Nice job on one of the tougher relativity questions, folk.
One quick comment: “C” is used to represent the velocity of light in vacuum, and that is what is a constant (the only constant) in relativistic equations. The speed of light in glass, water, or transparent penguin droppings can be whatever it’s measured to be, and will generally be less than “C” without confusing the issue.
I apologize in advance for this hijack…
[hijack] If you have a completely mirror lined room, what happens when you turn out the light? [/hijack]
I assume that since mirrors are not perfect, that the light eventually gets “absorbed”. How long would this take with current technology? (in other words, would there be a noticable delay?)
Similarly, what would happen if the mirror was “perfect” (ie-“reflected” 100 percent of the light)?
Wrong. Not trying to be confrontational, but when you start talking about light propagation in detail, it’s important to be very precise.
In the macroscopic world, light appears to move in a beam and appears to bounce off a reflector so the angle of incidence equals the angle of reflection. However, when you start looking at individual photons, neither of these things are happening.
It doesn’t know. Put very crudely and approximately, photons are emitted in all directions. The ones that are traveling in the “wrong” direction interfere destructively with each other and cancel out. The ones that are traveling in the “right” direction interfere constructively and add up to one photon traveling in the “right” direction.
The photon doesn’t bend, its apparent path (measured on a macroscopic level) bends. Our everyday mirrors do this because of the properties of the atoms (often silver) that make up the mirror. Better mirrors are made by depositing thin layers of other atoms; we can control the properties (thickness) of atomic layers much better than we can control the properties of individual atoms.
THere’s no better simple exposition of the answers to your questions, and others, than QED: The Strange Theory of Light and Matter.
The simplest answer to your question is, as someone already pointed out, that photons have zero rest mass. This doesn’t really explain much, though. This question is really like an onion in that there isn’t one answer, there are layers and layers of answers, each one correct and each one representing a different facet of what’s going on. Here’s my two layers for your consideration.
Light isn’t really moving like a large-scale particle, it’s propogating like a wave. It’s impossible to construct an analogy that won’t be sliced to ribbons, but think of it like this. Light is like sound. When you make a sound, it moves at a fixed speed – the speed of sound (which, I know isn’t a constant like c.). It doesn’t matter how loud the sound or what the frequency of the sound is, the sound wave always moves at the same speed. The reason is that it’s not really the air molecules that are moving (that’s wind). Rather, energy is being transmitted. The speed of the wave, therefore, depends on how fast the air “reacts” to the “stimulus” of energy being transmitted through it. As noted, there are enormous problems with this analogy. EM radiation doesn’t propogate through a medium, the air molecules are moving a little bit in a sound wave, etc. etc. However, I think the key point is the same. The photons aren’t really “going” at the speed of light like a particle would, space is “reacting” to the photon in such a manner as to cause the wave to propogate at the speed of light.
Even more cosmic answer. Who says the photon is moving at the speed of light? For the photon, everything is at rest. Suppose you could move along with the wavefront in a vacuum. You would be “moving” at the speed of light, or would you? From your point of view (remember, you’re not accelerating, just “moving” at c, so your frame of reference is just as valid as any other observer’s) time stops. Therefore, you would exist, simultaneously, along the entire path of the photon. As far as the photon is concerned this whole motion thing is an illusion!
Thanks for the answers folks, but while we’re on the subject of physics, I might as well ask another question since it isn’t worth its own thread. What would happen if two people are travelling apart and both are going .9c (or a significant fraction of c), i.e., how would they view one another? What if one of them tried to communicate with the other person via radio? Also, what if one of them had a propulsion system to accelerate towards the other person? What about away from?
I love that story, but it is kind of sad. It still haunts me.
But Einstein proved that light has mass, that’s how black holes pull in even light.
Fortunately this question is mostly Special Relativity, which I actually know something about.
The first way to find out how they look to each other is to discover how the other looks in each persons frame of reference. This is done using the relative velocity transformations shown here
http://cmt.hkbu.edu.hk/~bhung/rel/node5.html#SECTION00410000000000000000
with the proof of these equations being accurate shown here
http://cmt.hkbu.edu.hk/~bhung/rel/node24.html#vel
So he would see the other guy travelling at that speed and at a distance shown by the lorentz contraction equations which can be found here
http://www.phys.virginia.edu/CLASSES/252/lorentztrans.html
so now we can find out how far away person B looks to person A as well as how fast person B looks to be going to person A. At this point we can use the ‘light always travels at speed c through a vacuum’ principle to determine how long it would take a message from B to reach A (the same time it would take for A to see B waving since its all EM radiation)
Acceleration means General relativity, and is way outta my league, but I do find imagining relativistic collisions to be kinda fun, because while they might ‘appear’ to be going that much faster than they were a few seconds ago, the energy of the collision has just increased dramatically!
side note: y’know, I never really used google till I started reading this board…how did I ever survive?
Kierk
No, that’s a consequence of the fact that light has energy. Mass, energy, and even some weird things like pressures all couple to gravity: In all, there’s 16 seperate terms of what’s called the “stress-energy tensor”, which is what produces and is affected by gravitational fields. Mass is just part of that.
As for the calculus aside there, it’s possible (although maybe very difficult) to get something going at .9 c, or .9999 c, or .999999999999999999 c, or any finite number of 9s, but it’s not possible to get an infinite number of nines after the decimal point there.
A couple of years back, somebody slowed light in a near-vaccuum chamber to 38 mph. Now they say they can stop it dead, then restart it. Story below.
http://www.news.harvard.edu/gazette/2001/01.24/01-stoplight.html
If they can slow it down in one special medium, maybe they can speed it up in another. FTL fiber optic cables?
Note the distinction between mass and rest mass, Mass includes both rest mass and the mass equivalent of velocity. To give you a non-relativistic equivalent to clarify, obviously if a bullet fired from a gun hits you in the middle of the chest, it will penetrate, probably pierce a vital organ and kill you. But if you lie on the ground and I drop the same bullet that would have killed you onto your chest from a height of one foot, a minor discomfort from the impact is all you will feel. Force = mass x velocity.
Photons must travel at the speed of light. All objects in free fall with mass move in orbits around a primary, at a speed determined by the relative masses of object and primary and the distance from the primary. At the event horizon of a black hole, an abstract circumference figure around it, the pull of the hole becomes such that it reaches the speed of light. Any point within the event horizon therefore has an escape velocity greater than light, and nothing known to science can escape it, including photons.