How Time Passes Differently for Twins Traveling at Light Speed

[JesseM]

All right Jesse - I will try to say it in a way that conveys what einstein said as I see it unambiguously - let's keep it real simple. A and B at rest in the same frame separated by a distance d. Clocks brought to sync. B starts moving toward A at relative velocity v (a short acceleration to get up to speed - then cruises at constant relative v). Einstein says when B arrives the clocks will no longer read the same - B's clock lags (has logged less time - is younger - whatever you want to call it).

I am saying that this is a real difference - it is not an observational apparency - it is a real objective difference in the two clocks.

I think your question is - what if you consider things from B's perspective

Not exactly, I mean what if you consider things from the perspective of an inertial frame where B is at rest after B accelerates. In this frame, A and B will initially both be traveling at velocity v, then B will accelerate and come to rest, while I'm not sure if you would say this would be true "from B's perspective" (perhaps you would say that both A and B were initially at rest from B's perspective)--as always, it's tricky to talk about the "perspective" of an observer who accelerates at any point during the time period you're considering, it's better to analyze the whole problem from the point of view of a single inertial frame.

Alternately, if you don't want to talk about "frames", you could talk about the perspective of a third observer C who has been traveling at velocity v relative to A since the beginning of the time period we're looking at, who at first sees B traveling at v and then sees B accelerate and come to rest.

once B is in motion, according to the transforms and the fact that B is now in an inertial frame - why can't he say that A's clock is running slow. He will measure it to be running slower if he considers himself at rest and A moving toward him in his own frame.

But if B draws this conclusion, it cannot be a reality. There is only apparent symmetry. When the two clocks arrive, we cannot have a result where B's clock reads less than A's while at the same time A's clock reads less than B's. So if you try to do the problem in the frame of B you would get a different answer if you fail to include the initial conditions

I think the problem is that when you say "B's frame" you are considering a perspective where A is initially at rest and synchronized with B, but then after B accelerates A is moving with velocity v and running slow. But again, this isn't a valid frame, since acceleration was involved. If you consider things from the perspective of that third observer C who was always traveling at v relative to A, this observer C will initially see A and B traveling together at velocity v, and will see A's clock ahead of B's by vd/c^2. Then B will accelerate and come to rest, while A continues to move at velocity v in the direction of B. A's clock will be ticking slower than B's, but because A's was already ahead, A's clock will still be ahead when A and B meet. C's prediction about how much A's clock will be ahead of B's when they meet will exactly match the prediction made in A's frame, even though in this frame the explanation for why A's clock was ahead will be different.

So, do you agree that the description from C's perspective is just as valid as the description from A's perspective? If not, do you at least agree that all mainstream physicists, including Einstein, would say that the perspective of one inertial frame is just as good as any other?

But if you take into account the inital conditions (namely - how did the relative motion come about) you will get the correct answer in any frame in which the motions are transformed.

What if we only start looking at the problem at some time t after B has accelerated? Aren't the initial conditions at t enough to make complete predictions about what will happen in the future, without knowing what happened before t (ie without knowing if it was A or B who accelerated?)

 

[yogi]

Well - here is where I am probably going to differ from what you refer to as mainstream physics - but I think it is not only consistent with SR, it is also in conformity with all experiments that I am aware of . So, from the standpont of a third frame C, if we consider the velocities of A or B or both after they are up to speed relative to C, we would lose what I consider important, namely how did these velocities come about. Now on the other hand, if A, B and C were all at rest at some instant in the past, and all clocks calibrated and brought into sync, and then A or B or both where later accelerated - then the inital conditions are not lost - namely - which clocks were put into motion relative to C. The transforms would work to yield the actual age differences. For example if A had accelerated toward B we could calculate a spacetime interval for A in the C frame and likewise if B had been accelerated (perhaps a different amount of acceleration than A), then B's interval would have both a temporal component and a spatial component as did A's as observed from the C frame. And a straightforward application of Einstein's formula would give the actual age difference between B and A when the meet.

What i think Einstein did in his 1905 part IV which is significantly entitled "Physical Meaning of the Equations..." was to take the transforms to a different level - from their derivation based upon observations between relatively moving frames where each observer infers the other guys clock is running slow - to a full blown Minkowski space time where it becomes crucial to know which clock moved. Admittedly, once the B clock is in motion, everything looks perfectly symmetrical - but as you have pointed out, if the frames are symmetrical, why would there be a real age difference?

This was the point of my post on the cosmological twin paradox introduced by Garth - I don't see how it is possible to sync clocks on the fly - that is in relative motion - you can read a clock of course - as it passes by, but you have no way of knowing whether it is actually running faster or slower - so on any round trip, whether it be a circumnavigation of the universe or once around the earth, you don't have a way of determining whether the other clock is actually running at an identical speed -

As a matter of academic interest - I think it would be a very interesting to set up a PF pole and ask members if they consider the situation of the two clocks initally in sync and then have B move to A, constitutes a real objective age difference or not.

