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I Is time rate getting faster with cosmic expansion?

  1. Oct 2, 2016 #1
    Hi, layman here, but hopefully reasonably educated. I did not know whether this question might fit better under relativity or under cosmology so I'm posting it here.

    General Relativity tells us that time slows down in gravity wells. The cosmic expansion tells us that the energy density in space has been getting smaller and smaller since the very early epochs of the universe. Even if the dark energy remains constant, the matter (baryonic + dark) density is certainly getting smaller, so the overal energy density in space must be getting smaller.

    Consequently it seems logical to believe that the rate of time elapsing has been getting faster and faster as space expands. When the universe was very young and small it's energy density was very high some time must have run rather slowly. Conversely, in the current universe the average energy density is much lower so time must be running faster.

    I am aware that if these are universal statements, they may have no physical meaning. When talking about the rate of time elapsing in the universe, we have no external clock to compare to, so such a rate of time elapsing will always look the same to anything inside that universe. We may have the above theoretical reasons to believe that early in the universe time must have been ticking slower, and that now time must be ticking faster, but if there is no external clock to compare those to, they probably become meaningless.

    What can you say about this reasoning? Am I completely wrong in something? or partly right? Was time really running slower in the early universe than now, and if so does that have any significance, now or perhaps looking to a remote future when the rate of expansion will be much faster than now?

  2. jcsd
  3. Oct 2, 2016 #2
    Your logic doesn't seem have any mistakes in my account. However, because this is happening universally, time will seem to travel at a constant. Also, because the universe is enacted by gravity everywhere due to its infinite range, it would lead me to believe that time could also be reaching its maximum speed as the universe allows for less density.
  4. Oct 2, 2016 #3

    Vanadium 50

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    Let's do some science. Describe a measurement that you can make that would answer your question.
  5. Oct 2, 2016 #4


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    Prof. Richard Muller covers this very topic in his new book ''The Physics of Time'' and even proposes experiments to demonstrate ''cosmological time acceleration.''
  6. Oct 2, 2016 #5


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    To clarity your thinking for us, answer this: Do clocks in gravity wells tick slower than one second per second?
  7. Oct 2, 2016 #6


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    In stationary gravity wells. The universe as a whole is not stationary; it is expanding. So you can't apply this reasoning to the universe as a whole. That invalidates your argument.
  8. Oct 2, 2016 #7


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    This is not a valid source for PF discussion; it is speculative, and even though it proposes experiments, those experiments have not been done, so we can't discuss their results.
  9. Oct 3, 2016 #8
    Thanks. I already admitted in the OP that since there is no reference clock the reasoning may be meaningless, I understand that.
  10. Oct 3, 2016 #9


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    I'm not aware of any measurement you can make to determine the answer to your question. Which doesn't necessarily mean there isn't one - but I don't see how the question can be answered without a way, in principle, to test it experimentally.

    It may be instructive to take a brief digression into the so-called twin paradox of special relativity before attempting to answer the question you just asked. It's fairly well known that if you have two clocks in relative motion, if you choose a reference frame in which one of the clocks is at rest, the other clock will tick slower. And it doesn't matter which clock you pick, you can pick either clock, construct the appropriate reference frame, and the clock in the moving frame will tick slower. The very notion of this happening is inconsistent with the Newtonian notion called "absolute time", and I rather suspect that your question is based on this concept known by the name "absolute time". Since this notion of "absolute time" has been shown to be inconsistent with SR (and hence GR, which is based on SR), if your question is in fact based on the notion of "absolute time" it has no answer :(.

    For a discussion of the issues involved, read about any of "the twin paradox", "the relativity of simultaneity", or "Einstein's train" - there should be zillions of threads on this already on PF.
  11. Oct 3, 2016 #10


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    And you still have not answered the question that I asked you in post #5
  12. Oct 3, 2016 #11


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    It's not a matter of there being no reference clock. The entire reasoning you are using, about time going slower in a gravity well and faster outside it, is not valid for the universe as a whole, because the concept of "gravity well" does not even apply to the universe as a whole. It is meaningless, because the universe as a whole is not stationary, it is expanding. The fact that the density of ordinary matter and radiation in the universe has been decreasing over time does not mean the universe is a "gravity well" that is gradually getting weaker; that very concept is not valid for the universe. So the very first step of your argument is meaningless.
  13. Oct 4, 2016 #12
    Yes, clocks in a gravity well tick at 1 second per second of course.

    Thanks, I'm not sure I understand this though. If only as an intellectually exercise, if we attempt to view the universe as a block-time spacetime, we would observe regions of different energy density, both in space as in time. If we choose to view a slice of space of similar cosmic age, such as different space regions at the current age of 13.8 billion years, we will find regions of high density such as the surroundings of supermassive black holes and regions of low density such as great intergalactic voids. I think we can agree that even if we can not perform direct experiments we know that clocks in those highly dense regions must be ticking slower relative to those in the great voids.

