# Why is there a universal speed limit, c, and why is it what it is?

by CosmicVoyager
Tags: limit, speed, universal
 P: 1,102 Phew, thank you (i mean it sincerely) Cosmicvoyager for your reply. It demonstartes, to me, that my response was close to the right context for your question. "It wouldn't for me. It does not have a limit. That speed is the result of whatever propelled the expansion. It could have been faster or slower." Cool, I think that means you picture it the way I was trying desperatly to describe it.
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P: 1,849
 Quote by CosmicVoyager Yes, I mean what is holding the light back. It is like an invisible hand jumps up in front of things at c and stops them from going faster.
Maybe you are thinking, why can't you travel at 99% the speed of light, then go just 2% faster and find yourself at 101% the speed of light? Well, when you are travelling at 0.99c your notions of distance and time change. To the outside observer it looks like you have only 1% further to go, but from your own point of view you still have 100% to go -- the speed of light relative to you is still 299792458 m/s and you are no nearer to it than when you started. To look at this mathematically, velocities don't "add" as u+v but as
$$\frac{u+v}{1+uv/c^2}$$
In the example above, your final velocity isn't 1.01c but
$$\frac{0.99c+0.02c}{1+0.99\times0.02}=0.99039c$$
Another way of looking at this: the usual way to measure speed is to take distance on the observer's ruler divided by time on the observer's clock. But there is another way: take distance on the observer's ruler divided by time on the traveller's clock. This method is called "celerity" (or "proper velocity", a name I don't like). It turns out that the celerity of light is infinite, so if you translate your question from speed into celerity, "why is the universal celerity limit infinite?" it's a bit of a non-question.

You may well ask, "Why don't speeds add up" or "Why is the celerity of light infinite yet its speed is finite?" and most books will send you in a circle: "Because the speed of light is invariant" (the same for all observers), so it hasn't really answered your question. That's just the way the Universe is, who can say why?
 P: 1,102 Doc Al, "That's no excuse." That's subjective. "And yet, this is a physics forum." Actualy it's a physics forum.
 P: 13 http://golem.ph.utexas.edu/category/...thendieck.html 'One story has it that Grothendieck is now convinced that the Devil is working to falsify the speed of light. Schneps ascribes his concerns with the speed of light to his anxiety about the methodological compromises physicists make. He talks constantly, however, about the Devil, semi-metaphorically, sitting behind good people and nudging them in the direction of compromise, of the fudge, of the move towards corruption. ‘Uncompromising’ is the expression Schneps favours.'
 P: 7 I think I understand what CosmicVoyager is getting at. It is fascinating and illuminating to start gaining an understanding of the implications of relativity from basic principles, i.e. the experimentally verifiable facts that light is observed to have the same speed for every observer and also that every frame of reference is equally valid. From that, we can explain and describe almost everything we can observe. But what's missing is the 'why' bit. And whether you like it or not, it's the 'why' bit that is the fundamental part of human nature that drives us to discover more and more about the universe. CosmicVoyager is just wondering what it is about the fabric of the universe that makes things behave like this. Nitsuj talked about some 'medium' expanding, but actually it is space that is expanding in every direction. Isn't it the case that if time and space began with the big bang and has been getting bigger ever since, that the space I'm sitting in right now is an inflated bit of space that was once, and still is part of the big bang? It isn't unreasonable to muse on the possibility that this stretching of space time in all directions has something to do with what we observe as a speed limit.
 P: 178 Why is any constant what it is fine structure constant or c? It's a superbly interesting question with no real coherent answer, only plenty of good ideas. "There is only one thing faster than the speed of light and that is the speed of rumour." Terry Pratchett, I'm paraphrasing. Limits are troubling they make fools of us all I think.
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P: 17,530
 Quote by pip1974 But what's missing is the 'why' bit. And whether you like it or not, it's the 'why' bit that is the fundamental part of human nature that drives us to discover more and more about the universe.
hi pip1974, welcome to PF

Perhaps it is just the fact that I have young kids, but IMO "why" is generally not that important a question. any answer to a why question can be, and often is, simply followed by another why question. It is a game that any four-year old can play expertly. also, in my experience, generally a why question is asking for a bedtime story rather than a scientific experiment.
P: 178
 Quote by DaleSpam hi pip1974, welcome to PF Perhaps it is just the fact that I have young kids, but IMO "why" is generally not that important a question. any answer to a why question can be, and often is, simply followed by another why question. It is a game that any four-year old can play expertly. also, in my experience, generally a why question is asking for a bedtime story rather than a scientific experiment.
Why?

