Q: Why is the speed of light the fastest speed? Why is light so special?

Physicist: The best way to think about it is; there is a speed (C) that is the fastest speed and, by the way, light goes that fast. There’s nothing special about light, it’s just a useful way of describing C (“the speed of light”). Photons are just another podunk massless particle, whipping around the universe as fast as fast can be.
Historically, the derivation of the strange properties of C (relativity) relies on a pretty straight forward piece of Einsteinian logic, based in part on an understanding of light.

1) All the laws of physics work the same, whether you’re moving or not. There is no experiment that can tell you whether or not you’re moving.

2) Light is an electromagnetic wave, and the velocity of these waves can be derived from Maxwell’s laws.

3) Maxwell’s laws, like all physical laws, are independent of how fast you’re moving. So the speed of light must also be independent of how fast you’re moving.

4) So, there exists a speed (the speed that light travels at) that is the same to everyone, no matter how fast they themselves are moving. Holy crap! There’s your special relativity!

So when you see equations like E=MC^2 (“energy equals mass times the speed of light squared”), you may ask yourself “what in the hell does light have to do with how much energy is stored in the mass of an object?” Well, the answer is it doesn’t. C is just a speed, and E=MC^2 and all the other equations with C would stay the same even if light didn’t exist at all.

So why is C the fastest speed? A good way to think of it is to first ask; how do you know when you’re moving faster than something else? If you’re driving down the highway and you’re moving faster than the car in front of you, then eventually you’ll pass that car. However, C is the same to everyone, no matter what. So, say a photon goes past you, and you try to catch up. But no matter how much you speed up, the photon will always be moving away at the speed of light. You can never catch up (or even come close to starting to catch up). So, regardless of perspective, the photon is always moving faster than you.
Some of this may seem seem contradictory, but surprisingly, it’s all self consistent. Very surprisingly.

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18 Responses to Q: Why is the speed of light the fastest speed? Why is light so special?

  1. Janne says:

    A related question: Why is C a finite value, i.e. why is it not infinite?

    Or maybe another form of the question: is C just a fundamental constant the value of which cannot be explained, or can it be derived from other more fundamental constants/principles?

    OK you can say according to Maxwell c = sqrt(1/e0µ0), but this then just extends the question to e0 and µ0

  2. The Physicist Physicist says:

    Pretty much. There are many physical constants, and not as many equations relating them, so you’ll always end up with at least a few (19) variables that just are what they are. Your example above is about the best example. Of the magnetic permittivity of space, electric permittivity of space, and the speed of light, which is fundamental? There’s no way to tell for sure, but I cast my vote for C, and the electric permittivity.
    Magnetism can be derived from electric forces and relativity, but we could have it backwards, or it may not matter to the universe at all. In practice we have these constants measured, so we just use what we have, and don’t stress terribly on what came first (after all, you can eat eggs and chicken without too much trouble).

  3. Janne says:

    Thanks! Also for the subsequent post :)

  4. Pingback: Q: Why is the speed of light finite? « Ask a Mathematician / Ask a Physicist

  5. Chris says:

    Hi. This isn’t exactly related to the post, but regardless, I’m perplexed. What happened in this experiment that the scientists claim they’ve sent light faster than c? Is there no “universal speed limit”?
    http://www.cbsnews.com/stories/2000/07/19/tech/main216905.shtml

  6. The Physicist Physicist says:

    This is pretty tricky, but it comes down to a distinction between “phase velocity” and “group velocity”. Without going into detail (a long post) the experiment essentially requires a “standing wave” with waves at many wavelengths. These waves interact in such a way that they create peaks, like when you pluck two slightly-out-of-tune guitar strings and you hear a pulsing sound.
    These peaks move around in the standing wave region, and you can more or less keep track of where they are. In the middle of the region is a specially constructed cloud with extremely weird optical properties, that changes how fast light of various frequencies move through it (slowing only, but to various degrees).
    By changing the different frequencies you change how the peaks move around (making them faster than light in this case), however nothing is actually moving faster than light, just a non-information-carrying effect.
    Another example of this sort of thing is the “scissor paradox”. When you close a pair of scissors the point where the blades intersect is moving much faster than either blade, and if you were to construct a pair of scissors large enough then the point of intersection would move faster than light, but it wouldn’t be able to carry any kind of information (in part) because you’d already see the slower-than-light blades moving long before the intersection point got to you.
    This pulse thing is a similar “paradox”.

  7. Chris says:

    Hmm… kinda crazy. And cool. Thank you!

  8. The Physicist Physicist says:

    Update! The long reply above has been expanded into a post:
    http://www.askamathematician.com/?p=4037

  9. Positron says:

    Ok, this might sound a bit quirky, but how did Einstein really did get to know or derive or arrive at the conclusion that the fastest achievable speed is the light speed ? (1)
    (2)Well, he had a little doubt that what would happen if he were to travel next to a photon at its own speed. Let us consider that I can travel at the speed of light, even if relativity doesn’t permit me to. Then travelling next to a photon at its own speed, will I be able to see the oscillating electric and magnetic vibrations?

