# Does space expansion affect the rate of time?

1. Jul 11, 2015

### Gerinski

Time can have 2 different connotations.

One is inherent to an entity in spacetime by itself, say a lonely radioactive atom. It may decay or it may not decay, independently of what's going on around it.

But another involves interactions between particles, for example "it takes 60 seconds for microwave radiation of x frequency and amplitude to warm up water from 20C to 50C".

If we follow the assumed accelerated expansion of the universe, atoms and other structures will become farther away from each other, towards a heath death. There will be a time when particles will get so far away from each other, and space in between them will be expanding so fast, that interaction between them will no longer be possible.

In between now and then, all events which involve interaction between particles will gradually take more time, because the distance between them will be increasing. Perhaps the microwave source will need not 60 seconds but one month to warm up that water from 20C to 30C, because the space between the radiation source and the target is expanding.

Any chemical reaction which is now believed to happen at a certain rate will take much longer, and so on.

An hypothetical civilization living in that far future in an expanded space, will see the chemical reaction taking a longer time to happen than we do now.

If we understand Time as the rate at which events happen, could we say that the space expansion slows the rate of time?

2. Jul 11, 2015

### Staff: Mentor

There is no fundamental difference between those examples. Radioactivity is an interaction between elementary particles as well. And both are governed by the more general laws of physics, which do not care about our specific experiment we perform to measure time (as long as it is done locally).

That is not true (neglecting exotic concepts like a big rip). Structures like galaxies are bound, they do not expand. Some stars and some amount of gas get ejected over time, some parts will fall into black holes, but there will always be a significant mass concentration where a galaxy has been.

No, not at all.

3. Jul 11, 2015

### Chalnoth

There's no need to go through this long thought process. There's no meaning to either the statement, "the space expansion slows the rate of time," or "the space expansion speeds the rate of time." The rate of time is whatever a clock measures it to be. And it's just not possible to compare a clock at one rate of expansion to a clock at another rate of expansion.

So we just pick a set of clocks that are stationary with respect to expansion, and use those clocks as our time coordinate.

4. Jul 12, 2015

### Chronos

I agree chanoth.

5. Jul 12, 2015

### slatts

I think--and I could be wrong--that the OP may have lost sight of the fact that the space and time components of spacetime are integral with each other: If the space all around us is expanding, physicists appear to assume that time is (at least in its thermodynamic effects) moving forward, and if the space all around us is contracting, they appear to assume that time is moving backward.

Although I subscribe to them, there are two things that make me feel very insecure about these assumptions: The less significant of them is that I know even less about optics and biology than I do about physics in general, so I don't know whether a change in space that's actually a contraction might have been reversed in our heads. (That concern doesn't bother me much, because its effects would still be consistent.) The more significant is that the acceleration of the expansion, in the beginning of what I guess the multiverse freaks among us (probably the majority) would call our "local" universe, would seem to have changed the relation between space and time, consistent though it might have been either after that acceleration or (in localities identical to our own) before it. Since acceleration is indistinguishable from gravity in its effects, establishing the source of that acceleration may be impossible. The assumption that it was strictly temporal (with "time" used in a non-local sense) seems to be the usual one, although the possibility that it may originate from gravitational effects of a world on a scale different from any with which our own will ever be in contact has occasionally been addressed by cosmologists, and would seem to me to have been a purely spatial origin.

6. Jul 12, 2015

### timmdeeg

Yes, 'coordinate time' and 'proper time'.
No, we can't. Perhaps you are misinterpreting the meaning of the cosmological time dilation. E.g. one expects the supernova light curves to be broadened with increasing distance in the observer's frame. Any kind of clock far away from us will tick slower in our frame (in coordinate time) due to the expansion of the universe as it ticks in its rest frame (in proper time). So, in this context the slowing down of "the rate of time" is an apparent effect which depends on the choice of coordinates, whereas proper time is invariant.

Last edited: Jul 12, 2015
7. Jul 12, 2015

### rootone

If time is a measure of the rate at which things happen, then any change of that rate infers a secondary time dimension which is a measure of the change.
Spacial expansion does not equate to or imply a second dimension of time, and nothing else I have heard of suggests the existence of this unseen dimension.

8. Jul 12, 2015

### Staff: Mentor

This isn't an assumption, it's an observation. We observe that the direction of time we experience as the "forward" one (the one in which we can only anticipate events, not remember them) is the one in which the universe is expanding, and the "backward" one (the one in which we can only remember events, not anticipate them) is the one in which the universe is contracting.

9. Jul 12, 2015

### Staff: Mentor

No. The expansion can be defined in invariant terms, i.e., terms that don't depend on how we split up spacetime into space and time. So the correlation between our experience of time (in terms of anticipation vs. memory, as I noted in my previous post) and the observed expansion is also invariant.

How?

No, it isn't. The accelerated expansion can only be produced by a very particular kind of "stuff"--either dark energy, or something that behaves just like dark energy. The key characteristic of such "stuff" is that it has positive energy density and negative pressure, both of the same magnitude. No ordinary matter or radiation behaves like this.

I don't understand what you mean here. The accelerated expansion, like the expansion itself (see above), can be defined in invariant terms, i.e., terms that are independent of how we split up spacetime into space and time.

I don't understand what you're talking about here. Can you give a reference?

10. Jul 12, 2015

### slatts

The sense in which it would be an assumption would derive from that reversibility of time which I've heard described as characteristic of physics (i.e., that any instant of time can be considered real without regard to the direction of its connections with other instants in such spatial representations of them as movie stills or timetables), in combination with Aguirre & Gratton's model of past- & future-eternal inflation (described by them in

arXiv.org > gr-qc > arXiv:gr-qc/0301042, and more concisely by Vilenkin in
arXiv.org > hep-th > arXiv:1305.3836 ).

