The thing that is behind my last statement is that in order to measure the velocity of an object we have to see it. And we don’t see it where it is now but rather where it was a short time ago, that time being determined by its distance from us divided by the speed of light. So no matter what, the speed of light enters into our measurement of velocity.
And one last thing. It might help to not think “the velocity is” but rather think “we measure the velocity as.”
Pochacco , if this is true, then it seems that light follows the same rules as all other velocities. For example, again, using 10 km/hr, if I were moving 10 km/hr relative to an observor on Earth, and someone were moving 11 km/hr in my direction relative to Earth, I would see him moving at 1 km/hr, and the Earth observor would see him moving 1 km/hr faster than me, which is 11 km/ hr relative to him. So why is light special then?
Thanks so much for all the great answers! I really wish that theoretical physics had more of a popular appeal, because the ideas contained within it are really fascinating, and I’m sure if the average person could get over his fear of it, he would find it quite absorbing.
Gestalt
See Einstein’s book. At relativistic speeds, velocities add very differently than you expect them to. (They do at normal speeds, too, but at normal speeds the differencesw between relativistic addition and simply adding velocities is essentially indistinguishable.)
Wait, I thought the theory of special relativity says that light always travels at the speed of light, because it’s like, light? Regardless of the motion of the emitting body, the apparent speed of the beam never changes, it just gets redshifted or blueshifted depending on the relative direction of the emitter.
In fact the electrons moving in a wire at a “normal” level of direct current amperage is barely moving at all, as I discussed [post=8638221]here[/post]. In alternating current (AC) the electrons have effectively no net motion; they’re just vibrating back and forth in the metal lattice, transmitting their elevated state to the adjacent electron in solid state fashion. You can accelerate electrons in a vacuum pretty fast, and a small proportion–about 1%–of cosmic radiation is caused by incoming electrons moving at relativistic speed, but normally they’re pretty slow moving creatures.
I don’t know that I can add much more to the discussion other than that although we know that the speed of light is invariant down to our ability to measure it, we don’t really know why it is the value that it is, although we can describe the behavior extensively on both the broad scale (Special and General Relativity) and on the quantum level (quantum electrodnamics, or QED, and more generally, quantum field theory). We can talk of light relative to particles with invariant mass (which have to move slower than light), and we assume that all other massless particles like gluons and gravitons move at c though we’re not actually able to measure or indeed even see these directly.
Light as an aggregate in a medium moves slower than c because it ends up being absorbed and reemitted, giving it a finite (and often very short) free mean path. Photons emitted by fusion processes in the Sun, for instance, take tens of thousands of years to worm their way out to the photosphere. On the level of individual photons, however, they’re still moving at c; even physicists working in quantum field theory, who speak in terms of statistical distributions and don’t like to commit to any absolutes will admit that photons, on average, always go at c. More or less, anyway. Depending on the breaks, of course.
Stranger
Brian Greene’s book The Elegant Universe does an excellent job, in its opening chapters, of explaining basic relativity to the lay reader. Note, the book is a survey of the latest developments in superstring theory; the first quarter or so basically lays the groundwork of twentieth-century physics so the rest of the book has a foundation for twenty-first-century developments. Superstring theory is a real head-scratcher, to be sure, and if relativity puzzles you the last three quarters of Elegant Universe will be utterly confounding. That said, the beginning of the book, laying out the basics as a context for the more recent discoveries, is one of the better summaries of relativity intended for the lay reader. Check it out.
Well, it’s not really unexpected if you follow the scientific lead-up. A rough version follows.
Okay, so people measured the speed of light with various methods way back. Of course, there was a margin of error, so they didn’t really mind that it seemed to be the same answer all the time. It wasn’t until 1887 that Michaelson and Morley thought they had enough precision in their measurements that they could use the difference they assumed was there to measure the speed of the Earth.
At the same time, people studied electricity and magnetism. They found one constant involved in the electric force law and another in the magnetic force law, sort of like Newton’s G in his gravitational force law. These were duly measured, natch.
Then people figured that since changing electric fields make magnetic fields and vice versa, the two should be able to set up self-propagating “waves” of electro-magnetic fields. When they worked out the equations, the speed these waves would have to move at turned out to be the product of those two constants from the force laws. So take the measured values of the constants and multiply them to get… the measured value of the speed of light?
