Why is the speed of light a limit?

[Camacha]

As far as my failing memory tells me, universe needs maximum speed limit to avoid some funny things with causality

I feel that causality is something our monkey brains invented to deal with reality, but that is probably a different discussion

[undercoveryankee]

As to exactly why this occurs... well, it's a question on par with 'why is gravity an attractive force?' and 'why don't we see the effect of quantum fluctuations?'. We just don't know why the laws of physics in our universe are as we have observed them to be.

If you solve Maxwell's electromagnetic field equations for the speed of an electromagnetic wave, the figure that we call c pops out. There's nowhere in the math to correct for the motion of the source or the observer. If the speed of an electromagnetic wave were ever not c, Maxwell's equations would no longer hold.

Einstein postulated that the apparent oddity was not an accident or omission, but a law of nature -- that space-time has a structure in which that speed itself is the constant. He worked out what math would govern a structure that had that property and what some of the other consequences would be. All of those predicted consequences were confirmed by experiment as soon as experiments that could distinguish those predictions from the alternatives were designed.One of those mathematical consequences is that every mass, no matter how fast it goes, still has a speed less than the fundamental speed relative to every other mass in the universe.

The equations all imply each other. A philosopher who asks "why relativity" could equivalently ask "why do light and electromagnetism exist in the forms we observe"? There's a partial answer to that in the form of the anthropic principle -- it's hard to imagine any alternative laws of physics that support a rich enough variety of interactions for intelligent life to function -- but as far as observational science is concerned the answer is "because there's no good way to model these observations that doesn't imply these other things."

[Mr Shifty]

If you solve Maxwell's electromagnetic field equations for the speed of an electromagnetic wave, the figure that we call c pops out. There's nowhere in the math to correct for the motion of the source or the observer. If the speed of an electromagnetic wave were ever not c, Maxwell's equations would no longer hold.

I don't believe this is correct. The equation for the speed of sound in air also doesn't depend on local motions, but it's certainly possible for an object to overtake its own sound wave. (e.g when bullets arrive before you hear the shot.) It's assumed that the calculated velocity of the sound wave is relative to the medium it's traversing. Until Michelson-Morley, it was assumed that Maxwell's light speed was also relative to its medium (and it actually sort of is, if you consider that light's medium is space-time.)

[peachoftree]

For everyone wondering about what I meant when I said why, I wanted a mathematical / simply explained reason which I got. Thank you all! Sorry for the confusion.

Edit:

I thought of a good way to think of it

say all your energy was kinetic energy. From the Equasions E=mc^2 and KE = 1/2mv^2 we can substitute like so: 1/2mv^2 = mc^2 since v = c we find that 1/2m = m the only way this is possible is if m is 0 or infinity. We know it is not 0 so we can assume that we have infinite mass, which is both mathematically and realistically impossible. However, this does work for an object with 0 mass and is why photons travel at the speed of light.

Edited December 11, 2014 by peachoftree

[Mr Shifty]

say all your energy was kinetic energy. From the Equasions E=mc^2 and KE = 1/2mv^2 we can substitute like so: 1/2mv^2 = mc^2 since v = c we find that 1/2m = m the only way this is possible is if m is 0 or infinity. We know it is not 0 so we can assume that we have infinite mass, which is both mathematically and realistically impossible. However, this does work for an object with 0 mass and is why photons travel at the speed of light.

You can't quite do that. The mass-energy relationship applies when comparing rest mass to rest energy or total energy to relativistic mass, but you can't use it (as you're doing) to compare total energy to kinetic energy. The total energy includes the kinetic energy, but also the invariant energy of the particle due to its rest mass.

[cantab]

Let's go back to basics, and I'll try and put things in layman's turns.

The special principle of relativity is that the laws of physics are the same for everyone who isn't speeding up, slowing down, or turning. This dates back to Galileo and Newton, and replaced older ideas that the Earth is a special stationary thing. Nowadays we're familiar with this in everyday life; you can walk around and drink tea inside a train or plane and it feels just like doing so at home. If you don't look out the window and don't hit bumps or bends or turbulence you can't even tell if you're moving or how fast.

The speed of light isn't just any old speed, it's actually part of the laws of physics. It's related to a couple of other numbers in the laws of electromagnetism, and you can do an experiment with a capacitor and use those laws to work out the speed of light without ever measuring an actual light beam.

Now we have the idea of a light clock. It's just a couple of mirrors and a pulse of light bouncing back and forth between them. (Put the mirrors a foot apart and the clock ticks once a nanosecond.) If I have a light clock in my super-fast spaceship, then as I see it it that light pulse moves at the speed of light (dur) and so keeps good time whatever speed I'm going. I can check it against my wristwatch, my heartbeat and other body processes, even the radioactive decay of my ship's nuclear fuel, they all have to be in sync, otherwise I'd effectively be seeing different laws of physics at different speeds, going against the principle of relativity.

But if you watch me go past, then as you see it the light pulse has to go further between each bounce off the mirrors, because the whole thing is also moving along, as this diagram shows.

Since you also measure that light as moving at the speed of light, then you see my light clock ticking slowly. You also see my wristwatch, my heartbeat, and my fuel's radioactive decay, and indeed everything else on my ship, happening more slowly, otherwise things would just make no sense at all. Time itself on my ship passes differently as you see it than as I see it.

It's from these basic ideas of the principle of relativity, the speed of light being part of the laws of physics, and the light clock, that all the seeming weirdness of special relativity can be derived, including the speed of light being a limit for anything with mass.

(And yes, other hypotheses regarding how light behaves are reasonable. But Einstein's theory of special relativity is the one that experiments have shown to be correct.)

[Guest]

"... "magical" things that happen in particle colliders and such. Things that defy logical explanation."

