# Why no faster than c?

Why no faster than c?!!

Hi,

Nice basic question here, but why is it that nothing can travel faster than the speed of light? Im sure there is a simple thought experiment which explains it but I cant seem to find a decent explanation. Such a fundamental concept that I though I should really understand it.

Thanks!

Related Special and General Relativity News on Phys.org

You'll perhaps get a lot of "explanations" but that fact is: nobody knows.

Nor why the electromagnetic force is as strong as it it, nor why a proton has the mass it has, why time "passes" as it does, and so forth. One thing we do know is that if any of those were significantly different from observed values, either we would not be here or there would likely be no universe. We have no theory that adequately explains all those fudamental entities.

Einstein explained in his special theory of relativity why the speed of light is fixed, and why space and time are NOT fixed..prior to that most thought, from Newton's work, that space and time were absolute....and were unsure if light was really,really, fast(which was correct) ..or instantaneous. I think all four forces propagate at lightspeed...

You can read a brief explanation regarding mathematical limits of c here:
http://en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds

Basically, no matter can move at the speed of light because it's inertia, or more simply, it's mass if you like, would be infinite and it would therefore take infinite energy to propel it that fast. On the other hand, as it turns out in our universe, massless particles, like the photon, exist only at the speed of light.

JesseM

According to relativity, if you try to accelerate a slower-than-light object to the speed of light, the amount of energy required approaches infinity in the limit as the speed approaches c. This doesn't rule out tachyons which always travel faster than c (and whose rest mass would have to be an imaginary number), but according to relativity, if it were possible to transmit information faster than light it would also be possible to transmit information backwards in time (see this thread for a discussion), so this is a good reason for suspecting the laws of nature don't allow for such things.

Cheers for the replies!
Einstein explained in his special theory of relativity why the speed of light is fixed.
This is what I am looking for I think, all I can find/remember is that he just assumed it. Maybe I should read this >>>>>
According to relativity, if you try to accelerate a slower-than-light object to the speed of light, the amount of energy required approaches infinity in the limit as the speed approaches c.
If I am right in thinking (and I may well not be lol) that one of the assumptions of special relativity is that the speed of light is constant then how can it be used as a way of justifying itself?

Its not so much that it might be a limit but rather what is to say its a constant? What is wrong with it varying depending on where or when you are? I can remember reading something somewhere about light being slowed down but this was something to do with objects with an incredibly high refractive index or something and not really what I mean I don't think.

Still feel a little in the dark
(A bit like if I was moving faster than c maybe lol)

JesseM

If I am right in thinking (and I may well not be lol) that one of the assumptions of special relativity is that the speed of light is constant then how can it be used as a way of justifying itself?
Yes, that's an assumption. But I don't really understand what you mean by "justifying itself"--the only justification for believing that a given physics equation is accurate is that it matches up with experimental results, no? It's not like anyone is trying to prove that you can't reach the speed of light just by making a clever argument. Anyway, the claim that the speed of light is constant is logically separate from any claims about how much energy it takes to reach that speed or whether it's possible to pass it.

Janus
Staff Emeritus
Gold Member

Its not so much that it might be a limit but rather what is to say its a constant? What is wrong with it varying depending on where or when you are? I can remember reading something somewhere about light being slowed down but this was something to do with objects with an incredibly high refractive index or something and not really what I mean I don't think.

Still feel a little in the dark
(A bit like if I was moving faster than c maybe lol)
What is constant (or invariant), is "c" which is the speed of light in a vacuum. So you were right, the fact that light's apparent speed can change in a substance with a different refractive index doesn't count.

As to why the speed of light in a vacuum is is invariant, we can go back to the Maxwell equations. The Maxwell deal with the relation between magnetic and electric fields. On of the results of these equations is that they predict electromagnetic waves and how fast they travel. The answer came out to be almost exactly the same as the measured speed of light for that time. Light, it turned out, was an electromagnetic wave.

