this topic ,and acceleration in general, is going to require considerably more research and thought I ' m quite sure.

=sylas;2286898]Yes; it is the Pound and Rebka experiment, at Harvard, performed in 1959.
Shrug. I disagree; the experiment used clever techniques to detect tiny frequency changes, but there's nothing overly complex about it.

I wasnt refering to the complexity of their techniques which I am sure were fine. I was refering to the ambiquity regarding what exactly they were detecting. Was it doppler shift due to gravitational potential or was it time dilation? I understand you can say they are equivilent but at the same time they are two different phenomena. One is a modulation directly effecting a photon in transit. Eg; a photon from a source outside planet. Doppler shift.
The other is effecting the resonent frequency of electrons which then emit photons of a lower frequency. A la cesium. Time dilation.
I have had the same question regarding the redshift in spectra from the sum. It seems to be usually attributed to the potential effect on the photons in transit out of the well. So I have wondered why it wasnt assumed to be due to dilation effecting the source atoms. Or both. And how could we tell the difference?

I understand your reasoning when you view photon frequencies as "clock" periodicities.
But it also seems like there are real differences too, Light clocks have the same interval independant of the frequency of the light used. Frequency changes can occur without any temporal element involved , purely through relative motion. SO frequency change itself is not a sure indication of temporal dilation or expansion.
Be that as it may. The occurence of frequency shift would definitely indicate either relative motion between the front and the back or time dilation in the absorbing detector.

Or carry a clock slowly from one end to the other, leave it a while, and bring it back. Either way, you get a direct measure of the time dilation between clocks at the two locations.
Fair enough. This is plenty explicit and unambiguous.
Well thank you for your help and your patience with the communication confusion.
I have a lot of thinking ahead on these questions.

Ich

Jul31-09, 06:17 AM

And how could we tell the difference?

You can't, and that's because you're not talking about two different effects, but about two different descriptions of the same effect.

Austin0

Jul31-09, 08:59 AM

You can't, and that's because you're not talking about two different effects, but about two different descriptions of the same effect.

Fine, but consider this.
A photon traveling from a region of high gravitational potential to a lower, is lowered in frequency. SLower periodicity. Dillated.
A clock traveling the same path is increased in frequency. Faster periodicity.
And of course conversely. So the electron acts more like a clock and the photon acts like ,,well, a photon.
So it may ultimately be the same phenomenon and it all might be totally equivalent in the end.
Inertial motion,acceleration and gravity being simply different descriptions of a singular root but at this stage there appear to be relevant distinctions.
Thanks

Ich

Jul31-09, 10:54 AM

A photon traveling from a region of high gravitational potential to a lower, is lowered in frequency. SLower periodicity. Dillated.
...as measured with the clocks at the other location.
A clock traveling the same path is increased in frequency. Faster periodicity.
...as compared with photons coming from the other location.

Or, third viewpoint: neither the photon nor the clock is broken, it's just a different time there.

Al68

Jul31-09, 05:32 PM

Austin0

Aug3-09, 10:34 AM

austin0 _______
A photon traveling from a region of high gravitational potential to a lower, is lowered in frequency. SLower periodicity. Dillated.

=Ich;2292368]...as measured with the clocks at the other location.

austin0 _______
A clock traveling the same path is increased in frequency. Faster periodicity

...as compared with photons coming from the other location.

Also compared with clocks at either location. And the non-relative "actuality" of this can be empirically determined by simply leaving the moved clock in the new location for a period
and then by signal ,,comparing the elapsed time with the elapsed time on an unrelocated clock.

Or, third viewpoint: neither the photon nor the clock is broken, it's just a different time there .

You seem to be viewing this as a sort of SR ,, " which clock is really dilated" meaningless question.
I am looking at it from a completely different perspective. To me it seems that GR time dilation is purely a function of spatial location wrt the fixed gravitational space-time matrix.
As such it is absolute and not reciprocal wrt clocks at other locations.

If G is a clock on the ground at (g) and T is a clock at the top of the tower at (t) then the frequency ( f) of G = (f)[ G ,(g)] < (f)[ T, (t) ] not also (f) [T, (t)] < (f)[ G ,(g)]

If you want to consider photons as clocks then the analogous situation to what I described above would be : Two additional clocks E and P, colocated at (t) with (f)[ T, (t)]= (f)[ E, (t)] = (f) [P, (t)]

Moving them to (g) and finding that (f) [E (g)] = (f) [G (g)]
but ( f )[P(g)] > (f) [G ,(g)] or (f) [E (g)]

If we look at E and P as electron and photon with (f)[ E, (t)] = (f) [P, (t)] as meaning equivalence of resonance (f) for absorbtion and emission

then ( f )[P(g)] > (f) [E,(g)] presents several possible explanations for the observed frequency differential

1-- the photon itself was directly changed by the translation through the potential gradient. This is the interpretation I read and mentioned above. (f) [P ,(g)] > (f) [P,(t)]

2---the differential is due to the actual difference in E ,, (f) [E,(g)] < (f) [ E,(t)]
and the difference in (f) P is only relative [not actual]

3-- both effects take place.

Empirically this would resolve by.
1--- if the difference in (f) P (f)[ P, (g)] - (f) [P, (t) = (f)[E,(t) - (f)[ E,(g)]

it would seem logical to adopt #2 above. And consider the photon unchanged as it is with doppler shift due to motion.

