Is the Changing Clock Rate in Relativity Directionally Dependent?

[JesseM]

Jesse as to your post 67- yes - I think Einstein would have disagreed with that - I think he had doubts as to the validity of SR - he said he did not think it would survive the test of time

When did he say this? Can you give me the quote? Since GR incorporates SR, do you think he had doubts about GR as well?

the CBR is certainly different in different frames

the CBR is not a law of physics. The moon is different in different frames too, do you think that violates the principle that all inertial reference frames are to be treated equal?

Moreover, i do not think he would say, as to the two synced clocks which I described, where one is put in motion, that the one in motion would measure the non moving clock to be running slow (at least by the same factor)

He would certainly say that in the inertial reference frame where the accelerated clock came to rest after accelerating, the non-accelerated clock which is not at rest would run slow. To say he would disagree with this is to say he would disagree with one of the most basic principles of relativity as understood by all physicists then and now, yet for some reason he never noticed that all physicists were interpreting relativity differently from him or never voiced this difference of opinion. It's completely ridiculous, in other words.

He Never said this - some authors do - others stop short of making this statement - we have never made this experiment - and until we make a freespace experiment that shows that a pion traveling at 0.99c relative to the Earth will measure Earth time to be slow

How would this experiment work, exactly? The statement that a pion would measure Earth time to be running slow is simply a statement about the coordinate system we choose to define as the pion's "rest frame" in relativity. If you use the Lorentz transform to go between our rest frame and the pion's, this is automatically true. Of course, the Lorentz transform has to be physically motivated, and the pion's coordinate system can be defined in a physical way in terms of measuring-rods and clocks at rest with respect to the pion (as Einstein defined different coordinate systems in his 1905 paper), but if you grant that moving rods will Lorentz-contract and moving clocks will slow down in the earth's rest frame, and if the pion uses these rulers and clocks to define its own rest frame and uses the Einstein synchronization procedure to synchronize its own clocks, then it's automatically true that the Lorentz transform will give the correct relationship between our coordinate system and the pion's, and therefore it follows logically that in the pion's rest frame the Earth clocks must be running slow and the Earth rulers are Lorentz-contracted. It's logically impossible that things could work otherwise, provided Lorentz-contraction and time dilation hold in the Earth's own rest frame.

I think the question should remain unresolved - after all, relativity works fine whether or not all frames are perfectly equal.

Uh, how do you figure? Wouldn't that obviously violate the first of the two basic postulates of relativity, which Einstein laid out at the start of section 2 of his 1905 paper?

In short - I think the symmetry you demand does not comport with actual time dilation - it is consistent with apparent time dilation, and there is complete symmetry as to contaction - but as I have said - there is not complete symmetry when only one of two clock have been accelerated

Let me get this clear--are you arguing that even given the current known fundamental laws, which are definitely Lorentz-symmetric, you don't think there is a symmetry between the way the laws of physics work in each reference frame? If so you're talking obvious nonsense, the latter follows mathematically from the former, it's logically impossible that you could have Lorentz-symmetric fundamental laws and yet the laws of physics would not work exactly the same in all the inertial frames given by the Lorentz transformation.

But part of the problem is that you are maddeningly vague about what you mean by "symmetry", you often use this term in ways that totally depart from the standard meaning. Did you read and understand my post #27? Here it is again:

Your concept of "symmetry" is too vague. The symmetry is in the laws of physics as seen in different frames, but the specific situation you describe involving the two clocks is not symmetrical, because different frames disagree about whether the two clocks were synchronized at the moment before one accelerated (or the moment immediately after one accelerated, if you assume the acceleration was instantaneous). A symmetrical physical situation would be one where you could look at the situation in one frame, then exchange the names of the two clocks, and possible flip the labels on your spatial directions (exchanging left for right, for example), and then you'd have an exact replica of how the original situation looked in a different frame. For example, if clock A is at rest in one frame and B is approaching it at constant velocity from the right, and both clocks read the same time at the moment they meet, then if you switch the names of A and B and flip the left-right spatial direction, you have a replica of how the original scenario would have looked in the frame where B is at rest and A is approaching it at constant velocity from the left. But in any situation where the clocks read different times when they meet, there's no way you can exchange the names and get a replica of how the original situation looked in a different frame. Relativity does notdemand that specific physical situations be "symmetrical" in this way, only that the fundamental laws of physics be symmetrical (ie work the same way) in different frames.

If you understand this distinction, do you see why your comment about the CBR, for example, is a non sequitur?

 

[JesseM]

Pervect - When we attempt to remove one of two orbiting synchronized clocks to the top of one of the towers - as per jesse's query,do you think it will thereafter run faster or slower than the clock that remained in orbit,
(I know the math is messy - just looking for a conceptual answer if you have one).

There's no need for any tricky math here, because regardless of which scenario you look at:

1) two clocks are orbiting next to each other and then as they pass the top of the tower one instantaneously accelerates to come to rest on it while the other continues in its orbit

or

2) the two clocks are next to each other on the top of the tower and one instantaneously accelerates to go into orbit

...the paths of each through spacetime after this instantaneous acceleration will be exactly the same, and it's only the proper time along the two paths between the point in spacetime where they depart each other and the point in spacetime where they reunite that determines which has elapsed less time.

