How did Einstein prove nothing's faster than light?

[cmkeller]

The discussions of the "Faster than Light light-pulses" made me wonder:

I understand how certain parts of the theory of relativity were proven, e.g., that energy is just accelerated mass was proven by the way light bends around a large-massed body during an eclipse, and that time is relative to acceleration is proven by comparing clocks under the influence of different levels of gravity.

But what proved that light was the fastest thing in the universe? Surely it wasn't merely the fact that it was the fastest thing we humans have managed to observe. What makes scientists so sure that there's nothing out there that could possibly be faster?

[Myrr21]

Well, I don't remember the proof exactly, but it was done with one of his "thought experiments" and involved shining a beam of light inside a moving train. I remember vaguely that the most difficult math involved is just the pythagorean theorem. Course, I could be way off-base, but...

[Dinsdale]

An exhaustive series of time trials.
Light won consistently under all track conditions.

[manhattan]

Originally posted by Dinsdale

Light won consistently under all track conditions. Ha! Wait till next year when they introduce night racing. We'll kick them photon's ass then. Why, I'll bet the don't even qualify.

[Phobos]

My impression is that it comes from the mathematics & the description of spacetime.

good question though. Chronos?

[Whack-a-Mole]

It's all in the math. While I don't know the calculations (I'm sure Chronos or a few other can do them) it works out like this:

As you work the mathematics and increase your speed you get smaller and smaller numbers for the passage of time. If you plug in the speed of light you get an infinity...i.e. you'll never get there...time stops. You can go 99.99999999(ad infinitum)% the speed of light but you'll never cross that line.

Doing other calculations you run into other road blocks. How much energy does it take to go light speed? Do the math and it comes out infinite...there's not enough energy in the entire Universe to get you to that speed. The reason? As you increase speed you increase your mass. Reach light speed and you have an infinite mass (which would take infinite energy to move).

That last bit also has other implications that show light speed as a barrier. Time stops at light speed and you have infinite mass. You are, in effect, everywhere in the Universe at once.

I was never big on math in high school and college but it is kinda cool when you see things like the above pop out of equations. It all paints a picture if you know how to look at it.

[Dinsdale]

Sweet, manny!

[mrblue92]

Geez, I used to be able to do this (I minored in math and physics), but now four years out of college I'd probably have to look it up. IIRC, it can be done in a couple different ways, and the one that seems to come to mind used basic Newtonian mechanics combined with shifting frames of reference. The math is amazingly simple, at least for the Special theory...

[RussellM]

This is then end of a long discussion in Elementary Physics, Weidner & Sells which was the main standard text og my Physics degree.


T = T' / (sqrt(1 - v/c)^2)

This is the fundamental time-dliation equation. It is crucial that the meaning of the terms appearing in it be clearly understood. T' is the time interval elapsing between two events occurring at the same location and measured on the clock of an observer at rest at this location; T' is termed the proper time or rest time. On the other hand, T is the time interval between the same two events as registered on the clock of an observer travelling at speed v relative to the location at which the two events take place (and who, therefore, sees the two events taking place at differeny loactions relative to his rest frame). The clocks of the two observers when at rest give identical readings. This equation shows that in general T > T'; relative to a moving observer time intervals are increased, or dilated.



From this equation, we can see that as v approaches c, time intervals approach infinity - time slows down.

Experiments have shown this effect with short lived, high speed particles. From the same book

A muon is created when another unstable particle (a pion) decays; a muon decays in turn into an electron (together with two uncharged, massless particles called neutrinos). One cannot specify when any one muon will be created or decay, but the average lifetime of a large number of muons can be given quite precisely. The half life of a muon is 1.52x10^-6 seconds...if a large number of muons are in motion at speed v=0.98c, then the half life is 7.60x10^-6 seconds. Muons in flight at high speed live significantly longer than muons at rest.




Russell

[douglips]

The basic idea is that as you approach the speed of light it would take an infinite amount of energy to get you there, and your clock slows to the point where you can't do anything anyway.

I wouldn't say this 'proves' you can't go faster than the speed of light - this is a predicted limit from relativity. It is possible, though not likely, that relativity has flaws.

Finally, it is interesting to note that it is equally sound in the theory to discuss tachyons, particles whose speed can never be slower than the speed of light. It takes infinite energy to slow them down to the speed of light, and they go infinitely fast at zero energy. None have been observed, and they may not exist, but it is cool.

