Thursday, February 16, 2006

Q. How can velocities always be smaller than c?

A. "How can velocities always be smaller than c as required by special relativity - if there are two rockets moving away from each other with velocities of .5c each relative to the earth, won't they have a relative velocity of c to each other?"

In relativity, there is a formula for addition of relative velocities that limits the relative speeds to less than c:

this can be obtained from the Lorentz Transformations - the relations that give the transformations of space and time between observers with different relative velocities.

As can also be seen, in the classical limit of very small velocities, v1*v2/c2 is approximately zero, so the relative velocity goes to the classical, intuitive (Galilean) value.

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