Another thing that the equations show that if this speed was not invariant (remained the same for everyone despite their relative motions.), The wave equation describing the radiation goes away if the source and observer are moving relative to each other. Or in practical terms, you would not see the light produced by a candle moving with respect to you, because for you, that light wouldn't exist.

Since we do see the light from objects that are moving, for the Maxwell equation to be correct, the speed of light must be invariant.

If I am right in thinking that one of the assumptions of special relativity is that the speed of light is constant then how can it be used as a way of justifying itself?
No one is trying to justify that lights speed is constant. It is an assumption of special relativity based on very precise experiments that support it. The only thing that can be proved is that
If there exists some thing like the invariant speed then no one can travel faster than that speed. The special Theory of relativity does just that.

why is it that nothing can travel faster than the speed of light?
Here's a quote from the man himself. "The velocity of light forms the upper limit of velocities for all material bodies...The number expressing the velocity of light appears explicitly in the Lorentz transformation, and plays the role of a limiting case, like the infinite velocity in classical mechanics." (A. Einstein and L. Infeld, "The Evolution of Physics" (1938))

Did Einstein understand why light is the upper speed limit, and did he wonder why? Probably "No" and "Yes".

CompuChip
Homework Helper

Given his mathematical skills and excellent physical intuition, I personally have little doubt that he could explain why light is the upper speed limit as a consequence of the constancy of the speed of light in vacuum.

Whether he had any idea why the speed of light in vacuum should be constant, I'm not sure. I presume that he would view it as an experimental fact, or basic law of the universe.

I have a question; I know that looking at Einstein's equation for the energy of an object, if an object travels clossed to the speed of light , gamma approaches inifity , and hence the energy approaches infinity. Since , energy and mass are supposed to be equivalent physical quantities according to Einstein's theory of relativity, shouldn't the mass approach a value equal to inifinity; , since photons themselves are massless , how can a photon travel near the speed of light?

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Hi,

Nice basic question here, but why is it that nothing can travel faster than the speed of light? Im sure there is a simple thought experiment which explains it but I cant seem to find a decent explanation. Such a fundamental concept that I though I should really understand it.

Thanks!
If it's a thought experiment you want, here's a simple one. Certain specifics can get much more complicated but we will only take the limit as our defining point. Let's say that a ship has constant proper acceleration where a constant force is applied over steady time according to the ship clock. Assuming the two postulates of Relativity to be correct, we will find mathematically that a time dilation of the ship must take place for the ship as measured from another inertial frame of reference where an observer is considered stationary and does not accelerate. According to the stationary frame, the ship's clock time dilates by sqrt(1 - (v/c)^2) of the time that passes for a clock in the stationary frame. A stationary observer, then, will say that as the ship accelerates to a greater relative speed, the time on the ship's clock passes slower and slower. This means that if constant acceleration is being applied in constant time in the ship's frame, then since the stationary observer sees less and less time pass on the ship's clock, then less and less acceleration is being applied to the ship according to the stationary frame also, so while it is still accelerating, the amount of acceleration observed becomes less and less. At the limit, therefore, if the ship were to ever reach a speed of c to the stationary frame, the time dilation the stationary frame observes of the ship would be sqrt(1 - (c/c)^2) = 0, so no further time would be seen to pass upon the ship's clock, so no further acceleration would be seen to be applied to the ship according to the stationary frame either, and the ship would just continue along at c, gaining no greater speed ever, so that is why c is the speed limit.

Hi,

Nice basic question here, but why is it that nothing can travel faster than the speed of light? Im sure there is a simple thought experiment which explains it but I cant seem to find a decent explanation. Such a fundamental concept that I though I should really understand it.

