Is the Changing Clock Rate in Relativity Directionally Dependent?

[yogi]

Jesse - yes I was referring to the polygonal line statement - and i agree Einstein did not go further - what I am saying that every motion has some curvature most likely - but it does not show up in the results - why because acceleration per se does not affect clock rates - as i have said about 50 times. So the slight curvature is of no moment - if you were on that spaceship with such a low curvature you would feel perfectly justified in claiming yourself to be on an inertial platform (you could even straighten it out if you desired, as you passed A - it wouln't make any difference - when you attempted to use your slowly running clock to try to make measurments of the A clock as you passed by ...you would get the wrong answer - because the proper rate of the A clock in the A frame and the proper rate of the R clock in the spaceship frame is different by a factor of 2 whether you momentarily straighten out the spaceship path or not.

 

[JesseM]

My use of the word intrinsic is of course undefined in SR - - it is not the observed time - it is the difference between what two clocks that are in uniform relative motion will determine to have accrued on each clock when they are compared in the same frame. Let us proceed to use R and E as Hurkyl has chosen to illustrate - as long as they are in relative motion, we make measurements and get different results because relative velocity and distances are changing But what is being measured is a distortion - If R quickly stops halfway to Altare and interrogation signals are sent from E to R and from R to E - what do they report - after comparison R has fallen behind E by 1/2

Only if R "stops" in the inertial frame that E is at rest. But what if both R and E "stop" in some other inertial frame? If R has only made 1/4 of a full circle, I'm not sure if all inertial frames will agree that its average rate of ticking was slower than E (they would definitely agree on this if it made a full circle), and in any case it certainly won't be true that all frames agree that its average rate of ticking was 1/2 of E's. So what if, at the moment R has made it halfway to Altare both R and E stop in some inertial frame where R's average rate of ticking was 3/4 that of E's--in this case when they compare non-doppler-shifted signals, they will indeed find that during the journey R only elapsed 3/4 the time of E. Why should the comparison after both clocks "stop" in this frame be considered any less real than the comparison after R "stops" in the rest frame of E?

But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame. We can make this determination at any point we wish during the trip - and by asking the question: "What does your clock read" rather than: "how fast does time appear to be passing while we are in relative motion" we arrive at the correct physical reality...at all times during the voyage, proper time in the R frame accrues twice as fast as it does in the E, C, A frame. The result would be no different if R is in an orbit around some great attractor which C happended to be the center of - and it is no different on any other experiment - the invariance of the interval assures us that it is the high speed pion and not the Earth clock that runs slow - real time dilation is a one way thing.

Well, see above, there is no reason to consider the time comparison in E's frame any more of a "physical reality" than the time comparison in any other. No matter what frame you choose, if both clocks "stop" in that frame then when they compare non-doppler shifted signals they will conclude that one clock is behind by exactly the amount that frame's coordinate system would predict.

Let me ask you this, if you had an object moving inertially at 0.99c relative to the Earth and another object traveling in a circle at constant speed in the first object's rest frame, then would you consider the earth-frame's analysis of this problem to be "distorted"? Note that if the circular-moving object came to rest relative to the inertial one, and in their new rest frame they agreed that the circular-moving one had elapsed 1/2 the time of the inertial one, in the earth-frame the signals between them would still appear to be extremely doppler-shifted since one object is moving towards the other's signals at 0.99c while the second is moving away from the first one's signals at 0.99c. So we would not conclude that the circular-moving one had elapsed 1/2 the time of the other, you only get that conclusion if you assume that the relative velocity between each object and their signals is c, which is not true in our frame.

 

[yogi]

Only if R "stops" in the inertial frame that E is at rest. But what if both R and E "stop" in some other inertial frame? If R has only made 1/4 of a full circle, I'm not sure if all inertial frames will agree that its average rate of ticking was slower than E (they would definitely agree on this if it made a full circle)

I think you have a hang up on the necessity of a round trip - there is a physical thing going on - 1/8 of a circle is as good as a half which is as good as 3/4 which is as good as a whole. Look at the physical reality of what is actually taking place - there is no way that any of the clocks can change the rate at which time progresses in their own frame after R reaches crusing velocity - the A, C and E clocks remain in the same frame from beginning to end, the R clock rides on a spaceship that changes direction at a continuous rate but the tangent velocity remainst constant (there is no energy added or subtracted to or from the spaceship) What could possibly cause R to run a different rate at different parts of the voyage. if you prefer we can consider R tied to C by a long teather - there is unchanging continuity during the journey

Think about each clock as being powered by a frictionless flywheel which has been cranked up to speed and geared to drive the hands of the clock - it spins on for years at the same rate - when the R clock is launced, the angular momentum of the flywheel should not change (or perhaps you think it does - if so how and why) In any event - if it does not change, the hands should keep moving at the same pace as those of E, C and A - but SR tells us that the hands now go slower - something physical has occurred - this is the crux of the SR puzzle.

