by jinydu » Tue Aug 31, 2004 12:35 am
Ok, I'll do my best to answer some questons and show my thoughts.
For the question of why light doesn't travel at infinite speed, there are various ways I can try to explain it. For particles with mass, the amount of energy needed to accelerate the object approaches infinity as it approaches the speed of light. Thus, you could think that if the mass got smaller and smaller, it would take less and less energy to get closer and closer to the speed of light. If the mass reached zero, it would take no energy to reach the speed of light. However, the above explanation is flawed because it puts zero mass up against infinite energy, and assumes zero mass will win, which is not logically rigorous. Another way to think about it is that if light traveled at infinite speed, the Theory of Relativity would fall apart. Relativity does not try to prove that the speed of light is always constant at a finite speed. It takes that as a given (a postulate) and derives the consequences. On the other hand, Maxwell's theory of electromagnetic waves does derive (not assume from the start) that all observers obtain the same measurement for the speed of light. You could look into Maxwell's theory if you want to know more about why the speed of light is always constant and finite, but the mathematical calculations are quite complicated.
I'll interpret the second question as asking why the speed of light has the value that it does. The answer is that we don't really know. One idea is the anthropic principle: If the speed of light had a significantly different value, life would never have been able to form and we wouldn't be around to measure the speed of light. Since we are around to measure the speed of light, its value cannot have a significantly different value. For obvious reasons, many people don't consider this a very satisfying explanation. However, its important to keep in mind that in any theory, everything must be proven, in a finite number of steps, from basic postulates that are assumed to be true. A child can ask you "Why ____ _____ ...", and then use your answer to pose another why question, then use that answer to ask another why question, and so on. The child can keep asking why forever, but the rules of logical deduction say that at some point, you have to stop and say "That's just the way it is."
I learned in my Physics class that light does not have mass, but it does have momentum. The momentum of a photon is given by p = E/c, where p is the momentum, E is the energy and c is the speed of light. Thus, in the Theory of Relativity, there are things that have no mass but do have momentum and energy.
I assume that by "gap", you mean space that is not occupied by any particle, such as the vacuum (or very near vaccuum) of outer space. That space will never be filled up (unless the Big Crunch idea is correct, and the Universe contracts back into a singularity in a Big Crunch at some time in the future). Suppose you release a gas to fill up this space. As the gas expands to greater and greater volumes, you will eventually reach a point where there is, say, only one atom per cubic meter. But an atom is much smaller than a cubic meter, so you have mostly empty space.
I think that your question about infinity and zero is really a philosophical one, rather than a scientific one. Thus, I don't really know how it can be answered definitively. You could say that something with zero length doesn't exist, but relativity shows that things with zero mass can exist. As for infinity, if you claim that the singularity at the center of a black hole has zero volume, then you can say that the density at the singularity is infinite.
Well, those are my thoughts. Hope this helps.