  10. The Physicist The Physicist says:

    There were a series of experiments, most notably Michelson-Morley, that demonstrated that the speed of light seems to be the same regardless of how the experimental apparatus is moving. In the case of Michelson-Morley, they waited until the Earth was in different parts of its orbit (and thus moving fast in different directions), and even did the experiment on a boat so they could move around at will.
    The result was ultimately inescapable: the speed of light is the same regardless of how you’re moving. As a result, as you speed up, you’ll find that light is still passing by at the speed of light. You can never even get close!

  11. KeN says:

    example there is an infinite abyss then I throw a thing (like a piece of chalk) then it falls faster and faster. Is it possible to surpass the speed of light? then if it is possible, if I fell myself in the infinite abyss until I surpass the speed of light then i can travel through time? (by the way I’m just a kid and i just want to know those things XD )

  12. faheem says:

    Am I right vision speed is faster then light

  13. Chinmay says:

    Speed of light is not relative to speed at the observer is moving .
    In your words, ” the speed of light is the same regardless of how you’re moving. As a result, as you speed up, you’ll find that light is still passing by at the speed of light. You can never even get close!

    I have a problem here :
    If I am moving at speed , say, 1.0 * 10^8 m/s , and observing a speed of a photon.
    Myself and the photon started our journey at the same point.
    So, normally , I must observe the speed of the photon as 2.0 *10^8 m/s .
    But, according to special relativity, I see the speed as 3.0 *10^8,
    Then, I must say that “Real” speed of light or abstract speed of light is 4.0 *10^8 ?
    If I go ahead, I will find speed of light as infinite in nature?
    Were the greeks right in saying Speed of light is infinite?
    Is the value ,3.0*10^8, is a relative one ?

  14. The Physicist The Physicist says:

    The speed of light is always that same 3*10^8 m/s. If if you happen to be moving for someone else’ perspective, you’ll find that you always feel stationary. Photons always pass at exactly the same speed, both for you and for who ever thinks that you’re moving. It turns out that velocities don’t add the way we intuitively feel that they should. There’s an old post here about that here.

  15. Mariano Quiroga says:

    We can demonstrate it, but we still can’t explain why c = 299792,458 km/s. If we could experiment the universe travelling like a photon, it would be truly weird. Being massless and travelling at c, the whole eternity of time has passed in no time for your single experience. So you’d be standing away from the concept of time. Also, space would have shrunk enough so the whole universe would be infinetely small from your point of view. That is, you’d be everywhere in space, reaching any point at every time. That is, if you are massless. If you happen to have even a tiny amount of mass, then you’d also be infinitely dense and massive at c, perhaps shrinking all the mass of the universe in a singularity, like reversing the big bang.

  16. Mariano Quiroga says:

    Of course, you would require more than the energy in the whole known universe in order to attain c being massive. Perhaps the big bang is what happened when energy “decided” to slow down and become massive

  17. Walter Roberts says:

    After reading all the comments above the question of why the speed of light is the fastest thing in the universe has not been answered. The only thing for certain is that the speed of light appears to be constant.

    In Einstein’s postulates for the theory of Special Relativity he make a conclusion/assumption that the speed of light is the fastest thing in the universe, but failed to prove it experimentally or otherwise.

    In fact no one yet has been able to actually prove it. Einstein would have been better of saying he thinks the speed of light is the fastest thing in the universe.

    However that wouldn’t work for his theory. The problem with physicists and scientists is that they sometime accept these assumptions/statements as being 100% true and don’t challenge them. Maybe because it you can’t disprove it, it must be true.

  18. Phaedrus says:

    This gets into the question, why is there this general conception that the speed of light is a limit on how fast ANYTHING can travel. I haven’t thought of a good way (so far) to express this, to show a reason not to believe this, but I think the idea that nothing can go faster than c, the speed of light, is ridiculous. First of all, you have to understand, there is no such thing as an absolute speed. All motion is relative to something. Speed is a measure of how fast something is moving relative to something else.

