Speed of Light and Time

[Bob Hegwood]

You probably didn't expect to see a Brain-Dead geezer in
the Physics and Astronomy Forum, but I have a serious
question for those of you who are "In the Know."

How is it that the speed of light is as fast as anything can go?
How do we know this? From Einsten's equations? Hawking's?

Wasn't the speed of sound supposed to be the fastest speed
that an airplane could go at one time? And, why does time
slow down and eventually stop the closer one gets to the speed
of light?

Sorry, just curious. Is it not possible that particles, ions, or
rays of some kind which we know nothing about as yet could
be travelling faster than the speed of light? How would we
even know about them if such is happening?

Thanks, Bob

[granthutchison]

In the 1880s, a couple of scientists called Michelson and Morley did an experiment to find out how fast the Earth was moving relative to the "ether" - the mysterious, ethereal substance it was then imagined that light travelled in (in the same way sound travels in air).
This involved <skip lots of detail> measuring the speed of light on the surface of the Earth. You can imagine that if you were pelting along in an open train at 500mph and measured the speed of sound between the back and the front of the train, you'd end up with a figure of 200mph instead of the 700mph you'd measure in a stationary train ... the difference occurs because the train is moving through the medium the sound travels in. Since Earth had to be moving through the ether, Michelson and Morley expected to find a similar influence on the speed of light ... one that changed as the Earth moved around the circle of its orbit.
Instead, they found no variation in the speed of light with the direction the Earth was moving in - it was always the same.
This was a great puzzle, and it needed Einstein to come up with the weird predictions of Special Relativity in order to explain it. If we measure the speed of light to be always the same no matter what our state of motion, then something must be happening to our measuring system to make this so. He said that our time rate must be slowed and our measuring instruments shortened in the direction of travel. He also worked out that it would require infinite energy to accelerate an object with mass to the speed of light ... because we can't have infinite energy, it therefore follows that nothing in the Universe can accelerate a particle with mass up to the speed of light. Only massless particles (like photons) can travel at lightspeed (and they're forever fixed at that speed).
So it started with a puzzling observation, followed by an extraordinary explanation. Probably the most amazing thing about this is that Einstein's predictions for the behaviour of objects close to lightspeed have been extremely well-tested (using particle accelerators), and it would appear that the Universe does work to the laws of Special Relativity ... it does turn out to be harder and harder to accelerate a particle the closer it gets to lightspeed; and it does turn out that an unstable particle can exist for longer (from our point of view) before decaying if it is travelling at close to lightspeed (time is passing more slowly for the particle than for us).

(The problem with aircraft and the speed of sound was an engineering one, rather than a property of basic physics - engineers were worried they couldn't build an airframe and control surfaces robust enough to tolerate the shockwave generated when the aircraft hit Mach 1.)

Grant

[Bob Hegwood]

Hey Mr. Hutchison,

Thanks *very* much for that laymen's explanation. I even understood
it.

Basically, you're saying that - since there is no "Doppler" effect where
light is concerned, that THAT's why the special theory of Relativity had to
be constructed?

Interesting stuff. Surely there is more that we don't know though isn't
there? Mr. Hawking has modified the theory in some drastic ways
too, hasn't he?

At any rate, the explanation was much appreciated.

Thanks again, Bob

[granthutchison]

Basically, you're saying that - since there is no "Doppler" effect where light is concerned, that THAT's why the special theory of Relativity had to be constructed?

Not quite. The Doppler effect relates to changes in frequency (of sound or light) rather than speed. You can still see changes in light's frequency because it's coming from a moving source ... the "red shift" of distant galaxies because of the expansion of the Universe, for instance. But even though those galaxies are moving relative to us at a substantial fraction of the speed of light, Special Relativity says that physicists in those galaxies would measure the speed of light in their laboratories to be exactly the same as we find it to be on Earth. Einstein is saying that Michelson and Morley observed a fundamental law of the Universe ... the speed of light is always found to be the same, no matter how fast you're moving when you measure it.

Surely there is more that we don't know though isn't there?

I'm sure there is ... but Special Relativity is one of the best-tested physical theories ever; scientists have made careers out of looking for deviations in the umpteenth decimal place. So if there are deviations or loopholes, they're occurring under extreme conditions we haven't encountered yet ... which isn't to say such conditions can't possibly exist.

Mr. Hawking has modified the theory in some drastic ways too, hasn't he?

I'm no expert, but I don't think he's done anything to Special Relativity ... that's one of the "givens" underpinning the sort of stuff Hawkings is involved in, rather than an area theoretical physicists are going to be messing with.

At any rate, the explanation was much appreciated.