 

[Hurkyl]

As A passes through B, C, ..., Z, it will observe each of them as running slowly.

Hurkyl - i don't follow what you are saying - in my post 59 I intended to say that the A clock reads the time by looking at the visible counter attached to each tower B, C, D, ...Z the tower clocks always get progressively further ahead. This is not the same as making a measurement using the standard two clock method to determine apparent time dilation in a relatively moving frame - its a simple reading of the counter on the fly.

Yes, it's different -- one of my points was to make this clear. All you have done is to provide a convenient way for the orbiting clock to measure time according to the Earth frame. (As opposed to its own frame)



I was also leading up to a second hypothetical example. You seem to suggest that because the two clocks pass repeatedly, we can decide which time dilation is "real" and which is "apparent". However, consider this:

We just have the orbiting clock A and the tower clock B. However, B is mounted on an ultra-high speed elevator. When A is far away from B, we rapidly move B up and down the tower, and stop when A draws near from the other side.

In this scenario, we will find that B gains time on A after every orbit. So, your criterion would say that the fact B sees A run slow is the "real" time dilation, whereas the fact A sees B run slow is merely "apparent".

(Or we could set up a network of tower clocks that all do this. Then, B will see the time on consecutive towers lagging behind)


However, the time periods where A and B are near each other are exactly identical situations in both your and my scenarios.

In one scenario, A seeing B run slow was the "real" one.
In the other scenario, B seeing A run slow was the "real" one.
Yet, both scenarios are exactly identical during the interval in which the clocks can see each other.

Thus, your concept of "real" is ill-defined -- it is entirely inapplicable to time dilation (which is "local"), but instead a statement about the global behavior of a system.

Furthermore, I cannot figure out how you would be able to make a determination of "real" and "apparent" in a situation where there is no recurrence.

 

[yogi]

Hurkyl - I am obviously not making the point clear - in the experiment with one clock in orbit and the other fixed on the tower - there is a difference between the clocks when A flies overhead - each reads the other clock - there is an actual time difference - so best we distinquish this from what is traditionally referred to as time dilation - an experiment made between two objects moving at relative unifor velocity v - that requires two clocks in the measuring frame and it presupposes that the two inertial frames are identical - in that case the thought experiment leads to reciprocal measurments of slowing in the other frame.

So let's call my experiment intrinsic time difference - it corresponds to the time difference between the clock rate on Earth and the clock rate of high speed particles - this is a one way experiment - it is the same as the difference between the clocks when we speculate on space travel to a distant star - a one way trip - there is no requirement that the traveler return to Earth to reap the benefits of slowing time during the one way excursion. Unfortunately we are not able to make such experiments - but we can take note of the slowing of time in GPS satellites

In your up and down elevator experiment - yes - I would say that you could wind up with varying results - a common example in the literature involves two satellites - one in polar orbit - one in an equatorial orbit - during different times each will see the other as standing still - or having a varying relative velocity - it is not possible to synchronize 3 GPS satellite clocks with each other without a common reference frame

 

[JesseM]

Hurkyl - I am obviously not making the point clear - in the experiment with one clock in orbit and the other fixed on the tower - there is a difference between the clocks when A flies overhead - each reads the other clock - there is an actual time difference - so best we distinquish this from what is traditionally referred to as time dilation - an experiment made between two objects moving at relative unifor velocity v - that requires two clocks in the measuring frame and it presupposes that the two inertial frames are identical - in that case the thought experiment leads to reciprocal measurments of slowing in the other frame.

But pervect seemed to confirm my suspicion that a global coordinate system where an orbiting clock is at rest throughout the orbit cannot be called an "inertial frame"--in GR an object moving on a geodesic is only moving inertially in a local sense, not a global one. So there is no reason that the prediction of special relativity that two clocks moving inertially will each observe the other to be running slower in their own reference frame should be extended to general relativity in the case of two objects moving on geodesics (although the tower clock in your example actually isn't moving on a geodesic since it's not in freefall, but you could fix this by replacing the tower clock with a clock that is flying vertically away from the Earth at the time it passes the orbiting clock, then slows down and falls back towards the earth, passing the orbiting clock again on the way back down). In general relativity, I don't think the notion of each object having its own unique global "reference frame" even makes sense any more, so there wouldn't be a well-defined answer to the question of how fast one clock "observes" another distant clock to be ticking any more. Given a particular choice of global coordinate system you could answer this, but I don't think there's any "standard" choice of which coordinate system you're supposed to use for a given object moving on a geodesic, unlike in SR where there is a standard way to construct the coordinate system that is defined as the "reference frame" of an object moving inertially.

