rqr said:
Quoting JesseM re the Three-people case:
>There is no "objective differential aging" here because any claims
>about aging depend on your choice of simultaneity, which is totally
>arbitrary.
No, there is no "choice of simultaneity" involved. There are only
these two mutually exclusive physical possibilities involved:
[1] Ann is not the same age as Bob and Copy-Bob whenever the
latter meet
or
[2] Ann is the same age as Bob and Copy-Bob whenever the
latter meet
To say that these represent "physical possibilities" is to
assume that questions about relative rates of aging between observers in relative motion have some sort of "real" physical answer, and are not just dependent on your choice of coordinate system. But
why do you assume this is true? Why can't "relative rate of aging" be a coordinate-dependent notion just as much as velocity or x-coordinate? What would you say to someone who said:
There are only
these two mutually exclusive physical possibilities involved:
[1] Ann's speed is greater than or equal to Bob's speed
or
[2] Ann's speed is less than Bob's speed
Would you accept without argument that these are distinct "physical possibilities", or would you point out that "speed" is an intrinsically coordinate-dependent notion and that there are no physical reasons to believe in absolute velocity? If the latter, why can't you accept that the same thing might be true of relative rate of aging?
If there
is a truth about relative rate of aging, then do you at least agree that there would be absolutely no physical experiment that could determine the truth? That is all relativity is really saying, that there is no "preferred frame" in the sense of the laws of physics preferring one frame's point of view over another. You're free to adopt some sort of metaphysical belief that there really is an absolute truth about which frame's definition of relative aging rates or simultaneity (they are equivalent, of course) or velocity is the "correct" one, as long as you accept that only a god could know the true answer to this question, that there is no physical experiment
we can perform that will determine which frame is "preferred" in this metaphysical sense. I would tend to think that occam's razor favors the view that if the laws of physics don't distinguish between different frame's answers to these questions, then that's because there
is no physically correct answer and "relative rate of aging" or "simultaneity" or "velocity" are purely coordinate-dependent notions, but you're free to believe differently as long as it doesn't effect how you do physics.
rqr said:
Physical aging has nothing to do with your stated "arbitrary choice
of simultaneity." Aging has to do with internal bodily processes,
and each person will age in only one way in any given inertial frame.
And the laws of physics are sufficient to predict the outcome of any local physical event, like how old each person will be when they reunite in a single region of spacetime,
without assuming that there is any absolute truth about the relative rate that each person was aging at any single moment during the trip.
rqr said:
There is no "whim" involved when I say that either [1] or [2]
must occur during the Three-people experiment.
OK, if you have the philosophical preconception that there is an absolute truth about relative rate of aging/simultaneity, then yes, either [1] or [2] must be correct. But you must admit that there is absolutely no experimental test that could distinguish between [1] and [2], therefore it's just a philosiphical view and not one that can be justified using physics. Personally, I prefer the philosophical view known as
four dimensionalism (also known as
eternalism) which says that the reality is the 4-dimensional spacetime manifold, there is no absolute truth about which set of events on that manifold lie in "the present" and thus no absolute truth about simultaneity or how old two people are "at the same moment" (the alternative view, which you seem to prefer, is known as
presentism, it says that that there is a single objective "present moment" and thus an objective truth about whether two events happened at the same moment or different moments).
rqr said:
You kept on insisting on using worldlines. That is math. There is no
math involved, so you cannot use worldlines.
If you are a presentist than worldlines are just abstractions and the only reality is the arrangment of matter/energy in the absolute present. But for a four-dimensionalist, worldlines are actual 4-dimensional objects arranged in spacetime, and it's "the present" that's just an abstraction, a particular way of slicing up real 4D spacetime into a series of 3-dimensional spacelike surfaces, with the angle of the "slicing" depending on an arbitrary choice of coordinate system.
rqr said:
In the Three-people experiment, there are no clocks or rulers.
Therefore, there can be no usage of any math based on the use
of such instruments (such as Minkowskian math or SR math).
There can be no x, t, and v. No clocks, remember?
You cannot use any math, including any that contains
the standard variables x, t, and v.
This is a truly bizarre argument--do you believe that things cease to be true because they aren't measured? Do you think there can be no actual truth about whether the rest length of one object is greater than the rest length of another if we don't have a ruler to measure it? For that matter, how can you say that Ann or Bob is "10 years old" if you think there is no truth about statements concerning time elapsed when there are no clocks to measure it?
rqr said:
Quoting JesseM:
>Again, talking about a "rate of aging" at a single moment is
>meaningless in relativity.
I did not talk about "'rate of aging' at a single moment." I
am talking about "continuous (ongoing) rate of aging."
I said "at a single moment" to deal with cases where velocities change as in the standard twin paradox--there is obviously a definite truth about the total amount each one ages, my point is that there is no need to postulate a definite truth about the relative rate of aging when they have a particular relative velocity, like during the outbound phase of the trip. I suppose in your thought-experiment since no one changes velocity it doesn't matter, so in this case I'll say there is no need to postulate a truth about their ongoing rate of aging either. You can calculate things from the perspective of different frames which say different things about the rate they're aging, yet these different frames all make exactly the same predictions about local events like how old Ann and Copy-Bob are at the moment they pass. A presentist may say there is a "real" truth about which frame's definition of aging rates (or equivalently, which frame's definition of simultaneity) is the correct one, but they'd have to admit there's absolutely no physical experiment that can distinguish what this truth actually is, and a four-dimensionalist could simply dispense with the idea that this question has any single true answer, any more than the question of which person has a greater absolute speed.
rqr said:
Now that I have laid down the ground rules, I will continue
my above-started Three-people experiment discussion.
As I said above, there are two (and only two) mutually-exclusive
physical possibilities, viz,
[1] Ann is not the same age as Bob and Copy-Bob whenever
the latter two meet
or
[2] Ann is the same age as Bob and Copy-Bob whenever the
latter two meet
To reiterate, one of these two must occur regardless of any
clock synchronization or simultaneity schemes, math, or
worldlines. Also to reiterate, this has nothing to do with
any whims on anyone's part.
No, this is just a philosophical preconception. There is no need to believe there is
any sort of physical truth about which of these is correct, since if there is no absolute present then there is no objective truth about how old two people are "at the same time", the notion of "same time" would be just as coordinate-dependent as "same x-coordinate" from the perspective of a four-dimensionalist.
rqr said:
Indeed, I used both to cover all physical possibilties.
No, you ignore the possiblity that there simply is no physically true answer to the question about whether events that happen far apart from one another occurred "at the same moment" or "at different moments".