Speed of light - start or finish of arguent

Cecil's Columns/Staff Reports
1

As a reformed physicist, I know all too well that the speed of light in vacuum © is widely acknowledged to be the fastest than any message can travel - and therefore the fastest ANYTHING can travel. (True, light travels faster in some materials than in vacuum, but we have the argument that the speed a message travels depends on group velocity not phase velocity, and group velocity is always equal to or less than c.)

That said:

  1. The theory of special relativity, where all this comes from, starts rather than ends with the assertion that c is the fastest anyting can travel.

  2. Special relativity works (so far as we can tell) - its predictions are borne out in experimental results, mainly (for those experiments at any where near c) with sub-atomic particles.

  3. But for hundreds of years we were all perfectly content with Newtonian mechnanics, which basically placed no restriction on maximum speed. Einstein produced a fundamental update to Newton’s theories that said there was an upper limit.

  4. Sooner or later, there is going to be a major update to Einsteinian mechanics, which may or may not remove the restriction on faster-than-light travel. We may have to wait a couple of hundred years though…

Call it wishful thinking if you like, I have always intuitively felt that the restriction is too sweeping to be unbreachable. We’re not about to start swooshing around the galaxy like Captain Kirk anytime soon, but the unverse is an inconceivably large place and it would be odd if some beings somewhere were not several steps beyond Einstein in working out how to achieve faster-than-light travel.

2

Sorry, I meant to include the references. It is:

http://www.straightdope.com/classics/a2_095.html

3

It’s wishful thinking. But you’re certainly not alone in thinking it. :wink:

4

You can say that Einstein starts with the “assumption” that c is the maximum, if you like, but it is an observed fact, older than Einstein, that no matter how fast you chase light, it is always c faster than you. Space and time actually bend themselves to enforce this.

So “faster than c” looks a whole lot like “more perpendicular than 90 degrees”.

5

And, in fact, c being the ultimate speed limit is neither an axiom nor an absolute result of Special Relativity. Einstein assumed nothing of the sort, regardless of whether it was known experimentally or not (he did know about the constancy of the speed of light, but even there, he may not have known the experimental evidence).

Now, there are two results of SR which do seem to imply that c is the absolute limit. First, we have the result that any object with mass travelling at c would have infinite energy, and any object with (real) mass travelling at greater than c would have imaginary energy. Most things we’re interested in (includin, notably, ourselves) have real mass greater than zero, and so far as we know, infinite or imaginary energies are impossible to achieve. So this is a pretty stiff barrier to faster than light travel.

But what if it’s not exactly “travel”, per se? We might imagine something like wormholes, or warp drive, which take some sort of “shortcut”, and bypass the infinite-energy problem. Here’s where the second whammy comes in: Any possible method to get from Point A to Point B sooner than light travelling through empty space would get there, can also be used for time travel. Full-out, science-fiction, kill-your-grandfather time travel. If, as many folks do, you assume that this is impossible, then one must conclude that FTL is impossible.

Furthermore, if you take a step past Special Relativity to General Relativity, you’ll find that most or all of these hypothetical “shortcuts” would require the use of “exotic matter”: That is to say, matter with negative mass. This is, again, something which we strongly suspect does not exist.

Finally, while it is certainly probable that new advancements will be made (or even have been made, by unknown alien creatures) beyond Einstein’s theories, there’s no a priori reason to assume that such advancements will lift the speed limit. It’s either possible, or it isn’t, and it doesn’t matter one whit to the Universe whether we know it’s possible.

6

Chronos, I’ve seen you claim this more than once on this board, and I think you even said that you once showed how it was so. While I don’t disbelieve it in the slightest, do you have a link to your proof? I’ve been wondering about it for some time.

7

The Special-Relativity FTL “escape clause” requires matter with imaginary, not negative mass.

General Relativity has its own possible mechanisms for time travel, though requiring very large (perhaps infinite, but that hasn’t been determined) quantities of ultradense matter.