 

[yogi]

Jesse - Your post 71 - you obviously have a very different take on what Einstein would have said were he alive today, than I do - I am not going to bother answering all the your assertions because it leads too far astray - except to say - yes as to the fact that he (Einstein) had the same opinion on GR as SR - he stated only a few days before his death that he could not think of a single one of his works that would survive the test of time - if you doubt it - you should read more - you have a very narrow view of things -

I gave an answer to your question regarding the possibility that all inertial free float frames may not be idential - now you want to convince me its absurd - find one real experiment that demonstrates two inertial frames in relative motion measure the same dilation in the other frame - I will look at it - until then, I will retain my skepticism. Absolute equivalence between inertial frames is not necessary to any experiment result - at least not any I am aware of.

 

[JesseM]

Jesse - Your post 71 - you obviously have a very different take on what Einstein would have said were he alive today, than I do - I am not going to bother answering all the your assertions because it leads too far astray - except to say - yes as to the fact that he (Einstein) had the same opinion on GR as SR - he stated only a few days before his death that he could not think of a single one of his works that would survive the test of time - if you doubt it - you should read more - you have a very narrow view of things -

Then why didn't you answer my request to provide a specific quote? In any case, the question of whether the ultimate laws of physics are Lorentz-invariant is separate from the question of whether laws of physics such as time dilation must work the same way in different inertial frames given Lorentz-invariant laws--see below.

I gave an answer to your question regarding the possibility that all inertial free float frames may not be idential - now you want to convince me its absurd - find one real experiment that demonstrates two inertial frames in relative motion measure the same dilation in the other frame - I will look at it - until then, I will retain my skepticism. Absolute equivalence between inertial frames is not necessary to any experiment result - at least not any I am aware of.

So do you deny my claim that any laws of physics that have the mathematical property of Lorentz-invariance must automatically behave the same way in all the frames provided by the Lorentz transformation? Please answer this question yes or no. If you're just suggesting that we may find phenomena governed by new, non-Lorentz-invariant laws, fine, that's an experimental possibility. But if you're denying my claim above, this is analogous to denying that 1+1=2 or that the derivative of x^2 is 2x, we don't need experiments to prove beyond a shadow of a doubt that you're talking nonsense.

Also, are you ever going to address my point about your confusion between symmetry in how the laws of physics work in different frames vs. symmetry in how particular configurations of matter and energy look and behave in different frames? Like I said, there is no requirement that particular configurations look the same in different frames (as in your point about the CMBR, or about the situation where two clocks approach each other after one accelerates), only that the laws governing how they behave work the same way in each frame (for example, in the clock situation, the clock moving faster in a given frame will always be the one ticking slower, although the clocks may not have been synchronized in this frame to begin with so the one that ticks slower won't necessarily be the one that's behind when they meet).

 

[Hurkyl]

I'm trying to respond, but I'm having trouble pinning down exactly what you're saying.

But I did notice this:

what is traditionally referred to as time dilation - an experiment made between two objects moving at relative unifor velocity v - that requires two clocks in the measuring frame and it presupposes that the two inertial frames are identical

This is incorrect. Time dilation can be measured with nothing but light signals.

In fact, to even begin to talk about "two clocks in the same frame", one must be able to state what that means -- this is done via some protocol with light signals.

If we assume Minowski space from the start, we can talk about clocks with parallel worldlines -- but how do you experimentally determine if two clocks are in the same frame? With light signals! (Or, something relying indirectly on electromagnetism phenomena, such as a ruler)

 

[yogi]

Hurkyl: Here is what Resnic says at page 77 of Introduction to Special Relativity: "There are shorthand expressions in relativity which can easily be misunderstood...Thus the phrase "moving clocks run slow" means that a clock moving at a constant velocity relative to an inertial frame containing synchronized clocks will be found to run slow when timed by those clocks. We compare one moving clock with two stationary clocks. Those who assume that the phrase means anything else often encounter difficulties."

 

[yogi]

Hurkyl - Follow up to what i was trying to get across. So when we make these sorts of measurments using two synchronized clocks, we are determining apparent time dilation. And assuming arguendo, that the two frames are equivalent, each frame could carry two clocks and each would measure a clock in the other frame to be running slow. This is what I referred to as a traditional method of establishing time dilation.

The two frames would be equivalent if they were both initally at rest and then given equal accelerations until they reached a uniform relative velocity v - thereafter each frame would measure the apparent slowing of time in the other frame - when they are all returned to the same frame by uniform decelerations - the clocks should read the same (Case 1)

(Case 2) Contrast that with what occurs when only one of two synchronized clocks is accelerated to a uniform velocity v relative to the other as per Einsteins description in Part 4. When the two clocks are brought together they will not read the same - there is something different about the rate at which things occur in the frame which has been accelerated - or about the clock which has undergone acceleration - the two experiments give different results - in the second case there is a residual that can be measured - not so in the first case.

Now

 

[Peterdevis]

Since I won't be able to follow pervects mathematical solution to the removing of a clock in orbit - I will propose the following - initially we have 3 clocks J, K, and L on the Earth - at the top of the tower - then we put two (J and K) in the same satellite and launch them into orbit - they should both run at the same speed and slower than the third clock (L) left atop the tower - then we decelerate (K) so that it comes to rest on the tower - it should now run at the same rate as the stay behind clock (L) since it has been returned to the original frame where it was synchronized

On the other hand, from the perspective of the J clock still in orbit - (K) has undergone an acceleration, and it should now run slower than J while J is in orbit. So we have returned to the original puzzle - The orbiting clock J runs slower than either K or L on top of the tower - but K should run slower than the orbiting clock J.

