Originally posted by Hortlund
I'm sure you all remember this from high-school physics, but if you sit in a car that travels at 25 m/s and fires a gun forward, and the speed of the bullet is 300 m/s, then the speed of the bullet will be 325 m/s. And if you turn around and fire it backwards, the speed will be 275 m/s. The same is not true of the speed of light, because the speed of light is constant irregardless of the relative movement of the observing or moving body. That is what I mean when I say that the speed of light is a constant.
Take the sun as an example, it revolves around the center of our galaxy at a modest 217 000 m/s. A photon, or ray of light if you will, that leaves the "front of the sun" (i e in the direction of movement) will have the speed 299 792 458 m/s, and not (as one might expect from the car example) 299 792 458 + 217 000. Meanwhile a photon leaving the back of the sun will ALSO have a speed of 299 792 458 m/s and not 299 792 458 - 217 000.
I dunno if there are any physics nerds here who can tell me if we have found an explanation to this, because me being a law-nerd really have no idea, and back when I was in school, no one had the answer to that question.
The correct formula for adding velocities is not
V = u + w
... but ...
V = (u + w) / (1 + u*w/(c^2))
This is true for fast photons as well as for slow cars and bullets. It is just that when u and/or w are small, the denominator is very close to a 1, and the formula "simplifies" to
V = u + w
Since most of the velocities we dealt with until XIX century were very small in comparison with c, no one has noticed that V = u + w is not correct. The approximation is very close.
If one of the velocities you are trying to add is a c (u = c), the formula reduces to
V = (c + w) / (1 + c*w/(c^2)) = (c + w)/(1+ c*w/c^2)) = (c + w)/(1+w/c) = (c+w)*c/(c+w) = c
regardless of what w is.
Speed of lightThink about it this way. There is an absolute speed limit and it is exactly the same in all (not accelerating) frames of reference . Since all frames of reference are equivalent (a principle of special relativity), it follows that the max achievable speed should be the same in all of them. If it weren't you would be able to tell the difference between them and single out certain "special" frames of reference, which would violate the principle of the theory.
This speed limit is denoted as c.
Now, it just happens that photon in a vaccuum travel with the maximum achivable speed (c). As an unfortunate result physicists "equated" the two. This resulted in a very popular (but incorrect) statement:
"Speed of light is the maximum speed possible."
The statement above is false. What is true, is:
"The light travels (under certain conditions) at the maximum achievable speed c."