[Whack-a-Mole]

NOTE: The Speed of light as a speed limit only applies to 'things' that have mass. Obviously light moves at light speed along with a bunch of other massless particles. Tachyons, if they exist, have to be massless (or have negative mass which IIRC is what is required for FTL movement...needless to say none has ever been found and is hard to even conceive of as being realistic).

As an aside here's something I picked up from a semi-old sitcom with Dan Akroyd playing a single father/minister that helps you get your head around just how BIG infinity really is. In the show he was explaining to one of his sons how long 'forever' (basically infinity) is as a way to show him just how long burning in hell for his misdeeds would really take.

Imagine a giant, solid brass ball the size of the earth. Now imagine that once every hundred years a dove flies by and just brushes the brass sphere with one of its wings. When that ball is ground to dust forever will have barely begun.

Maybe it's just me but that's the best explanation I've ever had for getting a feel for how BIG infinity really is.

[Arjuna34]

As douglips mentioned, technically it's still not PROVEN, as nothing in science ever gets proven (unless make certain assumptions which reduces the question to a mathematical proof).

Countless experiements suggest that relativity is an accurate description of the world, but it could all come crashing down tomorrow with a new observation.

I wouldn't hold my breath though :)

Arjuna34

[handy]

cm, you need to understand what a 'theory' is. A theory is just that, it's NOT a truth.

As for light, surely anything that light is made up of must be faster than light itself, ja?

[KeithB]

As was pointed out, Einstein did not *prove* that the speed of light was the fastest thing in the universe. He axtually took that as one of the *postulates* for relativity. Though it is better stated that the speed of light is the same for all observers.

It was Michaelson and Morley that showed that light had the same speed for all observers. They showed that light coming directly towards the earth had the same speed as light coming from behind the earth, where "forward" and "behind" are relative to its orbital motion. This was a big surprise at the time.

[Phobos]

Originally posted by handy
As for light, surely anything that light is made up of must be faster than light itself, ja?

aren't photons fundamental particles? or are they non-baryonic?

[JonF]

As KeithB said, the principle that nothing can travel faster than light is essentially one of the postulates of special relativity, or it can be directly derived from alternate statements of the second postulate. That is, if things can travel faster than light then all the predictions of relativity are wrong to some degree, and many of the are way wrong. We know that the predictions of relativity are pretty darned good under all but the most pathological circumstances, therefore it is essentially impossible that information or known particles can travel faster than the speed of light. Foundations of Modern Cosmology - Chapter 7: The Special Theory of Relativity (http://astsun.astro.virginia.edu/~jh8h/Foundations/chapter7.html).

[Konrad]

I think KeithB has got it right. Einstein didn't prove that nothing can go faster than light. That was an idea that was being thrown around already. He just figured out what would happen IF it was true.

[Achernar]

Quoth Phobos: "aren't photons fundamental particles? or are they non-baryonic?"

Photons are fundamental particles, so as far as we know, handy, they're not made up of anything smaller. (Or did you mean that photons travel faster than light?) However, even if they were, I don't think that it necessarily follows that these sub-photons would go FTL. They're also not baryons, although I don't see what that has to do with it.

And I believe everyone else explained pretty well Einstein proving the Universal Speed Limit - Einstein didn't prove jack, or even try. He just sat around all day with his dusty old blackboard and his Nobel Prize, thinking stuff up, and made everyone else do the dirty work.

[DrMatrix]

I can see how "The speed of light the maximum possible speed" implies "The speed of light is the same for all observers". I don't see how the second statement implies the first. The second does imply that nothing can accelerate past the speed of light, but I fail to see how it implies nothing can go faster than light.

I'm not saying the two statements are not equivalent. I just don't see it.
Originally posted by Achernar
Einstein didn't prove jack, or even try. He just sat around all day with his dusty old blackboard and his Nobel Prize, thinking stuff up, and made everyone else do the dirty work. And that is why the man was a genius!

[Achernar]

DrMatrix, just when I was about to go through a big elaborate Mathematical proof showing you your shortcoming, I realized you were right. Special Relativity, as you noted, does not state that "The speed of light the maximum possible speed". Rather, it states, as you said, "that nothing can accelerate past the speed of light". In fact, particles travelling faster than light, like the tachyons mentioned by douglips, are consistent with the Theory. Of course, tachyons, while a cool idea, are not known to exist. Perhaps another way of stating this aspect of the Theory would be:

"As far as mundane objects, like atoms (and as far as we know, everything in the entire Universe), are concerned, nothing can go faster than c."