2 --- if (f)[ P, (g)] - (f) [P, (t) > (f)[E,(t) - (f)[ E,(g)] then it would appear that both were in effect.

The electron slowed down in E(f) and the photon actually increased P(f) while in transit.

SO does any of this clarify the question or make sense????
Thanks S

Ich

Aug4-09, 02:33 AM

SO does any of this clarify the question or make sense????
Not really.
But I like to emphasize that both "effects" are different viewpoints, so you certainly can't add their influence.
And that energy is intimately related to time, so a change in energy is a just different viewpoint of time dilation.
And that it does not matter whether the photon is unchanged or not. It appears differently to the upper observer, and GR doesn't care whether you explain that with a change of the observer or the photon.

Austin0

Aug5-09, 04:36 AM

=Al68;2292846]Well, logically, if time dilation exists for a clock moving relative to an inertial observer, then two clocks moving at two different speeds relative to an inertial observer must run at two different rates relative to the inertial observer.

Framed in this simple context the logic is both self evident and unquestioned.

But it seems to me that this situation is not at all that simple. That it implies and requires additional assumptions:

1-- Of course,, the axiom that everything is purely a coordinate transform and there are no physical implications to any relative effects..

2--That a single system can be considered as two independent frames. The fact that they are physically connected , not possibly having any effect or bearing on the consequences.

3-- That contraction is a purely spatial phenomenon. Negating any consideration that it may ultimately be a temporal displacement and may have unforseen effects on the clocks involved when acceleration is involved..

4--. That acceleration is fundamentally different from inertial motion. Is absolute not relative.

And the only way this is mathematically possible (if SR is correct) for two clocks "stationary" in an accelerated reference frame is if the clocks run at two different rates in the accelerated reference frame.

SO in this case we are calculating coordinate velocities and clock times in the rest frame and then jumping to the accelerating frame and assuming that they would apply there. At the same time assuming that the clocks in this frame are stationary wrt the frame and each other.
But viewed as two separate frames with different velocities they would not only, not be stationary , they would be at different distances from each other depending on which end you were measuring from.
Under the normal interpretation of SR , of course it is assumed that in whatever frame is under consideration the clocks are synchronized and the distances isometric. This would mean that whatever was calculated to be observed from another frame would be considered to be coordinate effects and would have no absolute interpretation. Like your transluminal velocities calculated for accelerating systems.

I cant help but think this is a little like calculating coordinate desynchronization as observed from one frame and then switching to the other frame and assuming the clocks are actually desynchronized.

I want to say again that I am not questioning the actuality or not of the phenomenon.
As to that, I have no view yet nor do I really care either way. It will just be another piece of the puzzle.
All of the above assumptions may be absolutely true.
I am just asking questions in the attempt to get together some kind of clear and logically coherant picture of the construct and how people interpret it. I think it is important , the whole question of acceleration , and so am spending a lot of time studying and thinking about it. But am finding it difficult to get definite answers. SO far on the invariance question I have received an unqualified yes, an unqualified no and an ,as yet ambiguous, yes and no.
DO you have a vote?? Thanks Stephen

Austin0

Aug5-09, 05:13 AM

=Ich;2296431]Not really.
But I like to emphasize that both "effects" are different viewpoints, so you certainly can't add their influence.

I wasnt adding their influence. I was simply saying that IF empirical tests produced results that exceeded the expected magnitude arising from the gravitational differential between the emiting and absorbing "clocks" THEN there would be reason to assume that the photons were also directly effected.
IF not THEN occams razor would seem to choose the dilation in the measuring electrons as a complete and sufficient explanation.
I dont know of actual empirical tests other than the tower experiment. In that case the explanations I have read attributed the initial lack of absorbtion to a blue shift of the photons due to gravitational effects on the photon. My original question was ,,,why was this the viewpoint they chose.

And that energy is intimately related to time, so a change in energy is a just different viewpoint of time dilation.

In this view what is the change of energy effected through translating a clock,cesium atom, electron , from a region of low gravitational potential to one of higher?
And likewise for a photon??

And that it does not matter whether the photon is unchanged or not. It appears differently to the upper observer, and GR doesn't care whether you explain that with a change of the observer or the photon

Quantitatively I see what you are saying but isnt it significant as far as understanding the interrelationship between photons and gravity???
Thanks

Ich

Aug5-09, 06:45 AM

My original question was ,,,why was this the viewpoint they chose.
Maybe because it's a quite common one: the photons gain potential energy while falling, just like any other thing would.
In this view what is the change of energy effected through translating a clock,cesium atom, electron , from a region of low gravitational potential to one of higher?
(in static spacetimes, like Schwarzschild)
Multiplication with g00, the time-time component of the metric.
For freely moving things like photons or falling clocks, g00 times particle energy (time component of its four momentum) is conserved.
I'm not sure this is helpful, however.
Quantitatively I see what you are saying but isnt it significant as far as understanding the interrelationship between photons and gravity???
It is significant to understand that it does not matter. GR has no mechanisms that change clocks or photons. It is about relations of space and time, not malfunctioning clocks or broken photons.

Al68

Aug5-09, 10:58 AM

Framed in this simple context the logic is both self evident and unquestioned.

But it seems to me that this situation is not at all that simple. That it implies and requires additional assumptions:

1-- Of course,, the axiom that everything is purely a coordinate transform and there are no physical implications to any relative effects..