    So similarly if we choose to view the block spacetime in a slice covering the universal history, we will also find regions of different density, and as average regions closer to the big bang will be denser than regions closer to our current universal age. So if we apply the same reasoning, even if only intellectually we should "know" that clocks in the denser regions must have been ticking slower relative to clocks in the less dense regions. I don't see where does expansion come into, I am thinking of a "snapshot" view of the block spacetime, a sort of static snapshot independent of whether there has been any expansion or not.

    Thanks again
  14. Oct 4, 2016 #13


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    No, we can't, because, as I've said several times now, the universe as a whole is not stationary. And that means there is no invariant way to compare our clock rate here on Earth, inside a gravity well (actually multiple gravity wells--see below) with the clock rate of a hypothetical observer inside, say, a great void a billion light-years away.

    The intuitive reasoning you are using works on the scale of a single isolated system and its immediate surroundings--for example, the Earth and its immediate surroundings (so our clocks here on Earth can be said to be ticking slower compared to the clock of a hypothetical observer out in interplanetary space and at rest relative to the Earth), the solar system and its immediate surroundings (so the clock of an observer out in interplanetary space but still well inside the solar system can be said to be ticking slower than that of a hypothetical observer out in interstellar space outside the solar system, at rest relative to the first), or even our galaxy and its immediate surroundings (so the clock of an observer in interstellar space, just outside the solar system, can be said to be ticking slower than that of a hypothetical observer just outside our galaxy and at rest relative to the first). But all of these localized systems can be considered stationary--not expanding. The universe cannot. It's not just a matter of galaxies and galaxy clusters moving apart. The spacetime of the universe itself is "expanding", in the sense that its geometry is simply not the same as the geometry of an isolated system surrounded by empty space, which is the kind of geometry for which your intuitive reasoning works.

    A snapshot is not spacetime, and it can't show you spacetime geometry. In particular it can't show you whether that geometry is static. The technical definition of "static" is that the spacetime has a timelike Killing vector field. Heuristically, this means that there is a family of timelike worldlines in the spacetime (curves describing the histories of a family of hypothetical observers), such that along each worldline, the geometry of space--i.e., the spatial geometry of each "snapshot" of spacetime at successive instants of time by your clock--is the same at all times. For example, if you are hovering out in interplanetary space high above the Earth, this will be true for you (at least to a first approximation, ignoring the effects of the Sun, other planets, etc.): the geometry of space that you see will be static, unchanging with time by your clock.

    However, for the universe as a whole, there are no observers, even hypothetical ones, for which this is true. On the scale of the universe as a whole, every observer, regardless of his state of motion, sees a changing spatial geometry. Since the change involves "comoving" observers--observers that always see the universe as homogeneous and isotropic--moving farther apart, we describe it as the universe "expanding". But however we describe it in words, this fact invalidates your reasoning, because your reasoning depends on the spatial geometry being static.
  15. Oct 4, 2016 #14
    I appreciate your answering, please don't get mad at me for asking further. Let's forget expansion for a moment. We know that there is a large gravitational potential close to Saggitarius a* at the core of the Milky Way. We know that between the Milky Way and, say Andromeda there is a significant void.

    We know by our experiments on Earth and its surroundings that the clock at the Earth's surface ticks slower compared to the clock in a space probe we send to Pluto once it's in that region. I believe that we need to take account of this when designing the communications and control of that space probe from Earth.

    If we know this, why can't we assume that the same must be true for the clock sitting very close to Saggitarius a* compared to the clock in the intergalactic void between us and Andromeda?. Again I don't see where universal expansion is relevant here, the Milky Way and Andromeda are not even getting apart from each other but rather the opposite.

  16. Oct 4, 2016 #15


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    Sorry, can't do that. Once more: the reasoning you are using no longer works once expansion is taken into account. Please read and re-read that until it sinks in. There is no point in discussing hypothetical situations where we ignore expansion, because the whole point is that the reasoning you use in those hypothetical situations is not valid when you take expansion into account.

    We can, but only because the Milky Way and Andromeda are both part of the same isolated bound system (our local group of galaxies). In other words, because we can get away with ignoring expansion in this particular case. But, once more: you can't ignore expansion on the scale of the universe as a whole. So, once more: the reasoning you are using is not valid for the universe as a whole. In particular, it doesn't work for comparing the early universe, with much higher average density than now, to now.

    There is no point in continuing to repeat what I have said and emphasized above. Thread closed.
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