max. rate of expansion of space?

by coyote2
Tags: expansion, rate, space
 P: 7 Since I see the Big Bang was the beginning of space; if space is infinite, does that mean that space can expand at an infinite rate? (Thanks in advance from this layman; I've started Brian Greene's "Hidden Reality" and despite laymen being it's target audience, I'm stuck on this question.)
 Astronomy Sci Advisor PF Gold P: 22,675 You have to be careful with popularizations. Many are written to make money, to sell to wide audience, rather than to honestly present the state of scientific observation and conjecture. Most working cosmologists do not accept or use "multiverse" models. (Yet Greene's book is largely about "multiverse" speculation.) So far there is no scientific reason to favor infinite over finite space. Both versions of the standard cosmo model may be used in the same paper. So far they fit the data about equally well, so it is an open question. Keep both possibilities in mind, is the idea. (If space is infinite now, then it always was. And expansion started from infinite volume.) So far there is no scientific reason to suppose that space and time "began" with the start of expansion or any other known event. There are models which do not go back further than the start of expansion, and there are models which do go back further in time. And both fit the data equally well. As more and better data accumulate we will be better able to distinguish and see which models fit best. There is actually some progress being made in this currently! It's exciting, but it's not over yet.
P: 7

max. rate of expansion of space?

Thank you very much for your wonderful replies, marcus.

I do understand that Green's book is largely speculative (and simplified), and I'm simply seeking a grasp of the bases of that speculation.

(Speaking of "speculation", I guess I'm interested in it because it seems to me that quantum mechanics seems strange enough, that an encompassing theory might well be rather surprising.)
 Quote by marcus (If space is infinite now, then it always was. And expansion started from infinite volume.)
Gulp. Is there a way I might understand how "infinite volume" could expand?

Are the vast differences between current and past expansion percentage rates simply proportional to the distances involved?
C. Spirit
Thanks
P: 4,752
 Quote by coyote2 Are the vast differences between current and past expansion percentage rates simply proportional to the distances involved?
If you are talking about the expansion of space itself then it is a function of time and is usually a power law.
P: 1,498
 Quote by coyote2 Gulp. Is there a way I might understand how "infinite volume" could expand?
Sure (but take a breath first). Imagine a rubber sheet with grid marks painted on it stretching out infinitely far in all directions from your position. Now imagine that the rubber sheet is stretched out isotropically from your vantage point. The grid marks will grow in size, charting the expansion of the rubber sheet. This is how an infinite volume undergoes expansion. The big bang in this case is the moment at which this expansion began.
P: 1,498
 Quote by coyote2 Are the vast differences between current and past expansion percentage rates simply proportional to the distances involved?
There are two things at play here: the expansion rate of the universe -- the rate at which the grid marks on the rubber sheet grow, and the speed at which distant objects attached to this sheet appear to recede from Earth. In a homogeneous universe, the rate of expansion is the same at all points in the universe, and is given by the Hubble parameter, $H$. (Really, it's determined by the rate of the change of the scale factor, $a(t)$, which governs how meter sticks grow in time. In terms of the scale factor, the Hubble parameter is $H=\dot{a}(t)/a(t)$, where $\dot{a}(t)$ is the time derivative of $a(t)$.) Now, the speed at which distant objects recede from Earth depends on how far away that object is. This speed, $v$ is given by Hubble's Law:
$$v = Hr$$
where $r$ is the distance to the object. So for a given, fixed rate of expansion (set by $H$), we find that objects recede from us at a speed that is proportional to their distance from us.

So to finally answer your question, in the real universe, the Hubble parameter is generally a function of time, and so the rate of expansion of the universe varies with time, but not location in a homogeneous universe.
P: 7
 Quote by bapowell Sure (but take a breath first). Imagine a rubber sheet with grid marks painted on it stretching out infinitely far in all directions from your position. Now imagine that the rubber sheet is stretched out isotropically from your vantage point. The grid marks will grow in size, charting the expansion of the rubber sheet. This is how an infinite volume undergoes expansion. The big bang in this case is the moment at which this expansion began.
Thank you bapowell, I may have a shot at understanding this.

Since this example uses a two-dimensional object (the rubber sheet) to stand for (three-dimensional) volume, does that mean that it's spacial expansion involves a dimension beyond three?
P: 7
 Quote by bapowell There are two things at play here: the expansion rate of the universe -- the rate at which the grid marks on the rubber sheet grow, and the speed at which distant objects attached to this sheet appear to recede from Earth. In a homogeneous universe, the rate of expansion is the same at all points in the universe, and is given by the Hubble parameter, $H$. (Really, it's determined by the rate of the change of the scale factor, $a(t)$, which governs how meter sticks grow in time. In terms of the scale factor, the Hubble parameter is $H=\dot{a}(t)/a(t)$, where $\dot{a}(t)$ is the time derivative of $a(t)$.) Now, the speed at which distant objects recede from Earth depends on how far away that object is. This speed, $v$ is given by Hubble's Law: $$v = Hr$$ where $r$ is the distance to the object. So for a given, fixed rate of expansion (set by $H$), we find that objects recede from us at a speed that is proportional to their distance from us. So to finally answer your question, in the real universe, the Hubble parameter is generally a function of time, and so the rate of expansion of the universe varies with time, but not location in a homogeneous universe.
First, as soon as I read WannabeNewton's reply, I realized my ambition was really just to know if despite the vastly different percentage rate of spacial expansion, the distance of the expansion was constant. After I googled "Power Law" I think I understood the answer was "no".