Pleasure. I have a bit of a bee in my bonnet about pointing out that Einstein didn't just make this weird stuff up for the heck of it ... it was very specifically tailored to explain Michelson and Morley while keeping the rest of physics intact.

Grant

[Guckytos]

So if i remember my books correct, the theory does not forbid the possibility, that particles with speeds greater than light exist. Scientists discuss about them and even make experiments to find out more.
BUT: The theory also says that if these particles exist, the speed of light is the lower limit of speed that they can reach. And these particles can't interact with normal matter.

So the speed of light could be described as a barrier between normal physics, as we know it, and a possible FTL-physic. One can't switch from one speed to other, at least as far as we know for know and probably for quite some time to come.[/b]

[Slalomsk8er]

Did you know, light can be a lot faster then light!!!

If you take light away the freedom to oszilate, updown movement is converted to forward movement (tunneling). This means as I understand, that it is possible to move faster then light moves forward but not fasters as the light total movement is!?

I am not sure on this but isn't the light forward speed diverent in diverent medias?

[ajtribick]

I seem to remember something along the lines that while it is possible to send light faster than light in a vacuum, no information can be transmitted in this way, thus preserving causality - same applies to spooky action at a distance.

[ElPelado]

I dont know if this is true, and we may never prove it, but I read once that traveling at normal speeds we go forward in time. Traveling near C we also go forward, but the time passes slower. If traveling at C time stops, and if traveling faster than C, time goes backwards, or, in other words, something traveling faster than C goes back in time...
But as I say, we may never prove that because we dont know anything traeling faster than teh speed of light.

Now that I remember, a couple of years ago(more than 3, maybe 5) I read in the newspaper that scientis had succed in making some particles(or mayeb atoms) to travel faster than the speed of light. It seems it was just a bad interpretation and it wasnt really faster than C...

[eburacum45]

The experiment at the NEC which sent a pulse of light apparently faster tham light in fact was a phenomenon linked to group velocity in the waveforms;
the waveforms travelled faster than light within a beam of light which itself was only travelling at light speed. No information can be sent by this method, and so relativity is still valid.

Quantum tunnelling occurs over small distances, and as I understand it cannot be used to tranfer information without the use of a classical light speed channel; so the speed of light remains an effective maximum for information transfer.

[Bob Hegwood]

Not quite. The Doppler effect relates to changes in frequency (of sound or light) rather than speed. You can still see changes in light's frequency because it's coming from a moving source ... the "red shift" of distant galaxies because of the expansion of the Universe, for instance.

Okay, Thanks again for the enlightenment. If I truly understand what your
trying to tell me then, the following would apply:

Measuring the speed of sound waves while you're travelling at 700 mph would
result in the measured sound waves travelling at 20 mph - relative to the observer.
Yes? That is, if the speed of sound is at 720 mph. Sorry, I forget the exact speed.

On the other hand, if an observer of the speed of light is travelling at 150,000
mph, you're saying that the measured speed of the light would still be 186,000 mph?

This is fascinating. Do I understand you correctly now?

Thanks very much for the watered-down explanations. I ain't much on
brains, but I *love* this stuff.

Also, if I understand you correctly again, you're saying that nothing with
mass can travel as fast as the speed of light, no matter *how* much
propulsion you use. Would this supposition also apply at the event horizon
of any good-sized black hole? Seems that the infinite supply of energy
- in the form of gravity - might be able to propel something with mass
at least very *close* to the speed of light. Yes?

Sorry for the dumb questions, but I really am interested in this stuff.
Thanks again for your patience in trying to explain it to me too.


Take care, Bob

[granthutchison]

On the other hand, if an observer of the speed of light is travelling at 150,000 mph, you're saying that the measured speed of the light would still be 186,000 mph?

You've got it (but that's 186,000 miles per second for the speed of light). And the observer we think is travelling at 150,000 mph would be quite entitled to consider herself at rest and to marvel at how we, travelling at 150,000 mph in the opposite direction, manage to also measure the speed of light at 186,000 mps. That's where the word "relativity" comes in - everything is relative, because there's no absolute standard of what is stationary and what is moving, simply because of this game the speed of light plays with us.

Also, if I understand you correctly again, you're saying that nothing with mass can travel as fast as the speed of light, no matter *how* much propulsion you use.

Yup. More and more energy required for each tiny additional bit of velocity.

Would this supposition also apply at the event horizon of any good-sized black hole? Seems that the infinite supply of energy - in the form of gravity - might be able to propel something with mass at least very *close* to the speed of light. Yes?

