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4D spacetime Light cone Twins paradox 
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#1
Oct2605, 06:48 AM

P: 22

I'm an "onmyownfreetime" armchair student of physics. Lol.
So if this question is way off the mark my apologies. Feel free to let me know where I’m off base. Anyway... For me, a great visual example of the twin paradox was found at this site: http://www.phy.syr.edu/courses/modul...k/default.html (Thanks Janus it was your link posted on another thread I used to get there) So, the second to last AVI or RAM at the bottom of the page shows the twins or (A) and (B)s full journey within their own world lines travelling through 4dspacetime. The twin (A) stays in his inertial frame and the twin (B) travels away from the first twin and then turns around. It was said that at the point of the turn it is revealed who has the preferred reference frame. So the paradox is resolved when the twin (B) turns around and returns to meet twin (A) Twin (B)s change of direction shows that he can no longer be considered to be in the preferred reference frame. He will age more slowly also the faster he goes. But my question is: When the twin (B) turns to return to twin (A) why can't it be said instead that twin (A) was the one doing the turning WRT to twin (B). Or a third possibility could be that they both share half the turn, if one can put it that way. So for the first half the trip twin (B)s clock runs slowly compared to twin(A) and for the second half of the trip twin (A)s clock runs slowly compared to twin (B)s. If they are doing a circular orbit around each other then perhaps the time dilation of both twins would just cancel out in real time. Sorry for the convoluted example but there you go. That’s my question. Is this possible? At the end of the trip both twins aged at the same rate? One can’t prove who was turning around whom and no one was discovered to be in the preferred inertial reference frame for the entire duration of the trip. Both reference frames during all turns or orbits equally cancel out each others time dilation. But time dilation still occurs as per usual. Sigh.. Hope that made some sense. Best Eon. 


#2
Oct2605, 07:09 AM

P: 2,179

Twin (B)s change of direction shows that he can no longer be considered to be in the preferred reference frame. In other words, it is twin (B) and twin (B) only that gets mushed up into the nose cone of his rocket when it slows down to turn around. That's how he knows he's the one that will be younger when the two meet up. 


#3
Oct2605, 08:42 AM

P: 22

Thanks for the reply.
What you say makes sense. But I'm still not sure on some of these points. Also... Let's say the acceleration or change in direction were slow enough or the orbit very large (computer controlled) as to make the change in G's unnoticable then why would anyone need to get mushed up or be aware that they were turning. It can be set up so that the twins are unaware of the flight path and unable to tell. The data for both twins trips could be compiled at the end of the journey.Do they suddenly age as soon as the data is compiled? Thanks again, Eon. PS... Please don't hit me with advanced maths of the lorentz tranformation as I'm sure I can plug in the numbers with a little help, but I'm trying to think through this conceptually. BTW I say that with humor..LOL...it's all good. 


#4
Oct2605, 09:00 AM

P: 22

4D spacetime Light cone Twins paradox
Many Thanks E 


#5
Oct2605, 09:15 AM

P: 2,179

2. A's inward leg. 3. B's outward leg. 4. B's inward leg. 5. The frame of the meeting point. It is common to think of this last frame as not moving in space, but in time only, although that is a frame dependent concept. Interestingly, travelling with this 'nonmoving' frame takes the longest proper time to traverse the two meeting events. That's how it is that the stationary twin ages more than the travelling one. 


#6
Oct2605, 11:26 AM

P: 22

Got it. Cool. The insight was yours. I just had a hunch. The rapid aging is strange but interesting. Appreciate your expertise and your time. Awsome. all the best, Eon. 


#7
Oct2605, 03:55 PM

Mentor
P: 11,864

What special relativity can't handle is situations where the effects of gravity are significant, that is, where you have to deal with curved spacetime. 


#8
Oct2605, 05:18 PM

P: 2,179

I'm not 100% sure that jtbell is right though. After all, acceleration is equivalent to gravity. How much acceleration do you need to curve space? I would have guessed any at all. A while back I was told that the concept of CMRF was a stopgap measure to approximate GR in the years between 1905 and 1915 when there was no GR. I was told that it is accurate enough and convenient enough for some calculations, but theoretically eclipsed after GR was introduced. Am I misinformed? 


