# Expansion of Space: Exploring Physics & Math Behind the Idea

• edpell
In summary, the expansion of space refers to the increasing distances between galaxies in the universe. This concept has a mathematical basis and is not simply "poof magic". The expansion of space does not drag along matter and energy, but rather is a consequence of the expanding universe. The conservation of momentum applies only on a local scale and is not affected by the expansion of space. The initial "inflation" at the beginning of the big bang, where the expansion of the universe was faster than the speed of light, does not violate the laws of special relativity. The Hubble law, which describes the recession rates of galaxies, is based on a particular moment in time and a specific type of distance measurement. This distance does not imply that galaxies
edpell
What does expansion of space mean? Is there an mathematical and or physics substance to this idea? Or is it just "poof magic happens" that is why the universe is very uniform in density distribution? How does expanding space drag along matter and energy with it? What about conservation of momentum?

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Conservation of momentum is a purely local consideration, like special relativity. Expansion works on scales where gavity is too weak to counteract this effect.

edpell said:
What does expansion of space mean? Is there an mathematical and or physics substance to this idea? Or is it just "poof magic happens" that is why the universe is very uniform in density distribution? How does expanding space drag along matter and energy with it? What about conservation of momentum?

Space isn't dragging anything. Expanding space should be regarded as consequence of expanding universe, not the cause. See https://www.physicsforums.com/showthread.php?t=283237" thread for more details.

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I am trying to ask about the initial "inflation" at the very beginning of the big bang. My limited understanding is people say the expansion went faster than the speed of light. This bothers me.

I am not asking about Hubble expansion I am cool with that.

This is quite a common question, and arises because "people" tend not to define what they really mean by a speed when they say that the universe "expanded faster than the speed of light". Maybe http://curious.astro.cornell.edu/question.php?number=575 and the links within will clear things up a little.

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edpell said:
I am trying to ask about the initial "inflation" at the very beginning of the big bang. My limited understanding is people say the expansion went faster than the speed of light. This bothers me.

I am not asking about Hubble expansion I am cool with that.

As you can see from the Cornell page Cristo linked ( [PLAIN]http://curious.astro.cornell.edu/question.php?number=575 ) many of the galaxies we are now looking at are currently receding at rates greater than c. That means the distances to them are increasing at rates greater than c.

That's what Hubble expansion says. So if you are cool with it, that's great!

It doesn't mean they are moving relative to us in any sense that would be governed by Special Relativity or would violate the Speclal Rel speed limit. "Receding" in this context refers to the Hubble law concerning the rate that distances increase at cosmological (very large) scale. Recession rates aren't governed by Special Rel. I'll put in my two bits on this in a moment. Here's Cristo's response:

cristo said:
This is quite a common question, and arises because "people" tend not to define what they really mean by a speed when they say that the universe "expanded faster than the speed of light". Maybe [PLAIN]http://curious.astro.cornell.edu/question.php?number=575 and the links within will clear things up a little.

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Ed, the Hubble law v = Hd
is about the expansion of distances, and whenever Hubble expansion enters the discussion we should have clearly in mind (maybe remind ourselves) what is meant by distance in that context.

You can see from the Cornell page that Cristo linked that the distance idea that fits in with Hubble law is what the author calls the "freeze-frame" distance. Or the now distance.

The distance to a galaxy now is what you would get if you could instantly freeze the expansion process, and then measure by radar or any other normal means.

Freezing means the distance doesn't change while you are trying to measure it, so it is fairly intuitive. And you can define distance analogously at any point in the past---think of freezing expansion back then and timing the exchange of light slgnals or radar beeps.

In the Hubble law, v = Hd, d is a distance measured in that way, and v is the rate at which that distance is increasing.

As a footnote, I'll mention that the law also refers to a particular moment in time. The distance is measured at that moment, and the rate of increase is current at that moment. So there is an implicit idea of simultaneity that is logically part of understanding what v = Hd says.

Also as a footnote, there are several alternative ways of defining distances in astronomy---and of coordinatizing the universe. For simplicity, when v = Hd is in the picture, we often just talk in terms of this one "freeze" or "now" type distance that goes with the Hubble law.

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Ed, since you are cool with Hubble-law expansion that might be a good place to start and do some calculation.

If we take the present value H0 of the Hubble rate to be 71 km/s per megaparsec (which is fairly standard to assume) and solve for d in the equation
c = H0 d
then we get d = 13.77 billion lightyears.

In other words any galaxy whose current distance is 13.8 billion ly from us is currently receding at the rate c.

Any galaxy at twice that distance is receding at 2c.

