What Causes Time Dilation in the Twin Paradox?

[atyy]

You are probably already aware of this, but the term "real" is very inappropriate. What these clocks would tell you is just what event on Earth your "now" is simultaneous with in A's frame. But A's frame is obviously not any more real than B's.

Within the framework of SR in which inertial frames are special, wouldn't A's frame be more "real" in the sense that it is a single inertial frame?

 

[matheinste]

Hello neopolitan.

Quote:-

---If I were designing a spaceship for "B", complete with a clock that shows "B" the time elapsed for "A", I would not plan on having that clock jump from 7.2 years to 32.8 years at turnaround. Nor would I have a clock which just quickly scrolled forwards to 32.8 years.----

But this is what happens from the point of view of B.When A and B are reunited there is an age difference, it is not just an optical illusion caused by light travel times.

The turnaround can take as long as you like if you want to limit the rate of advance of A's time as seen by B.

Matheinste

 

[neopolitan]

What you're defining here is just the future light cone of the local event. The apex of the light cone is not simultaneous with any other event on the light cone.

No, I was talking about the future light cone of the distant event. The information about an event, ie a signal, takes a period of x/c to reach a distant observer (and that has to be x in the observers frame). An event which occurred a period of x/c before this signal is received is by definition simultaneous with the event which transmitted the signal - in terms of the receiver's frame.

Oddly enough, you're getting this part exactly right. It's as if you're using the correct definition of simultaneity for this part, even though you just defined it incorrectly.

Yeah, odd isn't it.

This is just wrong. The deliveries obviously only depend on B's location in spacetime, but simultaneity only depends on velocity. So a change of simultaneity isn't going to make anything too weird happen to the deliveries.

This is pretty much my point. You won't get weird deliveries. The simultaneity confusion arises because you insist on trying to determine the time a signal was emitted in terms of a frame which was not valid when the signal was emitted. In the real world, you just won't do that.

Try putting it this way, call the midpoint of the turnaround an event. At this event, "A" and "B" have zero separation speed. There is a world-line joining these events (two, if you want to do one for "A" and one for "B"). There is causality linking all "B" events post this event and all "A" events post this event.

"B" could choose to stay in place until all signals which were en route catch up. Let's say 9.6 years. During this time, 16 years worth of signals would be received. Then "B" could head off again, same velocity and intercept 20 years of signals during 12 years of shipboard time (plus the 9.6 years worth of signals which were on the way).

Or, "B" could choose not to wait and head off instead. In this case, "B" would intercept 16 years worth of signals where were already on the way, plus the 20 years worth of signals which "A" sends during the 12 shipboard years it takes "B" to get back.

If "B" chooses to slow down on the way back, it will have two effects, one is that "A"'s apparent exuberance with signally will die down and the other is that "B" will intercept signals from "A" at a reduced rate.

"B" should then designate a new event, the slowing down event and consider what will happen with the flow of signals before and after this event. Again, "B" could chose to stop, gain zero separation rate with "A", receive all signals which were en route before stopping, and then keep going at a slower rate ... or "B" could chose to just slow down, receive those en route signals and then the ones sent after the event which simultaneous with the slow down (simultaneous according to "B", of course).



If you ignore these events, you will calculate discontinuities. This may be the accepted thing to do, but it's not characteristic of the real universe.

cheers,

neopolitan

 

[neopolitan]

Hello neopolitan.

Quote:-

---If I were designing a spaceship for "B", complete with a clock that shows "B" the time elapsed for "A", I would not plan on having that clock jump from 7.2 years to 32.8 years at turnaround. Nor would I have a clock which just quickly scrolled forwards to 32.8 years.----

But this is what happens from the point of view of B.When A and B are reunited there is an age difference, it is not just an optical illusion caused by light travel times.

The turnaround can take as long as you like if you want to limit the rate of advance of A's time as seen by B.

Matheinste

So if you were designing this clock, what would it do?