Yes. We can't see deeper into a black hole than its event horizon, which is the surface at which escape velocity reaches the speed of light. Now, if the escape velocity at the event horizon is equal to the speed of light, that also means that an object falling in from infinitely far away would hit lightspeed just as it crossed the event horizon. Objects going in from closer than infinity get close to light speed, but don't quite reach the mark (because they're not falling from high enough).
What happens deeper inside the hole? Well, we can't ever know directly, because there's no signal can reach us from in there!

Grant

[Cham]

Now, if the escape velocity at the event horizon is equal to the speed of light, that also means that an object falling in from infinitely far away would hit lightspeed just as it crossed the event horizon. Objects going in from closer than infinity get close to light speed, but don't quite reach the mark (because they're not falling from high enough).
What happens deeper inside the hole? Well, we can't ever know directly, because there's no signal can reach us from in there!

Grant

Actually, the observer's velocity at the horizon is always light speed, whatever his initial position and initial velocity, relative to any stationnary observer standing outside the horizon. But there's a very bizarre thing happening here : the falling observer appears to be "slowing down" in some way because he's taking more and more time to reach the horizon.

Actually, to the stationnary observers outside the horizon, the falling one is taking forever to reach it and never cross the horizon. I'm not talking about the gravitationnal redshift of light or about any Doppler effect. This stretching of time is a strange consequence of the non-euclidian geometry around the black hole.

A simple diagram of space-time could illustrate these weird effects, as the "light cones" becomes very stretched near the horizon and tend to tilt toward it.

[granthutchison]

Actually, the observer's velocity at the horizon is always light speed, whatever his initial position and initial velocity, relative to any stationnary observer standing outside the horizon.

Well, I can see how that works in a handwaving sort of way, when you reckon that infinite potential energy minus any finite quantity of potential energy still leaves you with infinite potential energy.

However, the space-time diagrams I've seen of stellar collapse or objects falling into black holes quite clearly show the infalling particle threading the tilted light-cones along a time-like path - implying that the crossing velocity is below the speed of light. Here's a sample of such a diagram (the first good clear specimen I ran across in a web search). Notice how the infalling particle doesn't go lightlike until it reaches the singularity. Am I missing some subtlety?

(Original context: http://www.etsu.edu/physics/plntrm/relat/blackhl.htm)

Grant

Edited to provide original context of diagram

[Cham]

Notice the vertical axis on this figure. It is not about the t coordinate versus the r coordinate. It's not about the local stationnary observers coordinates. It's using another coordinate system. When you draw the similar picture with t and r (the coordinates used for the Schwarzschild metric in its standard form), you get light cones which shows the falling observer is moving with the speed of light. I can find the proper drawing, but I can't paste it here (I don't have any iDisk, or something like this).

The point is, velocity is relative. For the falling observer, we can cross the horizon in a finite proper time without any trouble. But for the stationary observers (another coordinate system), we get another velocity (light speed). This is related to the fact that the Schwarzschild coordinates (t and r) are singular at the horizon.

[selden]

Cham,

What you need to do to post an image on the Forum is to put the image on a publicly readable Web page and insert its URL into your posting.

Unfortunately, most free web services don't allow direct links to images. They want you to use html pages so that people get to see the advertisements that are defraying their costs.

Of course, if you have a colleague who just happens to have such an image on the Web server where he works, then you could use that URL.

[granthutchison]

Oops, no, it's okay, I've just found Roger Penrose's Gravitational collapse: the role of General Relativity, which neatly shows the exact situation of interest in both coordinate systems - it seems all those pop-sci diagrams labelled simply but boldly Time (up), Space (across) are in Eddington-Finkelstein coordinates, for cryin' out loud. Sure enough the Schwarzschild coordinates show the light-cones smushing in a completely different way from what I've looked at in the past.
Thanks, Cham. I presume the E-F graph is common in pop-sci because people like to think about what happens to the infalling observer after the event horizon is crossed, which I see now that Schwarzschild can't portray.

Grant

[Cham]

Yes, there's a lot of confusion out there on the web, about general relativity. This is because we can use all sorts of coordinates system, and we CAN'T interpret the coordinates as something physical, like in the rest of physics.

For example, t and r (in the Schwarzschild metric, standard form) DO NOT represent the time and the radial distance, respectively. They are only labels, coordinates. This is very important to understand general relativity. Actually, t represent the true proper time of only the far away stationnary observers, which are standing at infinity. The r coordinate isn't even the radial distance from the black hole ! This is why many people got confused in the past.

[granthutchison]

Yes, there's a lot of confusion out there on the web, about general relativity.

Disappointing, though, to find Luminet and Thorne using the E-F diagram in popular books without providing a simple caution like yours. Fair enough, they often point out elsewhere that the Schwarzschild "radius" is an unfortunate and misleading derivation, but the power of a diagram can shove that knowledge to one side when you're looking at it.

Grant