Now plane moving to the past and future

rajeshmarndi,

See if this helps... http://physics.unm.edu/Courses/Finley/p570/Handouts/accelObserv.pdf [Broken]

from page 5
"As the accelerated observer moves the lines of simultaneity rotate “upward” as (tau) increases from zero, and “downward” as it decreases."

from page 10
"c. Thirdly, for events in quadrant IV, as the value of t increases the associated value of (tau) would decrease, so that the normal ordering given by the progression of time is reversed. This suggests that we have already passed into an unacceptable region. Only I is correctly treated by these coordinates."

 

The idea that the co-moving-frames ("CMF") analysis can be allowable in some circumstances, but not allowable in other situations, seems inconsistent to me. For example, in the standard idealized twin "paradox" scenario with an instantaneous turnaround, right before the turnaround, the traveler (he) says that the home twin (she) is much younger than he is. He then accelerates toward her to reverse course, and the CMF analysis says that (from his perspective) during the turnaround she rapidly ages, and after the turnaround she is then much older than he is. This analysis is usually considered to be acceptable.

But what if he then immediately accelerates in the direction away from her (so as to immediately achieve his original velocity away from her)? The CMF then says that she rapidly gets younger, and after this second turnaround, she is much younger than he is ... she is again the same young age that she was before the first turnaround. This application of the CMF analysis (with his acceleration being AWAY from her) is often said to be invalid (because it produces a previous age for her).

But what if he then immediately reverses course a third time? The CMF then says that she rapidly ages, and after the third turnaround, she is again much older than he is. So the third turnaround produces the same state that existed right after the first turnaround. For the first and third turnarounds, the CMF analysis is considered "proper", but for the second turnaround, the CMF analysis is considered "improper". But, in order that the state after the third turnaround be the same state that existed after the first turnaround, it seems to me that we either need to believe that all three CMF results are "proper", or else none of them is "proper". Saying that it's OK to use the CMF when he accelerates toward her, but that it's not OK to use the CMF when he accelerates away from her, appears to me to produce an inconsistency.

 

I tend to agree with this conclusion.

But if you realize as PeterDonis pointed out that we're talking about something that isn't a physical observable, then this is all nothing more than just different games played by different rules. It's only when a game has inconsistent rules that it no longer qualifies as a valid game.

By the way, none of these problems occur if you play the game according to the rules known as the radar method. But even then, it's important to realize that no additional knowledge or insight into a scenario is gained by playing these mind games. We do it just for the fun of it. (Or if you're lucky, like Brian Greene, you can also make a lot of money while playing these games.)

 

But the still unanswered question is this:

Does an immediate back-to-back (matched) pair of instantaneous course-reversals leave all ages the same as before? I.e., if the traveler instantaneously changes his velocity (wrt the home twin) from +V (away from her) to -V (toward her), but then immediately instantaneously changes his velocity from -V to +V, is the net effect the same as if there had been no reversals at all?

If the answer to that question is "yes", then it seems to me that the following is implied:

IF he is allowed to use the co-moving-frames (CMF) analysis for the first course-reversal, then he will say that her age suddenly increases during that first reversal. But if her age is the same before and after the matched pair of reversals, it is necessary that her age must decrease during the second reversal, by the same amount that her age increased during the first reversal. And this decrease in her age during the second reversal is exactly what the CMF says will happen.

 

It depends on how you want to play the game. In the game I play based on the radar method the answer is yes.

In the game I play, all the ages stay the same even in between the two instantaneous velocity changes. You don't have to play a game that creates discontinuities of age in remote objects under any circumstances.

A good reason not to play the game according to CMF rules and to switch to radar rules.

 

If simultaneity at a distance is as meaningless in special relativity as the prevailing opinions on this forum seem to indicate, it's odd that Einstein put so much emphasis on the Lorentz equations, which fundamentally are about simultaneity at a distance. I understand that coordinates are basically meaningless in general relativity, but I don't think that need be the case in special relativity, which assumes a flat universe of infinite extent, with no gravitational fields.

 

The Lorentz equations only apply to Inertial Reference Frames and they have become a standard convention.

You have been talking about non-inertial reference frames for which there is no standard convention and for which the Lorentz equations do not apply. You get to pick your own convention, establish a set of definitions and derive whatever meanings they lead to. But you should not think that any particular convention is more meaningful than another convention. That's like thinking the word "nine" is more meaningful in English than it is in German.