 Mentor P: 17,530 Once upon a time ...
P: 178
 Quote by DaleSpam Once upon a time ...

Oooh! Does it have dragons!

P: 3,188
 Quote by Calrid Why?
Yes exactly, why!
I agree with you. Children who never ask asking why (each time one level deeper) become scientists!

PS: the original popular reply to the "why" is because of the existence of a universal medium (Lorentz etc.), and the most popular reply today is because of the existence of a physical spacetime (Minskowski etc.). And likely there are numerous variants on those ideas and many other (such as post #16).
P: 7
 Quote by DaleSpam hi pip1974, welcome to PF Perhaps it is just the fact that I have young kids, but IMO "why" is generally not that important a question. any answer to a why question can be, and often is, simply followed by another why question. It is a game that any four-year old can play expertly. also, in my experience, generally a why question is asking for a bedtime story rather than a scientific experiment.
"Why?" is the most important question! And in science leads to the next level of understanding and more questions, that normally begin with "Why...".
Like, "Why do the planets appear to move the way they do?" Kepler already had equations to describe the motion of the planets and still Newton asked the question "why" because he felt that there were links to be made, patterns to be found and ideas to be brought together.
As I said before, it is human nature to ask the magic question "why" and to seek patterns in the things we experience and it is at the root of all scientific discovery. It is the same evolutionary trait that allowed our ancestors to be better hunter gatherers and to avoid predators that drives us to ask questions like "Why is there a universal speed limit".
Actually the simple answer to this particular question is that we don't know. Yes, we know that in the representation of the universe as we understand it that there is a speed limit, that there has to be one, and that it is based on the assumption that quite basic facts are true, but we do not know the real underlying nature of this speed limit or what the actual fabric of space itself is really like. We are still coming up with theories that try to model what the universe is really like deep down in the finest detail, but as we know the best theories are incompatible with each other.
And I think when kids want a story, and they ask "why this" or "why that" it's because we were all little scientists when we were kids. At some point, some people feel they have enough rules established to allow them to get by in their particular environment, whether they are a banker, a truck driver, an engineer or a physics teacher. But some people, bless them, just can't let things lie and keep on asking "why" and end up being scientists, philosophers, priests or artists.
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 Quote by CosmicVoyager ...It seems there is not reason there should be limits, and if there is, what is limiting factor? What is causing the restriction?
The reason there is a limiting factor for speeds is that the ever increasing speeds lead to a convergence of the X4 and X1 dimensions as they rotate toward each other (see sequence of sketches below). Then, the next "why question" is, "Why does the X1 coordinate rotate so as to maintain symmetry with X4 about the photon world line (note that this symmetry, with 45 degree photon world line, results in the same speed of light for all observers)?" A possible answer:

Nature wanted all observers to live with the same rules of physics, and this was the only way to do it (thus, nature contrived coordinates with invariance under Lorentz transformations)

 P: 1,102 pip1974 - "Nitsuj talked about some 'medium' expanding, but actually it is space that is expanding in every direction." The "medium" I talked about is space/time. To say it differently I was describing space/time as a medium. It is not just space that is expanding, time is as well.
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P: 17,530
 Quote by pip1974 "Why?" is the most important question! And in science leads to the next level of understanding and more questions, that normally begin with "Why...".
This is a very common misunderstanding. Science is fundamentally incapable of addressing "why" questions. Science can only answer questions of the following form: "Does the mathematical model X correctly predict the observation Y in experiment Z to within experimental error?". Even if the answer is "yes" the scientific method does not and cannot answer the question "why" the model works.
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 Quote by DaleSpam This is a very common misunderstanding. Science is fundamentally incapable of addressing "why" questions...
DaleSpam, what is your assessment of the "Theory of Everything"--assuming Stephen Hawking is proven correct in his pronouncements?
 P: 2,456 DaleSpam is right. But just 2 cents. Science is capable of answering "Why" questions (only to some extent) - using the Anthropic principle http://en.wikipedia.org/wiki/Anthropic_principle