Special relativity and acceleration

[Ich]

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]

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]

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]

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.

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. 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.

For a detailed derivation, I'd recommend Einstein's own derivation, but I can't find it on the net with a cursory quick search.

 

[Austin0]

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]

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]

=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 can't 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]

=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 don't 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 isn't it significant as far as understanding the interrelationship between photons and gravity?
Thanks

 

[Ich]

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 isn't 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]

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 can't 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]

=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 doesn't 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]

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 necessary 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 isn't 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 don't 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]

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 #2

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.

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 don't 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]

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]

=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 can't 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]

=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 don't 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]

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]

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]

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 isn't 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 [Bvelocity[/B]differential from 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]

=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 don't 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]

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]

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 [Bvelocity[/B]differential from 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]

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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.

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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 don't 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?
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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]

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 don't 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 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]

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]

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 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]

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]

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]

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]

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.