Why nothing can go faster than the speed of light

For those not familiar with RobotRollCall (the author of the linked comment) check out his profile and other answers. He is one of the best contributors to AskScience and can explain almost any theoretical physics topic in understandable terms. People joke that he is actually Neil deGrasse Tyson and that he should really get this own column / talk show.

I found that the author gave a great setup for an explanation, and then balked at giving the actual answer.<p>&#62; For right now, if you just believe that four-velocities can never stretch or shrink because <i>that's just the way it is</i><p>In other words, nothing can go faster than the speed of light because that's the way it is? The author needs to explain why the magnitude of this four-velocity vector is the speed of light! I was hooked after the first few paragraphs, but then felt like it dead-ended in a circular argument.

It's a shame that about 30% of the comments in this thread are about how the author of the Reddit comment is female. I have a feeling the discussion on Reddit actually trumps the discussion on HN for this one. What's worse is that you have to wade through this irrelevance to get to the "good" comments on here.

People keep asking this, and similar things like "if you were travelling in a vehicle at the speed of light and you turned on the headlights, what would happen?"<p>For me the easiest answer is to understand that from the point of view of the person travelling <i>near</i> the speed of light the beam of light moves away from them at the speed of light. So after ~1 second they are 300,000Km apart.<p>On the other hand, from the point of view of a 'stationary' observer, the light and the spaceship emitting it are moving at almost exactly the same speed. So after ~1 second they are maybe 1 meter apart.<p>How can this be? Our minds naturally want to reject this as nonsense. But the thing the gripping hand is holding that makes this true is that to the stationary observer and the person travelling near the speed of light time is moving at different rates.<p>The person who is moving ~1m slower than the speed of light is experiencing time enormously much slower than the person 'standing still'. The time difference is 300,000,000 times (sic).<p>Our brains reject this, because we think of time as an absolute rock solid constant, when in fact even with our primitive understanding and slow speeds we can demonstrate experimentally that time is in fact flexible, and it <i>does</i> slow down the faster you get.

Once you understand that, then read about (what I think is super-cool) : frame dragging.<p><a href="http://en.wikipedia.org/wiki/Frame-dragging" rel="nofollow">http://en.wikipedia.org/wiki/Frame-dragging</a><p>It causes satellites around earth to move a few feet each year.

Here is what seems like a reasonable "explanation" to me -<p>-- We figured out a few things about electric and magnetic fields. In particular, a changing electric field creates a magnetic field and a changing magnetic field creates an electric field. So if you setup a changing electric field in a specific way, you can setup a cycle between the two field types. Now, these fields hold energy and by virtue of this cycle, become capable of carrying away this energy - what we call "light" - just as waves on water carry energy away from the starting point at a certain speed. The strange thing about E and B though is that this "speed" is a constant that is independent of the reference frame you choose to monitor it. In other words, this wave would move at the same speed relative to you no matter how you happened to be moving and you can therefore never "catch up" with it. Therefore no "thing" (matter) can move faster than light. --<p>In physics, recursive "why"s always lead to "that's the way it is" tautologies. For instance, if atoms are mostly empty space, why don't we fall through the floor? Pauli figured out that no two fermions with same spin state can occupy the same space. Why can't fermions do that? They are spin-1/2 particles and their wave function amplitudes cancel out if you account for the fact that fundamental particles of the same type are indistinguishable. Why does the combined wave function cancel out? .. 'cos that's what seems to agree with experiment - i.e. because you don't see people falling through floors.<p>Progress seems to be about trying to extend this "explanation chain" by one step more. So string theory can step in and add "because vibrating strings, which is what we're made of, behave like this" .. and then it stops at some point again.