They don't describe subjective experience in either of its twin universes (a contracting one and an expanding one, both originating from the same three-spherical boundary surface), but a blogger (Aron Wall, with credentials far outshining my own) made the attempt, and arrived at a conclusion that they might be indistinguishable, which more-or-less matched my own impression. (For instance, an individual in the contracting universe would become animated only at the instant of their death, pass alive through a sequence of instants identical to those through which someone in the expanding one might've passed, and experience disappearance from the undivided entirety of their species upon whatever form of reproduction had isolated them within it, just as each of us feels that he or she did until their own individuation: The sensations involved, and even their linguistic expression, could be appropriately identical at every instant.)

Here I figure you're referring to such terms in the relativistic equations as pressure, energy, and mass, but please correct me if I'm wrong.

More-or-less in the same way that the clocks carried in opposite directions through the earth's gravitational field by jets registered the passage of slightly different amounts of time: If neither jet had accelerated, no such difference in the registrations of time would've occurred.

Sounds to me like there might be some overlap between the contracting zone and the expanding one, although not enough of an overlap to have factored much in the evolution of the species hereabouts.

The possibility that it occurred at a surface of time seems pretty common; I've seen one or two PF threads about the big bang occurring everywhere at once, and readings of Greene and Vilenkin have told me that time in the inflating region is kind of indeterminate. So, I figured that if the spatial contraction (intuitively seen as accompanied by an acceleration of time's passage, from an intermediate region's physically unattainable perspective) would've continued for enough fractions of a second, it would've dropped below the Planck scale, and it appears that Markov and Linde might've been thinking something similar, back when they were dreaming up the monopoles and other particles each containing a micro-universe that are mentioned in Linde's "Monopoles as Big as a Universe" at arXiv.org > astro-ph > arXiv:astro-ph/9402031, or alluded to in his "Monopoles as Big as a Universe and The Universe Inside a Bubble". Faraday knew more about magnetism when he was conceived than I know pushing 70, but it did also occur to me that some version of it might be holding the larger expanding sphere away from the smaller contracting one at its center, so the monopole may have been a logical favorite among such "seed" particles.

11. Jul 12, 2015

### rootone

Magnetic monopoles don't make sense to me.
They just don't.

12. Jul 12, 2015

### Chalnoth

They're perfectly sensible as an extension of Maxwell's equations. What it ends up looking like is two separate electric charges that act independently (and with different force strengths). So you could have moving magnetic monopoles creating an electric dipole, for instance. Magnetic monopoles are also a pretty generic prediction of grand unified theories.

13. Jul 12, 2015

### rootone

Right now I am stuck with the idea of something like a battery with only a positive terminal and no negative one.

14. Jul 12, 2015

### Staff: Mentor

The laws of physics are time reversible (with some minor exceptions involving the weak interaction that don't concern us here). But there are two ways that this can show up in the actual solutions to the laws, which are what we use to describe actual scenarios:

(1) The solution itself can be time-symmetric. An example would be a solution to the two-body problem in Newtonian physics: the solution looks the same if we reverse the direction of time.

(2) Solutions can occur in pairs, which each member of the pair being the time reverse of the other. This is what happens with the solutions to the Einstein Field Equation that we use in cosmology: our current best solution describes an expanding universe, and is not time symmetric; but there is a corresponding solution that describes a contracting universe (which is ruled out by observation).

This model describes a time-symmetric solution, yes, but even if we were living in such a solution, we would only be able to observe half of it, so observationally we can't distinguish it from a time asymmetric expanding universe solution.

Those are relevant in distinguishing one particular expanding universe solution from another, yes. But all such solutions will share the same invariant characterization of "expansion". The simplest way of describing that invariant is to describe it in standard FRW coordinates: it is just $\dot{a} / a$, where $a$ is the scale factor in the FRW metric and $\dot{a}$ is its derivative with respect to FRW coordinate time. But even though I've described this quantity in a particular coordinate chart, it can be shown that it is an invariant (by deriving it more laboriously from a manifestly invariant equation).

The kind of acceleration the jets experienced is not the same as the kind of acceleration we mean when we say the expansion of the universe is accelerating.

(Also, the reason the clocks in the Hafele-Keating experiment showed different times was not because of the acceleration of the jets; even the clock that stayed behind in the lab the whole time experienced proper acceleration. The reason the clocks showed different times was because of their different velocities relative to an inertial frame in which the center of the Earth is at rest. Proper acceleration, itself, has no direct effect on clock rates.)

What makes you think that? The entire universe is an "expanding zone"; there's no "contracting zone" to overlap.

Do you mean, that it started at some particular surface of constant FRW coordinate time? The accelerated expansion is occurring continuously now; it's not limited to any one particular surface of constant time. According to the simplest model, the universe's expansion did switch from "decelerating" to "accelerating" on some particular surface of constant FRW coordinate time, yes. But I don't know how much evidence there is that can test that against other possibilities.

The inflationary epoch is not the same as the current epoch of accelerating expansion. I thought we were talking about the latter, since that's what the OP was asking about.

15. Jul 12, 2015

### Staff: Mentor

Isn't that what a positive electric charge is?

16. Jul 12, 2015

### slatts

Sorry; I had, as you point out once or twice later, lost sight of the fact that the opening post was not about the inflationary epoch. Thanks for the various clarifications, especially re my particularly half-baked recollection of the clocks-in-jets experiment, which I guess would've worked the same if they'd been airborne since the formation of the earth.

Last edited: Jul 12, 2015
17. Jul 18, 2015

### KDO2001

Please explain further. Do you have references for the last sentence?

18. Jul 20, 2015

### Chalnoth

19. Jul 20, 2015