Thanks!
Hi,just look at this link from physorg

http://www.physorg.com/news182671620.html

CompuChip
Homework Helper

I have a question; I know that looking at Einstein's equation for the energy of an object, if an object travels clossed to the speed of light , gamma approaches inifity , and hence the energy approaches infinity. Since , energy and mass are supposed to be equivalent physical quantities according to Einstein's theory of relativity, shouldn't the mass approach a value equal to inifinity; , since photons themselves are massless , how can a photon travel near the speed of light?
Photons don't travel near the speed of light, they travel at the speed of light. This is a subtle but crucial difference.

Note that 'gamma' is a quantity which depends on one thing only, namely the velocity v/c of one frame with respect to the other one. So basically, sending it to infinity means transforming from one "rest frame" to a frame where the velocity approaches the speed of light ever more closely. The crux of the matter is, that for light no such transformation exists. Precisely because it moves at the speed of light for any observer, it is impossible for a massive observer to switch to the reference frame of a massless object. Therefore, it makes no sense to talk about, for example, what the universe looks like "from a photon's perspective" or "accelerating a spaceship to the speed of light". Indeed for photons, there is a different relation, namely E = hf, where h is Planck's constant and f is the frequency of the photon. Through E = mc2 you can - theoretically - assign a mass to the photon, and indeed in some cases this is useful. But the 'm' there does not correspond to something like the 'rest' mass of a photon, because there is nothing that we would want to call 'at rest'.

JesseM

Through E = mc2 you can - theoretically - assign a mass to the photon, and indeed in some cases this is useful. But the 'm' there does not correspond to something like the 'rest' mass of a photon, because there is nothing that we would want to call 'at rest'.
Yes, there are two ways of dealing with the energy of objects not at rest in your frame:

--you can use the "relativistic mass" M and then the equation is E=Mc2

--you can use the rest mass m, and then the equation is E2 = m2c4 + p2c2 (note that this reduces to E=mc2 in the case of an object at rest in your frame whose momentum p is zero)

according to relativity u can move faster than C for which u need infinite energy.

according to relativity u can move faster than C for which u need infinite energy.
Even with arbitrarily large amounts of energy, it would take an infinite amount of time to accelerate TO c nevermind past it. Relativity does not allow for FTL travel in our universe; why do you think Einstein had kittens when non-locality was presented?

Because Einstein don't know about entanglement at that time. Moreover, he don't want some one challenge his theory except Fock and Dirac attack his theory.

Because Einstein don't know about entanglement at that time. Moreover, he don't want some one challenge his theory except Fock and Dirac attack his theory.
Right, he had no notion of, and I quote Einstein now... "Spukhafte Fernwirking"?! Are you familiar with EPR?

EPR-Hidden variable. Yes i know ........Bell's experiment already reject this EPR.

what Spukhafte Fernwirking mean.........

what Spukhafte Fernwirking mean.........
It is german for "Spooky Action At A Distance", which is the phrase Einstein used to deride QM because of non-locality (i.e. Entanglement).

If you know about the EPR paradox, then how did Einstein, Podolsky and Rosen object to something they didn't KNOW ABOUT according to you?! "Because Einstein don't know about entanglement at that time."...

So... they didn't know about Entanglement, but they wrote a paper detailing a (percieved) paradox at the time, AND Einstein is quoted making fun of it? Teach me of swami, I clearly have much to learn from you.

Actually their claim was for the complete description of wavefunction some hidden varibale is needed, which Bell's shown that if there is a wavefunction there is no hidden varibale anymore.
"I am therefore i think.
I think therefore i am."

(How i can teach the native of F. Nietzsche).

Actually their claim was for the complete description of wavefunction some hidden varibale is needed, which Bell's shown that if there is a wavefunction there is no hidden varibale anymore.
"I am therefore i think.
I think therefore i am."

(How i can teach the native of F. Nietzsche).
Do you think I'm German (I'm not), and therefore "Cogito Ergo Sum" would be beyond me? Thanks. :rofl:

U have prove that u be my swami not i be ur swami.
Nice to meet u Swami Vivekanand.