Two comments. First, as she alludes to in her edit, the "rotated arrow" picture that RobotRollCall uses here is subtly backward. It does suggest the right things and I used to think of it that way, but it eventually gets you in trouble. (In actuality, as you start to move through space, your motion through time <i>speeds up</i>... but this still leaves your arrow the same length because the geometry of space-time is hyperbolic: the Pythagorean theorem reads "x^2 - t^2 = c^2" instead of "x^2 + t^2 = c^2". This ends up avoiding LOTS of issues, some of which were stumbling blocks for people in the comments to her post. But it's certainly harder to visualize!)<p>Second, several people have complained that RRC avoided the underlying question by saying "the arrow is always the same length". I think they may not be giving that answer the credit it deserves. Her claim isn't that the speed of light is the longest possible arrow (which I agree wouldn't help at all), but rather that <i>every</i> object's arrow has exactly this same length. That shifts the speed of light from being an arbitrary constraint to being simply a label for this universal fact. The question "Why is every arrow the same length?" is still valid, but there's much less reason to worry about it: no known process can change that length, just as no known process can change the rest mass of an electron.

No answer can be given to this question, it is one of the <i>axioms</i> of relativity theory. The explanation is trying to explain the axiom in terms of the theory built on it.<p>I found these answers to be more informative: <a href="http://physics.stackexchange.com/questions/2230/why-and-how-is-the-speed-of-light-constant" rel="nofollow">http://physics.stackexchange.com/questions/2230/why-and-how-...</a>

The top answer on Reddit was not helpful to me, and seemed tautological even in the face of its length.<p>WHY can't the arrow stretch? That is the crucial question; that is the original question. The original question was not "is there/why is there a tradeoff between space and time." The question was "Why can't the arrow stretch, why can't we go faster than light allows?"

I found her lengthy explanation patronising and unhelpful.<p>"you change your direction of motion through spacetime, but not your speed of motion through spacetime."<p>This is article a long-winded way of restating the question, and leaves the reader thinking they know the answer when they simply have a different understanding of the same problem.

I would just explain that a photon has zero mass, but nonzero energy and momentum and finite velocity. Intuitively (meaning: in a Newtonian universe), one would think that a particle with zero mass would have to have infinite velocity to have nonzero energy and momentum, right? And yet, its velocity is finite. That demonstrates that the universe is not Newtonian. It also sets up an intuitive connection (which is what we're looking for here, right?) between the speed of light and one's intuitive sense of an infinite velocity.<p>Again, of course, this brings us to the question of why the universe is this way: why it is Einsteinian rather than Newtonian. But that question really belongs to the realm of metaphysics, not that of physics.

What helped me with a better understanding of time dilation is short paragraph from RobotRollCall:<p>"""<p>If you're moving through space, then you're not moving through time as fast as you would be if you were sitting still. Your clock will tick slower than the clock of a person who isn't moving.<p>"""

Awesome explanation. But what I've never understood is what the universe looks like to photons. What does it mean for a photon to travel between two points from the frame of reference of the photon?

Stephen Hawking predicted that things can travel faster than the speed of light through quantum uncertainty. This is how information can escape from a black hole.<p><a href="http://en.wikipedia.org/wiki/Hawking_radiation" rel="nofollow">http://en.wikipedia.org/wiki/Hawking_radiation</a><p>Put simply it works like this: light travels at a constant speed, but due to quantum uncertainty nothing is in one exact place, it 'teleports' around an average point. Thus, if it 'teleports' in the direction that the light was travelling it has moved faster than the speed of light.