 

[yogi]

Jesse - As to some of your other questions - go back again to Part 4 - Einstein puts both clocks in the same frame and then moves one - when you introduce other moving frames you will again be mixing real time events with apparent measurments - we can only have two frames if we are going to follow Einsteins scenerio - obviously if we ever come to an agreement on something then we could extrapolate to other situations - in fact that was what I tried to do in my original statement of this thread -i then shifted to the orbiting GPS clocks and then the big voyage centered on clock C to make it easy to illustrate how REAL values could not be any other way - obviously I did not do such a good job - so I will restate what i am convinced to be correct - namely - it doesn't make any difference if the R clock travels in a circle or in orbit in a G field (freely floating fame) or a straight line or a polygonal path - the reality of the situation is that the clock which is accelerated to reach a constant magnitude velocity after initial synchronization will run at a constant slower rate than the one which remains fixed - we can only find out by how much if we ask the question - what does the moving clock read when interrogated - we can pose this question at any time during the travel period or we can ask it when the moving clock is brought to rest in the same frame from which it was launched - if we try to predict the results in third frames - it obscures the issue.

 

[JesseM]

I think you have a hang up on the necessity of a round trip

Only because that's the only case where all frames will agree on the time elapsed on both clocks.

there is a physical thing going on - 1/8 of a circle is as good as a half which is as good as 3/4 which is as good as a whole.

But with less than a full circle, there is no reason to prefer one frame over another. If you disagree, what reason do you think there is?

Look at the physical reality of what is actually taking place - there is no way that any of the clocks can change the rate at which time progresses in their own frame after R reaches crusing velocity - the A, C and E clocks remain in the same frame from beginning to end, the R clock rides on a spaceship that changes direction at a continuous rate but the tangent velocity remainst constant (there is no energy added or subtracted to or from the spaceship)

The tangent speed remains constant in C's rest frame, but the tangent velocity does not, because velocity is a vector, and the tangent velocity vector points in different directions as R moves along the circle. And in a frame where C is not at rest, the tangent speed isn't constant either.

What could possibly cause R to run a different rate at different parts of the voyage.

The fact that its speed is changing (in some frame other than the rest frame of A, C and E), and rate of clock ticking depends on speed.

Again, yogi, you didn't address my questions. When I ask you questions, can you please not just ignore them? Do you agree that if R and C both "stop" in some other frame other than C's original rest frame, and afterwards they compare their times using radio signals, they will get a different answer to how much R fell behind then if R "stopped" in C's original rest frame and they compared times with radio signals? And what about the question about the clock that is moving at 0.99c in the Earth's frame, with another clock moving in a circle relative to the first--is the earth-frame's perspective on this situation an incorrect one, according to you?

Think about each clock as being powered by a frictionless flywheel which has been cranked up to speed and geared to drive the hands of the clock - it spins on for years at the same rate - when the R clock is launced, the angular momentum of the flywheel should not change (or perhaps you think it does - if so how and why) In any event - if it does not change, the hands should keep moving at the same pace as those of E, C and A - but SR tells us that the hands now go slower - something physical has occurred - this is the crux of the SR puzzle.

Again, as long as the laws of nature obey equations which have the mathematical property of lorentz-invariance, then it's inevitable you'll get relativistic phenomena like time dilation. For example, since Maxwell's laws of electromagnetism have this property, if you built a "clock" which could be understood totally in terms of electromagnetic laws--say, a charge which oscillates back and forth at a regular rate, which can occur in EM--then it's necessarily going to be true that if are moving inertially and this clock moves away from you and then comes back, it will have elapsed less time than yours. No need to have a specific theory of relativity, this is guaranteed to happen just based on the equations of electromagnetism, and would have to be true even if you believed in an ether theory which obeyed the same equations in the rest frame of the ether.

Anyway, if you admit your own intuitions tell you a clock should not change its rate just because it moves, but you can see these intuitions are somehow incorrect, then why do you feel so comfortable trusting your intuitions about which reference frame's perspective is the "correct" one and which frame's is "distorted"?

 

[JesseM]

Jesse - As to some of your other questions - go back again to Part 4 - Einstein puts both clocks in the same frame and then moves one - when you introduce other moving frames you will again be mixing real time events with apparent measurments

What is a "real time event" and what is an "apparent measurement"?

we can only have two frames if we are going to follow Einsteins scenerio

No, his scenario is only that you have two clocks at rest relative to each other, and then one accelerates towards the other. He chooses to analyze this situation in the frame where they are originally at rest, but this is not part of the "scenario", it is fundamentally no different from a choice of where to place the origin of the coordinate axes or a choice of whether to use cartesian or polar coordinates.

the reality of the situation is that the clock which is accelerated to reach a constant magnitude velocity after initial synchronization will run at a constant slower rate than the one which remains fixed

But for an object moving in a circle, "constant magnitude velocity" itself depends on your reference frame. Likewise, "initial synchronization" of separated clocks also depends on your choice of reference frame. These things are entirely coordinate-dependent, there is no rational reason to treat one frame's view of them as more valid then another's, so your own preferences can only be aesthetic ones.

 

[Hurkyl]

But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame.

Aha! You have confessed to belief in absolute time. You have now unequivocally confirmed my suspicion that you are selecting one reference frame to be the preferred frame, and that all other reference frames are considered to be "distorted".

This is exactly what it means for one to consider time to be "absolute", or "universal", or such.