No, at the end K and L run at the same rate but clock K(pe 11:55) runs after on L (12:00). J will run slower then K and L not (only) because of its velocity but because the clock is constant accelerating (making a orbit).
So there is no paradox!

 

[Hurkyl]

yogi -- I figured out why I'm having trouble figuring out what you're saying: it's the same problem you chronically exhibit.

"two synchronized clocks" -- you've not specified how they're synchronized. (Is it that they always agree in a certain coordinate chart? Which one? Or are they synchronized by some light signal protocol? Or something else?)


"frames are equivalent" -- what do you mean by 'equivalent'? Given the context, the most appropriate meaning I could imagine is that it's referring to the hypothesis that the laws of physics remain identical in all reference frames... but your later usage disagrees with this interpretation.


"if they were both initally at rest" -- you've not specified how they're determined to be at rest. (Are you determining this according to a certain coordinate chart? Which one? Or something else?)


"given equal accelerations" -- how, specifically? First off, one cannot "accelerate a frame" -- a frame is simply a (nice) map from coordinates to space-time events. We use the word "accelerated frame" to denote a frame for which a particle that is always located at the spatial origin would not be traveling inertially.

Presumably accelerating a frames suggests accelerating some of the clocks too -- how is this going to be done? You've suggested in the past that you give all of the clocks "equal accelerations", but doing such a thing is "bad". (e.g. if I give the front and back of a train equal accelerations, as measured by the inertial frame in which it started at rest, it will rip apart)

When the two clocks are brought together they will not read the same - there is something different about the rate at which things occur in the frame which has been accelerated - or about the clock which has undergone acceleration - the two experiments give different results - in the second case there is a residual that can be measured - not so in the first case.

This is simply a property of their trips. One trip simply has a greater duration than another.

Incidentally, what you describe is only useful when the clocks start together and end together. It has absolutely no bearing on any scenario that does not satisfy this condition.

For example, this reasoning let's you say absolutely nothing about two clocks that are simply passing by each other. Each clock will observe the other dilated, but you have absolutely no justification for calling one "real" and the other "apparent".

 

[yogi]

Hurkyl - It should be obvious to what I am referring

Two synchronized clocks in the same frame (means at rest wrt each other) - used to measure a clock in a second frame that moves with uniform relative velocity v - The clocks are in sync in the frame at which they are at rest

Equivalent frames - any property you would measure in one frame would be the same as the property you would measure in another - Since I am not sure that all inertial frames are equivalent - then equivalent is a broader term

We can identify a frame with a spaceship - everything contained in the spaceship is a frame - included in the clocks on board -

For your edification ..the nomencalture "accelerating frames" is common in the literature
Take a look for example at Spacetime Physics - first edition at page 12
"...such an accelerated frame is a non inertial frame"

Things are at rest in the same frame when they are not moving wrt to each other

Now to your conclusions:

To say that "the time difference is a property of their trips" is to say nothing - one clock has not moved - only one clock took a trip

Only useful when they start and end together - how do you reach that conclusion - in reality, the only experments that start and end together are those like the GPS ones I described - or flying clocks around the world and bringing them back to the same place - but most of the experiments involve a particle that starts at one place in the Earth reference system and ends at a different. These are the experiments that show the most significant differences in time loss or gain

Finally - I have never labeled two clocks just passing each other as you have suggested ...one real and the other apparent - they are both apparent - all measurements made on the fly (while the clocks are in relative uniform motion) are apparent - but they may not measure the same rate on the passing clock - that would only be the case if all interial frames are not equivalent. That is the subject I have addressed above -

 

[yogi]

Peterdevis - a clock in orbit is in a freefloat frame - it feels no acceleration --- its rate is only determined by its velocity and its height - I proposed that the tower is at the same height as the height of the orbit - so there is no altitude correction required - all that is left is velocity -J and K run slower than L because J and K have been given a velocity relative to the tower, and all GPS clocks in orbit run slow because they have a velocity relative to the Earth frame in which they were originally synchronized.

If its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper, then when K decelerates, for example after one orbit, to reduce his velocity to zero ground speed to land atop the tower - it will appear from the standpoint of J that K has been put in motion - the question posed is whether, if J is later returned to the tower after many orbits - will there be a difference in the J and K clock readings that reflects the fact that K should be running slower than J during those orbits - whereas from the standpoint of L and K it is J that should show a slower time consistent with its orbital velocity

 

[Peterdevis]

f its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper,

Just like Einstein in 1905 you don't know anything about GR. But in difference with you Einstein understands that when you only can deal with inertial frames (where there is no good definition for) you' ve got to deal with a lot of paradoxes. He bypassed this problem by inventing GR.
So here is my suggestion: Study GR

a clock in orbit is in a freefloat frame - it feels no acceleration --- its rate is only determined by its velocity and its height

This is the only way you can describe it in SRT, but it is a simplification and it gives a lot of misunderstanding (this discussion is a fine example).
But there is a fundamental difference between a orbiting clock with a speed v (velocity is a vector) and a clock moving in een inertial frame with speed v. The first is moving in a curved spacetime, the second in a flat spacetime.

