How Old Is My Home Twin Right Now?

[Mike_Fontenot]

Halc believes that if he (as the traveling twin) is stationary in some specific inertial frame of reference, he is free to adopt multiple answers to the question "How old is my home twin (she) RIGHT NOW?". That is incorrect ... there is only ONE correct answer to that question, for ANYONE stationary in the GIVEN inertial frame. That single correct answer is, "Whatever the person (he), stationary in THIS inertial frame, who is currently momentarily colocated with her, says her current age is".

To understand the above last sentence, some elaboration is necessary. In that specific inertial frame of reference, any and all light pulses are guaranteed to be moving at 186,000 miles per second, relative to that frame ... that is the fundamental assumption of Special Relativity. If that light pulse is NOT moving at 186,000 miles per second, then Special Relativity is incorrect. Let's assume that Special Relativity IS correct.

The people who are stationary in the above specific inertial reference frame have established an array of clocks, stationary wrt the frame, that are all synchronized with each other. And the adjacent clocks are separated by a fixed, constant distance ... for example, by a yardstick. Those people have accomplished that synchronization by using their knowledge of the separation between the clocks, and by their knowledge of the speed of a light pulse in their frame.


When someone (say, Tom), stationary in that inertial frame, asks "How old is the home twin (she) RIGHT NOW?", the answer is "She is whatever age the person, named Steve, who is stationary in our inertial frame, and who is at this instant currently momentarily colocated with her, says she is.

Now, Halc, who is also stationary in the given inertial frame, says that "No, she can be lots of different ages right now: different inertial observers, who are moving wrt one another, give different answers to that question". Halc is right to say that inertial observers (in inertial frames moving wrt the given inertial frame) will disagree with those of us in the given inertial frame. But Halc is WRONG to insist that people stationary in our particular inertial frame aren't required to accept Steve's answer to the question. People stationary in our particular inertial frame MUST agree with Steve ... otherwise, they are REJECTING the fact that the speed of light is 186,000 miles per second in our inertial frame. And rejecting that fact is rejecting Special Relativity itself.

 

[Neddy Bate]

Halc believes that if he (as the traveling twin) is stationary in some specific inertial frame of reference, he is free to adopt multiple answers to the question "How old is my home twin (she) RIGHT NOW?". That is incorrect ... there is only ONE correct answer to that question, for ANYONE stationary in the GIVEN inertial frame. That single correct answer is, "Whatever the person (he), stationary in THIS inertial frame, who is currently momentarily colocated with her, says her current age is".

To understand the above last sentence, some elaboration is necessary. In that specific inertial frame of reference, any and all light pulses are guaranteed to be moving at 186,000 miles per second, relative to that frame ... that is the fundamental assumption of Special Relativity. If that light pulse is NOT moving at 186,000 miles per second, then Special Relativity is incorrect. Let's assume that Special Relativity IS correct.

The people who are stationary in the above specific inertial reference frame have established an array of clocks, stationary wrt the frame, that are all synchronized with each other. And the adjacent clocks are separated by a fixed, constant distance ... for example, by a yardstick. Those people have accomplished that synchronization by using their knowledge of the separation between the clocks, and by their knowledge of the speed of a light pulse in their frame.


When someone (say, Tom), stationary in that inertial frame, asks "How old is the home twin (she) RIGHT NOW?", the answer is "She is whatever age the person, named Steve, who is stationary in our inertial frame, and who is at this instant currently momentarily colocated with her, says she is.

Now, Halc, who is also stationary in the given inertial frame, says that "No, she can be lots of different ages right now: different inertial observers, who are moving wrt one another, give different answers to that question". Halc is right to say that inertial observers (in inertial frames moving wrt the given inertial frame) will disagree with those of us in the given inertial frame. But Halc is WRONG to insist that people stationary in our particular inertial frame aren't required to accept Steve's answer to the question. People stationary in our particular inertial frame MUST agree with Steve ... otherwise, they are REJECTING the fact that the speed of light is 186,000 miles per second in our inertial frame. And rejecting that fact is rejecting Special Relativity itself.

I agree to some extent. However, SR also states that any inertial frame is just as valid as another, so as long as he states which frame he is taking to be stationary, he can get different answers, regardless of which frame he is actually stationary in.

What bothers me more than saying there are multiple answers is saying that the question is meaningless. It seems very much meaningful to have a definition of simultaneity, even though ultimately it is just a convention.

The thing to keep in mind is that the round-trip speed of light is a known constant, but the one-way speed cannot be tested in any way. So there will always be the possibility that the speed of light is different in different directions, but we will never know. It makes sense to me to take the round-trip time and divide by 2, as Einstein did. That is the convention we should all use, but it is a convention none the less.

 

[Mike_Fontenot]

[...]
SR also states that any inertial frame is just as valid as another, so as long as (one) states which frame one is taking to be stationary, one can get different answers, regardless of which frame one is actually stationary in.

I think that language is too abstract. To get at the real meaning of special relativity, I think it is necessary to imagine oneself as REALLY being stationary in some inertial reference frame ... really having participated in the positioning of the clocks, and in the synchronization of the clocks, using only the assumption that the speed of light is 186,000 miles per second in your inertial frame. I.e., you don't "TAKE" an inertial frame to be stationary, you become stationary (and remain so for some amount of your life) in some inertial frame, and participate in the synchronization of the clocks. Once you've done that (or imagined doing that), you realize that to deny the meaningfulness of current age of the home twin ISN'T possible.

What bothers me more than saying there are multiple answers is saying that the question is meaningless. It seems very much meaningful to have a definition of simultaneity, even though ultimately it is just a convention.

