B Relativity: Twin Paradox - Is Age Determinable?

[Ibix]

Well, I wouldn’t say it is wrong

Taken on its own I agree. Leading into the next bit I quoted (edit: and the following bits about the "gravitational centre for all things"), however, I think it is actually wrong.

 

[Dale]

Taken on its own I agree. Leading into the next bit I quoted (edit: and the following bits about the "gravitational centre for all things"), however, I think it is actually wrong.

Excellent point!

 

[Bruce Wallman]

Easier or not, it's wrong.

The whole point of this scenario is to make students realize that this analysis is naive and, ultimately, incorrect.

Naive and simple yes. General relativity is about acceleration and gravity. Special relativity was written as being about velocity and the velocity of electromagnetic waves. What if I update my thinking about SR to GR standards and make it about velocity and the velocity of gravity? Then all velocities in the universe are measured against a gravitational frame and things like time dilation and mass increase become more intuitive.

 

[Ibix]

Naive and simple yes. General relativity is about acceleration and gravity. Special relativity was written as being about velocity and the velocity of electromagnetic waves. What if I update my thinking about SR to GR standards and make it about velocity and the velocity of gravity? Then all velocities in the universe are measured against a gravitational frame and things like time dilation and mass increase become more intuitive.

This is just nonsense.

If you don't understand special relativity well enough to be able to resolve the twin paradox without inventing reference to some illusory absolute reference frame then you aren't ready to try to understand general relativity.

 

[Herman Trivilino]

When reduced to movement relative to one another, then both twins are always moving at the same velocity and acceleration relative to one another, so there would be no difference in aging.

Neither your premise nor your conclusion is correct. In the typical presentation of the twin paradox only one twin has an acceleration. They do indeed have equal but opposite velocities relative to each other. And there is a difference in aging.

 

[Herman Trivilino]

Yes, we see slight effects at micro levels in current astronauts.

I don't understand. Micro levels of what?

I was thinking about a more noticeable age difference.

I'm not sure what you mean by noticeable. We can start with two identical clocks in the same location, and synchronize them. If the two clocks separate, take different paths through spacetime, and then reunite, it is as noticeable as it can possibly get when we observe that the clocks are no long synchronized.

This is a fact of life. We have observed it!

What physics does is provide an explanation. In this case, we can use it to calculate the path length of each clock, and compare it to the elapsed time on each clock. In all cases they match!

That's as noticeable as possible.

 

[Ibix]

Here are correct Minkowski diagrams (albeit for a slightly longer journey than Earth-Mars). First, in the rest frame of the planets (marked as blue worldlines):

The ship (red worldline) does 0.8c. I've marked black crosses, joined by a fine grey line, when the same proper time has elapsed since departure for both the traveller and stay-at-home. In this frame, the stay-at-home is older when the traveller arrives. Note that I have only drawn the traveller's worldline in transit - you may extend it inertially or treat it as taking off and landing. It makes no differece to the only thing that matters - the positions of those crosses.

We can also draw the same scenario in the frame where the ship and planets have equal and opposite velocities:

In this frame, the traveller and stay-at-home are the same age when the traveller arrives. And finally, we can consider the rest frame of the ship:

Here, it is the traveller who is older.

The point is that all of these diagrams are valid, and there is no reason to prefer one over another. So there is no unique answer to the question.

 

[PeterDonis]

@Elroch, you have now been banned from further posting in this thread. All you are doing is confusing the issue and repeating erroneous claims.

 

[PeterDonis]

Moderator's note: A number of confusing and erroneous posts and responses to them have been deleted.