Another way to look at it that is arguably simpler (and with greater loss, of course): Imagine the XY plane with every point described by integers in both X and Y marked. That is, (0, 0), (1, 4), (-2, -5), etc. Connect each of them to their four neighbors with a line segment. Now suppose you are at (3, 4) and you want to move to (4, 5), and you may only use the lines given to you. You move to the right, you move up, you're there. And you can move the other way, too, all the line segments are bi-directional.<p>That works in space; that does not work in time. You can't stop moving or change direction in time. You can put X and Y on that grid and have something meaningful, but you can't say it's X and T; that would imply the ability to freely move back in time or forward at your discretion, which is not true.<p>A simplified explanation of space and time's actual shape is that when you are at (3, 4) and you are moving through time (in the first coordinate, let's say), you've got lines that lead to (4, 4.1) and (4, 3.9) and so on, but the lines only go to a certain angle, which for simplicity's sake I'll say is the obvious 45 degree angle, which means you've got lines that go to (4, 3) and (4, 5), but nothing else below 3 or above 5. You can only move along those lines, and as there is no line to (4, -2) from your start position, there is no way to get there. The bound of those lines is the speed of light. The pictures of the "light cone" you may have seen are in some sense not merely a helpful picture but actually a true picture of the universe.<p>You can not move faster than the speed of light because you can only move between connected points in the universe, and to move faster than the speed of light is to bypass that restriction. The universe is literally not shaped that way. The shape of the universe forbids faster-than-light. You don't have any choices other than those lines and none of the lines go faster than light.<p>This is a grotesque simplification, but I think the core point is accurate. Exceeding the speed of light is impossible for reasons above and beyond the mere "exceeding the speed of sound" or other things were. To travel faster than the speed of light requires <i>changing the shape of the universe</i>. (And to the extent that certain theories permit it under some circumstances, such as the Alcubierre drive theory[1], I suspect that we'd find that even if we could implement one of these things the universe would still find a way not covered in those theories to shut it down, cosmic-censorship-style[2], or like [3]. I would also note that all "practical" FTL drives proposed to date have inevitably required the existence of at least one impossibility, such as stable negative mass, and it means little to prove that if I have one impossibility like stable negative mass I can have another like FTL.)<p>Also, because this is a grotesque simplification, please note that picking apart holes in my picture is not even remotely the same as picking apart holes in the theory of relativity, let alone picking apart holes in the Universe. In particular don't get caught up with things that may appear to be going backward; that's an illusion of this attempt to embed an explanation into Euclidean space, not a real problem with the physics.<p>[1]: <a href="http://en.wikipedia.org/wiki/Alcubierre_drive" rel="nofollow">http://en.wikipedia.org/wiki/Alcubierre_drive</a><p>[2]: <a href="http://en.wikipedia.org/wiki/Cosmic_censorship" rel="nofollow">http://en.wikipedia.org/wiki/Cosmic_censorship</a><p>[3]: <a href="http://books.google.com/books?id=_mo4AAAAIAAJ&#38;pg=PA132&#38;lpg=PA133&#38;ots=MPipJx9GjV&#38;dq=hawking+wormhole+time+machine+vacuum+explosion" rel="nofollow">http://books.google.com/books?id=_mo4AAAAIAAJ&#38;pg=PA132&#...</a> (reading pages 132 and 133)

I remember reading an article a while back:<p>"Scientists Make Radio Waves Travel Faster Than Light"<p>article:<p><a href="http://www.universetoday.com/33752/device-makes-radio-waves-travel-faster-than-light/" rel="nofollow">http://www.universetoday.com/33752/device-makes-radio-waves-...</a><p>the paper it's based on:<p><a href="http://arxiv.org/abs/physics/0405062" rel="nofollow">http://arxiv.org/abs/physics/0405062</a><p>Anyone with a Physics background care to comment on the validity of this study?

She's got a lot of good stuff in her comment history.<p>I really wish Instapaper worked with reddit comments. Lots of good reading there.

My gut feeling is that article is dragged :-) into somewhat irrelevant things like Poincare group et al.<p>Why maximum limit exist at all? How Universe without this limit will look like? How Universe with limit which is not equal to speed of light will look like?<p>Antropic principle inevitably pops up.

This explains why there's a limit to speed but not why this limit is light's speed.

What I want to know is what happens if the arrow is rotated more than 90 degrees?

eh, it's more fun to imagine we will one day surpass the speed of light. It hasn't been disproved so conclusively that I know about said proof, so as of yet I can continue imagining the barrier will be broken.