 

[JesseM]

If its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper

I'm pretty sure it's not. The satellite's motion is locally inertial, but I don't think there's any single unique global coordinate system that qualifies as an "inertial frame" in the sense that the satellite is at rest throughout its entire orbit in this coordinate system, and where you are permitted to assume that all the same rules that Einstein laid out for inertial frames in his 1905 paper would also apply in this coordinate system (for example, where the time dilation of the clock on the tower would simply be a function of its velocity in this coordinate system).

Can anyone confirm that an object moving on a geodesic in curved spacetime does not have a non-local "inertial rest frame" in this sense? Pervect? Hurkyl?

 

[RandallB]

If its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper,

No it's not an inertial frame in that sense - it's more like the traveling twin that continually departs and returns. Reversing frames at full speed instantly at each turnaround to return back to earth, just not stopping at the return to Earth (The tower); but continuing away again for another round trip of switching reference frames for each orbit to get back again. (If you want, wait till one of the big guys say the same thing.)
RB

 

[Hurkyl]

In Spivak, a frame is nothing more than an ordered basis for a vector space.

If we have a collection of (enough) everywhere linearly independent vector fields, then these define a frame for each individual tangent space. Spivak calls this a moving frame.


So, frames don't resemble coordinate charts at all.


Intuitively speaking, a frame for the tangent space of a point P does define an "infinitessimal" coordinate chart about P, but that's as far as that goes.

More rigorously speaking, this gives us tangent vectors (and we can talk about the corresponding cotangent vectors), so frames let us do calculus, even though they don't talk about coordinates.


We can take a frame and parallel transport it along an observer's worldline to speak about "his" frame. Presumably we'd like to pick the frame so that it's orthonormal, and so that the time axis is always the tangent to the worldline -- the observer would then be "at rest in this frame".

If my intuition in this context is worth anything, this would let us define an "infinitessimal" coordinate chart about the observer. Of course, it only let's us study things infinitessimally close to him.

The intuitive content of the equivalence principle is that infintiessimal regions behave as special relativity dictates, so this infinitessimal chart should behave as SR tells us.

But, just to emphasize it again, it would only apply to things infinitessimally close to the observer.

 

[RandallB]

But, just to emphasize it again, it would only apply to things infinitessimally close to the observer.

And since yogi needs to have a clock go by the tower (leave) and measure it going by again (return) frames that small won't work well.
Which is why the orbiting frame is much more like the traveling twin.

 

[Hurkyl]

Equivalent frames - any property you would measure in one frame would be the same as the property you would measure in another

Then two frames are equivalent if and only if they are exactly the same.

Given two different frames, I can easily find some property on which they would disagree. (Such as the coordiante velocity of a test particle)

To say that "the time difference is a property of their trips" is to say nothing - one clock has not moved - only one clock took a trip

No, both clocks took a trip. A straight-line path through space-time is still a path.

Only useful when they start and end together - how do you reach that conclusion

Because you are talking about clocks that started together and are eventually brought back together.

 

[pervect]

Here's an example of the sorts of problems that arise with accelerated observers.

Attached is a crude drawing of a space-time diagram. The thick red line represents an observer who accelerates briefly (time runs up the page), then stops accelerating. ([clarify] - He maintains his velocity that he picked up while he was acclerating). The section where he accelerates is dotted.

The black lines represent the initial coordinate system of the oberver. Horizontal lines represent his notion of "simultaneous events".

The blue lines represent the new coordianate system of the observer after he accelerates, then stops. Note that his defintion of simultaneous events changes after he accelerates (the blue lines representing simultaneous events, are no longer horizontal, but tilted).

We assume that the observer wants to use coordinates that are compatible with both his initial coordiante system (before he accelerates), and his new coordinate system (after he accelerates) to define his coordiante system.

In a well behaved coordiante system, an event is defined by a pair of coordinates which are unique. Thus lines of simultaneity can never cross, i.e. events where t=0 are always different from events where t=1, and the lines in the space-time diagram defined by "t=0" and by "t=1' never cross.

You can see, however, that the black lines do cross the blue lines!

There is no problem in the neighborhood of the observer, but it is not possible to define a well-behaved global coordinate system for our "briefly accelerated observer" when the region coverd becomes large enough.