Are you game?

ps - I know Minkowsk came up with the idea after 1905 - but as I read Einstiens's paper, I see it as implicit in his description.

 

[JesseM]

Well - here is where I am probably going to differ from what you refer to as mainstream physics - but I think it is not only consistent with SR, it is also in conformity with all experiments that I am aware of .

What is consistent with SR? The idea that B was objectively aging slower after it accelerated towards A, even though in C's frame it would be A that was aging slower? Or do you disagree that in C's rest frame, A would be aging slower?

So, from the standpont of a third frame C, if we consider the velocities of A or B or both after they are up to speed relative to C,

What does "up to speed relative to C" mean? C initially sees A and B moving at velocity v, then B accelerates and comes to rest in C's frame.

we would lose what I consider important, namely how did these velocities come about.

Velocities relative to what? Are you suggesting some concept of absolute velocity here? Why can't C and A have been moving at a constant velocity v relative to one another since the beginning of time? If C and A are just taken as the origins of inertial coordinate systems rather than real physical objects (after all, in relativity you are free to use 'reference frames' which no physical object is permanently at rest in), then the very definition of "inertial reference frames" demands that these two origins always move at constant velocity relative to one another.

Now on the other hand, if A, B and C were all at rest at some instant in the past

Nope, that's not the scenario I'm asking about. Again, the whole concept of an "inertial reference frame" presupposes that different frames are moving at constant velocity relative to one another for all time--if you want to consider what things look like from the perspective of a physical object which accelerates, you are not talking about inertial reference frames. Please don't duck the question--I'm asking whether the perspectives of different inertial reference frames are equally valid, not the perspectives of different physical observers who don't always move inertially.

By the way, are you saying that if our initial conditions at time t show A and B moving towards each other at constant velocity v, then in order to decide who is aging less we must know who accelerated last before time t? This is in clear contradiction of what you said on this thread, when I asked you:

Let me put it this way--do you agree that if we know the complete set of initial conditions at some time t in a particular frame (the position and velocity of both objects at t, the time on their own clocks, etc.) and we want to make some predictions about what will happen later, then since the laws of relativity are completely deterministic, these initial conditions at t are sufficient to make a unique prediction about the future? Do you agree that what happened before t is irrelevant, including the question of which of two clocks accelerated before t?

You replied "Yes - i will agree to that." So unless you misunderstood, or unless you are going back and changing your answer, that means if at some time t we see A and C moving towards each other at constant velocity, then the question of whether A or C accelerated at some time before t is not relevant to deciding any physical question, including the question of who is aging slower.

and all clocks calibrated and brought into sync, and then A or B or both where later accelerated - then the inital conditions are not lost - namely - which clocks were put into motion relative to C.

A was not put into motion relative to C during the period we are considering. A and C have been moving at constant velocity relative to each other since the beginning of the time period we are considering. If you like, you can consider them to have been moving at constant velocity relative to one another since the beginning of time, although as I said above this shouldn't be necessary if you agree that we don't need to know anything about times before our initial conditions to answer the question of who ages slower.

What i think Einstein did in his 1905 part IV which is significantly entitled "Physical Meaning of the Equations..." was to take the transforms to a different level - from their derivation based upon observations between relatively moving frames where each observer infers the other guys clock is running slow - to a full blown Minkowski space time where it becomes crucial to know which clock moved.

Well, that's just ignorant. Anyone who understands relativity knows that different reference frames disagree about which of two clocks is ticking slower, and that all frames are equally valid, the question of which clock accelerated in the past does not force you to choose one frame over another. This symmetry of different reference frames is a very basic part of "Minksowski space time", if you think that the question of which object "moved" (accelerated) is relevant to deciding which inertial reference frame to use, you're badly confused about how Minkowski space time works. The point of the twin paradox is not that one inertial frame is favored over another depending on who accelerated, it's just that you can't put the perspective of the non-inertial twin on the same footing as an inertial reference frame.

Admittedly, once the B clock is in motion, everything looks perfectly symmetrical - but as you have pointed out, if the frames are symmetrical, why would there be a real age difference?

How many times do I have to repeat this? The reason there is a real age difference is because different frames define simultaneity differently. Do you not believe me that C's frame will make exactly the same prediction as A's frame about what A and B will read when they meet, in spite of the fact that C's frame says A is ticking slower as they approach each other and A's frame says B is ticking slower as they approach each other?

I don't see how it is possible to sync clocks on the fly - that is in relative motion - you can read a clock of course - as it passes by, but you have no way of knowing whether it is actually running faster or slower

What do you mean by "sync"? Do you mean to make sure they're reading the same time? That's impossible if they're in relative motion, since they will be ticking at different rates. Or if by "sync" you just mean determining what one clock reads "at the same moment" that another clock reads a given time, like "when clock A read 2:00, clock B read 4:00" (ie the issue of simultaneity), then each frame can do this either using light-signals (taking into account the time the light took to reach you), or by using local readings on a network of clocks which are synchronized in that frame (the clocks are defined to be synchronized in this frame if light emitted at the midpoint of two clocks hits both at the same time according to their readings). This is the procedure that Einstein outlined in his paper, so even if you disagree with it, if you disagree that this is how Einstein defined simultaneity then you're just being ignorant.