"And that is why the man was a genius!" Yeah, I know. I'm just jealous. :) I've applied for the position of genius many times, but I keep getting turned down!

[RickG]

Originally posted by DrMatrix
I can see how "The speed of light the maximum possible speed" implies "The speed of light is the same for all observers". I don't see how the second statement implies the first. The second does imply that nothing can accelerate past the speed of light, but I fail to see how it implies nothing can go faster than light.

I'm not saying the two statements are not equivalent. I just don't see it.

It's all about causality. If the speed of light is the same for all observers, and it is possible to transmit information (information is what may not go FTL), then there exists an inertial frame in which some information is received before it is transmitted.

If we believe in causality (i.e. that observations must *follow* in time the events that are being observed), then one of the antecedents in the if-then statement above must be false. Since we have observed, to incredible precision, that light does indeed have the same speed for all observers, then it must be that nothing *can* go faster than light. Or strict causality may not be true, in which case all bets are off (since we could build a time machine and break the bank at every gambling establishment in the world :)).

Like it or not, it appears that our space-time is just built this way. Apparently, God must be a very good mathematician to have made this all work out so neatly :).

Rick

[Chronos]

Wow, a lot of these threads lately... Makes me feel right at home :) Wouldn't you know it, too, I'm exactly three posts too late to add anything to the discussion: DrMatrix mentioned the restriction on accellerating past c, and RickG mentioned the causality problems. Mind you, some of us don't really see why unidirectional causality is so necessary, but that's getting into philosophy, there.

Oh, and just so I don't waste this post, tachyons would have to have an imaginary rest mass, not a negative, in order for their relativistic mass to work out to be real. For some reason, nobody seems to want imaginary masses...

[cmkeller]

Chronos:

For some reason, nobody seems to want imaginary masses...

And certainly not the Pope. :D

Thanks for the replies, guys.

Chaim Mattis Keller

[PaulT]

All of you who are so anxious to postulate tachyons should remember why they are not believed to exist: anything travelling faster than light (in any medium) emits Cerenkov radiation, a sort of sonic boom of light waves. Tachyons, in addition to expending much of their own mass/energy creating that Cerenkov radiation, would also be easily detectable because of it. Until that radiation is detected, it's safe to say tachyons don't exist.

[Chronos]

Very true, PaulT, except that Cherenkov radiation requires that the particle be able to interact easily with some portion of its surroundings, most typically via an electric charge. All that the nondetection of tachyonic Cherenkov radiation prooves is that tachyons, if they exist, are very weakly interacting. If they were as elusive as, say, axions (a theoretical particle not yet observered) are believed to be, then there'd be no problem with us having not yet detected them. That said, though, they're still considered pretty durn unlikely.

[jb_farley]

also, PaulT, when a tachyon loses energy, it goes faster. it's the exact opposite of matter; the more energy you add, the slower it goes, but it can never get as slow as c.

so if they did expend their energy bustin out action cherenkov style, the would go faster, hence spouting out more c-type radiation. if tachyons were not weakly interacting, they would quickly blow the universe up in a rather graceless way.

but that's assuming that they exist.

[The Ryan]

Originally posted by PaulT
All of you who are so anxious to postulate tachyons should remember why they are not believed to exist: anything travelling faster than light (in any medium) emits Cerenkov radiation, a sort of sonic boom of light waves.
No, all accelerating particles emit radiation. If the paricle travels faster than the radiation, then the radiation is called "Cerenkov" radiation. Note that what one calls a type of radiation does not affect the amount of energy it carries.

[PaulT]

Okay -- so tachyons don't exist UNLESS they are not subject to accelerations -- i.e. massless, chargeless bosons. And last time I checked, the standard model predicted only one massless gauge boson -- the good old photon, which is NOT tachyonic.

Besides, if tachyons can't be accelerated, then they arent being acted on by forces, and are not only useless, but undetectable -- and possibly unfalsifiable.

[Chronos]

And last time I checked, the standard model predicted only one massless gauge boson -- the good old photon, which is NOT tachyonic.It also leaves the door open for other massless gauge bosons, such as the graviton. However, all of these particles travel exactly at the speed of light, not faster. As you said, tachyons are probably unfalsifiable, and so far as I know, they're not really required for any theories relevant to observable particles, either. The only useful purpose I know of for them, is they give the crew of the Enterprise something else to talk about.