Friday, 4 September 2009

FAQ about relativity

Einstein's Special Theory of Relativity is the key to understanding this particular question. Any reference on the subject (and I'm sure there are loads of them written for a wide range of students) will have some discussion on this. Briefly, to make an object accelerate from rest to any speed, we must expend some energy (by using a rocket engine, say). For low speeds (much less than the speed of light --- 186,000 miles per second; all all humans have traveled only at very slow speeds compared to that of light), an increase in the energy expended results in a reasonable increase in the speed of the object. However, as the SR theory says, when the object is traveling at very large speeds (= a considerable fraction of the speed of light), then an additional expenditure of energy will not result in as large an increase in speed as it would have at lower speeds. In other words, we have to expend quite a bit of energy to increase the speed by only a little bit, if the rocket ship is already traveling fast. If the rocket ship is traveling at 95% of the speed of light, a trememdous amount of energy will be necessary to make it travel at 96% the speed of light. In trying to make it travel at the speed of light, we would need to expend an infinite amount of energy --- in other words, we can't make it travel at the speed of light.
Now, every space ship, or other plane, etc., has traveled at a speed very small compared to light, so you might be wondering how we know the Special Relativity Theory is correct (why should we believe it without evidence?). Although, we have never made any large object (like a space ship) travel at a considerable fraction of light speed, experimental particle physicists are constantly making electrons and the like travel at speeds like 99% of the speed of light in particle accelerators. These accelerators only work properly because they are constructed obeying the laws of Special Relativity. To make the electrons accelerate, when they are already at 90% of the speed of light, does indeed take quite a bit more energy than would a comparable speed change when they are only moving at 10% of the speed of light. Special Relativity theory appears correct, in detail, even under the extreme speed conditions of a particle accelerator.
Since Special Relativity theory appears correct even under the extreme speed conditions of a particle accelerator, it is unlikely we will ever find a way to travel through space at a speed greater than (or even equal to) the speed of light. However, if your goal is to get from one place to another distant place in a time less than it would take to get there by normal space travel (at a speed less than light), there may be some way to get from one place to another without traveling "through the intervening space", by going through some sort of wormhole or other tunnel, but at the moment such ideas are nearly entirely speculative --- any progress in such a possiblility (if it's even possible), would have to occur in the future. But people are looking into it. An interesting reference on that would be Kip Thorne's book "Black Holes and Time Warps" which was published last year (I think).
Einstein said that if something could travel at light speed its mass would duplicate.
How could it be? Actually, here's the way it should be said: energy and mass are related. If you set up a "black box" (box you can't see into) containing some atoms, the total mass of the box and its contents will be equal to the sum of the mass of the box and mass of the individual atoms in the box. If you heat the box to a high temperature (so the atoms are moving around at high speed in the box, and thus have high energy), then the total mass of the box and its contents will be larger than if the temperature of the box is lower. Why? Because, the higher energy atoms contribute more mass to the total mass than before the box was heated. So, if you try to push on the box, you will discover that its inertia will be larger (it won't accelerate as quickly).
In a practical setup of this box containing gas, the actual change in inertia of the box (due to heating it) will be small. But, in principle, if the atoms are made to move at speeds nearing the speed of light, the mass of the box can be made very large --- even approaching infinity.



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