As a matter of academic interest - I think it would be a very interesting to set up a PF pole and ask members if they consider the situation of the two clocks initally in sync and then have B move to A, constitutes a real objective age difference or not.

Are you game?

Only if both the scenario and the question are phrased with enough detail so people don't misunderstand the question. For example, I might phrase it like this:

Suppose you have two clocks A and B which are initially at rest relative to one another and synchronized in their own frame, then B accelerates towards A and moves toward it at velocity v until they meet. Do you think it is objectively true that B was aging more slowly as it approached A, even though it is possible to view this situation from a frame where A and B are both initially moving at velocity v, then B comes to rest and A continues to move towards it at velocity v until they meet, so that in this frame A would be ticking more slowly after B comes to rest?

Of how about this:

Suppose two clocks start out at rest relative to one another and synchronized in their own frame, then one accelerates briefly and after that they move towards one another at constant velocity. If different inertial reference frames disagree about which clock is ticking slower as they move together, can we determine which frame is "objectively" correct by checking which clock was the one that accelerated?

 

[yogi]

Briefly - rather than go into all your misinterpretations as to what I have said - if you know the complete history of the two clocks - then yes, the predictions as to which is ticking faster, if either, is determined. By complete history you would have to know more than just the fact that the two frames have relative motion.

You can find recogonized authors that interpret Einstein's statement as real one way time dilation (age difference). John D Barrow for example explains the reality based upon the difference in the energy that can be attributed to the change in velocity - anyway - the primary experiments that are available to show time dilation are those dealing with high speed particles, H and K round the world airplane journeys, GPS, all of which are easily explained by taking Einstein's explanation at face value.

So let us see if we can agree upon a correct way to state the poll. I object to the words "objectively correct" I propose the following:

Einstein makes the following statement in part 4 of his 1905 paper under the Heading Physical meaning of the Equations in respect to moving Rigid bodies and moving clocks:

"If at points A and B there are stationary clocks, which viewed in the stationary system are synchronous, and if the clock A is moved with velocity v along the line AB to B, then on its arrival at B, the two clocks no longer synchronize, but the clock moved from A to B, lags behind the other, which has remained at B..."

Question for members - is this a real age difference or would the two clocks actually read the same when compared?

 

[Ich]

We´ve been through this - The time difference is real, it is the difference in proper time since the clocks of A and B have been synchronized in frame A.
The synchronization is of course frame dependent, and so is the time difference if you chose tho synchronize in a different frame.

 

[JesseM]

You can find recogonized authors that interpret Einstein's statement as real one way time dilation (age difference). John D Barrow for example explains the reality based upon the difference in the energy that can be attributed to the change in velocity - anyway - the primary experiments that are available to show time dilation are those dealing with high speed particles, H and K round the world airplane journeys, GPS, all of which are easily explained by taking Einstein's explanation at face value.

No, you are simply misinterpreting them, as usual.

Einstein makes the following statement in part 4 of his 1905 paper under the Heading Physical meaning of the Equations in respect to moving Rigid bodies and moving clocks:

"If at points A and B there are stationary clocks, which viewed in the stationary system are synchronous, and if the clock A is moved with velocity v along the line AB to B, then on its arrival at B, the two clocks no longer synchronize, but the clock moved from A to B, lags behind the other, which has remained at B..."

Question for members - is this a real age difference or would the two clocks actually read the same when compared?

yogi, this is a totally dishonest strawman on your part--you know perfectly well that I agree the clock A would be behind B when they meet, I just disagree that this means A was "aging slower" during its journey.

Let's say A and B start out 1 light year apart in their rest frame, and synchronized in this frame, then at the moment that both clocks read 2005, A accelerates to 0.5c and moves at constant velocity towards B. In this frame, A will reach B in (1 light year)/(0.5c) = 2 years, in 2007. But A was ticking at (1 - 0.5^2) = 0.866 of B's rate during this trip, so when it meets B it will only read 2005 + 2*0.866 = 2006.73.
So, in B's rest frame:
amount of time that B ages after A accelerates: 2 years
amount of time that A ages after A accelerates: 1.73 years

But in the frame of an inertial observer C who sees A and B initially moving at 0.5c, then sees A decelerate until it's at rest, things look a bit different. In this frame, A and B were initially not synchronized--instead, A and B were initially out-of-sync, with B ahead of A by 0.5 years. So if A read 2005 at the moment it decelerated, B already read 2005.5 at that moment. After that, B was moving towards A at 0.5c, and in this frame the distance between them was only 0.866 light years, so it takes (0.866 light years)/(0.5c) = 1.73 years for B to reach A. Since A was at rest during this time, its clock will elapse 1.73 years during this time, so it will read 2005 + 1.73 = 2006.73 when B arrives. But B is only ticking at 0.866 the normal rate during this time, so itwill tick 1.73*0.866 = 1.5 years in this time, and since it read 2005.5 at the moment A accelerated, it will read 2005.5 + 1.5 = 2007 at the moment it reaches A.
So, in C's rest frame:
amount of time that B ages after A decelerates: 1.5 years
amount of time that A ages after A decelerates: 1.73 years

So, both frames predict that B reads 2007 and A reads 2006.73 at the moment they meet, but in B's rest frame it was A who was aging slower after A accelerated, and in C's frame it was B who was aging slower after A decelerated. The question is, are both these descriptions equally valid? Am I correct in understanding that you would say both descriptions are not equally valid, yogi, but that the description in B's frame is somehow more correct than the description in C's frame? I promise that any relativist, including John D Barrow, would say both descriptions are equally valid.