The question is why should that particular frame be preferred? It is just as much as "formalism" as any other reference frame.

Why isn't, say, the Andromedra frame the preferred one? (In which ECA are all moving) Can you write down an experiment that would prove the ECA is the preferred frame, whereas the Andromeda frame is not?

(No)

 

[yogi]

Hyrkyl - There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times - For example let's take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light - each and every time it interrogates R and C it will find that the time lapsed on R is 1/2 that of C. In theory we can have an infinite number of these types of frames - all strung out along the rope joining R and C.

When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame - this is the bases of the twin thing and every other counterintuitive aspect of SR - if SR were nothing but an abstract theory of how things appear distorted in moving frames it would be of little use - in actuality, I see no justification for Einstein combining the equations as he did to arrive at the conclusion that one clock gets physically ahead of the other - it would seem that he should have said: The traveling clock appears to run behind the at-rest clock from the perspective of the at-rest clock and the at-rest clock appears to run behind the traveling clock when judged from the moving clock, and that both clocks read the same when the traveling clock is stopped so that it is at rest in the original frame. But he didn't say that - he went out on a limb and predicted a physical result that has fueled a 100 year debate. Actual time dilation does not follow from the mathematics - it is in fact a new postulate - couched in the mathematics of apparent observations, but not a logical consequence thereof. Einstein created a preferred frame thought experiment which results in the answer he had arrived at by intuition - as he said in one of his biographies - he had worked on the problem off and on for ten years - but it was always with me ... gradually I began to suspect time as the culprit. in actuality, Einstein turned a problem into a postulate. To get real time dilation, one frame had to be different from the other. If you choose to call it preferred - fine with me.

 

[yogi]

Jesse: "But with less than a full circle, there is no reason to prefer one frame over another. If you disagree, what reason do you think there is? "

There is every reason - because the C point I have chosen always gives the same value for the rate of the moving clock R. This is the same reason we choose the non rotating Earth centered reference system for GPS. The R clock should not change the pace at which it logs time during the voyage - the C clock measures this rate - i suppose you will say this is just its a convenience. True. Any clock on the ACE frame could be used to send and receive signals to R and as long as they ask the question "what does your clock read" we have an experiment that
comports with Einsteins 2 frame scenario. A third frame passing the whole experiment would raise the further issue - were the clocks in teh new frame ever properly synchronized in the ACE frame - that situation is undefined in Einsteins scenario

 

[JesseM]

Hyrkyl - There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times - For example let's take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light

J is not a frame in the first place. And how can J "measure" the speed of the R clock at all, without using some coordinate system? Presumably you just mean how fast J will see R ticking using light signals, but all inertial frames will make the same prediction about this, so it makes no sense to treat this as evidence for a "preferred frame".

When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame

No he didn't, because he'd get the same answer if he analyzed the situation in some other inertial frame.

Actual time dilation does not follow from the mathematics

Yes it does. Given laws whose equations have the mathematical property of Lorentz-invariance (which, remember, is not a statement about relativity at all, it's just a purely mathematical property of certain equations, like saying a given equation is a 'polynomial'), it is logically impossible that clocks obeying these laws would fail to show genuine time dilation as in the twin paradox. Do you agree with this or not?

 

[JesseM]

There is every reason - because the C point I have chosen always gives the same value for the rate of the moving clock R.

What do you mean "gives the same value"? Are you talking about how fast C sees the signals are coming in from R? You should know the difference between statements about how fast signals come in and how fast a clock is actually ticking in a given frame--because of doppler shifts, the two are not necessarily identical. And do you agree that all inertial frames will predict the same thing about how fast C sees the signals coming in from R? If so, isn't it obviously nonsense to say that something which all frames predict is evidence that one frame should be preferred?

This is the same reason we choose the non rotating Earth centered reference system for GPS.

No it isn't. We choose that reference system because it's the most convenient if we want to have a universal time system for people on earth. And I think the GPS system could easily be adapted to deal with situations like a satellite in an elliptical orbit, where the signals from the satellite would not be coming in at a constant rate as seen by an observer at the center of the earth.

A third frame passing the whole experiment would raise the further issue - were the clocks in teh new frame ever properly synchronized in the ACE frame - that situation is undefined in Einsteins scenerio

What do you mean "undefined"? If you know what the clocks read at a given moment in another frame, it is perfectly straightforward to figure out whether they are synchronized in the ACE rest frame--you just use the Lorentz transform, which Einstein had already derived earlier. Just like if you know the coordinates of A,C, and E in some coordinate system where they do not all lie along the same coordinate axis, it is perfectly straightforward to figure out if A would lie along the x-axis in a coordinate system where C and E did.

