I have a few questions about the speed of light and such. First, pretend that one was viewing a laser beam shooting across a vast space, and that the viewer was far enough away from it that he could actually see it progress across the distance. Now, if that viewer happened to have a stick or something that was long enough to reach to where the light was, could he swing it around so that the tip of the stick moved at or near the speed of the streaking light? Does this make any sense? Maybe another way of thinking about is, if a bicycle spoke were long enough, what is the maximum speed that the tip could ever achieve?
Thanks… Sorry these are dumb boring questions.
Oh, and here’s another one while I’m at it. If you set off a flash in a hollow, mirrored sphere, would the light just bounce around forever? How long would it take to dissipate into heat, etc? Hmmmmmmmm.
Hmmmm thanks for making me feel even more stupid… I’m 23 and out of college… Yeah my degree’s in music, but I got a 5 on my AP physics test in high school!
you could acheive near light speed like this… another way to thing of it is a giant pair of scissors, while the blade near the handle isn’t going very fast, the tip if the blade would be moving much faster…
or one of those really bright spotlights that car dealers sometimes have out at night… when it is cloudy, you can watch it high in the sky moving way faster than any plane could, yet the bottom of the light wouldn’t mover fast at all…
although einstein says you could never travel at the speed of light because if you did, you would have infinite mass and infinite gravity…
if you set off a flash inside a hollow, mirrored sphere, the difference in time from when the flash stopped, and how long before you couldn’t see it anymore would vary depending on how big the sphere is. if it was a small sphere, the difference may be to minute for you to notice. if the sphere was theoretically say the size of the universe, it would take some time, but it would not go on forever
Naw, those questions aren’t stupid. But then, I’m biased: I don’t think any physics question is stupid :).
First question: The end of the stick cannot move faster than the speed of light, because the stick can’t be perfectly rigid. When you move your end of the stick, the atoms at your end need to communicate to the next atoms in line “Hey, we’re moving!”. That communication is by electromagnetic forces, and electromagnetic forces travel at (you guessed it) the speed of light. Near the speed of light is a different matter: You can, in principle, get that stick going at any speed at all, so long as that speed is less than that of light (of course, this might be very difficult, but it’s possible). On the other hand, though, there really isn’t any such thing as “near the speed of light”: No matter how fast you go, you’re still just as far away from c as ever.
Second question: It depends on how big your sphere is, and how good your mirrors are. If your mirrors are perfect, and there’s nothing else in the sphere to absorb the light, then the light will indeed bunce around forever. But there’s no such thing as a truely perfect mirror, and using the best mirrors we can make, it’d still be over awfully darn fast.
First a nit. If I were located far away and shot a laser in any other direction than right at you, you would not see it. What makes a beam of light a beam, is that the photons are all going in the same direction. (Yes, even laser light will spread, but not so you could see that kind of thing.)
A better way to pose your question is to suppose a distant galaxy were to shoot some spectacular amount of mass at near light speed away from itself. This actually happens, and we see it because light is emitted every which way. You would have to move your stick very, very slowly in order to match that near light speed matter. For example, take a galaxy 1,000,000 light years away, that shoots stuff out so close to the speed of light as to make no difference. After 1 year, the speeding stuff will have moved about 1/60,000,000th of a degree.
MegaDave is talking about something quite different. Take that giant pair of scissors, say solar system size, made of some impossibly strong stuff. Try to close the scissors. While it is impossible to close the scissors so that any atom reaches the speed of light, the point at which the two “scisses” meet can exceed the speed of light. The same with shining a flashlight at the sky. No photon ever exceeds the speed of light, but the light spot can (theoretically at least) can appear to move faster than light.
Your question of the mirror also depends on the quality of the mirror. An ideal mirror, which by definition reflects all incident light at the same frequency as the incident light, would reflect the light forever. (I’m presuming that the flash mechanism is also either perfectly reflecting or totally consumed in the process of generating light.) The rate at which the light becomes heat would be a measure of the degree to which your mirror is not an ideal mirror.
Qazz, you feel bad because you’ve forgotten physics from a course you took 5 years ago??!!
The only way the scissors-cross-point could be moving faster than light is if the blades were already closing to cause this. You cannot possibly ‘close’ the blades from stationary in such a way to cause the point to move in that way because of what Chronos says – the scissors would bend.
If the blades were already moving thusly, then you orchestrated it beforehand by way of communication to rocket thrusters at light speeds.
You’re missing the point. “light speed” is a convenient but badly named label. Strictly speaking, its ‘information speed’. If you can construct an experiment where it appears that you are getting information (light, matter, anything) from point A to point B, even the closing scissor point, faster than light, then your experiment almost certainly has a flaw. Either that or you should provide overwhelming evidence to the contrary.
