The Reality of Relativity

yogi

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

yogi

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.

JesseM

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

JesseM

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

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 lets 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

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

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. 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:

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

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 accelarating (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 travelling 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)



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 lets 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

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

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.