 

[yogi]

Jesse I take issue with your reasoning on every point - you avoid the obvious conclusion that R and J cannot be inertial frames because of the slight curvature - no matter how small - that is a cop out. You keep asserting the transforms as controlling - but the issue is how they are to be applied - where is the symmetry - there is no sysmmetry between two frames in motion unless every experiment carried out in one frame gives the sames result when carried out in the other - but that is a yet to be proved assertion - assume R moves straight way toward A rather than in a circle - things are exactly the same - R is now a good reference frame even by your narrow standards - but when R interrogates C or A or E by asking the question "what does your clock read" he will find R is running slow by Gamma

A convenient aspect of the circular path is that C and R can not only use "What does your clock read" to determine relative rates - but either can signal the other using reflected light signals - if both R and C are equipped with a reflecting mirror - every time R bounces a signal off of C it will require "k" seconds to return back to R as measured on R's clock. But whenever C sends a signal to R it will return in "2k" seconds as measured by the C clock - if we do this enough times even you might conclude that the two clocks are running at intrinsically different uniform proper rates.

here is another heuristic experiment - let us launch a second spaceship from A headed in the opposite direction along the same circle and at the same velocity v - The second spaceship carries a clock Q. These two space ships pass at pi/2 and each uses the formalism of SR to conclude that the other clock is running slow - C of course will determine that each clock is running slow wrt to C by the same amount - so C will conclude that the actual clock rate of Q and R is the same. We will stipulate that Q and R straighen their orbits for a brief interlude while carrying out the experiment -

We next assume that Q is launched to (1/2)v rather than V so when the clocks meet after momentarily straightening their orbits - in the neighborhood of 135 degrees - will Q measure R to be running slow by the same amount that R measures Q to be running slow ?

 

[JesseM]

Jesse I take issue with your reasoning on every point - you avoid the obvious conclusion that R and J cannot be inertial frames because of the slight curvature - no matter how small - that is a cop out.

How is it a "cop out" when it's what the math tells you must be true, given the equations of the laws of physics? If you want to dispute that certain equations (Maxwell's laws of electromagnetism, for example) actually agree with experiment, fine, but if you somehow argue that conclusions which follow automatically from these equations are wrong, then you are in complete crackpot territory, akin to someone who accepts that a curve has the function y = x^2 but refuses to accept that its derivative is dy/dx = 2x.

You keep asserting the transforms as controlling - but the issue is how they are to be applied - where is the symmetry - there is no sysmmetry between two frames in motion unless every experiment carried out in one frame gives the sames result when carried out in the other - but that is a yet to be proved assertion

There is a symmetry if it can be proven mathematically that, given laws of physics that obey certain equations in one frame, the equations must be the same in other frames related to the first frame by the Lorentz transform. I thought you had already admitted this was true in your post #135:

If I have given the impression that I have any doubt about physical experiments producing different results in different frames - I did not intent to - Nor am I taking issue with the lorentz group of symmetries as a mathematical principle, although it is not always easy to see what is being conserved.

Now, do you agree or disagree that, given laws of nature whose equations have the mathematical property of lorentz-invariance when expressed in one inertial coordinate system, it is logically impossible that the laws of physics could fail to work the same way in other inertial coordinate systems related to one first one by the Lorentz transform? Please give a clear and unambiguous answer to this question. Since you have a tendency to not respond to direct questions from me whenever I write long posts answering your points in detail, I'm going to leave off responding to any more of your post for now and wait for an answer to this question.

 

[yogi]

Jesse. As to Galilean invariance - it would be very surprising if this were ever proved false - As to lorentz invariance - the issue arises as to "What constitutes a physical experiment within the inertial frame - Einstein took the position that passing light should be measured to have the same velocity in every frame - lorentz took the view that light always travels at c relative to the ether - both men were attempting to explain the nearly null results of MMx. I recently cited the CBR as an example of the fact that different inertial frames will get different results as to this phenomena - you came back with something to the effect that it wasn't an experment performed w/i the frame (can't remember what post or exactly what you said) But why could not the same argument be made wrt to passing light. Before relying too heavily upon the arithmetic, it would be nice to have some experiments conducted in a gravity free environment. Transforms are only as good as the conditions under which they are created - specifically the veracity of the assumptions and postulates. This thead calls attention to the fact that Einstein arrives at real time dilation only after he imposes strict initial conditions upon the two clocks. Your interpretation of the situation as you have championed in the past is that the accompanying frame of each clock (after the moved clock has reached a inform relative velocity) as as good an inertial frame as the other. You rely dogmatically upon the transforms - but alas - it is the transforms and their application to the case at hand that is in question

Anyway I appreciate your confining your comments to one specific point

 

[JesseM]

yogi, you're missing the point of my question. I'm not asking whether you think Galilei-invariance and Lorentz-invariance are ever going to be proven false experimentally (but why do you say of Galilei-invariance 'it would be very surprising if this were ever proved false'? Any law that is known to be lorentz-invariant, like Maxwell's laws of electromagnetism, must already violate Galilei-invariance). I'm asking whether, given laws whose equations have this mathematical property of lorentz-invariance when written in some inertial frame, you agree that it is logically impossible that these laws could fail to have the same equations when written in any other coordinate system related to the first by a lorentz transform. In other words, if you accept for the sake of the argument that a given clock can be understood wholly in terms of laws which are known to be lorentz-invariant such as Maxwell's laws, would you agree it automatically follows from this that the clock will obey the same laws in all the other frames generated by the Lorentz transform? You are free to accept this but to doubt that actual physical clocks actually do obey lorentz-symmetric laws, of course, this question is just about whether you agree that if they do, then there can be no further doubt about the laws working the same way in every inertial frame.

