I’ve read Asimov on Physics and Martin Gardner’s Relativity for the Million and various other popular-science works trying to explain Einsteinian physics to the layman. One thing I’ve never seen explained any of them: Why is the speed of light so special, such a unique speed, that it forms the ultimate speed limit, nothing can be accelerated past it, everything changes as you approach it, etc.? Can any Doper explain this in layman’s terms?
I’m not even close to a physicist, but I’m definitely a layman.
My understanding about why the speed of light is an upper limit is the boiled down physics concept that:
any object with mass needs infinite energy to be accelerated to the speed of light.
The closer you became to the speed of light, the more energy it would require to accelerate the object further, and this is an exponential increase such that to finally reach c, you need infinite energy. Obviously there’s no way to have infinite energy.
Unfortunately for laymen like me there are genuine examples of breaking the speed of light, but the general truism of “objects with mass can’t be accelerated to c without infinite energy, which is obviously functionally an impossibility” holds true.
Read about Cherenkov Radiation for at least one special case in which you can have something that goes faster than light.
I’ve also always heard that getting to c is a matter of acceleration, if something starts out faster than c, then this doesn’t violate any known laws of physics. (A tachyon is a theoretical particle that is constantly moving faster than the speed of light, but since it did not have to be accelerated from sub c to > c, this isn’t a problem.)
Yes, I get that part, but why the speed of light? Why not, say, the speed of sound?
One problem I’ve never understood is what happens when an object is accelerated to .6 c, and another object is accelerated to .6 c in the opposite direction. Both are theoretically possible speeds, but from the perspective of one of the objects, the other object is traveling 1.2 c. With that in mind, it should be theoretically possible to see objects travel faster than the speed of light. As an aside, would this cause a luminous-boom as you see with sonic booms on earth?
The other angle, BG, is just that it is. Science can, at least to a considerable degre, explain what is. It cannot really exaplin why it is, or even how it became so. It can describe the laws of the universe, but not why these specific laws and rules exist, or even if they could have been different. If you are not religious-minded and I believe you are not, you could perhaps wonder if there are other universe and/or some form of inter- or extra- universal space, which would have its own rules, etc. Still, there’s no intrinsic reason things are the way they are. The speed of light is a certain speed, and if it were different, it could radically alter the universe. Or maybe not. We don’t entirely know if the relationships we see among physical phenomena are intrinsic or created by circumstance - that is, if the speed of light directly affects the equation E= MC^2 or if that particularly relationship would be ever-so-slightly different if the sopeed of lgiht had always been different. My money is on the former, since such elegant mathematical relationships are rare, though not nonexistant, in nature.
It’s one of the physical constants, essentially one of the “laws” of the universe that humans have discovered over time.
It’s the same reason that a^2 + b^2 = c^2 (Pythagorean theorem) is true for a right triangle, that’s just one of the universal laws concerning objects of that shape, and even an (intelligent) alien would understand this with no cultural understanding or ability to even comprehend things in human terms.
Remember that everything is relative. That’s why they call it relativity. If a person sends to spaceships in opposite directions at 0.6c and observes them, to him, they will both appear to be going 0.6c. But if spaceship A observes spaceship B, it will appear to be going less than c, even though common sense would seem to dictate that the observed speed should be 1.2c. This is because at relativisitc velocities, speed, length, and time are all distorted – you can figure out by how much by using the Lorentz transformation.
As for why c is the specific number that it is, well you’d have to ask the guy who picked pi.
But a law of mathematics, logically necessary, is something fundamentally different from a physical constant, which has to be determined by experiment/observation, and might conceivably have proven to be something different than it is. Isn’t it?
I think part of the problem is maybe just the name “the speed of light”.
Light just happens to travel at c because it is (basically) massless. So it’s not really that “things cannot travel faster than light” (which wouldn’t a true statement anyway since light can be slowed far below c).
But it’s that light in a vacuum can get up to spacetime’s speed limit. Very nearly anyway.
I guess there are really three questions here:
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Why does the universe have an Ultimate Speed Limit, such that it is the same for all observers in all frames of reference, and nothing can go faster, and the velocities of objects in relative motion never add so as to exceed it?
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Why is that limit 299,792,458 meters per second?
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Why does electromagnetic radiation propagate at that speed?
Completely different kind of question. See post #8.
Because motion is relative, if you consider only those two objects and no other reference frames, both of them accelerating in opposite directions could be equally well described as one of them staying still, and the other moving away more quickly.
