Lets say that there are three objects in space. One object (Object A) is stationary (relatively speaking). Object B takes off in one direction away from A. Object C takes off in the exact opposite direction away from A. The two objects are moving at X speed, but wouldn’t they be travelling at 2X relative to each other? Wouldn’t that assumption mean that if Object A saw Object B going half the speed of light, wouldn’t Object C see B traveling at the speed of light? If that is the case, then shouldn’t 1/2 the speed of light be just as unattainable as the speed of light itself?
Let’s make B and C travel at .9999 light speed relative to A.
Observer A sees the separation of B and C increasing as though one of them is traveling away from the other at 1.9998 light speed. But when B or C actually does the measurement of the other’s speed, it’s always less than light speed.
In other words, none of the observers measure any of the others traveling at more than light speed relative to him (i.e., in his frame of reference).
Today we know that it is a mathematical consequence but at the time Einstein would’t have been able to realize that. He had to treat it as an assumption. It’s also not really clear whether he used the Michaelson-Morley experiment or not.
No, what it’s saying is that everything is relative. You can’t say “Bob is going half the speed of light.” You can only say “Bob is going half the speed of light relative to Alice”
Let’s go back to the OP’s example. B and C are both traveling away from A in opposite directions. From A’s point of view, both B and C are traveling at 0.5C.
Similarly, from B and C’s point of view, A is traveling away from them at 0.5C.
What about B’s view of C? According to Newtonian physics, the apparent velocity should be exactly 1C. But Einstein postulated (and experiment later proved) that when relativistic velocities are encountered, simple Newtonian math breaks down and no longer works. To find the apparent velocity, you have to use the Lorentz equation: 1 / sqrt( 1 - ( v[sup]2[/sup] / c[sup]2[/sup] ) )
B is traveling away from A at (for the sake of simplicity) 150,000 km/sec. That gives us a Lorentz change factor of roughly 1.15. That means three things:
If A could observe B’s mass, it would be 1.15 times heaver than when B was at rest.
If A could observe B’s length in the direction of travel, it would be 1.15 times shorter than when B was at rest
If A could observe a clock on B, it would be going 1.15 times slower than when B was at rest.
Similarly, an observer on B would notice the same thing about A. Because of this time and length dilation, any observations that B makes about C would be likewise affected. The net result is that to an observer on B, C appears to be traveling away at something less than the speed of light.
And to third it, particles are known that travel at .99 many nines % C.
If you do the math, two particles moving away from one another at .99 C have a relative velocity of .999949 C. Any speed short of C is attainable in theory.
On the other hand, you can’t really say that you can approach the speed of light, since no matter how fast you’re going, you’re always just as far away from c as when you started.