I would like to clarify.

cheers,

neopolitan

 

[neopolitan]

if all you want his clock to do is tell the 'real' time on Earth then by all means design it however you want. but if as an engineer you want his clock to be useful to him in timing events on board his ship then you should reconsider.

I had to laugh.

The clock in question has one specific function, which I stated. In the modern world we are overrun by ordinary clocks, I have about five in front of me (computer, alarm, wall clock, time on mobile, time on printer, oh, and one on the wireless phone unit, so it is six). I didn't even consider that designing a special clock to give time elapsed for "A" might cause "B" undue hardship :)

cheers,

neopolitan

 

[atyy]

If you ignore these events, you will calculate discontinuities. This may be the accepted thing to do, but it's not characteristic of the real universe.

Is your point that everyone ages according to his own proper time, and that B can calculate the proper time of A?

 

[matheinste]

Hello neopolitan.

Quote:-

---So if you were designing this clock, what would it do?---

Why would i need such a clock. Why not just calculate A's time. Should you wish for a display of the results of this time calculation then that is easy enough.

Matheinste.

 

[Fredrik]

The information about an event, ie a signal, takes a period of x/c to reach a distant observer (and that has to be x in the observers frame). An event which occurred a period of x/c before this signal is received is by definition simultaneous with the event which transmitted the signal - in terms of the receiver's frame.

(Units such that c=1). So if a signal is emitted at (0,0) and received at (x,x), the event that occurred a time x before the event (x,x) (at spatial coordinates x I assume) has coordinates (0,x) and is simultaneous with the emission (0,0). At least we agree about something. We have found that a simultaneity line is a line of constant time coordinate.

So far this definition of simultaneity agrees with the one I posted in #18, but have you really thought about what it means? Do you agree or disagree with my claim that the blue lines are simultaneity lines of the rocket when it's moving away from Earth? What about the simultaneity lines when the rocket has turned around?

This is pretty much my point. You won't get weird deliveries.

But your claim was of the form "if [something that's 100% true] then we get weird deliveries", so your point must have been that the true statement was actually false. (Reductio ad absurdum). But your claim was false. You were wrong to think that the assumption implies something obviously incorrect ("weird deliveries").

In the real world, you just won't do that.

This isn't a valid argument.

Try putting it this way, call the midpoint of the turnaround an event. At this event, "A" and "B" have zero separation speed. There is a world-line joining these events (two, if you want to do one for "A" and one for "B"). There is causality linking all "B" events post this event and all "A" events post this event.

I haven't been able to decrypt what you're saying here. What two events? I assume that one is (20,16) in A's frame, but what's the other one? Also, a world line is a curve that represents the motion of an object. You want to imagine something moving from (20,16) to some other event? Why?

(lots of sentences containing the word "signals")

You're much too focused on those signals. I don't see how they are relevant at all. You seem to think that they somehow forbid us from using the inertial frame associated with B's return trip, but you haven't given us a reason for that.

If you ignore these events, you will calculate discontinuities. This may be the accepted thing to do, but it's not characteristic of the real universe.

The way you talk about these things is pretty strange to me. How is it not a characteristic of the real universe that two different global coordinate systems disagree about stuff? And what "discontinuity" are you talking about? What function is supposed to be discontinous? All we have here are (at least) two inertial frames that describe things differently.

 

[Al68]

This might derive from my being an engineer by training rather than a physicist. We use the calculations as tools, rather than laws. If I were designing a spaceship for "B", complete with a clock that shows "B" the time elapsed for "A", I would not plan on having that clock jump from 7.2 years to 32.8 years at turnaround. Nor would I have a clock which just quickly scrolled forwards to 32.8 years.

If you were designing such a clock, how would it operate?

It would run slower than a "standard" clock (by the appropriate factor dependent on relative velocity) for all inertial motion. When it senses the acceleration (turnaround), it would run faster than "normal" by a factor proportional to the rate of acceleration and proportional to its distance from "A"s clock.