Note that when you analyze situations like Einstein's thought-experiment or the A,C,E,R scenario, you seem to grant for the sake of the argument that all the clocks in this scenario will slow down by the amount predicted by relativity in whatever frame you choose to analyze the problem, which is why I find it completely puzzling that you go on to question whether the laws work the same way in every frame even in your hypothetical scenario where you seem to be assuming for the sake of argument that the laws work the way relativity says they should in the frame where you have chosen to analyze the problem. If you want to question whether relativity makes correct predictions in any frame, that would be one thing, but once you have granted that relativity makes correct predictions in one frame that means it is logically impossible that the observed laws could fail to work the same way in other frames related to the first by the lorentz transform.

 

[Hurkyl]

There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times

Which, of course, begs the question of what we mean by "determine reality".

You assume a very special (and very nonrelativistic condition that "reality" has the property that there is a single, "real" way to compare the rates of any two clocks, and that this comparison has nice properties. (such as if A is faster than B, and B is faster than C, then A is faster than C)

I'll state it again: you are assuming absolute time.

And I'll state again the problem of absolute time: given all the laws of physics we currently know, we cannot even in principle figure out how to "determine reality". There does not exist an experiment that can confirm the hypothesis that the ECA-frame makes "real" measurements, and can deny that the Andromeda-centered frame does not.

This is why people question just how "real" the nonrelativistic view of reality is.

For example let's take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light

How do you figure that?

First off, as Jesse said, J is not a frame.

Secondly, why would R appear to be moving at all?

When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame

I have no idea what part 4 means, but I can still strongly suspect you have this wrong. When one does problems, it is usually most efficient to set up a choice of coordinates that simplifies the problem, and do the problem in those coordinates. This choice of coordinates is no more preferred than the choice of x and y-axes you might make when trying to solve a high-school geometry problem.

if SR were nothing but an abstract theory of how things appear distorted in moving frames it would be of little use

Wrong. If we take this interpretation of SR, it is still extremely useful, since distortions are all we can ever measure, even in principle. Therefore, it would be extremely practical to have the correct theory of distorted measurements.

To get real time dilation, one frame had to be different from the other.

To get real time dilation, you first must have a definition of what the phrase "real time dilation" means. (Well, you need a practical definition, one that can be determined by experiment. But to begin, I'll settle for any definition at all)

 

[yogi]

Hyrkyl

I am not assuming absolute time - I am reasserting as Einstein did, an unambiguous relationship between the rate of two clocks in uniform relative motion where they have been previously synchronized in the same frame and only one has been put into motion

If the Andromeda centered frame is not moving wrt to the ECA frame, it can make real measurements as to the rate of R, although not as conveniently as C. If it is moving wrt to the ECA frame it will make apparent measurments as to both distances and time


If you do not consider either J or R a frame - I say to both of you - you are hiding behind a slight curvature which doesn't affect the clock rates in order to avoid certain conclusions - To avoid that foxhole, I said do the same experiment with R traveling straight from E to A - you will get the same result - for Gamma = 0.5 the R clock will read 1/2 the C, E and A clocks upon arrival at A, and if it turns around and travels straight back to E at the same velocity (e.g., it slingshots back due to the gravity field of Altair) it will read again 1/2 that of clocks ECA.

Do you really want to stand on the statement: "Secondly, why would R appear to be moving at all?" I suppose you mean relative to J -



"I have no idea what part 4 means,"

That is what this is all about





]

 

[JesseM]

I am not assuming absolute time - I am reasserting as Einstein did, an unambiguous relationship between the rate of two clocks in uniform relative motion where they have been previously synchronized in the same frame and only one has been put into motion

Einstein asserted no such thing, and you will find no quote in his paper that implies anything like this. He simply chose to analyze the two-clock problem in the frame where they were initially synchronized and at rest, but he made no suggestion that the problem could not equally well be analyzed in any other inertial frame.

"I have no idea what part 4 means,"

That is what this is all about

Perhaps Hurkyl just didn't know what you meant by "part 4", ie that you meant part 4 of Einstein's original 1905 paper (you didn't specify this in your post), not that he had seen part 4 of the paper and failed to understand it.

 

[yogi]

Jesse - I am not avoiding your post - I drafted a response - but I wanted to think about it - so I removed it. It got me wondering about something you said.

Hurkyl - You asked for a defiition of real time dilation - rather that put into words - I will go back to the example I described previously - while R is pursuing its path on the tether - C sends signals to R. The over and back distance is always the same - and we take as fact in the experiment that light travels at the same velocity c in both directions - C notes the time the signal was sent and the time it is reflected from a mirror attached to R - we will say it is 10 seconds as recorded by the C clock. R sends similar signals to C and they are reflected back to R. The time recorded on the R clock is 5 seconds (you can debate this if you like - but for the purpose of defining Real time dilation, if the return time is 5 seconds we can say R runs at a rate of 1/2 that of C). There are no variables - the over and back distance is the same for both R and Cs transmissions - and they do not have to be correlated - any time R bounces a radar signal off of C it takes 5 seconds to return as measured on R clock ---any time C bounces a radar signal off of R it takes 10 seconds to return as measured on the C clock.