 

[yogi]

Jesse - you are weasel wording your way around again - you have previously taken the position that there can be no objectively real age difference in the situation I quoted in post 64.

 

[yogi]

Jesse - Here is one of my previous statements:
Originally Posted by yogi
Clocks in relative motion do record different absolute times whenever they have been synced at rest and one clock is put into motion - all evidenced by H and F airplane experiments, GPS, and the extended lifetime of high speed muons and pions that are created in the Earth reference frame and subsequently move relative thereto.

And your response:

None of these experiments show evidence for an "absolute" truth about which clock is running slow, all of them are perfectly consistent with the idea that each inertial frame sees clocks in other frames running slow, and that there is no way to settle which frame's point of view is the correct one. If you think Einstein would have disagreed, then you are completely misunderstanding his paper.

Did I use the word "correct" or preferred or universal -no as to each

I consistently said that when B moves to A and the two clocks are compared in the frame in which they were synced - A will have logged more time than B - there is a one way age difference, real and objective.

 

[JesseM]

Jesse - you are weasel wording your way around again - you have previously taken the position that there can be no objectively real age difference in the situation I quoted in post 64.

No, I explicitly said in many posts (I can quote some if you like) that in the scenario where the two clocks are initially at rest relative to each other and synchronized in their rest frame, and then one accelerates towards the other, then the one that accelerated will show a lesser time reading. My position has always been that although this clock shows a lesster time reading when they meet, that does not mean that the clock that accelerated has "aged less" between the time it accelerated and the time they meet. This is clear in the numerical example I give in my last post, where A accelerates towards B, and all frames agree that when they meet, A will read 2006.73 while B will read 2007. But you see that in B's frame, A ages 1.73 years and B ages 2 years between the time A accelerates and the time they meet; but in C's frame, A ages 1.73 years but B only ages 1.5 years between the time A accelerates and the time they meet. Are you saying that the description of the situation from C's perspective is any less valid than B's, or aren't you? Please give me a simple straight answer to this question.

I consistently said that when B moves to A and the two clocks are compared in the frame in which they were synced - A will have logged more time than B - there is a one way age difference, real and objective.

"Logged more time" since when? In C's frame, B only logs 1.5 years after A accelerates while A logs 1.73 years, but B still comes out ahead because A read 2005 at the moment it accelerated while B already read 2005.5 at the same moment.

To pin down what you mean here, let's imagine that A and B were out-of-sync in their own rest frame--at the same moment B read 2005, A already read 3164. Then A accelerates, and when they come together, B reads 2007 and A reads 3165.73. Would you say that A has "logged more time" simply because it reads a greater time when they meet, ignoring the question of whether they were in sync to begin with? Or would you say that the question of whether they were initially in sync is relevant to the question of which clock "logged more time"?

 

[yogi]

Don't add other factors - I am saying that, in the example I proposed as a PF poll question in post 64, between a first spacetime event defined as A and B at rest in the same frame and both set to read zero in the frame in which they are at rest, and a second spacetime event (B's subsequent arrival at A consequent to a short acceleration period followed by constant relative velocity v thereafter), then, if A and B both stop their respective clocks and the hands viewed, the clocks will read different (For example A could read 50 minutes and B could read 40 minutes).

 

[Ich]

there are 3 spacetime events involved.

 

[JesseM]

Don't add other factors

Those "other factors" are what our debate is about, since we both agree that in the scenario you proposed as a poll, A will read a lesser time than B when they meet. So now please address the two questions in my last post, which I think will clarify what it is we actually disagree about:

This is clear in the numerical example I give in my last post, where A accelerates towards B, and all frames agree that when they meet, A will read 2006.73 while B will read 2007. But you see that in B's frame, A ages 1.73 years and B ages 2 years between the time A accelerates and the time they meet; but in C's frame, A ages 1.73 years but B only ages 1.5 years between the time A accelerates and the time they meet. Are you saying that the description of the situation from C's perspective is any less valid than B's, or aren't you?

and

To pin down what you mean here, let's imagine that A and B were out-of-sync in their own rest frame--at the same moment B read 2005, A already read 3164. Then A accelerates, and when they come together, B reads 2007 and A reads 3165.73. Would you say that A has "logged more time" simply because it reads a greater time when they meet, ignoring the question of whether they were in sync to begin with? Or would you say that the question of whether they were initially in sync is relevant to the question of which clock "logged more time"?