2--That a single system can be considered as two independent frames. The fact that they are physically connected , not possibly having any effect or bearing on the consequences.

3-- That contraction is a purely spatial phenomenon. Negating any consideration that it may ultimately be a temporal displacement and may have unforseen effects on the clocks involved when acceleration is involved..

4--. That acceleration is fundamentally different from inertial motion. Is absolute not relative.

I'm not making the first two assumptions. For the third one, the clock hypothesis (that a clock is unaffected by proper acceleration) is an assumption, so any conclusion about the reading of a clock in GR/SR is only valid for clocks which are unaffected by proper acceleration.

For number 4, the time dilation between clocks in an accelerated frame is derived from relative coordinate acceleration alone, independent of proper acceleration, and does assume the clock hypothesis.

SO in this case we are calculating coordinate velocities and clock times in the rest frame and then jumping to the accelerating frame and assuming that they would apply there. At the same time assuming that the clocks in this frame are stationary wrt the frame and each other. Well, if a clock measures an elapsed time and stores the reading, the stored reading does not depend on any particular frame.
But viewed as two separate frames with different velocities they would not only, not be stationary , they would be at different distances from each other depending on which end you were measuring from. I can't figure out what you mean here.
Under the normal interpretation of SR , of course it is assumed that in whatever frame is under consideration the clocks are synchronized and the distances isometric. This would mean that whatever was calculated to be observed from another frame would be considered to be coordinate effects and would have no absolute interpretation. Like your transluminal velocities calculated for accelerating systems.

I cant help but think this is a little like calculating coordinate desynchronization as observed from one frame and then switching to the other frame and assuming the clocks are actually desynchronized.
Transforming coordinates from one frame to another is not "switching frames and assuming". Normally the transformed coordinates are correct by convention.

Similar to the way that 1 inch transforms to 2.54 centimeters. Sure assumptions are made, but the claim that 1 inch is "really" 2.54 cm is based on convention, not scientific theory. The way clocks are synchronized in SR, and coordinate times transformed between frames is based on convention, for simple convenience. There is no law of physics that says you must do it that way, but it's convenient to use a commonly used convention.

Austin0

Aug9-09, 04:56 AM

=Ich;2297818]Maybe because it's a quite common one: the photons gain potential energy while falling, just like any other thing would.

Could you explain what this means in the context of GR ???
In a classical interpretation, wouldn't it be said that; falling objects in a gravitational field loose potential energy while gaining kinetic energy or momentum [acceleration]
But as I understand GR the concept of acceleration does not apply in this situation and the path remains strictly inertial. If this is the case why would it be consistant to consider a photon gaining energy through translation through a potential gradient???
Does it also increase in velocity???
Are there test results as far as photon velocity with and against the gradient???

Based on the situation regarding frequency and your interpretation of it , I t would seem that with dilated clocks at higher potential areas [lower in the gradient] it would be expected that falling photons would be measured as moving at faster speeds by clocks with lower periodicity , than rising photons would be measured by clocks with higher rates.
Or at least this dilation factor would influence the actual measurements even if the empirical result was the opposite.
Is this the case????
I have read that photons actually travel slower in region of higher potential???

(in static spacetimes, like Schwarzschild)
Multiplication with g00, the time-time component of the metric.
For freely moving things like photons or falling clocks, g00 times particle energy (time component of its four momentum) is conserved.
I'm not sure this is helpful, however.

AS you surmised it is not immediately helpful. My knowledge of the mathematical structure of GR is only enough to instill a profound respect and give me a headache even contemplating actually learning it. A tensor in the neck.
AS regards falling clocks I can reach for an interpretation. As momentum ,velocity increase, conservation means that the time componenet must decrease ???

It is significant to understand that it does not matter. GR has no mechanisms that change clocks or photons. It is about relations of space and time, not malfunctioning clocks or broken photons

Isn't this generally true of physics??? That was a problem of Newtonian gravity or electrodynamics, even now. We have quantifiable effects with no comprehensible mechanism to explain them. GR didnt explain or dispel the action at a distance conundrum, it just changed the terms. Whether you view electromagnetic interaction as directly between particles or as a field phenomenon or wave interference doesnt really make a difference in this regard.
But does that mean that human intelligence should stop seeking to understand deeper levels of cause???
And clocks and photons do undergo change in our perceptual empirical reality without be broken.
Thanks

Austin0

Aug9-09, 06:45 AM

Originally Posted by Austin0
But it seems to me that this situation is not at all that simple. That it implies and requires additional assumptions:

1-- Of course,, the axiom that everything is purely a coordinate transform and there are no physical implications to any relative effects..

2--That a single system can be considered as two independent frames. The fact that they are physically connected , not possibly having any effect or bearing on the consequences.

3-- That contraction is a purely spatial phenomenon. Negating any consideration that it may ultimately be a temporal displacement and may have unforseen effects on the clocks involved when acceleration is involved..

4--. That acceleration is fundamentally different from inertial motion. Is absolute not relative.
__________________________________________________ __________________________
Hi Al68 I didn't mean to imply that you specificaly were making any kind of assumptions whatsoever. I was suggesting these particular ones as a partial list of implicit and neccessary assumptions for the theorem to be logically valid. Or in an other perspective ; if any of these (axioms, assumptions, hypotheses) are not true, then the validity of the theorem is in question.