Yogi's Rule: Two clocks in relative motion that maintain the same separation distance will exhibit real time dilation if reflected signals sent from one to the other require different times as measured by the clocks where the signal originated

 

[yogi]

Jesse - Just so you two are on the same page - do you agree that Einstein concluded that one clock was physically ahead of the other when they were compared - if you two havn't got past that point - there is no point in further discussion - either yes or no will do.

 

[yogi]

Jesse - Hurkyl is perfectly capable of telling what he meant - he doesn't need help - Do you do anything other than post on these boards??

 

[yogi]

Einstein asserted no such thing, and you will find no quote in his paper that implies anything like this. He simply chose to analyze the two-clock problem in the frame where they were initially synchronized and at rest, but he made no suggestion that the problem could not equally well be analyzed in any other inertial frame.

Ok - if you go ahead and analyse it in the moving frame - what will you get - will you get the same result that the moving clock is behind the clock in the stationary frame - let's see what you come up with

 

[JesseM]

Jesse - Just so you two are on the same page - do you agree that Einstein concluded that one clock was physically ahead of the other when they were compared - if you two havn't got past that point - there is no point in further discussion - either yes or no will do.

Yes! I have said over and over again that every inertial frame will make the same prediction about all physical questions like what two clocks read when they meet, and if this isn't completely obvious to you, then you need more practice analyzing the same situation in different frames. Just as an exercise, would you like to try transforming Einstein's problem into another frame to see how it works out? EDIT: I hadn't seen your last post suggesting this when I wrote that...

 

[JesseM]

Jesse - Hurkyl is perfectly capable of telling what he meant - he doesn't need help - Do you do anything other than post on these boards??

No need to be snarky. And if Hurkyl didn't already know that you were talking about Einstein's 1905 paper, your one-line response wouldn't clarify things for him, so that comment was as much for him as you.

 

[JesseM]

Ok - if you go ahead and analyse it in the moving frame - what will you get - will you get the same result that the moving clock is behind the clock in the stationary frame - let's see what you come up with

OK, Einstein does not give any specific numbers in his problem, but let's say that in the original rest frame of the two clocks, they are 12 light-seconds apart, with the clock 1 at position x=0 and clock 2 at position x=12 l.s. Assume they are also synchronized in this frame. Then when clock 1 reads time t=0 seconds, it accelerates instantaneously to a velocity of 0.6c in the direction of clock 2, and travels at this velocity until it reaches clock 1 at t=12/0.6=20 seconds in the coordinates of this frame. At the moment they meet, clock 2 will of course read 20 seconds since this is its rest frame, but clock 1 will have been ticking at $$\sqrt{1 - 0.6^2}$$ = 0.8 the normal rate, so it will only have ticked 0.8*20 = 16 seconds. Thus when they meet, clock 1 reads 16 seconds and clock 2 reads 20 seconds, according to this frame's prediction.

So, let's consider the coordinates of the following 4 events as seen in this frame:
EVENT A -- clock 1 reads 0 seconds and accelerates: x=0 l.s., t=0 s
EVENT B -- clock 2 reads 0 seconds: x=12 l.s., t=0 s
EVENT C -- clock 2 reads 7.2 seconds: x=12 l.s., t=7.2 seconds (the reason I picked this event will become apparent later)
EVENT D -- clock 1 and clock 2 meet, with clock 1 reading 16 s and clock 2 reading 20 seconds: x=12 l.s, t=20 s

In this frame, events A and B are simultaneous, because they both happen at the same coordinate time, while C is not simultaneous with either of them.

But now, let's transform events A, B, and C into an inertial frame moving at 0.6c relative to the first one, in the same direction that clock 1 moves afte accelerating. In this case the Lorentz transform for finding the coordinates of events in this frame would be:

x' = 1.25*(x - 0.6c*t)
t' = 1.25*(t - 0.6*x/c)

So, the coordinates of event A would be: x'=0 l.s., t'=0 s
The coordinates of event B would be: x'=15 l.s., t'=-9 s
And the coordinates of event C would be: x'=9.6 l.s., t'=0 s

So you can see that in this frame, it is events A and C that are simultaneous, while event B happened prior to both of them--in other words, at the "same moment" that clock 1 read "0 seconds" and accelerated towards clock 2, clock 2 was reading 7.2 seconds (that was the definition of event C, remember) and was at a distance of 9.6 l.s. away in this frame. And once clock 1 accelerates, it is at rest in this frame, while clock 2 is moving towards it at 0.6c. So in this frame, we conclude that it will take 9.6/0.6 = 16 seconds for clock 2 to reach clock 1 (and if you map event D into this frame using the Lorentz transform, you find it does indeed have coordinates x'=0 l.s., t'=16 s in this frame).

Now, if we assume the laws of physics work exactly the same in this frame as in all other frames, then since clock 1 is at rest in this frame it should be ticking at a normal rate, so it should have elapsed 16 seconds between the time it comes to rest and the time the two clocks meet; but since clock 2 is moving at 0.6c in this frame, it should be slowed down by a factor of 0.8, meaning it will have elapsed only 16*0.8 = 12.8 seconds between the moment clock 1 accelerates and the time they meet. But we already figured out that the time of clock 1 accelerating was simultaneous with the event of clock 2 reading 7.2 seconds in this frame (ie they were not synchronized to begin with), so it should read 7.2 + 12.8 seconds = 20 seconds when they meet.