Okay, so evidently light moves at the same speed as electromagnetic waves do, and it’s a short jump to realize that light is an electromagnetic wave. Cool.
Except for one weird thing: the speed of electromagnetic waves was calculated by multiplying two constants which have nothing to do with how the observer is moving or anything. So even when you and I are moving past each other we calculate the same constant value for the speed of light.
Where Einstein comes in is taking this fact from the model, combining it with the negative results from the Michaelson-Morley experiment, and saying that it’s not such a bad thing that c seems to be independent of the observer. Then he takes some math that Lorentz worked out and shows that if you use those rules for changing coordinates from one observer to another that everything in electromagnetism makes sense now. We just need to tweak classical (Newtonian) mechanics a bit to compensate.
And then gravity seems to break down. But that’s another story.
Some people like to use the convention that C = Einstein’s Constant, the speed of light that is an absolute maximum in all reference frames, and that c = the actual speed of light through a medium.
In most practical senses c in the [partial but almost complete] vacuum of space is so close to C that the difference is less than measurable experimental error. However, c can be much slower in other media like water or especially diamond.
It’s a worthwhile distinction for these threads when we are talking about mental experiments rather than reality.
It’s like so many things. If doesn’t make sense and then someone figures out how to explain it and it does.
My search-fu is weak. Is there a discussion in GQ about gravity and it’s relationship to “c”?
This thread, perhaps: [thread=311975]Why do light, radio and electricity all travel at the same speed?[/thread]
Here’s a thread that talks more generally about c and relativity: [thread=313761] Help With E=MC Squared[/thread]
And [post=8635111]here[/post] Chronos gives us the definitive answer on what we know about gravitons.
Stranger
Isn’t an absolute reference frame necesary? Consider a space ship that travels at .99 speed of light relative to earth and returns. Less time has passed on the spaceship during the trip, but relative to the spaceship the earth was what travelled at .99C. If there isn’t an absolute reference frame which frame of reference experiences the time dilation?
General Relativity deals with accelerating objects. That theory shows that time slows down on thing that accelerates. The space ship is the thing that accelerates. I’ll admit that I don’t quite understand this but someone will be along shortly I’m sure.
And the statement that you can’t tell one frame of reference from another should be that you can’t tell one inertial, i.e. constant velocity, frame of reference from another.
I like that answer David, I have not heard it before. Here’s another riddle I don’t have the background to figure.
Assuming the earth is travelling at some speed relative to the background. Does it take the same amount of energy to get to .99C in every direction?
I assume yes, but i don’t know how it works.
You assume correctly. This easy to see when you realize that you can consider yourself to be at rest in any inertial reference frame whatsoever.
As to how Einstein first came up with the idea that light must travel at c with respect to all inertial frames:
In other words he would see the electromagnetic wave to be spatial and non time varying. If the electric and magnetic fields aren’t time varying then there is no EM wave.
Look a little more closely at what I wrote and you’ll see the difference.
You’re moving at 99% of C relative to Earth. I’m on Earth watching you go by. You fire a laser beam from the front of the rocket.
You see the beam moving away from YOU at the speed of light. Since you’re flying past me at nearly the speed of light already, you naively assume that I see the beam moving at almost twice the speed of light.
But I don’t! I see the beam moving at exactly the speed of light. Since you’re moving at almost the speed of light, I naively assume that you see the beam slowly creeping ahead of you. Which, of course, you don’t.
This apparent paradox is resolved by the fact that when something is travelling at close to the speed of light time slows down and distances are compressed. So when you measure the speed of the laser beam you’re using a different clock and yardsick than I’m using.
I don’t know if it will be helpful but here is a graph that illustrates the difference in time measured by a stationary observer and one that accelerates. The chart is of the kind used by Sir Herman Bondi to explain relativity to the non-expert. If the chart is unclear and you want it cleared up just ask.
That link isn’t working for me… What page does that link from?
also… I realize that light slowed down by a medium is really not slowed down, it’s just being absorbed and reemitted… but what happens to light “slowed down” by magnetic fields?