Ready for the really goofy part? The two objects you are describing would NOT be traveling at 1.2c away from each other. As you approach the speed of light, speed in opposite directions is no longer additive. To put it another way, if you had one observer, and objects A and B traveling in opposite directions from each other at 0.6c with the observer staying motionless in the center, he would observe object A traveling at 0.6c in one direction, and object B traveling at 0.6c in the other. From object A’s perspective, it would be traveling at 0.6c away from the observer, and at 0.8c (not accurate, but close enough) away from object B. There is no combination of two speeds which exceeds C. If an object is traveling 0.9C in one direction, and another object is traveling 0.9C in the opposite direction, they are receding from each other at 0.99C.
Ready for the really REALLY goofy part? Some things are receding from us at faster than C, despite all that above. The reason for this is that space itself is expanding, and the further away something is from us, the more expanding space there is between us. This is different from actual motion. In these cases, there is no luminous boom or anything of the sort. We just simply can’t ever see things beyond the “observable universe”. It might as well be on the other side of an even horizon for us, because the light from those objects receding from us faster than C will never reach us.
ETA: beaten to the punch while typing this out. Oh well, my explanation was certainly not the best one anyway.
What is so special about c? As I understand it, basically, it is just because the math works out that way.
One thing about the speed of sound is that it isn’t constant. It depends upon the particular material in question (e.g. ~741 m.p.h in air at STP, IIRC). It is “special” in the sense that that is the speed a mechanical pulse will travel through a given medium.
Also, from reading a post of Chronos’s once, it may be possible that photons do in fact have a small rest mass, meaning that they don’t travel at c. In other words, if photons have a rest mass, the speed of light isn’t the speed of light. That said, c is still the upper speed limit for any object with a rest mass in a vacuum, even if photons can’t achieve it. It is also the fastest speed at which information can be transmitted. There are things that can travel faster than c, such as the expansion of space, but not Cherenkov radiation. You may get particles moving faster than photons, but neither is traveling faster than c.
Someone will be along shortly to clear up why you can’t add up velocities to achieve faster that light speeds who will do a much better job of explaining it than I could.
FWIW,
Rob
If things in Einstein’s Special Relativity were allowed to travel faster then light, then an observer could find a frame of reference where events proceed their causes. Since causation is pretty basic to physics, Einstein proposed that nothing could travel faster then light, and so far no one has found anything to contradict him. So I’d say the answer to your first question is: “to preserve causality”.
Well, the cheap answer is that a meter is defined as one-299,792,458th the distance light travels in a second. 
But the actual distance is a fundamental constant, there isn’t (yet) any known reason for it to be the size that it is. Indeed, lots of physicists like to play with theories that have the constant change over-time (though such theories haven’t been met with a lot of success).
All massless particles must travel at c. So since e&m radiation is transmitted by a massless particle, it has to travel by c.
Could you amplify this a bit with an example?
Thanks,
Rob
But, that still leaves the question: Why is there an Ultimate Speed, such that anything going faster would present a causal paradox, or involve going backward in time, or anything like that?
I don’t get this in particular. Does the paradox arise because light is how I perceive the event? In that case, it is no more causally paradoxical WRT the speed of light than WRT the speed of sound.
“Why” is a tough question. It’s such a tough question that some physicists want to bypass it altogether.
That’s part of the rationale beyond the hypotheses that many, possibly infinite numbers of, universes form all the time. Each of them would have a different set of physics, with different fundamental constants and different laws. Under this scenario we just happen to be living in a universe that is set up the way it is (and by various anthropic principles, is set up to allow life to exist to observe what the rules are).
Other universes may exist with different speeds of light and different fine structure constants and different particles and different masses for them. Whether we could ever observe any of these is a moot point.
For that reason many other scientists hate this notion passionately, as something so untestable that it’s not science. They insist that a more complete understanding of the basic laws of physics would help explain the why.
Your question really has two parts. First is the “why”. The second is answered more easily. Any finite speed for C produces causality problems. Information is mathematically equivalent to spacetime. (Oh, I can’t wait for the physicists to come down on this one. C’mon guys, you know what I mean.) The fastest you can transmit information is by photons or other massless particles which travel at C. If you can go faster than C by any means you can get information to a point that is earlier. So you can create causes that occur before effects. You have effectively traveled through time. It’s a direct consequence of C not being infinite.
The place where the explainers usually start is with light cones. See this Introducing the light cone page or Google it further.
But why is that? See post #17.
Point of order here:
Shouldn’t the youngest of all of us present be determined, in order to have that individual raise the question?
– In light of a recent Jewish Holy Day.
- Oddly yours, Og