I not only believe that the question is completely meaningful, I also believe that it is NOT "a convention", which would imply that it is somehow optional, or voluntary.

The thing to keep in mind is that the round-trip speed of light is a known constant, but the one-way speed cannot be tested in any way. So there will always be the possibility that the speed of light is different in different directions, but we will never know. It makes sense to me to take the round-trip time and divide by 2, as Einstein did. That is the convention we should all use, but it is a convention none the less.

The fact, that the one-way speed of light can't be measured, doesn't bother me at all. In particular, it doesn't keep me from concluding, beyond all doubt, that the one-way speed of light is 186,000 miles per second (in an inertial frame). For me, it's not a "convention", it's a reliable fact. I think doing physics without that fact would be futile.

 

[origin]

I think it is necessary to imagine oneself as REALLY being stationary in some inertial reference frame

What is that supposed to mean? Is really stationary different than just stationary? What exactly is the difference between those 2?

 

[Mike_Fontenot]

I (Mike Fontenot), had said:

"I think it is necessary to imagine oneself as REALLY being stationary in some inertial reference frame"

What is that supposed to mean? Is really stationary different than just stationary? What exactly is the difference between those 2?

I was responding to this statement from Halc:

Halc believes that if he (as the traveling twin) is stationary in some specific inertial frame of reference, he is free to adopt multiple answers to the question "How old is my home twin (she) RIGHT NOW?". That is incorrect ... there is only ONE correct answer to that question, for ANYONE stationary in the GIVEN inertial frame. That single correct answer is, "Whatever the person (he), stationary in THIS inertial frame, who is currently momentarily colocated with her, says her current age is".

 

[Halc]

That is incorrect ... there is only ONE correct answer to that question, for ANYONE stationary in the GIVEN inertial frame.

This is equivalent to the cop pulling you over and asking if you know how fast you were going. By your assertion, there is only ONE correct answer to that question, which is: "I was stationary officer. It was the road going too fast. Give the ticket to the road."

The choice of which frame to use is usually a matter of pragmatic utility. To the narrator of the twin scenario (you), sure, it has pragmatic utility to talk about frame changes and how that effects the symmetry of the situation. As for the traveling twin, he has almost zero pragmatic reason to care which event along some far distant worldline should be considered 'RIGHT NOW'. The Andromeda paradox illustrates the lack of utility in exactly this situation.

"Whatever the person (he), stationary in THIS inertial frame, who is currently momentarily colocated with her, says her current age is

I love how you just cannot say "her current age in the frame in which I'm stationary". No, you need a third person to be there to anthropomorphize the measurement, just like populating the universe with a web of rulers and clocks, and needing to put a helper friend at each one of them since a clock doesn't work unless it has a witness in its presence. Reminds me of Sigourney Weaver's role in Galaxy Quest whose job it was to simply repeat anything the ship computer had just said.
The point doesn't become more concrete with the 'helper friend'. We know what you mean. We also know what you mean when saying "I".

I also believe that it is NOT "a convention"

Simultaneity under SR is very much only a convention. Einstein was careful to evade any metaphysical meaning to it. The convention works even in the absence of isotropy of speed of light. Hence, even under absolutist theories which deny both premises of SR, the empirical predictions are the same. In such absolutist interpretations, the convention doesn't generate true simultaneity. Under SR, Simultaneity is merely an abstract convention, and there is no 'true simultaneity'.

 

[James R]

there is only ONE correct answer to that question, for ANYONE stationary in the GIVEN inertial frame. That single correct answer is, "Whatever the person (he), stationary in THIS inertial frame, who is currently momentarily colocated with her, says her current age is".

I disagree.

The problem lies with how the term "right now" is defined (as in "How old is my distant twin, right now?").

"Right now", for a specified observer, is the collection of events in spacetime that have the same time coordinate as that particular observer has, for a specified event on that particular observer's world line. Clearly, then, "right now" is dependent on which observer we are talking about and where that observer is on his own worldline. It is not just a matter of specifying a reference frame.

For instance, if you consider my personal worldline, then at precisely 9:30 am on 1 January, 2017 (as determined by the watch I wear), there exists a certain collection of events, among which is an event where Donald Trump was up to something or other. If, at that time, I had considered the question "How old is Donald Trump right now?", there is an unambiguous answer to that question that you and I can both agree on, but only by referring to my frame of reference and my location in spacetime at the time of my observation.

The answer to the question "How old is Donald Trump right now?" is different from my perspective at 12 pm on 1 November 2023, because we're considering a different point on my worldline to the previous one. This would remain true even if I had somehow remained completely stationary in the reference frame I used back on 1 January 2017, between then and 1 November 2023.

My answer to "How old is Donald Trump right now?" is not just a matter of picking a random person who is co-located with Donald Trump and stationary in Trump's rest frame. Remember, in this example, we are talking about just one reference frame, the whole time. But a person co-located with Donald Trump in 2017 is at a different spacetime event than a person co-located with Donald Trump in 2023.

Moreover, what Donald Trump thinks his age is at his "right now" time corresponding to some event on my personal timeline is completely irrelevant to me, because he doesn't necessarily share my frame of reference. If he doesn't, then his set of "right now" events, referenced from the particular event at which I saw he is 78 years of age, say, has no guarantee of containing the particular event at which I am considering his "right now" age.

The TL;DR version of this is: two people at different spacetime locations in the same reference frame can have different definitions of "right now", as can one person a single spatial location at two different time coordinates.

To meaningfully ask a question about something happening "right now" at a distance from an observer, we need to know the spatial coordinate of the distant point and the time coordinate of the observer at the time the observation is being made, both in the rest frame of that particular observer.