# Speed of Space

## Main Question or Discussion Point

Apololgies in advance for my complete lack of understanding of what are probably a well established facts but I have a few questions which have been buzzing around in my head (a rather empty head at that).

Why is the speed of light finite? Why can't it go faster? Is there an accelleration associated with light or does it just travel at a constant speed?

The reason I ask is that I have read that space can travel faster than light and that during the Inflation Period the Universe expanded very rapidly many times the speed of light. Expansion then continued at a slower and consistance rate until about 5 billion years ago when the expansion started to accerate and is continuing to accerate even today. The main reason given is that as the universe expanded it became less dense and allowed the 'dark force' to overcome the effects of gravity and so allow for accerated expansion.

My suggestion is that space has a natural tendancy to expand, in much the same way that light will radiate from a source, and does not require a 'dark force' to make this happen. What we see as a 'dark force' pushing the universe apart, is just space expanding with matter being carried along with the space.

This idea does raise a few question about how space, assuming that it does not require energy to expand (or very little), is then able to move matter, which requires a lot of energy (a awful lot of energy). I have no idea how matter and space are able to interact and even why matter should be carried by space.

I would be gratful if any geniuses out there have the answers, or can completely shoot me down in flames for such a ridiculous idea.

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bapowell
Thanks for the post AbsoluteChaos. May I just call you Chaos? Thanks.

According to Einstein's Relativity, the speed of light is the ultimate speed in the universe. Why this is the case is not addressed by the theory. One can establish analogies with the speed at which compressional waves travel in different media, and assign permittivities to the vacuum of space, but this doesn't really address the question. Light can change speed when it enters media other than the vacuum. For example, light slows down when it enters water.

During inflation, regions of the universe did indeed recede from each other at a relative speed surpassing that of light. However, objects in these regions are locally at rest -- it is the space between them that is expanding. In General Relativity, observers must obey the laws of Special Relativity locally, which they always do in cosmology.

Lastly, as far the 'dark force' you refer to, I suppose you mean 'dark energy'. Dark energy was proposed to account for the apparent acceleration of the present-day universe. It is not merely a device to facilitate the expansion of space, which happens with ordinary matter and radiation. In order to make the scale factor accelerate, we need a very exotic form of energy with a negative pressure. This is what dark energy is and also what inflation was.

During inflation, regions of the universe did indeed recede from each other at a relative speed surpassing that of light.
Do we know how much faster than c? Do we know the maximum value of expansion? Is there any upper bound?

bapowell
The speed at which distant objects are receding is determined by Hubble's Law:

$$v = Hr$$

where H is Hubble's constant and r is the distance to the receding object. You can see from this expression that at a special distance, namely $$c/H$$, distant objects are receding at superluminal velocities. This is a general property of expansion in a homogeneous and isotropic universe, and has nothing to do with inflation. In an infinite universe (if r is unbounded), then there is no bound on the recession velocity.

Now, the important thing about inflation is that the expansion is accelerating. The difference between non-accelerating and accelerating spacetimes has to do with the behavior of the special distance we identified above: $$r_H = c/H$$. How does this distance evolve in time?

$$\dot{r}_H = -\frac{c\dot{H}}{H^2}$$

When spacetime is non-accelerating, $$\dot{H}$$ is negative and larger than $$H^2$$ with the result that this distance is increasing at a speed greater than light. That's a bit of a mouthful: the distance at which objects begin to recede at speeds greater than that of light is itself moving away at a speed greater than that of light! The important conclusion is that a galaxy that was moving away from us at v = c yesterday is now moving away at a speed v < c today. In a non-accelerating spacetime, we eventually see all of the universe (given enough time).

During inflation, $$\dot{H}$$ is again negative but this time smaller than $$H^2$$. Now the distance $$r_H$$ is receding from us at less than the speed of light. A galaxy that is receding from us today at v = c will be moving at least this fast tomorrow. Main conclusion: during inflation there are regions of the universe that we will never see -- the distance $$r_H$$ marks an event horizon, much like that of a black hole (only in reverse).

EDIT: So, in my post above (#2), I was being a bit unclear about the fact that recession velocities greater than c are not a hallmark of inflation. It's $$\dot{r}_H$$ that results in inflation having such a dramatic effect on the observable universe.

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the speed of light is the ultimate speed in the universe
Is it even proper to speak of it as a "speed" as such? Isn't it a constant?