While such a clock would not be "needed", it is interesting to note how it would have to work. It would have to be rigged so that acceleration would cause it to speed up. Great question, neopolitan. Why am I the only person to even attempt to answer it?

Al

 

[matheinste]

Hello Al68.

This is purely a reply to your remark in #40.

To disagree with a point of view is absolutely acceptable as is my right to put forward my view, which on this subject is very much mainstream. I know you do not mean to criticize religion as such ( but it would not bother me if you do ) but the implication is that answers i have given to the best of my admittedly limited ability are given as a matter of unthinking, blind faith, in the manner of a crusade. My answers and those of many others on this question may in your eyes be incorrect but do not deserve to be called religious with all the underlying disparaging connotations of the word. The word itself is of course not offensive but its implications in your remark are.

Matheinste

 

[Al68]

Hello Al68.

This is purely a reply to your remark in #40.

To disagree with a point of view is absolutely acceptable as is my right to put forward my view, which on this subject is very much mainstream. I know you do not mean to criticize religion as such ( but it would not bother me if you do ) but the implication is that answers i have given to the best of my admittedly limited ability are given as a matter of unthinking, blind faith, in the manner of a crusade. My answers and those of many others on this question may in your eyes be incorrect but do not deserve to be called religious with all the underlying disparaging connotations of the word. The word itself is of course not offensive but its implications in your remark are.

Matheinste

Matheinste, my reference to religion was not to imply unthinking or blind faith, just to point out that in science, unlike religion, "well known and accepted" does not equal "correct and not subject to revision". Of course, I realized my remark was out of line when I reread it after posting. That's why I deleted it right away. My apologies.

Al

P.S. I don't believe your answer on this question is incorrect, just incomplete.

 

[phyti]

I can't fully understand why a person who makes a journey into space in a high-speed rocket will return home to find his age less than an identical twin who stayed on Earth. It makes since for the twin who stayed on earth, but for the twin who traveled into space, he sees himself at rest and sees Earth moving at constant velocity. so he should feel that time on Earth is moving slower than his time, this way he will find his twin younger than him not older. Please tell me what I am missing to help me understand this thought experiment.
Thank you.

You are missing the fact that the traveling twin, his clock, and everything in his space can/ship is functioning at a slower rate, therefore he ages more slowly. Referring to the drawing, he records 8 Earth years during his 7, while moving at .6c.

Jumping time is a misconception due to the instantaneous reversal of direction. In reality, it would be a gradual process and the Earth signal frequency would increase accordingly.

 

[neopolitan]

I haven't been able to decrypt what you're saying here. What two events? I assume that one is (20,16) in A's frame, but what's the other one? Also, a world line is a curve that represents the motion of an object. You want to imagine something moving from (20,16) to some other event? Why?

The two events are "A" and "B" at the time when "B" turns around. Since there is no separation speed there should be no simultaneity disagreement, both should (with the application of SR calculations) agree that these events are (t=20,x=0), "A"'s position according to "A" and (12,0), "B"'s position according to "B". (Couplets are: (20,0), (20,16) and either (12,-9.6), (12,0) or (12,0),(12,9.6) depending on "B"'s choice of origin since both choices have some merit even if the former is standard.)

The something moving from one event to another event is the information which I have discussed previously, a signal. A signal moving from "A" to "B". My contention is that even if "B" undergoes a change of frame, the calculations which "B" uses should not be used in such a way to indicate that this signal sent by "A" at (20,0) was simultaneous with any event at "B" earlier than (12,0).

That is a consequence of the implication in your diagram (http://web.comhem.se/~u87325397/Twins.PNG" ) that according to "B", "A" suddenly ages 25.6 years.

With the information that "B" has to hand, there is no need to make such a ridiculous claim - even if it may be standard simultaneity fare.

You're much too focused on those signals. I don't see how they are relevant at all. You seem to think that they somehow forbid us from using the inertial frame associated with B's return trip, but you haven't given us a reason for that.