Those "magical" things actually have logical explanations. And some of these "magical" things are the evidence you are asking for.

" I'm sure that I don't have to bring up the fact that at one time everyone knew the world was flat."

When was that time? And who thought that? As far as I know, every educated person in the last 2500 years knew the earth is round. The moment we could do experiments on the earths roundness (the greecs did it with shadows and sticks), we knew the earth was round.

"Well, everyone knows that you can't go faster than the speed of sound."

Who in history has ever claimed that moving faster than the speed of sound is impossible? We had bullets moving at supersonic speeds for hundreds of years. Just because some people believed it to be unlikely that supersonic airplanes are possible doesn't mean anything.

Next your are claiming that according to physics the bumblebee can't fly... You seem to be a walking textbook of science-history-misconceptions.

Edit:

And a quick google search didn't show anything? Wow... You really are a master of investigation!

http://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments

http://scholarship.rice.edu/handle/1911/18426

http://adsabs.harvard.edu/abs/1964AmJPh..32..551B

http://arxiv.org/abs/1108.5977

http://adsabs.harvard.edu/abs/2005JPhB...38S.741P

Thanks for the links. Did my post upset you? I wasn't trying to. Here's one for you : Mass does not increase with velocity :

http://henry.pha.jhu.edu/mass.pdf

I don't pretend to understand anything about the physics of electrons or any of the other things going on in particle reactors. I'm not arguing that. It's just when someone posted earlier in this thread that mass changes with velocity, that was the first I'd ever heard that. I understand the concept of time not being constant. I don't understand the physical mass of anything changing just because it changes velocity. Momentum, yes. Momentum includes time in the equation. Actual physical mass, no. My feeble mind can't get around that.

My analogy to some popular misconceptions in history wasn't meant to be an absolute proof of anything. I'm simply trying to elude to the fact that we don't understand everything about physics yet. The original topic of the thread was "Why is the speed of light a limit?". Well, maybe it isn't. We can't say for sure until we do understand everything. Consider some of the things that happen when the temperature approaches absolute zero. Strange stuff happens. :

And, by the way, a bumblebee shouldn't be able to fly. It's just too big for it's wings.(just kidding, it's a joke, don't go off on me)

[Z-Man]

Mass does not increase with velocity :

http://henry.pha.jhu.edu/mass.pdf

He is talking about the rest mass (I think. I don't like reading papers that SHOUT at ME. But the m in the final equation is that). That is indeed independent of the observer, it is an invariant quantity of an isolated system. All observers can agree on it. The quantity that is increasing with velocity is the inertial mass, the one that appears in the equation F = m a; different observers assign different values to it. To distinguish the two, the rest mass is usually labeled m₀.

[megatiger78]

the only way I know about to exceed lightspeed is the Alcubicure (did I spell that right?) drive.

[Yasmy]

"Why" is a philosophical or religious question. It requires faith to believe the universe exists the way it exists for some reason. We can never prove the existence of that reason.

As much as physicists like to think that certain theories are "natural", physics really can't explain why anything is true. Additionally, we can't even prove that theories are true, but only that they seem to work very well over the regime we can test them in. We can demonstrate that some theories are false though, by showing that some experiments contradict the theory.

"How" on the other hand, is the question that physics answers. "How is the speed of light a limit?" is a very simple question to answer, if you believe (faith) that the theory of Relativity holds. The answer has already been given: it would take an infinite amount of energy to accelerate a non-zero mass particle up to the speed of light. According to Relativity, the energy of a particle of rest mass m, moving at velocity v, is E = m c² / sqrt(1-v²/c²). If you plot that function, you see that the energy goes to infinity as the velocity goes towards the speed of light.

Note that we don't actually know that c is a fundamental limit. We have just never seen it violated. We know it takes incredible energy to accelerate tiny mass particles to near the speed of light, and we know we have never seen anything massive move at or above the speed of light.

[Yasmy]

The notion of relativistic mass is, thankfully, losing favor. Unfortunately most textbooks still use the concept. I'm in the camp that says there is no need for the concept. Just let the energy and momentum scale like gamma, and don't try to assign meaning to the quantity m*gamma, where gamma = 1/sqrt(1-v^2/c^2).

Suppose you are moving at velocity v in the x direction. Then the force laws are

f_x = m gamma^3 a_x

f_y = m gamma a_y

f_z = m gamma a_z

This suggests, if you believe in relativistic mass, that the mass is somehow different in the direction of motion than perpendicular to the direction of motion. The notion of relativistic mass comes from trying to make the mechanics look analogous to Newtonian mechanics (F = ma, p = mv) by letting m suck up the relativistic corrections. The analogy breaks down though, as above, where in the direction of motion there are a couple extra factors of gamma in the force to acceleration equation.

Note I generally frown on appeals to authority. It is not a good logical argument. But I'll just put this quote here from Einstein in 1948:

"It is not good to introduce the concept of the mass M = m / sqrt(1-v^2/c^2) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

(And to comply with the quote, the formulae for the energy and momentum are: E = m c^2 / sqrt(1-v^2/c^2) and p = m v / sqrt(1-v^2/c^2).)

Edited December 12, 2014 by Yasmy

[rtxoff]

Back to the OP's question, my answer is: Cause the supercomputer running the simulation of our universe would die an horrible BSOD.

[Guest]

Back to the OP's question, my answer is: Cause the supercomputer running the simulation of our universe would die an horrible BSOD.

Yeah, it's a good way to resolve overflows

[ZetaX]

Yeah, it's a good way to resolve overflows

Actually it is more a good way to resolve problems with numerics, i.e. rounding errors and such coming from an imperfect version of real numbers. Coincidentally (or not), the same reasoning would explain aspects of quantum mechanics. Some other aspects of QM could be meta-explained by what is called lazy evaluation.