 

[yogi]

I would concur that the frame attached to the clock in orbit must be local - at least from the standpoint of academic purity. I would also say that the analogy to the round trip twin is appropriate - in fact Einstein in his description in Part 4 referred both to a time discrepency for a round trip version and a one way vesion. So even if the free float frame has its limitations as an inertial frame - it is of no significance - there is little or no difference between doing the experiment using a circular orbit or replacing the Earth with a zero mass anchor point and tethering a rocket ship which travels the same path w/o gravity - i.e, the Eucledean space version previously raised as a question answered by pervect. What is at issue is why identical clocks record different times - we do not have to bring them together to examine them (although that is one way) but we can continually interrogate the moving clock wrt to the ground clock - and we will find that the clock put in motion falls behind - it is not an answer to say - the path length through space-time is different - we already know that - but how does the clock know its been put in motion after it has been synchronized. The fact that each clock runs at its proper rate in its own rest frame also tells nothing - there is an intrinsic difference between the rate of the Earth clock and the moving clock - whether it be in orbit or traveling the same path in Eucledean flat space - the error is small - The difference between the two clocks is given by the SR relationships between moving frames. SR is quite adequate to the job of predicting the time loss. So, while I proposed an orbit to dispell the argument that GR is a factor - there will always be those that claim otherwise, but it does not answer the question.

 

[Hurkyl]

If I have two pieces of string that begin and end at the same point, and I measure their lengths, should I be surprised if I find the strings have different lengths? And does this require an explanation of why the strings have different lengths?

I would answer no, and no.


Conversely, if I have two observers who start and end at the same point in space-time, and I measure the duration of their paths, should I be surprised to find they have different duration? And does this require an explanation of why the paths have different durations?

I would answer no, and no.


You disagree at least with the last question of this group. So let me ask you this: why do you think an explanation is warranted?

Different paths have different duration -- this should not be surprising. The only reason I could imagine that one would think that an explanation would be required is if you had some reason to think they ought to have the same duration.

E.G. if you adhered to some notion of universal tile. (As you tend to do -- you habitually ignore qualifying anything relative, and you often devise experiments so that all observers are making their measurements according to the same coordinate system... such as when you suggested that the oribiting clock should be reading the times on the network of tower clocks)

What is at issue is why identical clocks record different times - we do not have to bring them together to examine them (although that is one way)

How do you plan to go about examining them?

But that's just a tangential issue: what matters (to me) is how you plan on comparing them.

 

[RandallB]

What?

In a well behaved coordiante system, an event is defined by a pair of coordinates which are unique. Thus lines of simultaneity can never cross, i.e. events where t=0 are always different from events where t=1, and the lines in the space-time diagram defined by "t=0" and by "t=1' never cross.

To be a little clearer; I think you mean to ID the original ref frame as drawn in black with time lines t=0 & t=1. And a second ref frame ID as “primed” and blue with time lines t’=0 & t’=1.

Then you say:

You can see, however, that the black lines do cross the blue lines!

. . . it is not possible to define a well-behaved global coordinate system . . . when the region coverd becomes large enough.

What do you expect, of course a “well-behaved global coordinate system” will cross!
They are straight lines and don’t overlap; therefore they have to meet once!
The important point is THEY ONLY CROSS ONCE!
You only have a problem if you get these straight lines of SR relationships to cross TWICE!
That’s all yogi is doing – somewhere he has an error in his math or calculations that is giving him a point where these straight lines cross twice that’s all.
Till he can find where and how he is doing that, he won’t make any progress in moving from SR onto GR.
Confusing these simple SR issues by fussing over “brief accelerations” just distracts form the SR problem he is been having for so long.
GR issues are easily removed for SR problems by just using “Light Speed” (instant) transfers from one ref frame to the other (That means ZERO time change during a transfer that takes zero time in both frames).

Staying with the linear relationships (as shown by the straight lines in your graph) and CORRECTLY detailing all the times and locations as seen from all locations in BOTH reference frames is all that’s needed to get clear on SR “simultaneity”.
In yogi’s case, as I recommended earlier, one weekend on his own, NO beers! (Maybe one Barleywine) and he can “get it” right quick.
Till he can get that part understood; GR, Accelerations, local vs. non-local, and Rotations are just going to confuse the issue for him. Plus I don’t see how anyone can help him till he does this part of the work correctly in his own opinion, by crosschecking his own work. He certainly isn’t going to change the minds of the many here that have done the work and do “get it”.

My best advice for yogi – stay focused on SR alone till you either “get it”.
OR; On the chance that you really do know better, before you will having any credibility in discussing GR etc., you need to detail what you “know better” about SR, in a Logical and Complete explanation convincing enough to change the mind of at least one mentor. Till then don’t waste your time on GR, you will only get frustrated in long threads like this one.

 

[Hurkyl]

To be a little clearer; I think you mean to ID the original ref frame as drawn in black with time lines t=0 & t=1. And a second ref frame ID as “primed” and blue with time lines t’=0 & t’=1.

No, he meant to say they are the same frame. He's talking about a (hypothetical) globally defined non-inertial coordinate system... specifically, one that starts and ends looking like an inertial coordinate system.

So what you see in the picture is the black lines for t=0,1,2,3, and the blue lines for t=8,9,10

They are straight lines and don’t overlap; therefore they have to meet once!
The important point is THEY ONLY CROSS ONCE!

They can, in fact, meet zero times, and the fact they do meet once is a big deal! Because, in the diagram, the same event in space-time can be listed at two different coordinate times!