    “The motion of a body can only be described relative to something else – other bodies, observers, or a set of space-time coordinates.” – http://en.wikipedia.org/wiki/Inertial_frame

    An object in outer space does NOT have a speed. It has a speed in relation to other things. Every object in the universe could be said to have almost an infinite number of speeds, because there are an almost infinite number of other things to move in relation to. So to say that an object cannot move beyond the speed of light, that necessarily means you are saying that there is no thing in the entire universe which is moving at a speed faster than c in relation of this object you are talking about. When you talk about going faster and faster towards the speed of light, people think you are in this spaceship and the speedometer needle is rotating to the right more and more, but is slowing down as it approaches this RED line which indicates light speed. They think your space ship is going to start shuddering as you approach c, because you are going SO DAMN FAST! And the space ship is ready to explode or something. Your mass is increasing to infinity! Your time is slowing and slowing. The length of the ship and everyone in it is contracting and contracting, as per Einstein’s equations. But in reality, as I’ve said, motion is relative. If something on the other side of the galaxy is moving away from us here on earth, at a speed approaching c, then we are also, moving away from that object at a speed approaching c. So right now as you sit here reading this, you may very well be moving at a speed (in relation to another object in the universe, which is all speed is) that is close to the speed of light. Do you feel you are highly massive because of this? Do you feel your time is highly retarded? Do you feel you are thinner in one dimension than normal? No, you feel just fine. Oh, but the believers in special relativity will tell you, you aren’t going to feel these effects. Its only the people on that other object on the other side of the galaxy as they look at you on your planet earth, they will see these effects, such as your time being slowed down in comparison.

    Lets say you are going on a journey to another star, that is 4 light-years away from here. And let’s say you know the alien beings living on a planet orbiting around this other star, and you have sent them messages and talked with them. The aliens on the other planet (we’ll call it planet B) have decided they are coming to visit earth. We have shared technology and we both have a spaceship that can approach the speed of light (in fact, let’s say they sent us their plans so we have both built identical space ships). We both launch our rockets and start speeding towards each other’s planet. Both our ship and this other ship are now moving at .9 times the speed of light. By the way, let’s say that planet B’s sun and our sun are both still with respect to each other. So lets imagine a huge inertial frame in space that includes these 2 stars. That will be like an objective inertial frame over which these space ships will travel. When the 2 rockets, one from earth and one from planet B meet in the middle, they are both going .9 c with respect to this huge inertial frame that includes the 2 stars. Looking down on this inertial frame from above, the 2 spaceships are approaching one another at a speed of 1.8 times the speed of light. Now, in my view, that shows that things CAN travel at a speed greater than the speed of light. Because ship A (the one from earth) is moving with respect to ship B at a speed greater than light. But the special relativists will say, no, that’s not how you do it. We are talking about the speed that ship B will be perceived to be moving in relation to the inertial frame defined by space ship A. They give you these Lorentz equations and say, see that’s how you calculate the actual speed that passengers on ship A will see ship B as moving. Because of the relativity equations, you will see the ship is NOT moving (in relation to inertial frame based on ship A) at a speed greater than the speed of light. From ship A, if they look at ship B, it will be shortened in the direction of travel. The mass of ship B will be way up. The ticks of a clock on ship B will be way slowed down from those on the observers on ship A. But are all these effects really happening to ship B? Or are they just distortions based on the great speeds that are being attained between the 2 ships. I think if these effects actually happen as anticipated by the special theory of relativity, then I would say if anything they are distortions of perceptions from one ship to the other. If you really want to see whats happening between these 2 ships, you move up off the inertial plane which contains the 2 stars and the 2 star ships, and from that vantage point, you can see that the ships are approaching one another at a speed of 1.8 times the speed of light. So, I think what you want to do is, remember, that when you hear scientists and journalists talking about this idea that nothing can exceed the speed of light, what they really mean is that, no observer will ever directly measure some object or wave or whatever, moving at a speed greater than the speed of light. However, as I’ve shown, things can move with respect to other things at a speed greater than the speed of light, looked at from an objective point of view (or at least a more objective point of view than directly measuring objects’ speeds relative to the observer on another object he is observing from). The people on ship A will see time slowed down on ship B, but they will know that this is a perceptual distortion based on their moving past ship B at a very high rate of speed. They know that ship B’s ship has not really shrunk. They know ship B’s time is still ticking along as it always has been, from before the space ship took off. They know its mass hasn’t really increased (I wonder if special relativity predicts that since the mass of this object moving near the speed of light has increased substantially, would this cause their space ships’ path to actually be deflected more as they passed each other because of their masses bending space?). They know these are all distortions caused by fact they are moving with respect to each other at high rate of speed. But they know in reality both ships are the same. And if you look at things from objective point of view, they are approaching each other faster than the speed of light. Aha! So there! And remember, there is no such thing as absolute speed, right? There is only speed in relation to something else. And if you are flying in a space ship to another star system, it is perfectly reasonable for you to have a speed in relation to another space ship also flying to your star system. And thus your speed in this case is a speed that exceeds the speed of light.

    Notice that throughout this whole thought experiment, I am living within the constraints laid out by the special relativity theory. And still I came away with one object moving faster than the speed of light in relation to another object. And remember, that is all that SPEED is, it is motion per time in relation to something else. People talk about not being able to exceed the speed of light, like outer space is the big 3-D grid and everything is just sitting there in this grid and moving in relation to this grid. Well, that is old Newtonian thinking. Now, its true that I am sort of trying to critique the new Einsteinian view of things, but I do believe that there is not some absolute grid underlying space or something like that.

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