#9
Oct2605, 05:32 PM

Sci Advisor
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#10
Oct2605, 05:46 PM

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I think the equivalence principle does mean that if you have an object experiencing constant acceleration in flat spacetime, you can come up with a new coordinate system where the object is at rest and the Gforces experienced by the object are now explained in terms of a uniform gravitational fieldthat's what this page on the GR analysis of the twin paradox seems to be saying. A question for the GR experts hereI think I remember from a previous discussion someone telling me that in GR the curvature of spacetime does not depend on your coordinate system, so can a "uniform gravitational field" exist in flat spacetime? If the curvature of space alone can vary depending on your choice of coordinate system, does a uniform gravitational field in flat spacetime mean that space is curved even though spacetime is not? 


#11
Oct2605, 08:14 PM

P: 2,179

Here is my take on things. I don't think that use of the MCRF is strictly allowable in SR, you just get away with it because the calculations work. In that respect it is like using Newton's equations to calculate rocket trajectories. It is adequate for calculations, but theoretically incorrect. In other words, there are three ways of handling the twins: 1. SR 2. SR + MCRF 3. GR In this scheme, SR by itself is not adequate to explain the 'slowly accelerated' version of the twins seemingparadox. However, I agree with jtbell that for computational purposes, GR is not necessary either. Instead SR + MCRF can be used for the resolution of the seemingparadox. But only because it gets the right numbers. A full, theoretically correct analysis requires GR. These are the opinions of a nonphysicist. 


#12
Oct2605, 08:28 PM

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#13
Oct2705, 03:02 AM

P: 22

Is there a tension between the nonlocality of Q.M and the private nature of inertial frames and world lines in S.R?
In other words. Let’s say the twins make their flight and return. But the trip is done in a double blind way where the twins don’t know their flight path nor does the scientist. (at the NASA of the future let's pretend) Then the data is compiled. At the moment of compiling the data (doing the math) could some kind of nonbinary wave function collapse and suddenly one twin ages the correct amount according to S.R. LOL. I realise this is a complete fishing expedition and I’m just throwing out 3 ideas or more as a nonexpert but its interesting to me. Those concepts being: 1) nonlocality in Q.M. – Copenhagen interpretation or some other well respected one. 2) collapse of a wave function (state of existence?) (is the cat alive or not) and can this be applied to does one twin age or not only at the moment of observing the data and compiling it. 3) The rules of S.R stating that each world line is inertial and private? I’m so very much reaching here so I don’t mind if you all laugh. But can Q.M issues run into S.R. issues when dealing with the twin paradox? Best, Eon. 


#14
Oct2705, 04:19 AM

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#15
Oct2705, 04:30 AM

P: 863




#16
Oct2705, 04:41 AM

P: 22

I should have googled it first. When I did articles and papers from universities and arXiv.org came up on the subject of Q.M and S.R and the peaceful coexistence between the two for the most part, but not always. But as you say for the most part there is no issue. I believe. Thanks for the reply. best Eon. 


#17
Oct2705, 04:51 AM

P: 2,179

Edited to removed references to acceleration. 


#18
Oct2705, 06:28 AM

P: 2,179

I don't fully understand your distinction between acceleration curving spacetime and energy curving spacetime. Can there be acceleration without energy? Using an admitedly Newtonian point of view: Acceleration is proportional to force and an accelerating particle cannot be stationary for any period of time. Multiply the force times the distance moved and you get energy. Below is a famous picture of acceleration causing curvature. I have been told that there is a flaw in this picture, but I don't know what the flaw is, so I present it with the hopes that someone can explain it to me. Consider a disk spinning about its center like a roulette wheel. Consider a portion of the circumference small enough to be nearly linear. As the length of this small piece is parallel to its motion, a stationary observer at a point on the axis of rotation will observe a foreshortening. Now consider the radius connecting the center of the disk to the center of the small piece of the circumerence. This distance is perpendicular to the motion and so is not foreshortened. As the piece of circumference was arbitrary, the entire circumference is foreshortened. So the observer notes that one of the properties of flat space [itex]c = 2\pi{r}[/itex] does not hold. The cause is explained entirely by the acceleration of the disk without any mention of forces or energy. 


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