That doesn't mean the galaxy is moving, in the ordinary sense of going somewhere. There is no destination that it is approaching. It isn't outracing photons in its mad career.
It simply means that the current distance from us to it is increasing at a certain rate.
(And to be sure I mean the freeze-frame distance mentioned in the Cornell page Cristo cited, the type appropriate to Hubble law.)

A receding galaxy is not getting closer to anything, merely by virtue of the fact that it's distance from us is increasing. In that sense recession rates are intuitively different from ordinary motion that we are used to in our local surroundings.
==============

You might find it helpful to look at the first few posts on the Balloon Model stick thread.

marcus said:
... many of the galaxies we are now looking at are currently receding at rates greater than c ...

For any layman (like me) reading this, we might should explain two crucial facts...

1) Absolutely nothing can move faster than the speed of light (299,792,458 metres per second).

2) When a professional talks about galaxies in the observable universe receding at rates greater than the speed of light. He or she are not talking about a galaxy now visible at rates greater than c, but now calculated to recede at rates greater than the speed of light, based on the very old light, emitted a long time ago, hitting our eyes and camera lenses now, i.e. observable universe = calculated visible universe.

This almost drove me crazy some years ago, and it took a lot of time, and discussions with professionals (not on PF though!) before I got the solution to this mysterious 'enigma'. I even talked to a 'professional' who presented a theory of "variable speed of light", to get by the fact that locally nothing moves faster than c. According to this guy, light slows down when passing an observer, and then speeds up again when no one is looking!(!?) This theory of course didn’t help me much. When I found the real answer, and presented it to him – I never heard from him again...

Conclusion: The word observable can cause trouble for a layman, thinking of it like something we can observe – look at. For a professional observable implicitly mean – the ability to make scientific observations, including making mathematical predictions of an object. (I guess?)

Here’s an good article that I found on my way to solve this puzzle, by Michael S. Turner and Craig Wiegert : http://www.fnal.gov/pub/ferminews/ferminews00-05-12/p5.html"

(Hope this helps others from not falling into the same 'trap' as I did, but I guess your next posts 7 & 8 explains this better than me )

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...
Here’s an good article that I found on my way to solve this puzzle, by Michael S. Turner and Craig Wiegert : http://www.fnal.gov/pub/ferminews/ferminews00-05-12/p5.html"

(Hope this helps others from not falling into the same 'trap' as I did, but I guess your next posts 7 & 8 explains this better than me )

Thanks for the amplification! I'm glad you got over that confusion. There is one more hurdle, which I think is the hardest for most people to get over. As you indicate you understand, most of the galaxies we can see are currently receding at rates faster than c.

But it is also the case that most of the galaxies we can see today were receding faster than c at the time they emitted the light which we are receiving now. We see them as they were in the past, receding at greater than c rates.

This is explained in a good Scientific American article by a top cosmologist, Charles Lineweaver. You might ask, if they were already receding at > c, how did the light that they emitted then ever get here? The answer is that H has been decreasing, and was decreasing rapidly in the past. This means that the Hubble radius has a history of rapid growth. You can picture the expanding Hubble radius as "reaching out" to those struggling photons. Once a photon that is headed in our direction get within the Hubble radius, it is going to make it to us.

So photons emitted by a galaxy receding at >c do indeed lose ground at first. Due to expansion they at first get farther away from us even though they are traveling towards us as propagating waves. But the Hubble radius has historically extended rapidly outwards. It is the threshold so to speak, within that distance of us, expansion is < c and light will eventually get to us. Light that never gets within Hubble distance of us will never make it.

How are you on that? I have a link to Lineweaver's SciAm article in my signature at the end of the post. Let me know if you try it and the link doesn't work for you.

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marcus said:
How are you on that? I have a link to Lineweaver's SciAm article in my signature at the end of the post. Let me know if you try it and the link doesn't work for you.

The link is working fine. The article is helpful. It will take me some time to digest the "Can we see galaxies receding faster than the speed of light. Sure we can, because the expansion rate changes over time."

Marcus, in the article it says:

"One might conclude that the light beyond the Hubble distance
would never reach us and that its source would be forever
undetectable. But the Hubble distance is not fixed, because
the Hubble constant, on which it depends, changes with
time. In particular, the constant is proportional to the rate of
increase in the distance between two galaxies, divided by that
distance. (Any two galaxies can be used for this calculation.)
In models of the universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble
constant decreases. In this way, the Hubble distance gets
larger. As it does, light that was initially just outside the Hubble
distance and receding from us can come within the Hubble
distance. The photons then find themselves in a region of
space that is receding slower than the speed of light. Thereafter
they can approach us."

I can see that if the Hubble constant is decreasing the Hubble distance increases. But I thought the data of 1998 was that the Hubble constant is increasing?

