Voidmoon":38wumka3 said:

Thanks for the link, SpeedFreak. Would Chewie and Steve fall back into sync with one another if Chewie sat back down on the couch? I understand the thought experiment and the basics of the theory, but can't wrap my brain around how Chewie and Steve can be in sync one moment and then if Chewie gets up to walk around, this small movement is amplified so dramatically. So dramatically in fact that Chewie would now be 150 years in the past, according to Steve. I get the theory on a small scale, but just can't wrap my brain around it when very large distances are involved.

Well as you might suspect, this actually gets quite deep. What Greene is doing in the "Fabric of the Cosmos"

*(great book, by the way, I have it myself!)* is applying the relativity of simultaneity across cosmological distances. It is an extreme and exaggerated illustration of how two observers notions of "now" can shift relative to each other due to their relative motion, applied across absolutely vast cosmological distances, in order to show how the notion of simultaneity is essentially

*meaningless* at such distances.

Just as Special Relativity does not apply when considering galaxies that are apparently receding faster than light, the same can be said to be true of any notion of simulaneity - you cannot meaningfully synchronise two observers notions of "now", if they are on different sides of the universe. This is not due to the high apparent recession speeds themselves, it is due to the the fact that there is such a large slice of space-time between events and SR only works locally - any notions of simultaneity can only be applied locally in a meaningful way.

In the famous paradox of the twins, the difference in their ages can only be meaningfully compared if one twin turns around and returns to the other. It is the act of turning round, of changing your inertial frame of reference, that can be thought to cause the simultaneity shift. Aside from the difference in relative speed, it is the distance across space-time that determines the magnitude of the simultaneity shift. The further away the twin is when he turns around, the larger the shift in the two twins notions of "now".

If both twins remain in relative motion, and both twins remain in inertial frames of reference, then time-dilation is

**symmetrical** between them. Just as one twin calculates the others clock is running, say, at half the speed of his own,

*the same is true the other way round!* This is what causes the supposed "paradox" - time-dilation is symmetrical between observers in inertial frames of reference and so each twin thinks the other should age slower than himself.

Special relativity tells us that, if all the twins know about each other is that the other is moving away from them, then both twins calculate the others clock to be "running slower". That's it. In order for there to be a resolution of the paradox, the twins have to meet in the same place, in the same frame of reference. From afar, each twin can only assume the other is now ageing at a slower rate than themselves.

If one twin returns to the other, then on the return journey, as long as they remain in inertial frames of reference,

*once again there is symmetry in the time-dilation between them!* So if the time-dilation between them was symmetrical as the two of them separated, and was again symmetrical as the two of them converge,

*where did the difference in their ages occur?* Where was the shift in simultaneity, the shift in their individual notions of

*"now"*?

The shift in simultaneity happened when one twin changed his inertial frame, or moved between different frames. The shift occurred when one of them slowed down, turned around and sped up again.

If you consider what each twin would calculate from their observations (after subtracting out speed of light effects like Doppler or aberration) if they could see each other during the thought experiment, both would calculate that the other was ageing less than themselves during the time they were in relative inertial motion, but during the turnaround phase, the twin who was turning around would speed up tremendously to the twin back on Earth. The opposite is true from the point of view of the moving twin, who would calculate that, as he performed the turnaround, the twin back home would be ageing really slowly. Another way to think of this is that the travelling twin leaps forward in time during turnaround, so relative to him, the stay at home twin leaps backwards in time. The effect is magnified, the greater the distance the twins are apart.

So what Greene has done is taken this idea and applied it at universal scales. He is not actually concerned with the relative motions of the two distant galaxies, he is only concerned with the vast distance between them, as that alone would cause a huge shift in simultaneity for any small local movement from an occupant of one of those galaxies, relative to the other. Thus, as you pace up and down in your living room, centuries leap back and forth in a distant galaxy, but only

*relative to you*. The same is of course true the other way around, and this shows why any notions of simultaneity are actually meaningless across large distances. So, as an alien on a planet in a distant galaxy paces up and down, the time on Earth leaps backwards and forwards by centuries, relative to him/her/it!

Of course, we can safely assume that the above is

**not** a reflection of any true reality! It is a useful way to use Special Relativity to illustrate how time is relative and there is no absolute notion of simultaneity across the universe. It is also useful in showing how applying the postulates of SR across vast cosmological distances is an essentially meaningless exercise. In order to apply SR, you need a universe empty of any gravitational influence and path through space-time taken between events in order to compare those events. This is one of the underlying reasons why General Relativity was formulated in the first place!