Incidentally, when I talk about time running backwards at distant places in what I call accelerated reference frames, I'm talking about the phenomena prevect is describing here.

 

[pervect]

What? To be a little clearer; I think you mean to ID the original ref frame as drawn in black with time lines t=0 & t=1. And a second ref frame ID as “primed” and blue with time lines t’=0 & t’=1.

No, I meant what I said. Check out for instance MTW's "Gravitation", pg 168, section $6.3 entitled "Constraints on the size of an accelerated frame".

This is essentially a redrawing of their figure 6.2.

The intent is to explore to what extent it is possible to construct a "natural" coordinate system for a briefly accelerated observer, as a specific example which illustrates some unexpected problems in generalizing the notion of a natural coordinate system. We know that when an observer is not accelerated he has a natural coordinate system given by his inertial frame, so we ask if this idea can be extended to arbitrary observers.

If the briefly accelerated observer has a natural coordinate system, we can quite naturally require that it should be the same as the natural inertial coordinate system he has during the interval before he accelerated, and it should again be the same as his new inertial coordinate system he has after he stops accelerating.

At this point we haven't attempted to address the issue of what coordinates to use while he is accelerating, because the two requirements above already overconstrain the problem.

As the diagram illustrates,we cannot define a consistent uni-valued coordinate system that covers all of space-time and is consistent with both of the inertial coordinate systems that we have demanded it be consistent with. The best we can do is to define such a coordinate system that covers a limited, local region of space-time.

 

[RandallB]

No, I meant what I said. Check out for instance MTW's "Gravitation", pg 168, section $6.3 entitled "Constraints on the size of an accelerated frame".

Who is MTW ?
This looks to me like miss applying GR to an SR graph. But if I can find it I’ll take a look.

 

[Garth]

Who is MTW ?

Misner, Thorne & Wheeler, their textbook, https://www.amazon.com/gp/product/0716703440/?tag=pfamazon01-20, is a standard text of post-graduate gravitation and GR studies.

Garth

 

[RandallB]

Misner, Thorne & Wheeler, gravitation and GR studies.

Thanks –Wow, Expensive for a book from 1973,
found where I can borrow one tonight.

 

[JesseM]

I would concur that the frame attached to the clock in orbit must be local - at least from the standpoint of academic purity.

If you agree it's local, then do you understand this means you can't ask how fast the tower clock is ticking "in the orbiting clock's frame" once they are no longer at the same position?

there is little or no difference between doing the experiment using a circular orbit or replacing the Earth with a zero mass anchor point and tethering a rocket ship which travels the same path w/o gravity - i.e, the Eucledean space version previously raised as a question answered by pervect.

In this case, one clock is moving inertially and the other is not, so you can't ask how fast the tower clock is ticking in the orbiting clock's frame, because the orbiting clock doesn't have a single rest frame.

What is at issue is why identical clocks record different times - we do not have to bring them together to examine them (although that is one way) but we can continually interrogate the moving clock wrt to the ground clock

How do you "continually interrogate" one clock wrt the other if they are at different locations? Different inertial frames will have different definitions of simultaneity, and so will disagree about the relative rates of the clocks at different times. If you assume that the clocks obey Lorentz-symmetric laws of physics, then different inertial frames should be able to all use the same laws to predict how the clocks will behave (for example, each frame will predict a clock's ticking rate will be a function of its velocity in that frame), and they will all make the same prediction about what each clock reads when the two clocks reunite at a single location. Do you agree with this?

 

[yogi]

Jesse - we use the non rotating Earth centered reference system to interrogate GPS clocks all the time - we can calculate exactly what their daily drift is and correct them - if instead we do not preset a clock in satellite Earth orbit to compensate for the post launch orbital velocity - we can send a radio signal any time no matter where it is in its orbit and we will find it has a slower rate by the same amount relative to the tower clock - moveover, we can of course put different clocks at diffeent heights - e.g., we can arrange a launch platform at 100 milles up and a second at 200 miles above the Earth surface etc - and if both satellite clocks are synced respectivly to adjacent Earth tower clocks and launched into orbit at 100 miles and 200 miles respectivly, and no correction is made for the orbit velocity of either - when they are in orbit we can interrogate each of the two clocks from the tower at any point in their respective circular orbits. What will we find. The rate of each clock no matter where it is in its orbit, will be running uniformly slow with respect to the tower time - and each is slow by an factor that corresponds to its orbital velocity - i.e., each clock is running at its own uniform intrinsic rate at all times.