I am saying that, in the example I proposed as a PF poll question in post 64, between a first spacetime event defined as A and B at rest in the same frame and both set to read zero in the frame in which they are at rest

As Ich says, this is not a "spacetime event". A spacetime event is something that happens at a single point in space and a single moment in time--any description of two clocks separated in space cannot qualify as a single event. But this is just an issue of your using incorrect terminology, I understand the scenario you are describing and as I've said practically every time we discussed this scenario, I agree that the clock that accelerates will read a lesser time when they meet. If you ever thought I disagreed about this, you haven't been reading my posts very carefully.

 

[yogi]

No Ich says there are three events - which is correct - however I am only concerned with the reading of clocks in the rest frame starting at the time B begins to move and the time both clocks are stopped. Tell me Ich - would you agree that it makes no difference whether A and B are initally separated and then B moves to A - or If A and B were initally together and B moves the same distance as he did in the first case - and when he stops at the same point and simultaneously stops his stopwatch (clock) - if he sends a signal back to A - would you that in this case the transmiited signal would indicated the same time - e.g. B would send "my clock reads 40 minutes at the time I reached the destination. And A, Knowing the distance, could then calculate the time that passed on his clock from the time B left up until B signalled - and would he conclude that his clock read 50 minutes as before.

Jesse - the way you frame the problem always leads to diversionary tangents - I know how most SR types like to transform from one frame to another - blindly using the formulas - but not keeping in mind the limitations that - measurements of space and time in another relatively reference frame are illusory - and this leads to the abstruse analysis that colminates in shifting hyper planes and Earth clocks jumping ahead by thousand of years because the traveler turns around and so on. When you are all done, that type of analyis leaves one not knowing reality from squat. No wonder Einstein said "Now that the mathematicians have gotten involved in relativity, I am not sure I still understand it myself "

 

[JesseM]

Jesse - the way you frame the problem always leads to diversionary tangents

So do you refuse to answer my questions?

but not keeping in mind the limitations that - measurements of space and time in another relatively reference frame are illusory

Illusory? What the hell does that mean? If A and B are out-of-sync in C's frame, is this somehow more "illusory" than the fact that A and B are in sync in B's frame. If so, then it seems you do indeed think the description in B's frame is more valid than the description in C's frame, even if you are not willing to be straight with me and come out and say it in response to my question about this.

and this leads to the abstruse analysis that colminates in shifting hyper planes and Earth clocks jumping ahead by thousand of years because the traveler turns around and so on.

Not if you are consistent about which inertial frame you use throughout the problem. The shifting hyperplanes only happens if you insist on trying to understand what things look like from the perspective of a non-inertial observer, meaning you have to switch from one frame to another in the middle of the problem. But really, the theory of SR was never meant to tell you anything about the "reference frame" of a non-inertial observer, it is just supposed to tell you how a given physical situation can be understood if you analyze it from beginning to end in one inertial frame or another. In the case of the A-B scenario, if you analyze the whole thing from the perspective of B's frame, or if you analyze the whole thing from the perspective of C's frame, there is no shifting of hyperplanes or sudden jumps in clock readings whatsoever.

No wonder Einstein said "Now that the mathematicians have gotten involved in relativity, I am not sure I still understand it myself "

Yogi, you sound like a creationist taking quotes by scientists out-of-context to make it sound like they're supporting positions they obviously don't. If you notice, the only mathematical ideas I'm using in discussing how things would look in B's frame vs. C's frame are the Lorentz transformation equations, which Einstein himself derived in section 3 of his 1905 paper! And the whole concept of the Lorentz transformation is not that they represent some arbitrary mathematical transformation, they are the formulas for relating physical measurements made on systems of measuring-rods and synchronized clocks of different observers. If observer B has a system of measuring-rods spread throughout space which are at rest relative to him, with clocks mounted along them that are synchronized using the assumption that light travels at a constant velocity relative to B, and C also has a system of measuring rods at rest relative to him, with clocks mounted on them that are synchronized using the assumption that light travels at a constant velocity relative to him, then what the position and time coordinates they get by reading off their respective measuring-rod/clock systems will be exactly the ones I gave in my numerical example earlier. For example, if C sees that the clock in his system that was next to A when it accelerated read 2005 at that moment (at which moment A's own clock also read 2005), then if he looks at the moment that B was next to a different clock in his system that also read 2005, he will see that B's own clock read 2005.5 at that moment. This shows the physical meaning of the statement that in C's frame, the event of A accelerating, and of A's clock reading 2005, happened at the same moment that B's clock read 2005.5. So don't give me that nonsense about this being just a matter of abstract mathematics, Einstein explains in detail the physical meaning of the coordinates of different inertial observers in section 1 of his 1905 paper.