If you were moving in a "completely horizontal" direction, wouldn't you not be moving through time at all, but only through space? That means you could move infinitely fast, not with a strict limit.

It's a good explanation, really, but do we need to have only one? Can't we keep Reddit things in Reddit and HN things in HN?<p>If I am in a Reddit mood, I will go to Reddit. If I'm more in a HN mood, I will come here.

Oh, finally we got here cool discussion. Here is how I explain that one "could" travel faster then the speed of light! HOWEVER, and this is VERY IMPORTANT, this depends on your definition of the speed. So imagine following experiment:<p>There are two space ships which are built like these russian matroshkas. One smaller space ship is in the hangar of a bigger one. The bigger one starts from the earth and accelerates to the speed of light (or just until 0.999c). Now, the smaller ship starts and can again accelerate from the bigger ship point of view until 0.999c. So, if there is just a simple velocity measure instrument, which is measuring acceleration by F = m*a, and we know the relative space ship mass "m" as it was relative to the earth, then knowing how much force our engine produces we can compute the acceleration. And hence our velocity measurement device will add small "a" to the current velocity by every thrust of the engine.<p>So given that type of measurement, our smaller space ship can accelerate to the speed of 2c relative to the earth. HOWEVER, due to the relativistic effects the people living on the earth would never ever realize that this ship was moving with 2c, since they are measuring speed by looking how far the ship went in the certain amount of time. And due to the time dilation they will never realize that this ship was actually much farther away then it looks like.<p>So, regarding to this experiment, we can travel faster then the light. However, this is only due to the definition of the speed.<p>A counter argument would be that the mass "m" is also changing. However, one could argue that the mass is represented by the amount of particles per volume unit and hence remain constant if volume remain constant. Ok, another guy could argue again that the size of the volume shrinks, but I could then argue that if size of the volume shrinks, then the density of the particles per volume unit from the earth point of view would increase and could end up in a singularity or just black hole, so big bang ?:confused:<p>This kind of experiment fits well into my experience of the world, where I just cannot accept some of the constraints we get from the nature :) Yes, you cannot travel faster then the speed of light, BUT this is only because I stay at the earth and measure your speed by looking how fast you come back. But this pure guy who is traveling could measure the speed as I've proposed and would then realize that, in deed he was faster then the "earth's speed of light" :)

Wave cannot travel faster than speed of wave in medium.<p>Matter is form of electromagnetic wave, thus matter cannot travel faster that speed of electromagnetic wave in medium ("vacuum").<p>Everything that is not a form of electromagnetic wave, OR disconnected from electromagnetic medium, will be not bound to speed of light.<p>Imagine water and water waves. Water waves will never travel faster than speed of wave in water.<p>BUT, you can freeze water and push it faster than water wave just because it is not a part of water anymore.<p>I hope, super-cold vacuum (below 0K) or matter in cocoon of super-cold vacuum will be able to travel faster than speed of light.<p>PS.<p>Of course, I cannot even imagine, how we can freeze vacuum, because we cannot even interact with it.

Good explanation of space/time -- in short, you're always moving in space and time, and the more you move in space, the less you move in time. Vice-versa.<p>Brian Greene does a pretty good job of explaining all this in the Elegant Universe. If you're into this kind of thing, check it out.

Does it work in the other direction, or can you only take away time velocity to give to space velocity?<p>i.e., can you make your time slow down by coming to a full and complete "stop" in space, since I assume nothing in the universe is truly at rest?

what I don't understand is why the light is the point of reference. Just because it's the fastest "thing" we know ? Or is there some other reason ?

<i>The motion I'm referring to is motion in the futureward direction.</i><p>May be you should consider the fact, that while you are not moving- let's assume that your are in space and way far from earth or any other thing-, your brain, heart and blood do. If they don't, you wouldn't exist. It's in my believe that we are living in a single dimension world, and it's not quite different than a dream; actually it's the same thing. Just think about it ;)