Now you can say that each clock runs at its own rate because of the invariance of the interval, or the difference in the space time path, or some other factor that is part of SR ...a lot of true statements - but not an explanation - what I would like to know is how do the two clocks in different orbits know at what rate to run relative to the Earth frame. Each clock has its own uniform intrinsic rate relative to the tower in accordance with their velocity relative thereto. - if that question doesn't bother you - so be it

 

[yogi]

Randall - i am astonised you would lecture on GR having never heard of the MTW - I got my first copy about 10 years ago - seemed like it was about $90 then - later a picked up a slightly used copy for $4 in the Escondido Library used book department - Of course having two copies doesn't make it easier to understand

 

[JesseM]

Jesse - we use the non rotating Earth centered reference system to interrogate GPS clocks all the time

How does that contradict my point? Once you make an arbitrary choice of which inertial reference frame you want to use, you can of course compare different clocks in that frame. But the choice is totally arbitrary, you could equally well have used some other inertial frame, and using the exact same laws you'd get all the same predictions about what clocks read when they meet, but different answers to how fast their respective rates are when they're apart. Do you disagree?

we can calculate exactly what their daily drift is and correct them - if instead we do not preset a clock in satellite Earth orbit to compensate for the post launch orbital velocity - we can send a radio signal any time no matter where it is in its orbit and we will find it has a slower rate by the same amount relative to the tower clock - moveover, we can of course put different clocks at diffeent heights - e.g., we can arrange a launch platform at 100 milles up and a second at 200 miles above the Earth surface etc - and if both satellite clocks are synced respectivly to adjacent Earth tower clocks and launched into orbit at 100 miles and 200 miles respectivly, and no correction is made for the orbit velocity of either - when they are in orbit we can interrogate each of the two clocks from the tower at any point in their respective circular orbits. What will we find. The rate of each clock no matter where it is in its orbit, will be running uniformly slow with respect to the tower time - and each is slow by an factor that corresponds to its orbital velocity - i.e., each clock is running at its own uniform intrinsic rate at all times.

Yes, and we could make similar corrections if we wanted to have the clocks be synchronized in an inertial frame moving at 0.99c relative to the earth, as opposed to the frame where the Earth's center is at rest. Do you disagree?

a lot of true statements - but not an explanation - what I would like to know is how do the two clocks in different orbits know at what rate to run relative to the Earth frame. Each clock has its own uniform intrinsic rate relative to the tower in accordance with their velocity relative thereto. - if that question doesn't bother you - so be it

The question doesn't bother me, but my answer is simple: the laws governing the clocks are known to have the mathematical property of Lorentz-invariance, which insures they must behave the same way in different inertial reference frames related to each other by the Lorentz transform. I've asked you several times whether you agree that given Lorentz-invariant laws, it is logically impossible that clocks would fail to behave as predicted by relativity or that they would not work the same way in different inertial reference frames, but you've never responded. Can you please do so now?

If you want to argue that the fundamental laws of nature might not be Lorentz-invariant, or that there has to be some conceptual reason they are all Lorentz-invariant, that's fine. But so far a lot of your arguments have seemed to take for granted that clocks follow known relativistic laws in some given frame (say, the frame where two clocks are initially at rest before one accelerates in your previous example), but then you question whether these situations could really be analyzed just as well from the point of view of another inertial frame. But this is a truly incoherent line of argument, because again, if you take for granted that clocks obey the known Lorentz-invariant laws in one inertial frame, then it's logically impossible that they would fail to obey the same laws in all other inertial frames.

 

[pervect]

Let me add my $.02.

If we have an inertial observer, and someone moving via a powered orbit in a circle around the observer, the two observers are always a constant distance apart.

Because they are a constant distance apart, the travel time for a light signal will always be constant, and everyone will agree that the observer traveling in a powered orbit has a clock that is ticking slower. Constant travel time makes direct comparison of the rates of clocks possible

The obserer in a powered orbit will not have a "frame" that covers all of space-time. However, he will have a local frame that includes the inertial observer.

The observer in the powered orbit will see the inertial observer's clock as ticking faster, due to "gravitational time dilation" in his local coordinate system, as the inertial observer will always be "above" him.

So, there isn't any ambiguity here - the inertial observer thinks the accelerating observer's clock is ticking slowly, and the accelerating observer thinks the inertial obserer's clock is ticking fast.

This is perfectly consistent with the simple idea that the clock following a geodesic in flat space-time is always the clock that experiences the most time.

 

[RandallB]

Randall - i am astonised you would lecture on GR having never heard of the MTW - I got my first copy about 10 years ago -

I’m not lecturing on GR I’m talking about SR. And is there some list of acronyms that we should all know so we don’t wise cracks from you guys about not knowing what MTW stands for here? Tens years working on getting SR is more astonishing than having to learn acronyms of others.
Do you have an acronym for your version of relativity; LR BR YR (Lorentz, Broken, Yogi) it sure isn’t SR.

And if you think your issues in this thread are GR, you’re wrong it’s SR where you’re still having problems. Until you understand SR, how can you hope to work from an understandable vocabulary with any mentor that’s not on the same page as you with what ever version of SR you’re using?

If you’re trying to learn the correct way to understand it. Stick with SR alone first. They won’t be able to help you in GR if you don’t have SR down first.

But, if your purpose is to convince someone of your view, do it in a SR environment; in GR you’ll never be able to communicate effectively if they don’t understand your version of SR. And be clear about your purpose if this is the case; at least be fair to the mentors that are only trying to help you see SR, if that is not your intent. I really don’t thing any are looking to pick up a new view of relativity, but some may be willing to look at your augments differently if you’re actually trying to bring forward a new view of relativity.
I honestly cannot tell which you are doing.