oldprof
Newbie

Posts: 16
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« Reply #3 on: July 17, 2011, 10:39:53 AM » |
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There are actually two theories: the special and the general. The special assumes a non accelerating reference frame and platform, and the general makes no assumption. So the general is just a less restrictive case of the special.
The STOR began when AE asked, "How can W = V + C = C" where V is the speed of an observer and C is the speed of light. W is the speed of light relative to the observer. That W = C no matter what V was doing is what Michelson Morley uncovered with their famous experiments. As you've read so much about the STOR you've probably heard of them; so I won't go into that.
After doing some mind experiments, AE decided that W = V + C = C could only happen if space dS and time dT adjusted to make C a fixed value no matter what. In other words, if the speed of light is C = dS/dT in normal space and time, then it had to be C = ds/dt when space contracted to ds < dS and time slowed to dt < dT. Or, conversely, when space expanded from ds to dS, time had to speed up from dt to dT. It's all relative (get it); it can go either direction, but C still has to be C because the experiments showed that to be true.
Once Al figured that out, he spent the rest of his days leading up to publishing the STOR figuring out the equations that would predict by how much space contracted and by how much time slowed for any platform speed V to keep C at C no matter what. And that how much is encapsulated in the Lorenz Transformation, L(V/C) = sqrt(1 - (V/C)^2). [Some write it as G(V/C) = 1/L(V/C), but I see no advantage in that.]
We find L(V/C) in dT = dt/L(V/C), M = m/L(V/C), and dS = ds/L(V/C), where dT, dS, and M are normal time, space, and inertia as seen by a reference frame, like your bedroom, for V, the speed of some moving platform, like a spaceship. We call your bedroom the reference frame because the speed of the spaceship is relative to your bedroom. Which means dS, dT, and M are relative to your bedroom as well.
Now, on board that spaceship. The relative speed of the crew is V = 0 as they are not moving relative to the ship. So their normal time is dT = dt, their normal space is dS = ds, and their normal mass is M = m, where m is the rest mass of their ship before it took off. In other words, on board that ship, everything seems, well, "normal."
But, for you, back in your bedroom, nothing is normal on that spaceship. If it were, W = V + C wold be true and experiments have shown over and over that can't be true. So you see that their normal space is actually ds < dS in your reference frame, and their time interval is shorter than yours, and their inertia is greater than it was back before the ship took off. And that, sports fans, is why W = V + C = C.
By the way. After doing a series of L(V/C) on V and C and their associated time intervals, we find that W = (V + C)/(1 + VC/C^2) is the real relative speed of light coming from that platform. For example, let V = .25 C, the ship is going 1/4 light speed. Then W = (.25C + C)/(1 + .25C^2/C^2) = 1.25C/1.25 = C. Voila, the speed of light is C no matter what that space ship is doing. QED.
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