As far as I have understood inflation, it's a rapid increase of space, i.e. the structural conditions of the universe, rather than anything which is *existing* (in the physical sense).

bapowell
Is it even proper to speak of it as a "speed" as such? Isn't it a constant?
Speed is constant. The speed of light, $$c = 3\times 10^8 m/s$$, is a constant.

As far as I have understood inflation, it's a rapid increase of space, i.e. the structural conditions of the universe, rather than anything which is *existing* (in the physical sense).
Well, I guess it comes down to whether you consider space as existing. And be careful -- time is involved too. I consider spacetime a very real thing in the sense that gravity is a manifestation of it.

whether you consider space as existing
Well... I kind of think of space as the canvas and *physicality* as the brushstrokes of colour (or whatever else) that you layer opon it. But you have a point here... I haven't really been thinking about the connection between spatial inflation and *time* in a continuum. Hmmm. Now there's another abyss! Than you very much, like!

marcus
Gold Member
Dearly Missed
...During inflation, regions of the universe did indeed recede from each other at a relative speed surpassing that of light. However, objects in these regions are locally at rest -- it is the space between them that is expanding...
Do we know how much faster than c? Do we know the maximum value of expansion? Is there any upper bound?
Edpell, the rate that distances increase depends on the size of the distance. The Hubble law is essentially a percentage increase rule. So longer distances increase more (in km per second terms, or in comparison with the speed of light.)

We don't know the "maximum value" or "upper bound" in terms of speed, because we don't know an upper bound for the size of the universe. And looking back to the beginning of expansion the picture gets somewhat conjectural---there are different inflation scenarios, different assumptions.

In reply to your question "Is there any upper bound?" I think the answer is No, we don't know of any upper bound.
===================

But if you just focus on conditions in the universe TODAY you can get a kind of practical upper bound of around 3c
(not absolute, just for the stuff we can currently see radiation from).

Today the farthest material we can see is the stuff which radiated the CMB radiation. It was originally reddish light like from the surface of a star at a temperature of around 3000 kelvin. And it comes to us with a redshift z = 1090. That's essentially the stretchout factor.
That farthest visible stuff (which has doubtless by now cooled and condensed to make stars planets galaxies etc like our stuff has, so it doesn't look the same as when it radiated the reddish light as a hot gas) is now about 45 billion lightyears away, and receding at a rate of slightly over 3c.

You can calculate this easily for yourself. Google "cosmo calculator" and type 1090 into the z-box. It will tell you the current distance (that goes into Hubble law) is 45 billion ly. (actually 45.5, I'm rounding off the numbers).

But the Hubble distance Powell was talking about, the distance at which things recede at exactly c, is 13.7 billion ly. And the recession rate is proportional. So you just have to divide 45/13.7----it comes to about 3, or 3 and a fraction. So 3c, three times speed of light.

Or google "cosmos calculator" (with an s) for a different one----but then you have to first put in .27 for matter fraction and .73 for cosmological constant and 71 for Hubble rate (the other calculator automatically assumes those standard values, saving bother). The good thing about "cosmos calculator" is that when you put in the redshift number it tells you the recession rate. More trouble setting up but less afterwards.

By upping the redshift you can push "cosmos calculator" back closer and closer to the start of expansion, and you will see the recession speed go higher and higher, and the Hubble parameter (which is now 71 km/s per Megaparsec) go up into the millions. Those calculators embody the standard model that cosmologists use. OK but they are not reliable when you get too close to the start. You can get some qualitative impressions but actually the standard classical model is likey to go wrong very near start and will need some quantum corrections. So it is speculative. Proceed with caution.

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Speed is constant. The speed of light, $$c = 3\times 10^8 m/s$$, is a constant.

But physicists have been able to slow the speed of light down to 38 mph. See http://www.news.harvard.edu/gazette/1999/02.18/light.html

To paraphrase an Einstein question, if you jump off a light wave travelling at 38 mph are you travelling faster than the speed of light?

marcus
Gold Member
Dearly Missed
We're talking speed of light in vacuum, Ray. Those experiments where they get different speeds of light involve some kind of medium. Even water will slow light down to about 3/4 speed. Various types of glass slow it to around 2/3 speed.

What Powell referred to is the speed with nothing else around affecting the speed. Vacuum.

