# Questions about the speed of light and the extent of the universe

What is the reason that speed of light is the maximum speed in the universe? Why there is no speed swifter than light? Or is it just we haven't found yet? A similar question is like this: why the light speed in vacuum has to be 299,792,458 m/s? Why couldn't it be faster? Who or what is controlling this speed in vacuum? Who is stopping it from being faster?

Another question confusing me is this, if light from a far away Galaxy travels to us and we see the stars tonight, couldn't it be fully possible that at this time, they actually are already dead? Which means by modern scientific methods, there is absolutely no way to know what is really happening out there, all we know is just what was there, right? So our knowledge is going to be forever limited unless we have something that can travel much faster than light?

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Daniel -- some of your questions are answered here: physics.stackexchange.com/questions/3644/… –  Johannes Dec 11 '12 at 16:40

Just wondering what is the reason that speed of light is the maximum speed in the universe?

I like the term which was used in the second volume of Landau and Lifshitz books. They started the argument by saying, that there is some finite interaction constant, which defines, how quickly the information is travelling. Which basically means, that there is no such thing as a rigid body starting instantaneously rotating as different sections of it find out that the body starts rotating at different times. Probably it's not an answer to this part of the question, but it's a different way to think.

Why there is no speed swifter than light? Or is it just we haven't found yet?

If you regard the speed of light as the interaction constant, according to which all the matter is interacting, then these questions should not be there at all, as they contradict to the assumption of interaction constant. However, this once again doesn't answer the question, but instead, pushes these fundamental questions further.

A similar question is like this: why the light speed in vacuum has to be 299,792,458 m/s? Why couldn't it be faster? Who is or what is controlling of this speed in vacuum? Look, in vacuum, who is stopping it from being faster?

I think, that teh speed of light magnitude is irrelevant, as it is just a numerical value which by luck happens to be this. And the value is this because of our chosen units. In other unit systems it is different (or it can be set to be equal to one).

Another question confusing me is this, if from a far far away Galaxy, its light travel to us and we see the stars tonight, couldn't it be fully possible that at this time, they actually are already dead?

Yes, as there is no way we can know what is exactly happening there at some particular moment.

So our knowledge is going to be forever limited unless we have something that can travel much faster than light?

Defintely, but this would mean the invention of a time machine, which would would break the causality phenomenon, which wouldn't be good. In a way, we will never explore the whole universe, as we are always limited by the age of the universe (or rather the distance light can travel during the age of the universe), and beyond there is the unknown.

Hope my rambling was at least a bit helpful.

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Ultimately, it comes down to special relativity. There are at least two ways of approaching this.

The first is to follow the historical development of electrodynamics. Maxwell's equations predict the existence of electromagnetic waves. Those waves must travel at the speed $c =\frac{1}{\sqrt{\epsilon_0\mu_0}}$. $\epsilon_0$ and $\mu_0$ are the permittivity and permeability, respectively, of free space. These are experimentally measurable constants. If you plug in their values in your favorite system of units, you get $c = 2.998\times 10^8 \mathrm{m/s}$. In a completely unrelated set of measurements, we can measure the speed of light. We get the same value, which strongly suggests that these electromagnetic wave are actually light.

I mention all that as a setup to special relativity. SR makes the claim that the laws of physics have the same form to all observers in inertial reference frames. It also makes the claim that Maxwell's equations establish the speed of light as a law of nature, so it should have the same value for all observers. It's a simple bit of algebra to get from that fact to the Lorentz transformations and to the result that $m \rightarrow \infty$ as $v \rightarrow c$. This is the typical derivation given in introductory classes in the United States. It's a bit unsatisfying, as it really only demonstrates that it would take an infinite amount of energy to accelerate an object with non-zero mass to the speed of light.

The other approach is group-theoretic, and the math is given in a section of the Wikipedia article devoted to the Lorentz transformations. You start by assuming that the laws of physics obey linear and temporal translational symmetry. If they do, then a coordinate transformation between two inertial reference frames should be linear. So it will be a matrix with parameters that don't depend on the relative positions or times of the two reference frames. You then require that that set of transformations forms a group, that is, that there is an identity transformation, every transformation has an inverse, that any two transformations combine to form another transformation, and that they follow the associative rule. That last requirement doesn't provide any new information. The rest impose a set of restrictions on the transformation matrix, leaving you with one free parameter, which I'll call $k$, and which has units such that $1/k^2$ is a speed. $k$ can be greater than zero, less than zero, or equal to zero. $k > 0$ allows transformations that violate causality, so we reject it. $k = 0$ recovers the older Galilean transformations. $k < 0$ allows us to define a maximum speed $c = -1/k^2$. This gives you the Lorentz transformations.