 

[yogi]

Its not abstract math - it is measurement math - the measurements made in a relatively moving frame are only apparent - they are true in the sense that the measurements are true - but to introduce additional clocks and frames is not necessary for the situation involved in the simple example Einstein gave - at no time in his explanation of the physical meaning of the equations does Einstein make any claim about what the moving (B clock) measures in the A frame. (Its not important) The reciprocity of the frames is not discussed by Einstein in part 4 when he describes the physical meaning. So why consider anything other than the simple fact that the clocks don't agree when the one way journey is completed. As you say "SR is meant to explain what happens from beginning to end in one inertial system" dido to that.

Me a Creationist...In the beginning there was nothing, and God said let there be light. And still there was nothing, but you could see it.

 

[JesseM]

Its not abstract math - it is measurement math - the measurements made in a relatively moving frame are only apparent

All frames are "relatively moving" relative to something--for example, the frame where B is at rest is moving relative to C. Again, are you saying there's some reason to believe the measurements in B's frame are any less "illusory" or "apparent" than the ones made in C's frame?

but to introduce additional clocks and frames is not necessary for the situation involved in the simple example Einstein gave - at no time in his explanation of the physical meaning of the equations does Einstein make any claim about what the moving (B clock) measures in the A frame. (Its not important)

Just a quibble--in Einstein's example it's the B clock that is the inertial one, the A clock is the one that accelerates. But even if you switch the letters, I'm not sure I understand your point--he certainly talks about what the clock that was moved measures, he says that it lags behind the clock that didn't move by (1/2)t(v/c)^2. Maybe that's not what you meant by "what the moving clock measures in the clocks' frame", but if so, what did you mean? Did you mean that Einstein doesn't talk about how things look in the frame of the clock that was moved? Well, I don't either, since the clock that was moved (A) moved non-inertially and thus doesn't have a "frame" in SR. I did talk about how the whole situation would look from the frame of a third observer C who is moving inertially at velocity v relative to the inertial observer B. So is your point just that Einstein didn't talk about how the whole situation would look in a different frame? No, he didn't, but anyone who comprehended the previous sections of the paper would understand that Einstein believed it's an arbitrary choice which frame you use to describe a given physical situation, no inertial frame is more valid than any other. Would you disagree that this is clearly Einstein's view?

The reciprocity of the frames is not discussed by Einstein in part 4 when he describes the physical meaning.

Yes he does. He first talks about how objects look in a reference frame K (which he has labeled 'the stationary system') when they are moving relative to K, then he says "It is clear that the same results hold good of bodies at rest in the 'stationary' system, viewed from a system in uniform motion".

So why consider anything other than the simple fact that the clocks don't agree when the one way journey is completed.

Because that's not all that you consider. You also say that the clock which moved "logged less time" than the other clock, or that it "aged less". And you also seem to think it is somehow more valid to say that the two clocks were initially in sync than it is to say they were initially out-of-sync. If you want to renounce all such statements and just say that in Einstein's scenario, the clock that accelerated will be behind the clock that didn't when they meet, then I certainly agree with that much, but if you continue to make statements which go beyond that and seem to implicitly privilege B's frame over other frames, then I still say you're wrong.

As you say "SR is meant to explain what happens from beginning to end in one inertial system" dido to that.

Yes, but SR also says that the only truly physical facts are the ones that would be true in every inertial frame. The fact that A is behind B when they meet will be predicted in every frame, but the statement that A and B were initially synchronized is not a frame-independent truth, nor is the statement that A's clock was ticking more slowly as A and B approached each other.

Me a Creationist...In the beginning there was nothing, and God said let there be light. And still there was nothing, but you could see it.

I wasn't accusing you of being a creationist, just of taking quotes out of context like a creationist.

 

[yogi]

What I have attempted to say - many times - is that the A frame is the frame where the clocks are brought in sync - we never do any syncing in the B frame (I am calling B the traveling clock) - everything is determined in A frame - once B is up to speed it is also a valid inertial frame - but it is different than the A frame

To restate: B is initially at rest in the A frame and in sync with A clock - B leaves the A frame (via acceleration that produces a relative velocity) and returns to a different spatial point in the A frame (or B could return to the same location as A). I am saying that this return does not have to be a physical pulling up to a stop in the A frame adjacent to A - it can be passing any known spatial point that was measured off (a proper distance in the A frame) and B's clock will be read by A either because B physically stops at one of these points or passes by and transmits a radio signal to A.

In contrast to venturing to a distant star and returning to effect real age difference (classical twin paradox) - real age difference is brought about whenever one clock leaves the frame in which it has been calibrated and later returns to any point in the frame in which it was calibrated. That is the essence of einstein's explanation in part 4

If you do not agree - that is ok - but then show me a single experiment that disproves my interpretation (don't give me the mainstream authority argument - give me an experiment)

 

[jdavel]

yogi and JesseM,

Two clocks, A1 and A2, at rest wrt each other, separated by a distance L, synchronized as defined by SR.

A third clock, B, moving at v wrt A1 and A2, passes A1 (on his way to A2) and, at the instant he passes A1 he synchs with A1.

Do you guys disagree on what B and A2 read when B passes A2?