=Al68;2298039]I'm not making the first two assumptions. For the third one, the clock hypothesis (that a clock is unaffected by proper acceleration) is an assumption, so any conclusion about the reading of a clock in GR/SR is only valid for clocks which are unaffected by proper acceleration.

I am not familiar with the origen or timing of the "clock hypothesis" as such ,but I do know that as of very recently in this forum,, there were knowedgeable people who expressed views that acceleration did in fact induce dilation.
At this point it appears to be more than a mere assumption, as it has so far been validated by empirical testing.
But if you look at #3 I was not talking about dilation due to acceleration but about contraction and the possibility of it having a temporal origin and unkown effects on clocks. Ie: The possibility that the apparent movement through space [closer to the front] was in actuality a movement through time.

For number 4, the time dilation between clocks in an accelerated frame is derived from relative coordinate acceleration alone, independent of proper acceleration, and does assume the clock hypothesis.
Well this is a somewhat different interpretation from what it seemed Sylas was saynig.
Which seemed to be that the difference was relative velocity between the front and the back. Which does imply #2
In light of your interpretation I have a question.
What is the difference btween proper acceleration in the system and coordinate acceleration as viewed from another frame?? If it is not empirically detectable as proper acceleration does giving it another name then make it observable?
If it is an actual phenomena why isnt it observed?? Simply because the magnitude is so slight as to be undetectable at our present state of technology??Or other????

Well, if a clock measures an elapsed time and stores the reading, the stored reading does not depend on any particular frame.

This is of course absolutely true wrt real world clocks. But we are talking about hypothetical readings which may not be so independant

austin0
But viewed as two separate frames with different velocities they would not only, not be stationary , they would be at different distances from each other depending on which end you were measuring from.
__________________________________________________ ________________________

I can't figure out what you mean here.

I think Sylas explained this nicely in the thread Invariance of c in ACCEL frames

Transforming coordinates from one frame to another is not "switching frames and assuming". Normally the transformed coordinates are correct by convention.

I completely agree , with regard to inertial frames.

Similar to the way that 1 inch transforms to 2.54 centimeters. Sure assumptions are made, but the claim that 1 inch is "really" 2.54 cm is based on convention, not scientific theory. The way clocks are synchronized in SR, and coordinate times transformed between frames is based on convention, for simple convenience. There is no law of physics that says you must do it that way, but it's convenient to use a commonly used convention

I dont think this analogy really applies. It is not a question of 1 in =2.54 cm but 4.67cm in S being equivalent to 7.9cm in S'

Isn't it actually the physics of the real world that determines the mathematical transform and the method of synchronization??
Thanks

Al68

Aug9-09, 08:25 PM

I am not familiar with the origen or timing of the "clock hypothesis" as such ,but I do know that as of very recently in this forum,, there were knowedgeable people who expressed views that acceleration did in fact induce dilation.
At this point it appears to be more than a mere assumption, as it has so far been validated by empirical testing.The clock hypothesis says that a clock is unaffected by proper acceleration, eg: applied force, not coordinate acceleration, which is just the coordinate rate of velocity change in a specified reference frame. Those other knowledgeable people must have been referring to coordinate acceleration, which doesn't affect a clock's rate directly, but is a measure of the rate of change of coordinate velocity in a specific frame, which does affect a clock's rate (in that frame).Well this is a somewhat different interpretation from what it seemed Sylas was saynig.
Which seemed to be that the difference was relative velocity between the front and the back. Which does imply #2The front and rear of an accelerating spaceship would be at two different (but not independent) velocities with respect to an inertial frame. This is a consequence of SR, not an assumption.In light of your interpretation I have a question.
What is the difference btween proper acceleration in the system and coordinate acceleration as viewed from another frame?? They are equal if the other frame is the instantaneously co-moving inertial frame. But since that frame is different from moment to moment, they are rarely used as reference frames in a scenario, except sometimes one of them. Proper acceleration depends on force applied (thrust) and the mass accelerated, and is the same value in any frame. Coordinate acceleration, like coordinate velocity, depends on reference frame.I dont think this analogy really applies. It is not a question of 1 in =2.54 cm but 4.67cm in S being equivalent to 7.9cm in S'But the reason for that is convention as well. It's based on the SR simultaneity convention. If the proper length of my spaceship is 20 ft long, and an observer in relative motion at 0.6c measures the spaceship length by using light signals, he would use the SR simultaneity convention to determine the location of each end, and determine the ends to be 16 ft apart at a specified moment. Assuming a constant invariant light speed, the length of the ship in the other frame is 16 ft by convention. Length contraction is a result of convention, and invariant light speed.Isn't it actually the physics of the real world that determines the mathematical transform and the method of synchronization??Only in the same way as the standard method for converting inches to cm. The SR simultaneity convention, like other conventions, isn't a law of physics.

Neither is the clock hypothesis. It's a standard for what type of clock is valid in SR/GR. And of course there is no perfect clock, but some are close enough to that standard to give results consistent with SR/GR within a very small margin of error.

These conventions are used in a physical theory not as claims, but as useful tools. Alternative conventions could be used, and the final results would be the same, if the theory using the other conventions was otherwise equivalent to SR/GR.

Ich

Aug10-09, 04:46 AM

In a classical interpretation, wouldn't it be said that; falling objects in a gravitational field loose potential energy while gaining kinetic energy or momentum [acceleration]
Of course. I'm sloppy most of the time.

