Re: Is faster than light motion impossible due to spacetime contraction?

Date: Mon Mar 13 06:23:45 2000
Posted By: Samuel Silverstein, faculty, physics, Stockholm University
Area of science: physics
ID: 951981080.Ph

Message:

William,

You have clearly spent quite some time reading and understanding the relativistic formulas, and certainly have a good idea of how they work. If I understand your questions correctly, you want to know "why" light is constrained to be constant by the theory of relativity. Unfortunately this turns out to be a "chicken and egg" sort of question, as I will try to explain...

The Special Theory of Relativity is based on two postulates, or assumptions which themselves need to be accepted before you accept the theory. This is not unique to Relativity; any logician will tell you that it is impossible to build any theory without some independent postulates. The trick is to use postulates that you can trust. :-)

Anyway, the two postulates of Special Relativity (SR) are, simply stated:

The laws of physics are the same, no matter what inertial reference frame you choose to do an experiment in, and
The speed of light in vacuum is a constant, in any reference frame that you choose to measure it in, and independent of the velocity of the source.

The first postulate is often called the "relativity postulate", and is based on our "common sense" understanding of the everyday world. The second postulate, which says that the speed of light is constant, is based on years of scientific evidence, going back to the Michelson-Morley experiment in 1887. These postulates must be taken "for granted" if you use SR. So far, they have withstood the test of time.

So the constancy of c as a cosmic speed limit is "hard-wired" into SR. You can't actually derive it from the theory, since it was there from the start.

Regarding accelerating a massive particle to a speed faster than c: you can try, but it wouldn't work. As you know, the energy E of a massive particle is:

              2
            mc 
E = -----------------
               2   2
    SQRT( 1 - v / c )

You can get the particle going really close to c, but the closer you get the smaller the denominator becomes. At v=c, you are dividing by zero, and E becomes infinite! Therefore, you would need an infinite amount of energy to accelerate a massive particle to the speed of light. That means that not even an infinite amount of energy is enough to get a massive particle going faster than c!

I think of the imaginary numbers that you get when you calculate the masses, energies or dimensions of superluminal objects as "non-physical" quantities. That is to say, you could never see them within the boundaries of our universe. Beyond the event horizon of some black hole is another story, but since you can't get any information on your observations back out of the black hole, then we're safe :-)

A very good introductory textbook on SR is Introduction to Special Relativity by James H. Smith. It is a thin book with a lot of good explanations and examples, as well as a straightforward, algebraic treatment of the math. I would recommend it to anyone wishing to understand relativity.

I hope this helps.

Cheers,
Sam Silverstein

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