1) Absolutely nothing can move faster than the speed of light (299,792,458 metres per second).
There is one thing that should be mentioned everytime this argument shows up: accusations of something going FTL are always referring to a special coordinate system
Dave Rothstein said:
If we use the definition of distance given above (and only if we use this definition and no other)
that has nothing to do with the coordinate system in which "nothing can move faster than the speed of light" holds. The cosmological coordinate system is not the one we (and, for that matter, SR) are used to. Just be aware that what cosmologists call "recession speed" is not the "normal" speed.
While agreeing almost totally with him, I must criticize this setence of marcus:
It doesn't mean they are moving relative to us in any sense that would be governed by Special Relativity
They surely are moving, in a SR sense. You just can't exactly, unambiguously, quantify their speed.
edpell said:
But I thought the data of 1998 was that the Hubble constant is increasing?
No. The Hubble constant, multiplied by the scale factor, is increasing. H itself is monotonely decreasing.

Ich said:
No. The Hubble constant, multiplied by the scale factor, is increasing. H itself is monotonely decreasing.

What is the scale factor?

http://en.wikipedia.org/wiki/Scale_factor_(Universe)"

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edpell said:
Marcus, in the article it says:

"One might conclude that the light beyond the Hubble distance
would never reach us and that its source would be forever
undetectable. But the Hubble distance is not fixed, because
the Hubble constant, on which it depends, changes with
time. In particular, the constant is proportional to the rate of
increase in the distance between two galaxies, divided by that
distance. (Any two galaxies can be used for this calculation.)
In models of the universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble
constant decreases. In this way, the Hubble distance gets
larger. As it does, light that was initially just outside the Hubble
distance and receding from us can come within the Hubble
distance. The photons then find themselves in a region of
space that is receding slower than the speed of light. Thereafter
they can approach us."

I can see that if the Hubble constant is decreasing the Hubble distance increases. But I thought the data of 1998 was that the Hubble constant is increasing?

No, the Hubble constant is decreasing and will continue to do so. And it has decreased much more rapidly in the past.
The accelerated expansion that was detected in 1998 does not contradict this. It says that the scalefactor a(t) is increasing at an increasing pace. Expansion means that a'(t) is positive (the time derivative of the scale factor). Accelerated expansion means a''(t) is positive.

The Hubble constant is defined to be a'(t)/a(t). What it does depends on both the numerator and the denominator. As long as a(t) is growing fast enough to overwhelm the slow acceleration, the growth in a'(t), the Hubble rate, which is that fraction, will continue to decline.

marcus said:
... How are you on that? I have a link to Lineweaver's SciAm article in my signature at the end of the post. Let me know if you try it and the link doesn't work for you.

Oh MAN! Thanks! I’m drooling over this fantastic article and extremely nice pictures!

...though I have a slight feeling that 'God' (Albert Einstein) in his heaven is laughing big time at me right now ...since it seems I’m back on that crazy square ONE!?

But I’m not giving up, no way. I’ll digest this new info and – I’ll be back!

Ich said:
1) Absolutely nothing can move faster than the speed of light (299,792,458 metres per second).

There is one thing that should be mentioned everytime this argument shows up: accusations of something going FTL are always referring to a special coordinate system
...

Agree, and maybe the (obvious) fact that the speed of light in a vacuum is a universal constant (c).

In water, for example, it’s only 0.75c and we could get an (electron) speed greater than the speed of light in that medium, resulting in http://en.wikipedia.org/wiki/Cherenkov_radiation" :

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## 1. What is the expansion of space?

The expansion of space is a theory in cosmology that suggests the universe is constantly expanding and has been since its beginning. This means that the distance between galaxies, stars, and other celestial bodies is increasing over time.

## 2. How is the expansion of space measured?

The expansion of space is measured through the use of redshift. This is a phenomenon where the wavelengths of light from distant objects appear longer (shifted towards the red end of the spectrum) due to the expansion of space. The greater the redshift, the faster the object is moving away from us.

## 3. What is the evidence for the expansion of space?

There are several pieces of evidence for the expansion of space, including the observation of redshift in distant objects, the cosmic microwave background radiation, and the large-scale structure of the universe. These all support the idea that the universe is expanding and has been for billions of years.

## 4. How does the expansion of space affect the motion of objects in the universe?

The expansion of space does not impact the motion of objects on a small scale, such as within our own galaxy. However, on a larger scale, the expansion can play a role in the motion of objects as they are carried along with the expanding space. This is known as the "cosmological expansion."

## 5. What are the implications of the expansion of space on the fate of the universe?

Currently, the expansion of space is believed to be accelerating, meaning that the universe will continue to expand indefinitely. This could lead to the "heat death" of the universe, where all matter and energy become evenly distributed and the universe reaches a state of maximum entropy.

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