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Twin paradox and the size of the universe

  1. Dec 14, 2014 #1
    Ok, let's take the standard twin paradox, Alice leaves on a trip in her rocketship near the speed the light, and comes back to Earth some time later to find herself 5 years younger than her twin, Bob.

    Now they go out to lunch and strike up a conversation as to how old the universe is. Alice says it's ~13.8 billion years old and is such and such a diameter across. Bob says, no no no, the universe is ~13.8 byo + 5 years and has an accordingly larger diameter. Which one is correct? How do we reconcile this? I mean, if each are living in a different-sized universe, how are they able to have lunch together? For instance, how are the physical properties of the restaurant not affected, etc.?
  2. jcsd
  3. Dec 14, 2014 #2


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    Indeed, you hit the nail on the head: how are they able to have lunch together?

    The answer is because they have matched velocities and are in the same rest frame. Thus, they measure the universe identically.

    Sure, while on their trips they made all sorts of measurements. (Hey look, that restaurant passing by my windows at .999c looks massively longitudinally contracted - as does my local universe! And everything is now moving verrrry slowly.)

    But those measurements are relative. When they slow their ship and turn around, they will get different answers. They know they are changing their velocities, so they will certainly know their measurements will vary accordingly.

    (Ah, now that I am in the same rest frame as the restaurant, it looks quite normal, as does my local universe.)
    Last edited: Dec 14, 2014
  4. Dec 14, 2014 #3


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    Bob is correct, because (by hypothesis) he has remained at rest in "comoving" coordinates--physically, he has continued to see the universe as homogeneous and isotropic. To relate how old you think the universe is to its diameter in the way you are assuming, you have to be such an observer--one who has always seen the universe as homogeneous and isotropic. Since Alice is not such an observer, she has to apply a correction when deriving the diameter of the universe from how old she thinks it is; with the correction applied, she gets the same answer Bob does.

    (Note that the above applies to Alice after she has come back and met up with Bob again, so she is now at rest relative to Bob. During Alice's trip, the "diameter" she assigns to the universe in a frame in which she is at rest will be different because of her motion relative to Bob, and the relationship between this "diameter" and the age Alice assigns to the universe will also be different. I put "diameter" in quotes here because Alice's surfaces of simultaneity while she is in motion are different from Bob's, so the "diameter" she is assigning belongs to a different slicing of spacetime into space and time. Discussions of cosmology almost always assume "comoving" observers, like Bob, and the corresponding slicing; so if you deviate from that, you have to be careful not to make assumptions that are only valid for that slicing.)

    (Also, I assume that the "diameter" you mean here is the diameter of the observable universe. According to our best current model, the universe itself is spatially infinite.)
  5. Dec 14, 2014 #4


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    A short answer - there is no absolute time in special or general relativity, so there is no true "absolute age" of the universe. We do have certain conventions, those conventions are used when "the age of the universe" is given. These conventions are that we measure the age in a co-moving frame, one in which the CMB is isotropic.

    Seems simple to me, but it appears people have difficulties with giving up the idea of "absolute time".
  6. Dec 14, 2014 #5


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    Well, maybe, but I don't think that's the issue here. The issue is how can the age of the universe from a single event in spacetime (the simulataneous co-existance of Bob and Alice at the same point in space) experience the age of the universe in two different ways. I had exactly the same idea as Dave but I'm still mulling over Peter's analysis.
  7. Dec 14, 2014 #6
    Yeah, that's exactly my point. My point is that, as they are having lunch together and look through the telescope the waiter brought them, they each look through the lens and see a different universe? With a different age and diameter? (visible universe, that is).

    PeterDonis says Bob is correct. Does that mean that when Alice looks through the telescope, she sees the universe as Bob sees it? Is that how this is reconciled?
  8. Dec 14, 2014 #7


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    Of course not. They are both at the same point in spacetime, with the same velocity, so they see everything the same. How they got there does not affect what they see at that moment; it only affects the elapsed times on their respective clocks.

    Yes. But she calculates a different relationship between what she sees and the elapsed time on her clock, because of her different history of motion compared to Bob.
  9. Dec 14, 2014 #8


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    Because they arrived at that point in spacetime by different routes, and the "age of the universe" that you experience depends on the route, not just on the point in spacetime you are currently at. More precisely, the relationship between what you currently observe (which is the same for all observers at the same event with the same velocity), and the "age of the universe" that you experience, depends on the route.
  10. Dec 15, 2014 #9


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    Makes sense. Thanks for continuing to clarify that for us. Now that I think about it, a thought experiment using the decay of a radioactive element shows clearly that the age would be different for Bob and Alice. I just hadn't thought it through.
  11. Dec 15, 2014 #10
    That doesn't really make complete sense to me... If the age (of the visible universe I'm assuming) would be different for Bob and Alice, then they would not see the same thing looking through the telescope, would they?

    Ok, sounds like there may be differences, but...

    Ok, that sounds like there are no differences...

    Could you elaborate on that a little bit? What kind of different relationship? I'm imagining her looking through the telescope and looking at her watch and going, ahhh, I get it. But I don't get it.
  12. Dec 15, 2014 #11


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    Yes, as Peter explained, they WOULD see the same thing, but that is NOT relevant to the age that they see the universe as being. Just using the differences in their ages should be enough to make that clear but somehow, for me, it didn't so I thought about a radioactive element. Use magic to consider that this radioactive element has been around since the beginning of the universe and is exactly 13,000,0000,000 years old (round number for ease of demonstration). They break it in half and one half goes on the trip and one half stays home. When the traveling half gets back it's, say, 13,000,0000,005 years old, BUT ... the half that stayed home is 13,000,0000,020 years old. They have taken different paths through spacetime and thus have different ages. Similarly, Bob and Alice had taken different paths through spacetime and so see the age both of each other and of the universe as being different.
  13. Dec 15, 2014 #12

    What is special about universe, so that universe is not just another aging object?