Had I stuck with my plan to take more math and major in physics decades ago, I'd have had a much better shot at fully grasping bapowell's reply (my fault, thank you bapowell)!
P: 1,498
 Quote by coyote2 Since this example uses a two-dimensional object (the rubber sheet) to stand for (three-dimensional) volume, does that mean that it's spacial expansion involves a dimension beyond three?
No, it's just lower-dimensional for ease of explanation. To get our universe, you just have a 3D volume undergoing expansion in the same manner.
P: 1,498
 Quote by coyote2 Had I stuck with my plan to take more math and major in physics decades ago, I'd have had a much better shot at fully grasping bapowell's reply (my fault, thank you bapowell)!
Don't give up! It's difficult sometimes to gauge the level of people on the forums -- I apologize if I spoke passed you or used terms/concepts with which you are not familiar. Feel free to ask for clarification!
P: 7
 Quote by bapowell No, it's just lower-dimensional for ease of explanation. To get our universe, you just have a 3D volume undergoing expansion in the same manner.
Thank you bapowell. I'm afraid I'm not quite there yet...

Perhaps my problem is that, in terms of area, "3D volume" and "space" seem equivalent to me. Which leaves me still wondering how "infinite volume" could expand. I'm sure it's just my limited imagination, I don't see how an infinite amount of volume can increase.

Or maybe my problem is I don't understand "infinite". (In two dimensions, I think of "infinite" length as going on forever, endlessly. Such that infinity + 1 = infinity.)

I promise if I can't get it this time, I'll stop wasting your time!
P: 4,678
 Quote by coyote2 Since I see the Big Bang was the beginning of space; if space is infinite, does that mean that space can expand at an infinite rate?
Well, there isn't any known fundamental limit to the expansion rate, however an infinite expansion rate would require infinite energy density. And that can't happen.
 Sci Advisor PF Gold P: 9,090 The observable universe is temporally finite [~13.7 billion years] and contains a finite quantity of baryonic, non-baryonic, spatial and energy components. It is hard enough to wrap your head around that without introducing indeterminate quantities of unobservable and exotic components.
P: 7
 Quote by coyote2 Perhaps my problem is that, in terms of area, "3D volume" and "space" seem equivalent to me. Which leaves me still wondering how "infinite volume" could expand.
I think I get it now. I thought "volume" here meant an "amount of space, measured in cubic units"; but since "expansion started from infinite volume" was (I believe) referring to the Big Bang then "volume" there couldn't have meant an "amount of space", since at the moment of the Big Bang there was not an infinite amount of it (just google tells me a "singularity...the size of a dime").

I apologize, I guess I needed to take more deep breaths. I hope there aren't too many like me who stumble in here needing clues, overwhelmed from reading pop physics.
 Sci Advisor P: 1,498 Right. Don't think about expansion as some region necessarily increasing in volume (in a finite universe, this would indeed be the correct view). Instead, just think of expansion as the increase in size of the grid marks you paint throughout your volume. In general relativity, this is precisely the way expansion works -- as an increase in distance between points drawn on the grid.
P: 7
 Quote by coyote2 Thank you bapowell. I'm afraid I'm not quite there yet... Perhaps my problem is that, in terms of area, "3D volume" and "space" seem equivalent to me. Which leaves me still wondering how "infinite volume" could expand. I'm sure it's just my limited imagination, I don't see how an infinite amount of volume can increase. Or maybe my problem is I don't understand "infinite". (In two dimensions, I think of "infinite" length as going on forever, endlessly. Such that infinity + 1 = infinity.) I promise if I can't get it this time, I'll stop wasting your time!
 Quote by bapowell Right. Don't think about expansion as some region necessarily increasing in volume (in a finite universe, this would indeed be the correct view). Instead, just think of expansion as the increase in size of the grid marks you paint throughout your volume. In general relativity, this is precisely the way expansion works -- as an increase in distance between points drawn on the grid.
Thank you bapowell, this reply plus time pondering helped me imagine it better at all scales.

I'd heard about (but not understood) the Big Rip hypothesis; it didn't occur to me that expansion was a factor at very small scales.

I see that "the electromagnetic forces hold... molecules and atoms together" now (but perhaps not forever if "the energy density of dark energy increase[s] without bound"; then "Finally even atomic nuclei will be torn apart").

Knowing that electromagnetic forces now keep atom nuclei from being torn apart leaves me still wondering: that means the atoms aren't expanding at all yet, right? (I'm guessing that based upon atomic particles having quantum states.)

I shudder to think how far off the rails I might be here.