Re: Is the speed of objects relative to each other limited to the speed of ligh

Hi Steve,

	I don't think you're HOPELESSLY confused about anything. Relativity
*is* confusing, especially at the start. That's what made Einstein
such a genius. He was willing to postulate that something was true --
namely that the speed of light is constant, nothing can travel faster
than it, and (here's the fundamental part) no matter what the observer
is doing, they will ALWAYS measure the same value for the speed of light,
even if they are moving at nearly that speed themselves. This seemed
"crazy" to many people then and now, but it turned out to be true!

    Here's how it works. The physics of everyday life is familiar to 
anyone who studies Newton's laws of motion and all that. Normally 
you think that velocities are additive: if two objects are traveling
in opposite directions at 100 mph, then each one "sees" the other as
moving away at 200 mph. It all makes perfect sense, and you can do 
experiments to prove that it works out that way. 

    HOWEVER, when things are moving at a significant fraction of the
speed of light (c = about 186,000 miles/sec), the simple, intuitive
picture breaks down. Our intuition is based on everyday life where nothing 
ever goes that fast, so it doesn't really "make sense" but experiments
have in fact confirmed that Einstein was right. Using relativity theory
the "addition" of velocities is a bit more complicated:

To use your example, suppose you have two objects A and B. Each one is 
moving at 0.75c (three-quarters the speed of light) relative to a 
stationary observer between them. What is the speed of one, relative to
the other?

Let's call the answer v', and the speed of A = u, the speed of B = v
and in this case u = v = 0.75c

The formula that gives the correct answer is the following:
    

             u + v          0.75c + 0.75c         1.5c
     v'  =  --------   =    -------------     =   ----------- = 0.96c 
                  uv              (0.75c)^2            9 c^2
             1 + ----        1 +  ---------       1 +  ------
                  c^2               c^2                16 c^2


You can prove to yourself that this more complicated formula still works
for everyday speeds, and gives the usual result that when both are much
slower than c --  the velocities are additive in the normal way. This 
formula is more general than the usual v' = u + v because it holds for all 
possible velocities from zero up to c, but no one ever realized that things
are more complicated when the speeds get really large, unitl Einstein
gave us his theory (special relativity). I hope this helps. And don't
worry, the more physics you study them more examples you'll find of things
that don't behave the way we expect, if the conditions are far removed
from what we normally experience. Quantum theory describes how tiny
particles and waves behave, and weird things can happen at very low
temperatures (like superconductivity or superfluidity) as just a few
examples. Physics is actually fun, you know!