But as I understand GR the concept of acceleration does not apply in this situation and the path remains strictly inertial. If this is the case why would it be consistant to consider a photon gaining energy through translation through a potential gradient???
What is gravitational potential? If you look at it closely, it is not some local property of space. You can't measure the potential at any position.
Potential is an expression for a relation: the potential difference between two points is a number that tells you, for example, how much more energy a photon will have when measured at point 2 as when measured at point 1.
This is exactly how GR works also: there are no local circumstances that change clocks or photons. They always work fine.
Instead, GR describes the relation of spacetime at one event to spacetime at another event, with explicit predictions of how this relation shows up in measurements.
Generally, the relation is complex and path dependent.
In weak fields, at low speeds, however, the relation can be expressed as a single number. This number corresponds to potential in Newtonian gravity.

When light gains energy, it doesn't get faster, however.

Austin0

Aug12-09, 06:55 AM

=Ich;2303278]

What is gravitational potential? If you look at it closely, it is not some local property of space. You can't measure the potential at any position.
Maybe I am once again misunderstanding but I thought that, as abstract constructions , the basis of both GR and electrodynamics was exactly that; assigning local values to points in the coordinate space? That those values [scalars, vectors, tensors etc]. were determined by the global conditions but were still local properties of space.
It is understood that you cant directly measure gravity at all

This is exactly how GR works also: there are no local circumstances that change clocks or photons. They always work fine.
Why do you keep making comments like this implying that I am suggesting that one clock is right or another is broken???

When light gains energy, it doesn't get faster, however
Does this mean the measured velocity ,both empirically and theoretically, is invariiant , in this context, the same up and down the potential gradient???
Thanks

Austin0

Aug12-09, 07:42 AM

=Al68;2302912] ]
The front and rear of an accelerating spaceship would be at two different (but not independent) velocities with respect to an inertial frame. This is a consequence of SR, not an assumption .

Subtle distinction there between different and independant

originally austin0
__________________________________________________ ________________________
In light of your interpretation I have a question.
What is the difference btween proper acceleration in the system and coordinate acceleration as viewed from another frame??

They are equal if the other frame is the instantaneously co-moving inertial frame. But since that frame is different from moment to moment, they are rarely used as reference frames in a scenario, except sometimes one of them. Proper acceleration depends on force applied (thrust) and the mass accelerated, and is the same value in any frame. Coordinate acceleration, like coordinate velocity, depends on reference frame.

I understand the definitions of proper and coordinate acceleration. That was not my question. If acceleration of a frame results in dilation what difference does the semantical distinctions make with regard to its observation from another inertial frame.
Ie: Whether you call it proper acceleration or coordinate acceleration or consider it a velocity differential due to acceleration,,, why is it not detectable in the acceleration testing performed so far???

original quote austin0
__________________________________________________ ________________________-
I dont think this analogy really applies. It is not a question of 1 in =2.54 cm but 4.67cm in S being equivalent to 7.9cm in S'

But the reason for that is convention as well. It's based on the SR simultaneity convention. If the proper length of my spaceship is 20 ft long, and an observer in relative motion at 0.6c measures the spaceship length by using light signals, he would use the SR simultaneity convention to determine the location of each end, and determine the ends to be 16 ft apart at a specified moment. Assuming a constant invariant light speed, the length of the ship in the other frame is 16 ft by convention. Length contraction is a result of convention, and invariant light speed.Only in the same way as the standard method for converting inches to cm. The SR simultaneity convention, like other conventions, isn't a law of physics.

I think we completely disagree on this one. The Lorentz math is no more a convention than the inverse square proprtionality in gravity and electrostatics. There is no other possible expression. This is a description of fundamental aspects of reality and physicists of Andromeda would inevitably discover the same expressions although undoubtably with different conventional units.

These conventions are used in a physical theory not as claims, but as useful tools. Alternative conventions could be used, and the final results would be the same, if the theory using the other conventions was otherwise equivalent to SR/GR.

Thanks

Ich

Aug12-09, 09:51 AM

Maybe I am once again misunderstanding but I thought that, as abstract constructions , the basis of both GR and electrodynamics was exactly that; assigning local values to points in the coordinate space?
GR is formulated via local quantities, the curvature. Those quantities cannot be measured strictly locally, by their very nature you need to survey some finite region to measure them.

Also with EM, there are local quantities that define the field at each point. But these are locally measurable.

And the point I'm trying to drive home is that all those locally measurable quantities are totally independent of these local GR quantities. Local curvature doesn't influence the local E-Field in the least, both are independent by their very mathematical definition - where vectors and tensors "live in the tangent space".
Does this mean the measured velocity ,both empirically and theoretically, is invariiant , in this context, the same up and down the potential gradient???
As long as they are measured in a local free falling frame: yes.

Al68

Aug13-09, 12:46 AM

I understand the definitions of proper and coordinate acceleration. That was not my question. If acceleration of a frame results in dilation what difference does the semantical distinctions make with regard to its observation from another inertial frame.
Ie: Whether you call it proper acceleration or coordinate acceleration or consider it a velocity differential due to acceleration,,, why is it not detectable in the acceleration testing performed so far???I'm not sure I understand what you mean by "not detectable", but the difference between proper acceleration and coordinate acceleration is not semantical. The coordinate acceleration of any object can be made equal to any arbitrary value simply by the choice of a suitable reference frame. I think we completely disagree on this one. The Lorentz math is no more a convention than the inverse square proprtionality in gravity and electrostatics. There is no other possible expression. This is a description of fundamental aspects of reality and physicists of Andromeda would inevitably discover the same expressions although undoubtably with different conventional units.Length contraction relies on not only the SR simultaneity convention, but the invariance of the speed of light, which is considered a law of physics. When I said that length contraction was based on convention, I should have said that the specific example (proper to coordinate length ratio) was based on convention, not the phenomena of length contraction itself. My bad.

