# Expansion of space or accelerating speed?

1. Feb 22, 2010

### harrietjob

Are objects in space moving apart at an increasing rate relative to one another, or is the 'space' between them expanding?
For example, using red-shift to explain the differential causes:
If an object is moving away from Earth, the electromagnetic waves it emits are red-shifted. This would be because the initial standardised wavlength for the emission in question is preset, given, if you will, but in addition to this, you have the velocity of the celestial object, thus adding a two-point dependancy to the given wavelength - that is, if the objects are moving apart relative to one another. But what if the force we imagine to be propelling these objects apart is in fact non-existant? If the reason for the increasing rate of expansion of the universe is down to space expanding, then red-shift would still occur. To imagine the expansion of 'nothing' is a difficult concept to imagine, but it would be clearer as to why the rate of expansion is accelerating - Hubble's Law clearly relates distance with the rate of expansion, but what is causing the accelerating rate of which the universe is expanding? For eample, if you had 4 cubic metres of 'space', and the amount of 'space' doubled every minute, then after one minute you would have 8 cubic metres, then after two, you would have 16 cubic metres, and so on - directly demonstrating the relationship between time and 'space', so to speak. I have many more questions, but I would be interested to hearyour views on what I have written so far.

2. Feb 22, 2010

### marcus

There are various different coordinate systems that can be used and different ideas of distance. How one describes, how one talks about cosmology depends on that.

The Hubble law uses a particular concept of distance and for starters, as a beginner, it's a good idea to focus on that concept first and get a solid understanding of Hubble law.

So first I'll say what ("freeze-frame") distance means---the distance that works in v = Hd.

Imagine that at a certain moment in time you could freeze the expansion process. Then our (freezeframe) distance to some galaxy at that moment is just the ordinary distance measured by timing a radar or light signal. If it takes a billion years for a light signal to travel to the galaxy then the distance at that moment is a billion lightyears.

The point of defining distance that way is that the distance doesn't change while the signal is traveling, so it is a pretty simple distance concept. (There's an interesting technicality about what "at a certain moment" means, which we can deal with after taking a look at Hubble law.)

The freezeframe distance is not the same as the "light travel time" distance, where you use how long it actually took for some light to get here from a galaxy as a measure of how far away the galaxy is. Light travel time is radically affected by the past expansion history, past slowing down and speeding up. The distance when the light started will be different from the distance when it arrives here, and neither have any simple relation to how long it took. Light travel time is not appropriate to use with Hubble law.

When someone starts talking to you about distance in cosmo the first thing is to get clear on what concept of distance they are using. Here I am talking freezeframe distance ( technically called "proper" and in other contexts "comoving"). The distance to some galaxy NOW is the distance you'd measure by freezing expansion right now. The distance to that same galaxy THEN is what you would have measured if you froze it then.

These are the distances you get from the cosmos calculator here
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html
Or just google "cosmos calculator" and you'll get it.
Check out the calculator. You put in the redshift number, for some light you are seeing, and you want to know how far away the source is. Where it says distance now, and distance then, those are freezeframe distances now when you are receiving the light, and back then when the light was emitted.

When you see the Hubble law v = Hd,
d is a freezeframe distance and v is the rate at which that distance is increasing. Since all these quantities depend on time, and change, we could make the equation messier and put in time-dependence:
v(t) = H(t) d(t)
But it's easier on the eyes to just write v = Hd

If you want to experiment with the cosmos calculator, the usual numbers to put in for matter density, cosmo constant, and Hubble are .27, .73, and 71. You type in those three numbers (in the first three boxes) first and then you put in whatever redshift numbers you want.

Last edited: Feb 22, 2010
3. Feb 22, 2010

### marcus

Harriet, one thing you will have noticed when you've taken the trouble to check out Morgan's cosmos calculator is that it's perfectly all right for distances to be increasing at several times the speed of light.

The distance to some photon of light that is far from us can be increasing at 3 times the speed of light. It's common for the distance to another galaxy to be increasing at twice the speed of light.

This is an obvious consequence of Hubble law. Since v = Hd, you just have to take d big enough and you can get v to be several times c.
Most of the galaxies we observe today have redshifts greater than 1.4, and the distance to any such galaxy is increasing faster than c. The light from them started on its way to us when they were closer to us. Many of them could not now send us a message because they are receding at such a high rate (the message, sent today, would never arrive.)