If you allow a medium, then it is easy for things to travel faster than light. In a tank of water you can have electrons traveling faster than light, and they make an eerie glow called the Cherenkov effect. So your thought experiment could be reformulated for someone riding on an electron: "if you are riding on an electron going 8/9 of c in a tank of water, and if you jump off, are you going faster than light?" Yes, because you are going 8/9 c and the speed of light in the medium is only 3/4 c. So you (and the electron you rode in on) are both going faster than light.

c typically means "speed of light in vacuum"

Chalnoth
Why is the speed of light finite? Why can't it go faster?
Fundamentally, I think it has to do with causality. All of the fundamental laws of physics of which we are aware of are local: things have to actually be in contact to interact. Long-range forces like electromagnetism and gravity act over distance only by the exchange of mediating particles, photons or gravitons in these cases. So what happens is two particles come together, perform some interaction, then travel apart.

Now, these particles, if they traveled at infinite speed, would lead to non-local behavior: particle A could interact with particle B far away instantaneously, and the laws of physics would no longer be about two things interacting with one another locally. So, there has to be some maximum finite speed at which particles can move. Light happens to travel at this speed in a vacuum, and so we call it the speed of light.

Chronos
Gold Member
The speed of light is predicated by two fundamental properties of empty space - permittivity and permeability. And, no, this has nothing to do with aether. It has a great deal to do with Coulomb's law.

Chalnoth
The speed of light is predicated by two fundamental properties of empty space - permittivity and permeability. And, no, this has nothing to do with aether. It has a great deal to do with Coulomb's law.
This is nitpicking a little bit, but I think the causality argument is actually more fundamental: the laws of E&M had to work out at a macroscopic scale such that light waves travel at the speed of light in vacuum because light waves are made of photons, and photons have zero mass. Zero mass objects travel at the maximum speed possible.

Chronos
Gold Member
Agreed, but, it is fundamentally important to understand that Einstein's relativity is deeply based on Coulomb and Maxwell's theories.

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Chalnoth
Agreed, but, it is fundamentally important to understand that Einstein's relativity is deeply based on Coulomb and Maxwell's theories.
Fair enough. Just saying that he uncovered a richer and deeper reality than Maxwell, Coulomb, and the other physicists involved in developing E&M dreamed of.

bapowell
Fundamentally, I think it has to do with causality.
I would think that causality is a consequence of a finite speed of light. Not the other way around.

Not necessaraly. Concept of causality is needed to be in place in order to introduce notion of finite speed, or speed at all. I think that it is chicken-egg question.

Chalnoth
Not necessaraly. Concept of causality is needed to be in place in order to introduce notion of finite speed, or speed at all. I think that it is chicken-egg question.
Yup. Once you have the notion that all fundamental laws of physics are inherently local, that is talking about how things interact when they come into contact with one another, a finite speed becomes a necessary outcropping of that.

bapowell
Not necessaraly. Concept of causality is needed to be in place in order to introduce notion of finite speed, or speed at all. I think that it is chicken-egg question.
Actually, it seems they are one in the same. Can someone remind me why this is being discussed in a physics forum and not the philosophy forum?

bapowell
Yup. Once you have the notion that all fundamental laws of physics are inherently local, that is talking about how things interact when they come into contact with one another, a finite speed becomes a necessary outcropping of that.
Right. But why elevate locality to some bedrock principle?

Chalnoth
Right. But why elevate locality to some bedrock principle?
To be fair, we don't know the most fundamental laws of physics at the current time. All we have are a variety of approximations that have different ranges of applicability. But we can look at what direction our current physical theories are moving, and try to get a handle on the features of the most fundamental theory of physics. One major feature appears to be it must be a quantum theory (which appears to be derivable from Bell's inequality). Another appears to be locality, as the "action at a distance" behavior has dropped away as we've learned more about the long-distance forces.

This could be wrong, of course, but I'm reasonably confident that whatever fundamental theory we finally arrive at, it will turn out to be a local quantum theory.

bapowell
Another appears to be locality, as the "action at a distance" behavior has dropped away as we've learned more about the long-distance forces.
I follow this. But why can't locality arise from a more fundamental need for a finite speed of information propagation.

Chalnoth
I follow this. But why can't locality arise from a more fundamental need for a finite speed of information propagation.
The two are basically one and the same statement. What I was saying was something slightly different: that if we have locality, then all "stuff" must travel at or below a certain speed. That is to say, the speed limit "c" is fundamental, and the field equations of electromagnetism are forced to produce waves that travel at this speed because the particles that make up said field have no mass. Put another way, "c" is more fundamental than "$\epsilon_0$" and "$\mu_0$".

bapowell