Does Time Contraction Change Substance?

[ghwellsjr]

2. Focusing on symmetrical and arbitrary time dilation examples instead of more realistic roundtrip travels gives people the false impression that time dilation is totally arbitrary and has no real connection with observed reality. IE, that when two objects approach from a distance, both will observe the other's clock ticking faster than their own and both would be right (even accounting for doppler effect). But while it is true that if you are dealing only with frames of reference or hypothetical snapshots of objects that magically appear from nowhere it can be viewed that way, but in real-world situations it is not at all arbitrary: Objects have histories and through those histories, the "true" time dilation - the one that is recorded on their clocks when they are brought together - is uncovered, even before you observe that reality is observed by comparing the clocks.

If an astronaut is traveling away from earth, both witness the other's clock ticking slower, but the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving and when he returns, his clock will read a shorter elapsed time and he'll be younger than his twin because of it. You can't make that go away by arbitrarily changing reference frames.

I have made some spacetime diagrams showing an astronaut traveling away from Earth and returning. The first one depicts the Earth rest frame, the one you claim has the "true" Time Dilation for the Earth and the astronaut.

Of course it is true that this diagram depicts the "true" Time Dilation of the Earth and the astronaut for the rest frame of the Earth but after this I'll show some other IRF's which also show "true" Time Dilations for the Earth and the astronaut. Note in the above diagram that the astronaut, depicted in red, travels at a speed of 0.8c so he is Time Dilated by the factor of 1.6667 which is the ratio of the accumulated Coordinate Time to the accumulated Proper Time (depicted by the dots) and that after 3 years of Proper Time for the astronaut on his way out, 5 years (3 times 1.6667) of Coordinate Time has transpired and the same for the way back. People on the Earth (depicted in blue) are at rest so they are Time Dilated by the factor of 1 and they age by 10 years (10 times 1) while the astronaut is gone. Please note how I specifically referenced the Proper Times of the astronaut and the Earth separately to the Coordinate Time of the IRF rather than to each other. That's very important to a correct understanding of Time Dilation.

Now let's transform the above IRF to one in which the Earth and the astronaut are departing away from each other at the same speed, 0.5c:

At 0.5c, the Time Dilation factor is 1.1547 so after 3 years of Proper Time for both of them, 3.5 years of Coordinate Time has transpired. That's when the astronaut fires his rocket to return home exactly how he did in the first IRF but now it gets him to a speed of 0.929c with a Time Dilation of 2.7 and it takes him 8.1 years of Coordinate Time for his 3 year of Proper Time. The astronaut's total Coordinate Time for his trip is 3.5+8.1 = 11.6 years, the same as the Coordinate Time it takes for the Earth to progress through 10 years of Proper Time at 0.5c with a Time Dilation of 1.1547. This is the first example of where the Time Dilations are "true" but different than the Earth's rest frame.

Now we'll do the IRF in which the astronaut is at rest during the first part of his journey. This puts the Earth traveling at 0.8c and experiencing the Time Dilation of 1.6667 while the astronaut has none (actually 1):

During the second part of the journey, the astronaut reaches a speed of 0.9756c and a Time Dilation factor of 4.55 and so when he gets back to earth, after 13.667 years of Coordinate Time (3 times 4.55) for a total of 16.667 years, it matches the accumulated Coordinate Time for the Earth (10 times 1.6667), another "true" example of Time Dilations.

Let's do another one, the IRF in which the Earth and the astronaut approach each other at the same speed:

This one is similar to the second one in this post, so I'll let you out the details.

Finally, the IRF in which the astronaut is at rest while returning:

This one is similar to the third one in this post so I won't go into the details.

I hope these diagrams have helped to show the difference between Time Dilation and Differential Aging.

 

[ghwellsjr]

If an astronaut is traveling away from earth, both witness the other's clock ticking slower, but the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving and when he returns, his clock will read a shorter elapsed time and he'll be younger than his twin because of it. You can't make that go away by arbitrarily changing reference frames.

I'd like to further disabuse you of the notion that the astronaut is the one "actually" moving because he is the one who fired a rocket and that automatically guarantees that he will be the younger one when they meet up together later on.

Let's consider an astronaut (red) leaving Earth (blue) at 0.8c but some time later, another astronaut (black) leaves Earth at a greater speed, 0.9756c to eventually catch up to the red astronaut:

In this case, it's the black astronaut that ends up younger when they meet up together.

The oft repeated "rule of thumb" that it's the twin who accelerated that ends up younger leads to misunderstanding because it leads people to believe that it's acceleration that is important in resolving twin-type scenarios even if is does work in some cases (those where only one twin accelerates). It's better to understand that Time Dilation, like speed, is frame dependent and that if you add up accumulated time for each segment of each twin's progress, you always get the correct answer.

 

[PeterDonis]

the reality is that only one of them fired a rocket to get away from the other. The astronaut is the one "actually" moving

As ghwellsjr points out, this rule of thumb doesn't generalize. It only works in flat spacetime, and only if one of the twins is inertial the whole time. The rule that generalizes, as he says, is to compute the proper time along each worldline and compare the answers.

It's true that the "standard" twin paradox is set in flat spacetime, and only one of the twins in that scenario accelerates, so the rule of thumb works in that case, and that's the case that's usually given as the "standard" example of differential aging. But given the number of threads we get here in which somebody assumes that that rule of thumb generalizes, and starts applying it to more complicated cases where it doesn't actually work, and then wonders what "really" causes the difference in aging if it isn't acceleration, there is at least a case to be made that, for pedagogical purposes, we should skip the rule of thumb and go straight to the general principle: add up the proper time elapsed along each worldline and compare them.