 

[JesseM]

What I have attempted to say - many times - is that the A frame is the frame where the clocks are brought in sync - we never do any syncing in the B frame (I am calling B the traveling clock)

OK, I have been calling A the traveling clock since that's how Einstein wrote it in his example. But I'll switch from now on so we're using the same convention.

- everything is determined in A frame - once B is up to speed it is also a valid inertial frame - but it is different than the A frame

To restate: B is initially at rest in the A frame and in sync with A clock - B leaves the A frame (via acceleration that produces a relative velocity) and returns to a different spatial point in the A frame (or B could return to the same location as A). I am saying that this return does not have to be a physical pulling up to a stop in the A frame adjacent to A - it can be passing any known spatial point that was measured off (a proper distance in the A frame) and B's clock will be read by A either because B physically stops at one of these points or passes by and transmits a radio signal to A.

Sure. Or this other point could have a clock that was synchronized with A's clock in A's rest frame, and then you could compare what B's clock reads at the moment it passes this clock, and you'd see B was behind this other clock. This would be the idea described in section 1 of Einstein's paper, where the coordinates of an event (in this case, the event of B's clock reading a certain time) are determined by local readings on a network of measuring-rods and clocks spread throughout space which are all at rest relative to the observer and with the clocks synchronized according to Einstein's procedure.

In contrast to venturing to a distant star and returning to effect real age difference (classical twin paradox) - real age difference is brought about whenever one clock leaves the frame in which it has been calibrated and later returns to any point in the frame in which it was calibrated. That is the essence of einstein's explanation in part 4

What I am saying is that this is not a "real age difference" unless they meet, because nothing is physically "real" in relativity unless it is agreed upon in all frames. It's true that if B reads 2010 at the same moment he's passing a clock in A's network which reads 2015, then at that moment B is five years younger than A, in A's frame. But in C's network of clocks, at the moment B reads 2015 he may be passing a clock in C's network that reads 2020, and at the moment that A passes a clock in C's network that reads 2020, A may read 2014. This would mean that in C's frame, A is one year younger than B. Since the question of whether B is older or younger than A at the moment that B reads 2015 cannot be decided in a way that doesn't depend upon an arbitrary choice of reference frame, there is no physically real age difference between them until they meet at a single point in space.

If you do not agree - that is ok - but then show me a single experiment that disproves my interpretation (don't give me the mainstream authority argument - give me an experiment)

I am not sure what your interpretation actually is. Why is it, exactly, that your interpretation tells you that the age difference in A's frame is more "real" than the age difference in some other frame? Is it simply because Einstein chose to describe this example from the point of view of this frame? Or is it because they were initially brought into sync in this frame? If they had been initially brought into sync in some frame other than their rest frame, would you say that the "real age difference" would be the one in this other frame, or would you say that their real age difference should still be viewed in terms of their initial rest frame, but that it would no longer match the difference in their clock-readings since they were out-of-sync in their initial rest frame? If you want me to try to find an experiment that shows why your interpretation doesn't make sense, then please answer these questions about how your interpretation works.

 

[JesseM]

yogi and JesseM,

Two clocks, A1 and A2, at rest wrt each other, separated by a distance L, synchronized as defined by SR.

Synchronized in their rest frame, presumably?

A third clock, B, moving at v wrt A1 and A2, passes A1 (on his way to A2) and, at the instant he passes A1 he synchs with A1.

Do you guys disagree on what B and A2 read when B passes A2?

No, I'm pretty sure we both agree that B would be behind A2. But I think yogi would say this means that B really aged less than A2 did between the time it passed A1 and the time it passed A2, while I would point out that in B's frame, A2 aged less than B between the times of these two events, and I'd say that no inertial frame should be preferred over any other.

 

[jdavel]

So,

Two clocks, A1 and A2, both at rest in S, separated by a distance L, synchronized as defined by SR.

A third clock, B, at rest in S' which is moving at v wrt S, passes A1 (on his way to A2) and, at the instant he passes A1 he synchs with A1.

Suppose you define 3 events, E1, E2, and E3 and use the notation:
event: En[x, t, x', t']
gamma = Y

Then the three events and their S and S' coordinates are:

E1[0, 0, 0, 0] "B passes A1"

E2[0, L, YL, -YLV/C^2] "A2 is set to 0"

E3[L, L/v, 0, (L/v)/Y] "B passes A2"

JesseM, when you say "...in B's frame, A2 aged less than B between the times of these two events" which two events do you mean?

 

[JesseM]

So,

Two clocks, A1 and A2, both at rest in S, separated by a distance L, synchronized as defined by SR.

A third clock, B, at rest in S' which is moving at v wrt S, passes A1 (on his way to A2) and, at the instant he passes A1 he synchs with A1.

Suppose you define 3 events, E1, E2, and E3 and use the notation:
event: En[x, t, x', t']
gamma = Y

Then the three events and their S and S' coordinates are:

E1[0, 0, 0, 0] "B passes A1"

E2[0, L, YL, -YLV/C^2] "A2 is set to 0"

E3[L, L/v, 0, (L/v)/Y] "B passes A2"

JesseM, when you say "...in B's frame, A2 aged less than B between the times of these two events" which two events do you mean?