I’m trying to see the thought processes behind this whacky assertion but the best I can come up with is that if an observer were moving at the speed of light then light would still travel away from them at the speed of light – Is that what you’re driving at?
Quantum mechanics has produced results that seem to flout this no action at a distance - nothing-propagates-faster-than-the-speed-of-light conclusion.
Indeed, it is one of the great conundrums of modern physics – the theories of Quantum Mechanics and Einstein’s Relativity seem to be at odds with one another.
This doesn’t necessarily mean that the tip of a stick can move faster than light.
The quantum mechanics experiments that appear to show “action at a distance” in no way show that information can ever be transmitted faster than the speed of light.
If an experiment can ever show information travelling faster than the speed of light, then it also shows a time-travelling machine.
And what Chronos means is that the speed of light in a vacuum is always constant. That means that, no matter how fast your are travelling with respect to any inertial reference frame, the speed of any light that you observe will always be traveling at ~3 x 10[sup]6[/sup]km/s with respect to you. You and an observer in the other frame of reference will disagree on the wavelength of the light in question, though.
William_Ashbless, point taken about the information already having been transmitted to close the scissors. I was trying clarify what I thought MegaDave was bringing up. (The scissors example was one way of explaining why phase velocity can exceed the speed of light when I was an undergraduate. I never have bothered to see if you could set up two intersection lines so that the ends do not have to exceed the speed of light in order for the crossing point not too.) But given that you’ve set it up before hand, what information is moving faster than the speed of light when you close the scissors?
I also have a slight hijack question. Special Relativity is based on two postulates, that the laws of physics are the same in all inertial reference frames, and that the speed of light is the same in all reference frames. (I always thought the second postulate was redundant given that Maxwell’s equations show that the speed of light is determined by two constants of nature, but that is irrelevant.) From whence comes the statement that information can not travel faster than light?
I meant to add that the scissors example is a nice visual for explaining how nothing can move faster than the speed of light. In this case, “nothing” is a conceptial point, not an actual object. (Clearly the example is bogus, as the ends of the line must move at length*angular seperation/time to close, while the intersection point only moves at length/time to close.)
I also should rephrase my question about information. I too have made that claim when explaining why neither quantum teleportation nor variations of Bell’s experiment violate relativity. But, I have only seen the claim made, and then demonstrated for particular instances. I have never seen a proof that Special Relativity requires that information can not move faster than the speed of light.
the problem is you would still need to provide the energy to make the tip of the “pole” move at the speed of light. Basically it would require infinite force on your end to make the other end reach that speed.
When I studied Special Relativity the two postulates were the Postulate of Equivalence (the laws of physics and therefore the speed of light are the same in all inertial frames of reference) and the Postulate of Simultaneity (a definition of what it means for two events to be simultaneous).
If you work from there you discover that simultaneity varies from frame of reference to frame of reference, and you end up deriving the Lorentz transformations. When you examine these you discover that anything that is faster than light travel in any inertial frame of reference is travel backwards in time in certain other inertial frames of reference. Since it is taken as axiomatic that information cannot travel backwards in time, it follows that it cannot travel faster than light either.
Agback, I understand 2. I know that no material object can move faster than light, and that massless objects must move at the speed of light.
But, phase velocity can certainly exceed the speed of light. Also, some quantum experiments have been done where light exits a chamber faster than light can propagate through a vacuum. It is not obvious to me that there is some law of nature prohibiting gleaning information faster than light in such examples. All I have ever seen are demonstrations how in any given particular case, information does not exceed the speed of light.
There must be some proof along the lines that even though information is not a physical object, it must always be transmitted by a physical object (vice phase velocity, e.g.).
Agback just gave the proof that information cannot exceed the speed of light. If you can transmit information FTL, then you can also transmit it back in time. And if you can transmit information back in time, then you get all sorts of fun things like the Grandfather Paradox, which most people consider to be impossible.
As to how a perfectly rigid scissors (if such could exist, which they can’t) could transmit information FTL: Suppose I have a pair of scissors stretching from here to Alpha Centauri. Since the Centaurians can’t get ESPN, they’ve asked me to let them know how the Superbowl goes. So, we agree on a code where one scissor-closing means the AFC team won, and two closings mean that the NFC team won. Five minutes after the end of the Superbowl, I go out and squeeze the handles of the scissors, either one or two times. They were never opened very far, and it only takes me a couple of seconds for each squeeze. So minutes after the end of the Superbowl, sports fans four lightyears away know who won. Beecause of the causality problems mentioned above, this isn’t allowed. What’s wrong? The scissors can’t really be perfectly elastic, like I assumed.
I’m 23 and out of college… Yeah my degree’s in music, but I got a 5 on my AP physics test in high school!