8

Chronos is correct. General Relativity allows for wormholes in the presence of negative energy densities. Here is a Scientific American cite:
http://www.sciam.com/askexpert_question.cfm?articleID=000998FD-65C6-1C71-9EB7809EC588F2D7&catID=3

Feel free to correct the way I think of Special Relativity’s restrictions on accelerating one of us to the speed of light. The faster you travel compared to me, the slower your time appears to pass. At the speed of light, time does not pass for you (from my perspective). (That seems to imply that a massless object, which must travel at the speed of light, can not decay.) If you were to exceed the speed of light, then I would perceive your time as running backwards - thus reversing “time’s arrow”. That, in turn, would imply the actions happened “after” their causes, which would violate causality.

9

I’m not totally sure, but I think there’s an error here. The gamma factor is the mathematical representation of dilation and contraction in Special Relativity, and it’s a function of your speed. So, when you’re still, gamma = 1. As you speed up, gamma gets greater and greater, and time slows down. As you approach the speed of light, gamma goes to infinity, and time stops.

Now, what happens when your speed becomes greater than the speed of light? Does gamma become negative, which would imply that time runs backward? No, as a matter of fact, gamma becomes imaginary (square root of a negative), which would imply… I know not what.

10

Can someone explain to me why Gamma would be infinite if the velocity is c? Just look at the equation:

u²= (1/(v²-c²))

Wouldn’t that mean that if v is the speed of light, there would be no value for gamma?

11

Sorry, this is the equation, u being gamma, v velocity, and c speed of light:

u²= (1/(1-v²-c²))

My question is still valid though.

12

Make that:

u²= (1/(1-(v²/c²)))

13

Yes, time dilation goes imaginary if v>c.

Yes, 1/0 is mathematically forbidden. However, light itself demonstrably travels at c, so it must do something. In this case, it appears that 1/0 means an effective infinity, even though it’s bad math. Offhand, I believe the various algebraic lines of analysis that cause 1/0 to be forbidden break down when you try to apply them to these relativistic “word problems”, so it all works out in the end. (If there’s a fallacy in the universe and no-one can detect it, is it still wrong?)

(It is believed that light is able to travel at c because photons have a rest mass of zero. Therefore, their mass at c becomes 0/0; the answer to “What is 1/0?” is “nothing”, but the answer to “What is 0/0?” is “anything”.)

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Right, the relativistic mass of a photon can be thought of as 0/0. However, I think it’s possible to construct some physically meaningful limit that has the correct value (E = pc) as v approaches c.

15

Quoth SlowMindThinking:

That is correct. Unless, that is, it interacts with some other particle, in which case the center of mass frame has a speed less than c (it’s the center of mass frame which is most relevant in collisions). So a photon travelling through vacuum will just keep on going forever, as would a graviton (also massless), or a gluon (if you were able to get an isolated gluon, which you probably can’t).

Achernar, I went through the argument in detail in the thread The Past Through Tomorrow, but that might be a bit of a weighty read, since I was working from first principles. The gist of it is that simultenaity isn’t well-defined in SR. So if in one frame, event A occurs at the same time as event B, in another frame, A will be before B, and in yet another frame, A will be after B (but in all cases, they’ll still be spacelike separated: That is, the space part of their separation is larger than the time part). We can turn this around, as well: Given any two events A and B which are spacelike separated, I can find a frame of reference where A occurs before B, and one where A occurs after B. But this is exactly what we have in any effective FTL scheme: The two events are me leaving Earth, and me arriving at [symbol]a[/symbol] Cen, and for it to be FTL, the time at [symbol]a[/symbol] Cen must be less than four years after the time I left Earth, and the events are spacelike separated. So I can find a frame of reference, just as valid as any other frame of reference, where my arrival comes before my departure. Then, I can even find another frame of reference for the return trip, such that I end up back on Earth before I left Earth.

16

You know me; I wouldn’t have it any other way. :wink: While that answer is good, I guess it’s nothing I couldn’t have figured out myself. Correct me if I’m wrong, but if you require that dt/d(tau) > 0 in one specific frame, then you can’t time travel in that frame? And you can certainly have FTL while requiring dt/d(tau) > 0.