    Alice: "During my 1 year trip universe and Bob aged so quickly that they aged 6 years."

    Bob: "During Alice's 6 year trip universe and me aged 6 years. But Alice aged so slowly that she aged 1 year."
    Last edited: Dec 15, 2014
  14. Dec 15, 2014 #13


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    Nothing. The universe IS just another aging object, but like Bob and Alice, and everything else, how you measure the age of the universe depends on your path through spacetime.

    Yes, so?
    Yes, so?

    What you seem to not be getting is that the age of an object ALWAYS happens at one second per second for that object, BUT ... when compared to the age of a different object, then what matters is the path through spacetime that each have taken.
    Last edited: Dec 15, 2014
  15. Dec 15, 2014 #14


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    The age of the universe is not something you directly observe; it's something you calculate, and the calculation depends on your own past history, not just on what you're currently observing. Bob and Alice each have the same current observation, but they have a different past history, so they calculate a different age for the universe.

    What this really means is that the term "age of the universe" is really something of a misnomer for what we are all talking about. See below.

    You're imagining it way too simply. Alice's watch registers the proper time elapsed along her worldline, and Bob's registers the proper time elapsed along his worldline. If we suppose (which of course can't be the case in a real scenario) that both watches were set to time zero at the Big Bang, then the reason the two watches read differently is simply that Alice and Bob followed different worldlines to get to the same current event in spacetime. So the readings on their watches aren't really telling you "how old" the universe is, because the readings don't depend on the universe itself--both worldlines are in the same universe. They're just different worldlines, and the watch reading depends on the worldline. So Alice should not expect a simple relationship between her watch reading and what she sees through the telescope, and she certainly should not expect to see the same relationship as Bob does.

    When cosmologists use the term "age of the universe", what they really mean is the proper time elapsed since the Big Bang along a "comoving" observer's worldline, like Bob's. The special property that picks out "comoving" worldlines from all other worldlines (like Alice's) is that "comoving" observers always see the universe as homogeneous and isotropic; observers following any other worldline will, for at least some portion of their history, see the universe as non-isotropic or non-homogeneous (like Alice does during her trip). So the "age of the universe" in cosmology is really "the proper time elapsed since the Big Bang along a comoving worldline". A non-comoving observer, like Alice, can still calculate this number from their watch reading and what they see through a telescope, but the calculation won't be as simple as it is for a comoving observer, who can just read it directly off his watch (again, assuming an idealized case where the watch is set to time zero at the Big Bang).
  16. Dec 15, 2014 #15
    Ah yes, the "co-moving" term I've been coming across most frequently recently and have been putting off investigating in full. I guess that's going to be my project for tomorrow. I'll give you the report :redface:
  17. Dec 16, 2014 #16
    I'm sorry if this answer isn't in the spirit of the thread...
    Alice and Bob, both knowing she would be making this trip at a significant and measurable fraction of the speed of light, would adjust Alice's clock just like we do for the clocks on GPS and other satellites. They would agree on the amount of time passed and the corresponding expansion of the universe.
  18. Dec 16, 2014 #17


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    What do you mean "the amount of time passed" ??? This whole thread has been about explaining that there is no "THE" amount of time passed, just the differing amounts of time passed relative to each other. They are not the same amounts of time for Bob and Alice. Do you dispute that?
  19. Dec 16, 2014 #18
    The universe is a composite object, with no detectable center. All its components are moving at varying velocities, with varying degrees of time dilation. On that basis the universe has a range of ages. Alice has made an excursion relative to Earth. On reuniting, her accumulated time is 5 yr less than that for Bob, and anything else still existing there. This difference only applies to the Alice-Earth system. When they observe a distant component, it is only a relative doppler effect, i.e. a comparison of frequencies (clocks).
    I agree with pervect, as to the CMB being the only thing serving as a "fixed" reference, since events don't move.
    Considering the distances involved, any age comparisons of the universe with any component would be vague and uncertain.
  20. Dec 16, 2014 #19


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    In relativity, there is no preferred frame of reference, but in cosmology, there certainly is. (The most obvious frame is the one where the cosmic microwave background is closest to isotropic. We call this the co-moving frame.)
  21. Dec 16, 2014 #20
    These comments makes sense to me. I like using the standard of the observer always seeing the universe as homogeneous and isotropic as the "comoving" frame. A few questions:

    1) So in the scenario above, are we assuming that Bob is "comoving" or in the same comoving frame as the CMB, that this qualifies as Bob and the CMB being in the same inertial rest frame (IRF), and the "test" of such is that the universe appears to be homogeneous and isotropic, to Bob?

    2) There is a galaxy with an earth-like planet far far away receding from the Earth at 0.9c, Does an inhabitant on that planet also see the universe as homogeneous and isotropic as well as being in the same rest frame or comoving with the CMB? We can say that Alice during her trip breaks symmetry with Bob and travels a different "distance" through spacetime due to her departing from Bob's (and the CMB's) IRF, and thus shows a different age when she shows up back on Earth. But what about the guy in the receding galaxy? Is he also traveling a different distance through spacetime than Bob seeing as he's traveling at 0.9c relative to Bob? Or is there some special feature about this scenario whereby the guy in the distant galaxy also sees the universe as homogeneous and isotropic? In other words, does a symmetry apply in this case where it doesn't in Alice's case.
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