Austin0

Aug14-09, 06:52 AM

Originally Posted by Austin0
I understand the definitions of proper and coordinate acceleration. That was not my question. If acceleration of a frame results in dilation what difference does the semantical distinctions make with regard to its observation from another inertial frame.
Ie: Whether you call it proper acceleration or coordinate acceleration or consider it a velocity differential due to acceleration,,, why is it not detectable in the acceleration testing performed so far???

=Al68;2307175]I'm not sure I understand what you mean by "not detectable", but the difference between proper acceleration and coordinate acceleration is not semantical. The coordinate acceleration of any object can be made equal to any arbitrary value simply by the choice of a suitable reference frame.

I will try to express myself more clearly. I was not suggesting that the difference between coordinate and proper acceleration was a matter of semantics.

You have a singular accelerating system and a unique set of observations as recorded in the system and an inertial frame. This is an unambiguous situation. Time dilation is either detected or it isnt as determined by comparison of proper elapsed time between the accelerated clocks and the inertial clocks after acceleration.
According to the actual real world tests performed so far to my knowledge,,,, there is no additional dilation due to acceleration. The dilation that has been recorded is totally accounted for by the dilation due to relative velocity. Ie: Due to the instantaneous velocities but with no additional factor due to the change in velocities.
This theorem posits that there is no dilation due to proper acceleration. There is no dilation due to coordinate acceleration. BUT there is additional dilation taking place due to the velocity differential resulting from acceleration.
That is what I meant about semantics. Simply calling it dilation due to a differential from [B]acceleration doesn't alter the fact that so far it is not detected.
I ,of course ,,cannot say that this is neccessarily true and is not simply a result of testing limitations etc etc. I also am taking the conclusions derived by the various mathematicians as valid without being able to perform the calculations myself. But can you simply dismiss the data in favor of a theoretical hypothesis???
Thanks

Austin0

Aug14-09, 07:22 AM

=Ich;2306276]GR is formulated via local quantities, the curvature. Those quantities cannot be measured strictly locally, by their very nature you need to survey some finite region to measure them.

OK this makes sense ,,,I wouldn't expect to be able to directly measure the field itself.

And the point I'm trying to drive home is that all those locally measurable quantities are totally independent of these local GR quantities. Local curvature doesn't influence the local E-Field in the least, both are independent by their very mathematical definition - where vectors and tensors "live in the tangent space".
Vectors and tensors may live in "tangent space" but clocks dont. SO I dont follow how these local measurements can be totally independant of the field or curvature either. I thought particles were totally effected by the curvature and local quantities both in there paths and periodicity.
___________________________
Previous austin0
Does this mean the measured velocity ,both empirically and theoretically, is invariiant , in this context, the same up and down the potential gradient???
___________________________

As long as they are measured in a local free falling frame: yes

Do you know of any actual tests done either from static locations at differing G altitudes or actual free fall tests????

Ich

Aug14-09, 03:16 PM

I thought particles were totally effected by the curvature and local quantities both in there paths and periodicity.
See, that's why I keep reminding you not to think of broken clocks. A clock's "periodicity" is in no way effected bv local quantities. The best mathematical representation of "ticking rate" is indeed a vector (four-velocity), and as such lives in tangent space. Comfortably, I am told.

It's different with the path: local curvature defines how vectors, tensors and such change when being "transported" from one event to another. "Transport" can be a real transport, like moving a gyroscope around and observing how its axis - a vector - changes. Or a mathematical concept, like shifting A's four velocity through curved spacetime to the position of B's four velocity. That's the only way to compare vectors in GR, you have to bring both together, and it does matter how you do that. If the comparison shows that both don't point in the same direction: that's called time dilation.
Do you know of any actual tests done either from static locations at differing G altitudes or actual free fall tests????
I don't know any tests of light speed under awkward circumstances. But GPS, for example, depends on light behaving exactly like GR says, which, in turn, should coincide with what I say.

Al68

Aug15-09, 01:11 AM

According to the actual real world tests performed so far to my knowledge,,,, there is no additional dilation due to acceleration. The dilation that has been recorded is totally accounted for by the dilation due to relative velocity. Ie: Due to the instantaneous velocities but with no additional factor due to the change in velocities.
This theorem posits that there is no dilation due to proper acceleration. There is no dilation due to coordinate acceleration. BUT there is additional dilation taking place due to the velocity differential resulting from acceleration.
That is what I meant about semantics. Simply calling it dilation due to a differential from [B]acceleration doesn't alter the fact that so far it is not detected.
I ,of course ,,cannot say that this is neccessarily true and is not simply a result of testing limitations etc etc. I also am taking the conclusions derived by the various mathematicians as valid without being able to perform the calculations myself. But can you simply dismiss the data in favor of a theoretical hypothesis???I see your point here. And you're right. What you say is not only supported by the data, but by theory as well. That is the crux of the clock hypothesis.