So, to sum up: in the first frame, both clocks read a time of 0 when clock 1 accelerates, and it takes 20 seconds of coordinate time for them to meet, so that the slowed-down clock 1 only reads 16 seconds while the at-rest clock 2 reads 20 seconds when they meet. But in the second frame, clock 1 reads 0 but clock 2 reads 7.2 seconds at the moment clock 1 accelerates, and it takes 16 seconds of coordinate time for them to meet, so clock 1 elapses 16 seconds while the slowed-down clock 2 only elapses 12.8 seconds, meaning that it reads 7.2+12.8 = 20 seconds when they meet. So in both frames you predict that clock 1 reads 16 seconds and clock 2 reads 20 seconds when they meet, even though the two frames disagree about which was running slower as they approached each other, and they also disagree about simultaneity (ie what clock 2 read 'at the same moment' that clock 1 accelerated).

 

[Hurkyl]

I am not assuming absolute time

Yes you are (or at least you are assuming something logically equivalent to absolute time), and you did it yet again in this very post when you said:

"If the Andromeda centered frame is not moving wrt to the ECA frame, it can make real measurements as to the rate of R, although not as conveniently as C. If it is moving wrt to the ECA frame it will make apparent measurments as to both distances and time"




Now that I know the paper to which we're all referring, allow me to remind you that Einstein is in no way suggesting that any frame is truly stationary.

In the opening paragraph of section one, he states:

"Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ``stationary system.''"

Emphasis mine. The ``stationary system'' of his paper is simply a co-ordinate choice in which Newton's laws are valid to a first approximation. He merely wants to use the phrase as a convenient way to refer to the co-ordinate system whose coordinates he wants to label with x, y, z, and t. He even puts "stationary" in quotes at the beginning of the next few sections to remind us that he's not talking about anything truly stationary.

In no way is the stationary frame to be construed as being "special". To wit, you could simply choose any other frame you like in which Newton's laws are valid to a first approximation, and "the stationary system" now refers to the new choice throughout the entire paper.


I got to go; I'll make a further response later.

 

[yogi]

So in both frames you predict that clock 1 reads 16 seconds and clock 2 reads 20 seconds when they meet, even though the two frames disagree about which was running slower as they approached each other, and they also disagree about simultaneity (ie what clock 2 read 'at the same moment' that clock 1 accelerated).

Quite right Jesse - good show. You can analyse the problem in either frame - and if properly done, the answers should agree, which they do - somehow you led me to believe during one of our earlier debates that you did not concur with actual time difference in the one way trip i.e., I got the impression you were saying - from the #1 clock perspective, #2 would be found to be in arrears when the meet whereas from #2 perspective, #1 would have logged less time.

 

[yogi]

Hurkyl - Einstein used the word stationary - and we all know what was meant - it did not convey the idea of absolute rest

When I say you can use the moving Andromeda frame to make your analysis, you will be doing the same thing Jesse just did - which I have said before, will get you the right answer - all the apparent lengths and times combine to yield the same time difference. You can say the time for a clock to travel from here to Alpha at Gamma factor of 0.5 is shortened because the distance is half (Rindlers approach) or you can say that the traveler is halfway ahead on the time clock when he starts (an analysis I received from you). These methods all lead to a correct result.

 

[Janus]

I am not assuming absolute time.

Maybe not by your definition of "absolute".

But you certainly are assuming something closer to "absolute time" than the "relative time" used in Relativity.

What you seem to be calling "relative time" is limited to only a certain aspect of the full picture painted in Relativity.

It is as if you were treating time like the directions North and South. Two observers can be relatively postioned with respect to each other by varying degrees, But both will agree which is the most Northernly.

In Relativity, time is more like Left and Right. Two observers relatively positioned to each other, depending on how they are facing, may not agree as to who is to the right. Both may equally claim that they are on the right, and both can be correct.

 

[yogi]

So if we are in agreement that the coordinate frame of EAC is not preferred in the sense of an absolute rest frame - it is a frame where radar samplings can be made from C to R and from R to C at every point along the path of R to verify the difference in the clock rates.

R and C are identical clocks - the only difference is that R has been accelerated - thereafter R runs at a slower rate than before - any problems with this statement

 

[JesseM]

So if we are in agreement that the coordinate frame of EAC is not preferred in the sense of an absolute rest frame - it is a frame where radar samplings can be made from C to R and from R to C at every point along the path of R to verify the difference in the clock rates.

What do you mean when you say "it is a frame where radar samplings can be made"? If you agree that all frames make the same physical predictions, then all frames should predict the same thing about what a particular clock will read when a particular signal reaches it, so the radar samplings aren't associated with anyone frame. Of course, when any observer uses the raw data from clock-readings to try to calculate the rate at which the signals were "actually" emitted (taking into account doppler shift), he has to pick a particular reference frame for figuring out how far the signal had to travel, making the assumption that the signals travel at c in that frame, and calculations based on different frames will give different answers.