So if you have played around with Siobhan Morgan's calculator (she is a university prof in Iowa who teaches astronomy and she put the "cosmos calculator" up on the web for her students to use) and if you have noticed this thing about rates of distance increase, then you might want to ask about it. Asking questions is the clue to learning this stuff.
(and examining your assumptions, making sure you don't assume stuff unconsciously, and understanding the concept of distance applied in a given situation.)

4. Feb 23, 2010

### Chalnoth

One way I like to think about this is to just write down the Einstein field equations:

$$G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$

On the left hand side, we have what is called the Einstein Tensor, $$G_{\mu\nu}$$. This is a quantity that encodes the behavior of space-time. For instance, if space is expanding, then we see it in the behavior of $$G_{\mu\nu}$$.

On the right hand side, we have the stress-energy tensor, $$T_{\mu\nu}$$. The stress-energy tensor encodes the energy, momentum, pressure, and stress (e.g. twisting) of matter. If bits of matter are moving away from one another, then that movement will be encoded in the stress-energy tensor.

And what do the Einstein field equations say? Up to a little bit of unit conversion (given by $$8\pi G/c^4$$), the two are equal. This means that if you look at the stress-energy tensor and say, "Hey, things are moving apart!", then you can also just take a look at the Einstein tensor and say, "Looks like space is expanding!" The two statements are equivalent descriptions of the exact same behavior, in other words.

5. Feb 23, 2010

### marcus

That's a nice way to put it, Chalnoth!

The nutshell epigrammatic version of general relativity.

Space is not a separate thing that exists independently of matter. You need one to describe the other. I would call the lefthand side of the equation "geometry" and the righthand side "matter".
The stuff with 8 pi, and Newton's constant G, in the middle, like you say is just units of measurement conversion factors. If you adjust the units you can make the stuff in the middle go away and just have G = T.

What you say can seem a bit [I don't know, radical? cryptic?] but it's not incorrect. I think it's fundamentally the right way to look at it.

Einstein said in 1915 that his theory deprives space and time of the last shred of objective physical reality. By themselves they simply are not. They only mean something in conjuction with material events....substance. Because they are the web of relationships of events.

6. Feb 23, 2010

### harrietjob

i am [as you can tell] fairly new to all this, but what if 'space' is more similar to matter we know of today than we think, or [i have no evidence to base this upon, just a suggestion] is it a possibility that 'space' is actually our word for whatis actually 'dark-matter' of which the properties are yet hidden, hence the sub-title 'dark'?

7. Feb 23, 2010

### marcus

Hello Harriet,
I'm glad to see you came back.
Persistence in asking questions is vital to learning in this context. You don't always get exactly the answers you need the first time or even the first ten times, I expect.

You could give some feedback on the responses. Was my post #2 too technical for you?
Did you by any chance click on the link to Siobhan Morgan's online calculator?---it embodies the standard model that cosmologists are currently using.

I'm curious to know because it's possible to be allergic to simple mathematical models of the universe---which means you rely entirely on verbal metaphor models. Or one can be the sort of person who is potentially comfortable with both.

I'm a fan of Siobhan Morgan---never met her in person. She likes dogs, collects old superhero comic books, and has a sense of humor---which are admirable qualities.
She also seems to know how to explain and teach cosmology to extreme beginners in northern Iowa.

I'd be delighted if you would give her model universe (in the form of a kind of 4-button calculator) a try.

Einstein said already in 1915 that space does not exist. Geometry is what we are talking about. The dynamic changing geometry of the real world, not the static foursquare axiomatic geometry of Euclid. We don't know yet whether we should think of "dark energy" as a built-in feature of geometry. or alternatively as a kind of material. perfectly uniformly distributed.

You suggest on philosophical grounds that there is no dichotomy. It could be both. Both a feature of how geometry evolves (to be built in to the basic equation of general
rel.) and a kind of substance. OK. A lot of us like that idea. But right now we don't have enough chops to decide the issue.

Cosmology is a simple mathematical science that involves fitting a math model to observational data. And the model keeps getting better and better. It is more intelligent than any one human being and eventually the model will reveal to us something about existence. It will tell us how nature's dynamic geometry and it's ever moving substance are one and the same, how they grow from the same root, and then we will understand why and how they interact. Why it is that matter curves geometry and that geometry guides motion. But we aren't there yet and it is no good guessing the answer. We just keep on refining the model to get a more elegant and precise fit, and listening to what it tells us.

Probably the most important quantity, the central quantity, is redshift. The letter z is used to stand for it. If you want to understand cosmology you should get a hands-on feel for what redshift is. Ask some questions about it. At this point I would advise not asking about "space". Too nebulous. One needs a quantitative handle.

8. Feb 23, 2010