- #36
Ich
Science Advisor
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You can't, and that's because you're not talking about two different effects, but about two different descriptions of the same effect.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.And how could we tell the difference?
Ich said:You can't, and that's because you're not talking about two different effects, but about two different descriptions of the same effect.
...as measured with the clocks at the other location.A photon traveling from a region of high gravitational potential to a lower, is lowered in frequency. SLower periodicity. Dillated.
...as compared with photons coming from the other location.A clock traveling the same path is increased in frequency. Faster periodicity.
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.Austin0 said: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.
=Ich;2292368]...as measured with the clocks at the other location.
...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 .
Not really.SO does any of this clarify the question or make sense?
=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.
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.
=Ich;2296431]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
Maybe because it's a quite common one: the photons gain potential energy while falling, just like any other thing would.My original question was ,,,why was this the viewpoint they chose.
(in static spacetimes, like Schwarzschild)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?
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.Quantitatively I see what you are saying but isn't it significant as far as understanding the interrelationship between photons and gravity?
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.Austin0 said: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.
Well, if a clock measures an elapsed time and stores the reading, the stored reading does not depend on any particular 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.
I can't figure out what you mean here.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.
Transforming coordinates from one frame to another is not "switching frames and assuming". Normally the transformed coordinates are correct by convention.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.
=Ich;2297818]Maybe because it's a quite common one: the photons gain potential energy while falling, just like any other thing would.
(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.
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;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.
.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, if a clock measures an elapsed time and stores the reading, the stored reading does not depend on any particular frame.
.I can't figure out what you mean here
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
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).Austin0 said: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 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.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
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.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??
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.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'
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.Isn't it actually the physics of the real world that determines the mathematical transform and the method of synchronization??
Of course. I'm sloppy most of the time.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]
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.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?
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.=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.
Why do you keep making comments like this implying that I am suggesting that one clock is right or another is broken?This is exactly how GR works also: there are no local circumstances that change clocks or photons. They always work fine.
Does this mean the measured velocity ,both empirically and theoretically, is invariiant , in this context, the same up and down the potential gradient?When light gains energy, it doesn't get faster, however
.=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
.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
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.
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.
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.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?
As long as they are measured in a local free falling frame: yes.Does this mean the measured velocity ,both empirically and theoretically, is invariiant , in this context, the same up and down the potential gradient?
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.Austin0 said: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?
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.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.
=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.
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.=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".
As long as they are measured in a local free falling frame: yes
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.I thought particles were totally effected by the curvature and local quantities both in there paths and periodicity.
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.Do you know of any actual tests done either from static locations at differing G altitudes or actual free fall tests?
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.Austin0 said: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?
____________________________________________________________________________=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.
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
That's what I wrote, butSee 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.
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.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.
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.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?
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" .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.
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.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
sylas said: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