But semantically, I would disagree with the way you word this: "There is no dilation due to coordinate acceleration", simply because, by definition, this is the equivalent of saying: "There is no dilation due to coordinate velocity changes", which you point out, is not true.

Gravitational time dilation is both predicted by theory and supported by data, there is no contradiction. But whether the detected dilation is "gravitational" or "velocity based" depends on which coordinate system we choose. It's the same effect either way, both in theory and practice. Using the phrase "gravitational time dilation" is just a convenient way to explain the dilation of clocks which are "stationary" in an accelerated frame, but is the same dilation that would be referred to as "velocity based" when observed from an inertial frame.

Austin0

Aug18-09, 06:53 AM

--------------------------------------------------------------------------------
austin0
I thought particles were totally effected by the curvature and local quantities both in there paths and periodicity.

=Ich;2309199]See, that's why I keep reminding you not to think of broken clocks. A clock's "periodicity" is in no way effected bv local quantities. The best mathematical representation of "ticking rate" is indeed a vector (four-velocity), and as such lives in tangent space. Comfortably, I am told.

It's different with the path: local curvature defines how vectors, tensors and such change when being "transported" from one event to another. "Transport" can be a real transport, like moving a gyroscope around and observing how its axis - a vector - changes. Or a mathematical concept, like shifting A's four velocity through curved spacetime to the position of B's four velocity. That's the only way to compare vectors in GR, you have to bring both together, and it does matter how you do that. If the comparison shows that both don't point in the same direction: that's called time dilation._________________________________________ ___________________________________
__________________________________________________ _________________________

See if I have this right. A clock at a specific location has a defined four-vector (periodicity). Translation to another location and comparison of four-vectors with a resident clock reveals that they dont point in the same direction =time dilation.

Is it not true that once colocated for comparison they will then have vectors that point in the same direction? That the time dilation is revealed by the difference in elapsed proper time , the clock reading. That the change in the moved clocks vector is not a SR result of its motion,, but is an incremental change due to the local curvature. Ie: measuring and responding to the local condition in the same way your gyroscope did.

I must be seriously misunderstanding here but I thought that tensors did not move but were constant values with fixed locations within the overall field??????

austin0___________________________________________ ______________________________
Do you know of any actual tests done either from static locations at differing G altitudes or actual free fall tests????
__________________________________________________ _____________________

I don't know any tests of light speed under awkward circumstances. But GPS, for example, depends on light behaving exactly like GR says, which, in turn, should coincide with what I say

Good idea. But from what I have been able to find it was not explicit if the transit time compensation was calculated at exactly c or not. But it did seem to be a single figure which should mean that the time from earth to satellite is the same as satellite to earth.
Ill keep looking unless you have more defintie info.
Thanks

Ich

Aug21-09, 09:48 AM

See if I have this right. A clock at a specific location has a defined four-vector (periodicity). Translation to another location and comparison of four-vectors with a resident clock reveals that they dont point in the same direction =time dilation.
That's what I wrote, but
1. my description is not entirely correct (in fact it's wrong, but ok for the purpose),
2. I meant "difference in clock rate" instead of "time dilation".
Is it not true that once colocated for comparison they will then have vectors that point in the same direction? That the time dilation is revealed by the difference in elapsed proper time , the clock reading. That the change in the moved clocks vector is not a SR result of its motion,, but is an incremental change due to the local curvature.
All true. But like motion, that is a change relative to some other observer. While there is no locally defined "absolute direction" of said vector, just like there is no absolute velocity.

I must be seriously misunderstanding here but I thought that tensors did not move but were constant values with fixed locations within the overall field?
If you take the spin direction of a gyroscope as an example: that can be thought as fixed to the gyroscope's position and moving with it. Generally, we're talking about this (http://en.wikipedia.org/wiki/Parallel_transport) abstract mathematical procedure. Pure geometry, nothing to do with physics - except that SR and GR are also pure geometry, the latter at least with a coupling to mass.

Quentin

Aug25-09, 01:25 PM

I have been following with great interest the discussions in this thread, the comments on the interaction of gravity with light being of particular interest. I wonder if the following possibility has ever been considered:

Suppose that the presence of a gravitational field resulted in a modification of the product of the electric permittivity ε and the magnetic permeability μ of free space, which is the quantity which determines the velocity of light in free space according to the relation c^2 = 1/( ε. μ ) .

Suppose further that this resulted in a refractive index in a gravitational field which was a function of that field, possibly even a linear function. That would mean that the deflection of a light beam could be attributed to refraction by a changing refractive index, rather than directly to a gravitational force.

All the relevant equations could be changed by the inclusion of suitable factors which linked the value of refractive index to the gravitational field, thereby modifying the value of c to produce the same end result in every case. One major difference would be that it would no longer be necessary to deal with the distortion of space-time, because the resulting deflections could then be attributed to effects caused by changes in the refractive index of free space due to gravitational fields.

This interpretation would not for example change the result of the Pound-Rebka Harvard Tower experiment. The time-dilation produced by the gravitational red-shift would instead be interpreted as a change in the value of c, caused by the change of the refractive index, (due to the gravitational field) between the source and emitter, leading to the mismatch between the photon energies.