The signals are an attempt to get you to understand that it is unreasonable and unnecessary to state that "A" suddenly ages 25.6 years. The signals are also representative of the information flow from "A" to "B". There is real information about "A" which is accessible to "B", but it is speed limited so "B" will never get it instantaneously. The best "B" can do is use the information received to make projections which are valid for the prevailing frame.

The way you talk about these things is pretty strange to me. How is it not a characteristic of the real universe that two different global coordinate systems disagree about stuff? And what "discontinuity" are you talking about? What function is supposed to be discontinous? All we have here are (at least) two inertial frames that describe things differently.

This sudden ageing of 25.6 years is the discontinuity that I am referring to.

The 25.6 years is based on realigning the frames with the end result, so that "A" is a nice 40 years old when "B" gets there.

However, it is not real. The clock I discussed with Matheinste won't suddenly scroll forward from 7.2 to 32.8 years. And here is why not ... the 32.8 year figure is based on "A" not moving at all during the 20 years. That means that the clock would have to somehow predict the future.

This is totally separate from the issue that the calculation behind the 32.8 years is based on a combination of situations, the bastard son of two frames, and that the calculation totally ignores how information flows in the universe.

"B" should, at the turnaround, make a projection that "A" has aged a total of 20 years. Not 32.8 years.

cheers,

neopolitan

PS Perhaps you might like to create a chart which maps the "A" events which are, according to "B", simultaneous with "B" events. Make all the events ageing events, ie '"B" has aged x days, this is simultaneous, according to "B" with "A" having aged y days' and plot y against x.

In my version, there will be a straight line (with a little bump in the middle if I am going to be pedantic), since "B" effectively maintains the same speed the whole time (0.8c) and I will not be ignoring the information that "B" receives.

In your version, there will be three straight lines - (0,0) to (12,7.2), (12,7.2) to (12,32.8) and (12,32.8) to (24,40).

Which sounds more representative of a realworld situation?

PPS phyti has approximately the right sort of diagram. His figures are for a shorter trip and show the situation in a different way, but at each end of phyti's diagonal lines are the simultaneous events which I suggest you chart, Fredrik.

 

[Al68]

"B" should, at the turnaround, make a projection that "A" has aged a total of 20 years. Not 32.8 years.

I think everyone agrees with that, assuming that you mean when the ship comes to momentary rest with earth. That's when Earth's clock will read 20 yrs. The 32.8 yrs is what the Earth clock will read according to "B" after the acceleration and the ship is headed back. The Earth clock readings of 7.2, 20, and 32.8 yrs are only a "jump" in time seen by the ship if we consider the turnaround instantaneous. We could just as easily say Earth's clock jumps from 7.2 to 20 during an instantaneous deceleration, then from 20 to 32.8 during an instantaneous acceleration. And we could break it down into segments as small as we like, and for each segment during the acceleration, Earth's clock will advance more than the ship's clock according to "B" (or co-moving inertial observers).

Al

 

[Fredrik]

The two events are "A" and "B" at the time when "B" turns around.

That's what I thought you meant, but you said weird things like that there's a world line that connects them.

...that according to "B", "A" suddenly ages 25.6 years.

With the information that "B" has to hand, there is no need to make such a ridiculous claim - even if it may be standard simultaneity fare.

You seem to be missing the point of the twin paradox. The false conclusion that there is a paradox was found by considering both twins' points of view, and doing it incorrectly. You can't solve that problem by saying that B's point of view is unnecessary. A resolution must explain why B is younger when they meet again, even though B can say (correctly) that his brother is aging at a slower rate at any point during the trip except the turnaround

This sudden ageing of 25.6 years is the discontinuity that I am referring to.

I know. I didn't ask because I needed to hear that part of the answer. I asked what function is supposed to be discontinuous to get you to think about how you can't even specify that function without explicitly mentioning the switch from one inertial frame to another.

