# I Time and the expansion of space.

1. Dec 4, 2017

### Mayed Al-Tunaiji

Before I get to a question that's been on my mind for a while, I would like to make it clear that I am a high school student with no understanding of physics beyond my school's curriculum and some books that I've read, so excuse me if this sounds rather absurd.

I know that the expansion of space doesn't have anything to do with the passing of time although they are embedded together (that's from what I understood while reading about relativity) I still don't get why if the expansion stopped time would still pass. So if my limited understanding of the relation between time and space is correct, then why doesn't the expansion affect the passage of time the way large objects do due to their gravity?

2. Dec 4, 2017

### Ibix

I don't think this question has an answer because it doesn't really make sense. Time is a direction in spacetime, so it's defined whether or not the universe is expanding.
Because they're different situations, basically. It's common, but incomplete, to say that time runs slower close to a massive body. Actually, a clock close to a mass ticks more slowly than a clock further away. The point is that you have to compare one clock to another in order to say which one is running faster. There isn't any way to do that with the expanding universe. What would you compare to what?

3. Dec 4, 2017

### timmdeeg

You might like to google 'Friedmann equations' to see the time dependence of the scale factor which describes the dynamical evolution of the universe. Depending on its 'ingredients' it expands, contracts or is static. In the latter case time doesn't stop, instead the derivative of the scale factor with respect to time is zero.

Last edited: Dec 4, 2017
4. Dec 4, 2017

### Staff: Mentor

What have you read? It's always good to give specific references.

First we need to be clear about what "expansion of space" means. Assuming you have seen this term used in reference to cosmology, i.e., to our current model of our universe as expanding, the term "expansion of space" refers to the fact that the scale factor of the universe is increasing with time. But putting it that way raises two obvious questions: what is the scale factor, and whose time is it increasing with respect to?

To answer these questions, we consider a particular family of observers in the universe called "comoving" observers. These are observers that always see the universe as homogeneous and isotropic (the same everywhere and in all directions). These observers have a built-in notion of "time": the time that observer has experienced since the Big Bang. (Note that these "observers" are mathematical constructs; we are not saying that any real observer has to have existed and been experiencing time since the Big Bang. Based on the observations of actual observers like us and our telescopes and instruments, we can reconstruct what a comoving observer would experience.) And these observers also have a built-in notion of "space": the set of all events that happen at the same time according to them. Finally, these observers have a built-in notion of the "scale factor" of the universe: how far apart any given pair of comoving observers are at some instant of their time.

When we say that "space is expanding", what we mean is that the scale factor is increasing with time (where "scale factor" and "time" are the built-in notions described above). This is just another way of saying that the comoving observers are moving apart--i.e., that the universe is expanding. (The latter way of putting it is, in my opinion, less potentially misleading than "space expanding".) So "space" is not really a separate "thing": it's just a way of referring to the scale factor, i.e., how far apart comoving observers are at some instant of their time.

Next, we need to be clear about what "gravity affecting the passage of time" means. Suppose we have a large, static gravitating mass like a star, and we have two observers: one is at rest relative to the star but far away from it, in free space; the other is "hovering" at rest at some low altitude above the star. If these two observers compare the rates of their clocks, for example by exchanging light signals, they will find that the second observer's clock is running slow; this is because of the star's gravity. But in order for them to make this comparison, they have to be at rest relative to each other and to the star; that is what gives them a common reference for what events happen at the same time, so they can compare their clock rates. This common reference also gives them a common notion of "space", and this "space" is static, because the star itself is static.

Now we have enough information to compare the two cases, and we can see that they are different in at least two crucial respects:

(1) In the case of the universe, all of the matter is uniformly distributed, whereas in the case of the star, all of the matter is concentrated in the star. In other words, the second observer in the case of the star is clearly much closer to the matter, and is therefore more affected by its gravity. But in the case of the universe, all comoving observers are equally "close" to the matter, since it is uniformly distributed everywhere, so whatever effect the matter has is the same on all observers.

(2) In the case of the star, "space" is static; in the case of the universe, "space" is expanding. However, as noted above, this can be better expressed as follows: in the case of the star, the observers are not moving apart; in the case of the universe, they are.

The question is, which of these two differences explains the different effects on the comparative "rate of time flow" of the observers? It seems obvious that it is difference #1. Why? Because, as we've already seen, in both cases the observers have a common notion of what events happen at the same time, even though the universe is expanding while the star is static. That only leaves the different distribution of matter, relative to the observers, as a relevant difference.

5. Dec 4, 2017

### martinbn

Imagine a vertical cylinder. The horizontal cross-sections will be circles, and all of these circles will be the same. Now imagine a cone that opens upward. The sections will be also circles but they will be bigger as you go up. In the first case the size of the circles doesn't change, in the second it does (they expand). But in both cases you can go up, nothing prevents the existence of the up direction. In a way it is similar with time, it goes on regardless of whether the universe expands or stays the same.

6. Dec 4, 2017

### nitsuj

"Time and space are embedded" may not be the right concept to approach an understanding of passing time / expanding space. geometrically, measuring comparative motion, "time and space are embedded", however with the expanding universe, not a relative motion, it is specifically space that is expanding.

I like the word continuum for "passing of time"