R and C are identical clocks - the only difference is that R has been accelerated - thereafter R runs at a slower rate than before - any problems with this statement

Yes, there's a problem. Although R's average rate over an entire orbit will be slower than C in all inertial frames, it is not true that R's rate will be slower than C at every moment in all inertial frames, so if you accept that any frame's analysis of the situation is equally valid, you can't say "thereafter R runs at a slower rate than before". Also, if you combined the raw data from the radar signals and clock-readings with the assumption about light moving at c in some frame, along with that frame's answer to how far the emitter was when the signal was sent, then this analysis of the data will agree with the abstract calculation of how this frame should expect R's ticking rate to vary. Again, there is nothing about sending radar signals that will force you to prefer one inertial frame over another.

 

[yogi]

Janus - whether time is absolute on some cosmic scale is yet to be proven - but it is not part of the premise of this thread - we start with a reference to Einstein 1905 part 4 - and we follow the arithmetic to arrive at Einstein's conclusion that as between the stationary frame and the moving frame, the clock which moves loses time relative to the stationary clock - that is all ...what I always wind up doing on this board is defending the notion that the moving clock (the one that got accelerated at the start of the journey is always losing time at every point in the trip) This is the source of the twin thing - turnaround does not create the problem - turnaround is only incidental in the sense that it provides a convenient place to compare readings back at the origin. Einstein makes it very clear, on the one way trip, the clocks will read different when they meet each other after following any pologonal path or whether the moving clock returns to its origin.

 

[JesseM]

we start with a reference to Einstein 1905 part 4 - and we follow the arithmetic to arrive at Einstein's conclusion that as between the stationary frame and the moving frame, the clock which moves loses time relative to the stationary clock

Einstein doesn't even talk about a "moving frame" in that problem, he just analyzes everything from a single frame, the one he calls the "stationary frame". Don't confuse frames with actual physical clocks! And Einstein does not conclude the accelerated clock "loses time", he just concludes it's behind when they meet. But every frame agrees it's behind when they meet, even frames that say the other clock lost time (see my earlier analysis, where in the second frame the accelerated clock ticked forward 16 seconds while the inertial clock only ticked forward 12.8 seconds--wouldn't you agree that in this frame it's the inertial clock that 'loses time'?)

 

[Hurkyl]

Well, much of what I was going to say now seems irrelevant, so I will skip ahead.

Hurkyl - Einstein used the word stationary - and we all know what was meant - it did not convey the idea of absolute rest

Okay -- so the question is why are you conveying the idea of absolute rest?

You continually pick out the ECA measurements as being "real", and everything else merely apparent. This conveys many absolute ideas:

Absolute time - Since using the ECA-frame is the only way to make "real" measurements, this gives us an absolute standard of time: the duration measured by ECA-clocks. All other durations one might measure are merely "apparent".

Absolute distance - Since using the ECA-frame is the only way to make "real" measurements, they give us an absolute standard of distance: that which is measured by ECA-rulers. All other distances are merely "apparent".

Absolute rest - Since using the ECA-frame is the only way to make "real" measurements, this gives us an absolute standard of rest: something is at rest if and only if its position remains constant according to ECA-rulers. All other notions of rest are merely "apparent". (Actually, this could be defined as saying that the absolute distance traveled by an object is zero)

Absolute simultaneity - Since using the ECA-frame is the only way to make "real" measurements, they give us an absolute standard of simultaneity: two events are simultaneous if and only if ECA-clocks say they happened at the same ECA-time. All other notions of simultaneity are merely "apparent". (Actually, this could be defined as saying the absolute duration between events is zero)

Need I go on?

 

[Hurkyl]

This is the source of the twin thing - turnaround does not create the problem - turnaround is only incidental in the sense that it provides a convenient place to compare readings back at the origin.

The twin paradox is the following (invalid) series of statements. (but with more or less detail, depending on the arguer)

(1) The earthbound twin has an inertial reference frame in which he's stationary.
(2) The spacebound twin is always moving in the earthbound twin's frame.
(3) Therefore, the spacebound twin's clock is always running slower than the earthbound twin's clock, as measured by the earthbound twin's frame.
(4) Therefore, when they meet, the spacebound twin's clock will read less than the earthbound twin's clock.
(5) The spacebound twin has an inertial reference frame in which he's stationary.
(6) The earthbound twin is always moving in the spacebound twin's frame.
(7) Therefore, the earthbound twin's clock is always running slower than the spacebound twin's clock, as measured by the spacebound twin's frame.
(8) Therefore, when they meet, the earthbound twin's clock will read less than the spacebound twin's clock.
(9) This is a contradiction.

If you think the twin paradox is anything other than the above argument, then you are not talking about the twin paradox -- you are talking about some other thing that involves a similar setup.

The turnaround is crucial to the refutation of the twin paradox, because it is the reason statement (5) is wrong. The spacebound twin is moving in a noninertial manner during the turnaround, and that is the only reason why he cannot have an inertial frame in which he's stationary. If you could somehow get rid of the turnaround, the argument would be rock-solid, and we'd have a true contradiction on our hands.