The clock I discussed with Matheinste won't suddenly scroll forward from 7.2 to 32.8 years. And here is why not ... the 32.8 year figure is based on "A" not moving at all during the 20 years. That means that the clock would have to somehow predict the future.

No, it just has to keep track of the rocket's position and velocity at all times. The rest is a straightforward calculation. And yes, if you slow down on the way back, it will go backwards. If you programmed it right, that is.

...the calculation totally ignores how information flows in the universe.

It should ignore that. Think about what a coordinate system is. It's just a function that assigns numbers (coordinates) to events.

"B" should, at the turnaround, make a projection that "A" has aged a total of 20 years. Not 32.8 years.

Half way through the turnaround, yes. (When A and B have the same velocity). But not when the turnaround is complete.

PS Perhaps you might like to create a chart which maps the "A" events which are, according to "B", simultaneous with "B" events. Make all the events ageing events, ie '"B" has aged x days, this is simultaneous, according to "B" with "A" having aged y days' and plot y against x.

Check out for example the second text box from the bottom in my spacetime diagram. It states both what B is experiencing at the event where the blue line intersects B's world line, and what A is experiencing at the event where the blue line intersects A's world line. (Reminder: the blue line is a simultaneity line of B).

...at each end of phyti's diagonal lines are the simultaneous events which I suggest you chart, Fredrik.

Simultaneous? They aren't simultaneous unless the signals are transmitted by tachyons moving at 1.25c.

This discussion doesn't seem to be going anywhere, so I might withdraw from it after this.

 

[Al68]

The clock I discussed with Matheinste won't suddenly scroll forward from 7.2 to 32.8 years.

No, but if it works the way I described earlier, the time (according to the "normal" clock "B") it would take for this special clock to advance from 7.2 to 32.8 yrs would be inversely proportional to the rate of acceleration. Since the rate of acceleration can't realistically equal infinity, the special clock won't "jump" time, some time will elapse on the "B" clock while the special clock advances from 7.2 to 32.8 yrs smoothly (assuming the rate of acceleration is constant). And this special clock would not need to predict the future, if the ship stops accelerating at any time, the clock would sense the lack of acceleration and resume running slow by the gamma factor compared to clock "B".

Al

 

[yogi]

I have a different take in the twins thing - first of all, solve the problem by reducing it to two one way trips - and double the result to get the total age difference - so on the outward bound one way trip use two clocks, one on earth, one at the destination - they are synchronized in the Earth frame and always read the same - the distance to the traget is vt where t is the lapsed time in the earth-target frame, and ct is the temporal distance the Earth frame has moved during the one way trip - so the space time path followed by the traveler is a composite of the the space and temporal increments - during this interval, the travelers clock logs a time t' and the temporal distance for the traveler is ct'

so (ct)^2 = (ct')^2 + (vt)^2 from which you get Gamma and the amount of time that difference between the two frames, that is t' = Gamma(t)

You don't have to send signals, you don't need to get involved with turn around accelerations, and it doesn't make any difference whether the earth-target frame is moving or the traveler - all you need is Minkowski orthogonality of space and time and realize that each frame has taken a different space time path so since one frame has moved only in time and the other frame has experienced both a space and time increment - the intervals will be equal, but the components of the interval in each case will be different

 

[neopolitan]

Fredrik and Al,

Perhaps we can break the deadlock if you explicity state the assumptions of your conclusion(s).

Here are the assumptions of my conclusion, as far as I can tell:

• "B" keeps track of signals from "A".
  
• "B" is aware of accelerations undergone.
  
• "B" assumes under the conditions of the experiment that "A" does not undergo any significant accelerations.
  
• "B" is aware of relativity and uses that knowledge appropriately in calculations.
  
• "B" calculates "A"'s age on an ongoing basis.
  
• Most significantly: "B" does not at any time assume that the prevailing inertial frame is eternally valid (due to awareness of accelerations).

I do think that the last is important, and is possibly the sticking point.

