What does the term "age" mean in descriptions of the twin paradox?

[Peter Strohmayer]

TL;DR

Does it make sense, independently of any reference system, to say: "All people born at the same time and resting in different places always have the same age and always celebrate the same birthday at the same time"?

In other words: Does a reference system, in the relationship between the displays of its synchronised clocks, have a specific property that is independent of any reference system? Is this particular relation of events in the form of displays of spatially distant clocks at rest the same from the point of view of all reference systems?

 

[Dale]

In the twin scenarios “age” is synonymous with “proper time”.

 

[jartsa]

"Age" in twin paradox means how old a twin appears to be.

And the twins do not have any diseases that make a person appear to be older or younger than the person's real age.

The twins are like clocks. There is probably some reason twins are used instead of two clocks.

 

[Ibix]

Does a reference system, in the relationship between the displays of its synchronised clocks, have a specific property that is independent of any reference system?

Only inasmuch as there's a coordinate free definition of the clock synchronisation process. In the usual Einstein synchronisation, for example, if clock A and clock B are at mutual rest and synchronised and clock A bounces a radar pulse off clock B, the time shown on clock B at the reflection event will be half way between the times shown on A at the emission and reception events. That's completely coordinate free and all frames (and weirder coordinate systems) will agree, although the will not agree in general that A and B are in sync by their own standards.

So the coordinate free-ness comes from there being an operational definition of "synchronised". The coordinate dependence comes from there being a lot of choice over what operational procedure to use.

As @Dale says, "age" in the twin paradox is usually a synonym for "proper time since the start of the experiment".

 

[Orodruin]

"Age" in twin paradox means how old a twin appears to be.

I would strongly discourage the usage of the words ”appears to be” in conjunction with this. It seems to indicate that there is a subjectivity attached where the resolution is that there is no subjectivity whatsoever.

 

[vanhees71]

In the twin scenarios “age” is synonymous with “proper time”.

Yes, and just to make it very clear: This implies it's independent of the choice of any (inertial or non-inertial) frame. The proper time of each twin along his time-like trajectory is
$$\tau=\int_{\lambda_1}^{\lambda_2} \mathrm{d} \lambda \sqrt{g_{\mu \nu} \dot{x}^{\mu} \dot{x}^{\nu}}, \quad \dot{x}^{\mu}=\frac{\mathrm{d}}{\mathrm{d} \lambda} x^{\mu}(\lambda).$$

 

[Nugatory]

TL;DR Summary: Does it make sense, independently of any reference system, to say: "All people born at the same time and resting in different places always have the same age and always celebrate the same birthday at the same time"?

No, because “at the same time” is always dependent on some reference frame. Talking about “the same time” independently of any reference system is like talking about left and right without considering the direction we’re facing.

 

[Nugatory]

@Peter Strohmayer you have been asking the same question and getting the same answers over and over again in multiple threads - clearly the way we’re explaining this stuff isn’t helping you see or clear up your misunderstanding.

You might be better served by a different approach: get hold of a copy of Taylor and Wheeler’s “Spacetime Physics” and work through it from the beginning. Do not speed through the early chapters thinking you understand that basic stuff - you don’t. The first edition is legal and free on the internet, and we can help over any hard spots if you get stuck.

Please don’t just post the same old stuff here without having gone through that exercise or something similar. This thread is already on the wrong side of the forum rule about restarting closed threads and another like it won’t help anyone.

This thread is closed.