This means that when we look at far away objects, we are actually seeing them as they were a long time ago, not as they are right now. This does limit our knowledge, but not entirely. In the example you gave, we have some understanding of the lifecycle of stars, which allows us to infer how old a star was when its light left it, based on what the light looks like when it gets to us. So we can make a guess of whether or not the start is still alive "now."

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what is the reason that speed of light is the maximum speed in the universe?

That's the way the universe was made.

why the light speed in vacuum has to be 299,792,458 m/s?

It's a fundementel property of the nature of electro-magnetism in our universe.
The explanation in many intro books is confusing because it typically says "you can't go faster than light because you would know things had happened before you see them". Of course this is silly, a blind species would think that sound was the fastest thing for the same reasons.

In fact the speed of light value drops out of a couple of equations describing electro-magnetism. It's almost a coincidence that this is also the speed that light goes at (it's because light is an electro-magnetic effect).

couldn't it be fully possible that at this time, they actually are already dead?

Yes. The furthest objects we see are almost certainly not there anymore. The most distant thing we see is the microwave background. Which is (sort of) the flash of the big bang once it had cooled enough to be light.

So our knowledge is going to be forever limited unless we have something that can travel much faster than light?

Yes, we are forever limited to the observable universe. In simple terms this is the sphere around us where light has had time to travel since the beginning of the universe. Signals from anything outside that will never get to us.

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If so, then theoretically speaking, isn't it fully possible that there is not just one big bang, but many big bangs, some are even happening right now, but we never will know during our limited years and limited sphere and knowledge. Because there is just one single big bang seems to be weird to be? Why there is just one. OOPS :) –  Daniel Dec 10 '12 at 20:55
@Daniel we can be pretty sure there is only one big bang in our universe. But there may be other big bangs creating other universes "outside" our own, or before/after ours. (Although before/after doesn't really mean anything outside a universe!) We can never know - so it's arguable if it's physics or philosophy to talk about them. –  Martin Beckett Dec 10 '12 at 20:59
The speed of light is a feature of relativity, i.e. the nature of space and time; the fact that light travels at this speed is due to the fact that photons (like gravitons) are massless. –  Dave Dec 10 '12 at 21:35
@Dave 299,792,458 m/s is a feature of Maxwell's equations. That electro-magnetism has anything to do with space is a feature of relativity. My complaint is the circular argument about 'c', relativity and causality in a lot of explanantions –  Martin Beckett Dec 10 '12 at 21:52
@MartinBeckett so you'd disagree with an answer like this: (physics.stackexchange.com/questions/7041/…) ? –  Dave Dec 10 '12 at 21:56

Because moving clocks don't stay synchronised.

If you and I meet up and synchronise watches, go our own ways, and come back later, generally our watches will not be synchronised anymore.

At everyday speeds and distances, this effect is very difficult to detect. If you take an airplane trip around the world, and I stay put, we're about talking less than a millionth of a second difference when we meet again. Nevertheless it is a real difference and can be measured with precise atomic clocks. And it's not the fault of our clocks, anything that "marks time" undergoes the same desynchronisation. It seems to be built into the very geometry of space and time itself. (Italicised phrase to be pronounced in an ominous voice.)

Now, the centre of the galaxy is about thirty thousand light-years away. This doesn't actually stop you from getting there in your lifetime: that is not the sense in which the speed of light is a speed limit. In theory you can get there as fast as you want.

But if you and I meet up and synchronise watches, and you take a forty year journey (*) to the centre of the galaxy and back, and I stay put, you would find that I am long dead and my watch has rusted to nothing. Our watches are out of synch by about sixty thousand years.

So it's not just a question of trying to go faster. In one sense, there is no speed limit. You can get to the centre of the galaxy in your lifetime, just not in mine (unless I go with you, but I kind of like it here and I think I'd rather stay).

(*) Forty years is about the time it would take for a 1G rocket to get there and back: 1G acceleration to the mid point and then 1G deceleration to the centre of the galaxy, and the same back. For mathematical details, Wikipedia's time dilation article is a great start. There are all sorts of practical issues with a 1G rocket, but it is perfectly possible in theory.

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