Please present your assumptions, then have a go at mine, if you so wish.

cheers,

neopolitan

PS as yogi points out, signals are not really strictly necessary, assumption 4 would eliminate the need for assumption 1. But I keep the signals to force some real universe thinking in the example.

 

[Al68]

I asked what function is supposed to be discontinuous to get you to think about how you can't even specify that function without explicitly mentioning the switch from one inertial frame to another.

I think he might be referring to a function describing clock "A" in B's frame, which would have a discontinuity if we assume the rate of acceleration to be infinity, and the elapsed time on clock "B" to be zero during the turnaround. The Earth's clock would read 7.2 then 32.8 yrs, but not values in between. But this is just an artifact of treating the turnaround as instantaneous. If we say the turnaround is just "near" instantaneous, then the Earth's clock will advance from 7.2 to 32.8 very quickly according to clock "B", but it will read all times in between with no discontinuity.

Al

 

[Al68]

Fredrik and Al,

Perhaps we can break the deadlock if you explicity state the assumptions of your conclusion(s).

Here are the assumptions of my conclusion, as far as I can tell:

• "B" keeps track of signals from "A".
  
• "B" is aware of accelerations undergone.
  
• "B" assumes under the conditions of the experiment that "A" does not undergo any significant accelerations.
  
• "B" is aware of relativity and uses that knowledge appropriately in calculations.
  
• "B" calculates "A"'s age on an ongoing basis.
  
• Most significantly: "B" does not at any time assume that the prevailing inertial frame is eternally valid (due to awareness of accelerations).

I do think that the last is important, and is possibly the sticking point.

Please present your assumptions, then have a go at mine, if you so wish.

cheers,

neopolitan

Hi neopolitan,

I actually see what you're saying, I think. I answered your question about how a clock would work that is supposed to show Earth time on the ship. And I agree with you that there is a discontinuity associated with instantaneous turnaround, but it's not real because instantaneous turnaround is not possible. Such a clock would simply run fast relative to clock "B" during any acceleration (toward earth). And it would always show the time on Earth simultaneous with any moment on the ship (or a co-moving inertial frame).

I would use your assumptions, although #1 wouldn't be necessary.

Al

 

[neopolitan]

I think he might be referring to a function describing clock "A" in B's frame, which would have a discontinuity if we assume the rate of acceleration to be infinity, and the elapsed time on clock "B" to be zero during the turnaround. The Earth's clock would read 7.2 then 32.8 yrs, but not values in between. But this is just an artifact of treating the turnaround as instantaneous. If we say the turnaround is just "near" instantaneous, then the Earth's clock will advance from 7.2 to 32.8 very quickly according to clock "B", but it will read all times in between with no discontinuity.

Al

No, I am as against quick advancing of the clock (I called it scrolling) from 7.2 years to 32.8 years as I am against the clock being 7.2 years one moment and 32.8 years the next.

Acceleration qua acceleration has no effect on timing, only as a consequence of the altered relative speeds. (And simultaneity is only altered as a consequence of altered relative velocities.)

cheers,

neopolitan

 

[matheinste]

Hello neopolitan

As regards the turnaround, it need not be abrupt, it does not matter how long it takes. For the sake of my present post let us assume that it is takes a finite time. Now this finite time could be almost instantaneous, fairly fast………very slow, imperceptibly slow.. If the turnaround took a long time and was smooth and continuous and the clock showed a very slow advancement ( the one with B telling A’s time ), would you accept this. If you would, then let us crank the rate of turnaround up a notch and ask if you would accept this also ( assuming you accept the first degree of slowness ).
Obviously you see where I am going. If the discontinuity bothers you, by the way I think it makes for a bad scenario and would not have used it myself, let's just do away with it. If that was your worry would you accept scenarios with increasingly fast but smooth turnarounds and if not, at which point would they cease to be acceptable, assuming you accept accelerated rates of clock advancement of A’s clock from B’s point of view, at at all?

Matheinste.

 

[Fredrik]

• "B" calculates "A"'s age on an ongoing basis.
  