Would the concept of ‘gravitational time dilation’ even be necessary if what was really happening were changes in the value of c caused by a variable refractive index. The term ‘gravitational red-shift’ however, would still be entirely appropriate, since the result would still ultimately be due to the gravitational field, but by modification of the refractive index rather than by ‘time-dilation’.

Ich

Aug25-09, 02:19 PM

Would the concept of ‘gravitational time dilation’ even be necessary if what was really happening were changes in the value of c caused by a variable refractive index.
Of course. The idea of an effective refraction index is not new, a quick search gave me this paper (http://homepages.ecs.vuw.ac.nz/~visser/Seminars/Conferences/refractive-index-2.pdf).
GR can't be reduced to a scalar theory, as the refractive index would be. So that's not an intrpretation, it's a new theory which contradicts some experiments (I don't know which at the moment, you can look it up in MTW's Gravitation).
Even in cases where a scalar quantitiy is enough, it is not evident how a refractive index should produce real time dilatation, the one accumulating over measurement time.

Quentin

Aug26-09, 09:02 AM

Thanks for the quick reply and the reference. My comment on the 'gravitational time dilation' was only in the context of the Harvard Tower experiment. Just to clarify the gist of my argument:

Suppose that a rocket containing an atomic clock was accelerated on an outward journey and was then decelerated to return to the starting point. If the refractive index was affected as suggested by the gravitational fields generated in the acceleration/deceleration periods, then the clock frequency would be reduced for both those periods and would of course show a corresponding cumulative time dilation.

Ich

Aug26-09, 10:45 AM

Suppose that a rocket containing an atomic clock was accelerated on an outward journey and was then decelerated to return to the starting point. If the refractive index was affected as suggested by the gravitational fields generated in the acceleration/deceleration periods, then the clock frequency would be reduced for both those periods and would of course show a corresponding cumulative time dilation
But time dilatation is proportional rather to the total time you spend on the journey, not to the acceleration phases. You can't model this "SR" time dilatation with a local refraction index.
You can express time dilatation in static spacetimes with a single parameter, but I don't see how this would be due to a different refraction index. But as I said, the theory can't replace GR anyway.

Austin0

Sep4-09, 08:52 AM

It does: and this is what I describe above in the previous post.

Note that you cannot simply compare an accelerated observer with an unaccelerated observer, because in that case you also get an increasing velocity difference, and that dominates any time dilation.

However, if you have a long spaceship experiencing a constant acceleration at all points, it turns out that the front has slightly less acceleration than the back, and there is a time dilation between the front and the back of the ship... but no change in the distance between them, as measured by anyone on the ship. THIS is what turns out to be exactly analogous to the time difference of two observers at different altitudes in a gravitational field.

Cheers -- sylas

Hi sylas I am still thinking over this topic.
I did a work up of a hypothetical case but my math is rusty so I thought I would run it by you.
Inertial frame F
Accelerating System S'
rest L'= 1 km
a= 1000g= 10km /s^{2}

Range .6c ===> .7c
.7c-.6c =.1c = 3 x 10^{4}km/s

Time dt= (3 x 10^{4}km/s)/(10km/s) =3000 s

Contraction v_{i}=.6c ------- \gamma=1.25 --- = L'_{0}=.8 km
v_{f} =.7 -------- \gamma= 1.4 --- =L'_{1} =.71km

Difference in length over course of acceleration = .09 km
.09km/ 3000s = 3 x 10 ^{-5} km /s

relative velocity between front and back v_{fb}= (3 x 10 ^{-5} km /s) /(3 x 10 ^{5}km /s ) = 10^{-10}c
Additive average relative velocity between front and back = (.65+10^{-10})+ .65c = .65+ (1.7316 e^{-10} )

average velocity difference v_{d}= 1.7316 e^{-10} c
avg \gamma= 1 +( 2.9484 x 10 ^{-20} ) between front and back

Relative to inertial frame F ,,, S' avg v=.65c \gamma= 1.32
dt/1.32 = 3000/1.32 = 2,273 s = overall elapsed time on S'

2,273 / 1 +( 2.9484 x 10 ^{-20} ) = 6.782 x 10 ^{-17} s
elapsed time difference between back and front.

As I said I am rusty and could have easily dropped an exponent or counted all the zeros or 9's on the calculator screen wrong but does this seem in the ballpark???
Or is there some other fundamentally different way to calculate?
I assumed constant acceleration as observed in the inertial frame , of course the calculated (a) factor wouldn't neccessarily be healthy for humans but it made for smaller numbers
Thanks cia0

Quentin

Sep9-09, 10:55 AM

Silas:
I was notified that your reply to AustinO (the quote in message #64) pertained to a question that I raised in message #63 and indeed it does. I get the point about the acceleration on a long rocket being different at each end, because of time dilation over the length of the thing, due to the gravitational field which it generates being different from end to end.

Can you give me some idea of what the polar diagram for the field looks like? Surely it cannot have anything to do with the position of the propulsive force. Suppose for example the source of this force was situated at the centre of the rocket, rather than at the rear end, would that change the polar diagram of the gravitational field? I can't imagine that it would.

For example what would the field look like if the accelerating object was not a rocket but a spherical mass with the propulsive force being a point source at the centre of the sphere? Don't ask me how such an arrangement could be devised without a radial hole to the centre for the gas or the ions or whatever to escape and provide thrust, but let's assume that it is in the realms of mythical frictionless surfaces and perfectly reflecting ones along with the other mythical assumptions which are made to illustrate a basic principle.