In B's frame, the event of E1 does not happen simultaneously with E2--instead, at the moment B passes A1 and both read 0, A2 reads vL/c^2. So, define the event E2b: "A2 reads vL/c^2". If you want to compare how much A2 ages vs. how much B ages in B's own rest frame, then you must compare how much time elapses on B between events E1 and E3 with how much time elapses on A2 between events E2b and E3. Saying that event E2 is somehow more important than E2b is equivalent to saying that one inertial frame's definition of simultaneity (the A1/A2 rest frame) should be preferred over another inertial frame's definition of simultaneity (B's rest frame).

 

[jdavel]

Ok, how's this?

Two clocks, A1 and A2, both at rest in S, separated by a distance L, synchronized as defined by SR.

A third clock, B, at rest in S' which is moving at v wrt S, passes A1 (on his way to A2) and, at the instant he passes A1 he synchs with A1.

Suppose you define 4 events, E1, E2a, E2b and E3 and use the notation:
event: En[x, t, x', t']
gamma = Y

Then the four events and their S and S' coordinates are:

E1[0, 0, 0, 0] "B passes A1"

E2a[L, 0, YL, -YLv/C^2] "A2 is set to 0"

E2b[L, vL/c^2, L/Y, 0] "A2 reads vL/c^2"

E3[L, L/v, 0, (L/v)/Y] "B passes A2"

 

[yogi]

djavel - I do not know what is meant by syncing a clock that flies by - we can read its instantaneous value, but we do not have a way of determining that the flyby clock is actually running at the same speed as the two clocks that were in the same rest frame. For example a GPS clock that flies over the North Pole will not be in sync with a clock at the North Pole unless it had been preset to run at the same rate as the clock in the non rotating Earth centered reference frame located at the same height as the satellite

Jesse - I do not understand why the B clock has to be adjacent (physically return to the same point occupied by the A clock) for a real time difference to have elapsed.

 

[JesseM]

Jesse - I do not understand why the B clock has to be adjacent (physically return to the same point occupied by the A clock) for a real time difference to have elapsed.

As I said, because I'd say the only "real" physical quantities are those that all frames agree on. Do you agree that as long as the two clocks are separated in space, different frames will disagree on the time difference between them? Are you saying the time difference in A's frame is more "real" than the time difference in C's frame?

 

[JesseM]

Then the four events and their S and S' coordinates are:

E1[0, 0, 0, 0] "B passes A1"

E2a[L, 0, YL, -YLv/C^2] "A2 is set to 0"

E2b[L, vL/c^2, L/Y, 0] "A2 reads vL/c^2"

E3[L, L/v, 0, (L/v)/Y] "B passes A2"

Yes, this looks fine to me.

 

[Dragongod]

the problem is that Einstein never actually proved his special relativity theory. Its based on his assumption that in space-time, which according to him is some kind of forth dimension, time isn't universal. He just merely stated that. He never proved it with logical reasoning. So according to his assumptions, if you have twin at point A and twin at point B if one moves faster than the other over, automatically because time isn't universal, one will have to be older. It doesn't actually make sense. Whether you travel at the speed of light or not, and i can say at the speed of light because it hasn't been proven that the speed of light is actually some kind of cosmic speed limit, the distance you travel over in no way should effect time. Time within a system (the Universe) should be constant. According to Einstein its not but that is irrevelent because who is to say he is right - it is not proven that time isn't constant. And logically, it should be. All that changes, within a system where time is constant, is the distance traveled by the body in that period of time. It doens't destort time itself. Special Relativity Theory is based on Einstein's assumptions about Spacetime.

 

[Dragongod]

According to Einstein Time is a subjective thing. Time according to me is not. Time exist whether we do or not and always moves forward at an instanteous rate that we cannot measure. For example, the second you try to measure an instant, you are already too late. Time is always moving forward and cannot be distorted, especially by different frames of reference. Whether i am at point A or you at point B or C or D or F it has no baring on the time that is constantly moving forward regardless of anything.

 

[DaveC426913]

Dragongod, are you aware of the countless experiments that have demonstrated beyond a shadow of a doubt that objects traveling at relativistic speeds experience time at a different rate?

We don't need spaceships and distant planets and thought experiments. This is real laboratory experimentation. Particles fired at relativistic speeds in accelarators die at a different rate than if they were not moving. Those rates are predicted with exquisite accuracy, time and time and time again, by einstein's theory.

Relativity is one of the most tested theories in the history of science, and it has passed spectacularly every time.

Einstein's relativity is not merely the best theory going, it is the only theory that even makes the trip downtown, let alone into the ballpark.

 

[Dragongod]

That doesn't prove that the particles are somehow not governed by the same dimension of time. The fact that that happens (particles moving at a faster and rate and living longer than those that are not moving as fast) could be due to the fact that as particles move over a DISTANCE not TIME, they gain more mass and therefore gain more energy. That experiment doesn't necessaritly prove what Einstein was proving - that it is due to different TIMES.