• Most significantly: "B" does not at any time assume that the prevailing inertial frame is eternally valid (due to awareness of accelerations).

And what would you say that A's age according to B is right after the turnaround? If it isn't "original age" + 32.8 years, then you have two major problems: 1) The time dilation formula says that A will only age another 7.2 years during the return trip, and he's going to have aged 40 years when B gets home, so your result contradicts time dilation. 2) Your result defines some other line than the red line to be B's simultaneity line, and that implies that B won't agree that the speed of light is =1 (i.e. =c).

 

[Antenna Guy]

As regards the turnaround, it need not be abrupt, it does not matter how long it takes.

If B's trajectory is circular in A's frame, the "turn-around" would take the entire trip to complete.

Regards,

Bill

 

[Dale]

This is exactly why I dislike this resolution of the twins paradox. It always leads inevitably to this discussion because simultaneity is fundamentally difficult to define in a non-inertial reference frame.

I much prefer the spacetime geometric resolution. It is simple, clear, and universal.

 

[atyy]

Is Michael Weiss claiming this question is not even meaningful?

"How much Terence ages during the turnaround is not something you can directly observe, according to SR. The Doppler Shift Analysis focuses on what Terence and Stella actually see through their telescopes, which avoids the difficulty."
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_distance.html

Edit: Is this at all related to how we observe distant galaxies, but we don't say anything about how old they are now, but we do at least colloquially say that this gives us information now about how the galaxies were then?

 

[Antenna Guy]

I much prefer the spacetime geometric resolution. It is simple, clear, and universal.

I agree.

The peculiar aspect of the circular trajectory is that the magnitude of B's velocity in A's frame could be constant for the entire trip (changing only in direction).

Regards,

Bill

 

[neopolitan]

Is Michael Weiss claiming this question is not even meaningful?

"How much Terence ages during the turnaround is not something you can directly observe, according to SR. The Doppler Shift Analysis focuses on what Terence and Stella actually see through their telescopes, which avoids the difficulty."
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_distance.html

Edit: Is this at all related to how we observe distant galaxies, but we don't say anything about how old they are now, but we do at least colloquially say that this gives us information now about how the galaxies were then?

Even more interesting are the two diagrams under this by the same author:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#gap

Pretty much the same thing that I have been talking about, so thanks atty :)

For the ever-snarky Fredrik, look at the angle of the red lines in the second of the two diagrams in Figure 2. Note that this angle is much more acute than the angles in the diagram posted by phyti and you made the comment about tachyons ...

cheers,

neopolitan

 

[Fredrik]

This is exactly why I dislike this resolution of the twins paradox. It always leads inevitably to this discussion because simultaneity is fundamentally difficult to define in a non-inertial reference frame.

I much prefer the spacetime geometric resolution. It is simple, clear, and universal.

I assume that you mean that the final ages of the two twins follows immediately from the fact that "what a clock measures" is the "proper time" (defined as an integral) along the curve in Minkowski space that represents the clock's motion

I agree that this is all you need to determine their final ages, but in my opinion, a "resolution" of the paradox should also explain what's wrong with the argument that lead to the conclusion that there's a paradox. The resolution discussed in this thread does that. It tells us that if you only take the time dilation into account, you get a paradox, but if you also take the "simultaneity shift" into account, you don't.

 

[atyy]

Your result defines some other line than the red line to be B's simultaneity line, and that implies that B won't agree that the speed of light is =1 (i.e. =c).

It always leads inevitably to this discussion because simultaneity is fundamentally difficult to define in a non-inertial reference frame.

Fredrik's comment about the speed of light is good. Is it possible to state, considering DaleSpam's comment, that a non-inertial frame only has a local plane of simultaneity? If so, how is "local" to be defined?

Edit: There seems to be no problem with the global planes of simultaneity, at least in this particular version of the twin paradox. However, we also don't require the speed of light to be constant in a non-inertial frame.