|MadSci Network: Physics|
Dear James, This is an excellent question and it hits upon the fundamental idea behind Relativity – the universe doesn’t know the difference. That is to say, for a rocket moving past the Earth at 0.95c, the rocket will measure a clock on the Earth do exactly the same thing as the Earth would measure a clock on the rocket do. Both would measure the other as going slow. How is that possible, and what does it mean? We are used to thinking that time and space are two separate and distinct things. This is not correct when things start moving around at high speeds. The problem here hinges on the concept of simultaneity, or being able to say that two things occur (in physics we would say two events occur) at the same time, that they are simultaneous. Let me refer to the ship and Earth as “frames of reference”, this is the standard term that is used in relativity. In general, two events that are simultaneous in one frame are not simultaneous in another. To understand this, we must ask ourselves to be very precise about how one frame would measure a clock in another frame. Let’s say that the Earth wants to measure the rate at which a clock is ticking in the rocket ship. To compare two clocks, they must be side-by-side, if not, you would have to worry about the time it takes for the light to go from one clock to the other, and the frames might disagree as to the amount of time the light spent traveling. To avoid this, we will say that clocks must be next to each other to compare them. Let’s say that the Earth will measure how much time it take for the rocket’s clock to tick from 12:00:00 to 12:00:01 , that is, one second in the rocket’s frame. Since the rocket’s clock is moving during that one second, the Earth would have to have one clock stationed at the place where the rocket’s clock will be at 12:00:00 and another clock at the place where the rocket’s clock will be at 12:00:01. The Earth must then use two clocks to measure the rate at which the rocket’s single clock is ticking. The Earth synchronizes its clocks with the rocket clock as it passes the first clock, that is, it sets both its clocks so that they read 12:00:00 just as the rocket’s clock passes the first of them. Then, as the rocket passes the second clock, the Earth’s clock will read about 12:00:03 . Both the rocket and the Earth will agree that the rocket’s clock is about 2 seconds behind the Earth’s second clock. What will each conclude from this? The Earth will conclude… 1. My clocks are synchronized. 2. The rocket’s clock only ticked one second for my three seconds. 3. The rocket’s clock is running slow! The rocket will conclude… 1. My clock read 12:00:00 at exactly the same time as the first Earth clock read 12:00:00. 2. My clock read 12:00:01 at exactly the same time as the second Earth clock read 12:00:03. 3. This proves nothing because THE EARTH’S CLOCKS WERE NOT SYNCHRONIZED!! The second clock was set ahead of the first one! The rocket will then argue that it is really the Earth’s clocks that are running slow, and to prove it, the rocket sets up two clocks to check the rate of one of the Earth’s clocks… and I think you get the picture. The Earth and rocket will agree with any comparison of two clocks when they are right next to each other, but if two clocks are at different places and are simultaneous in one frame, the other frame will not agree! The other frame will claim that one clock was set ahead of the other. This also explains how both frames will claim that a meter stick in the other frame is actually shorter than one of their meters. To measure the length of a moving object, you need to locate the two ends SIMULTANEOUSLY. It makes to sense to see where one end is, wait as it moves along, and then see where the other end is; this will not give you the correct length. The measurements have to be done at the same time, and that is where the argument comes in. If the Earth measures the rocket’s meter stick, the rocket will claim that the Earth actually measured the front end first, then the back end afterwards, after the stick had moved a bit, so of course the Earth would think the rocket’s stick is short. The Earth would make the same argument about the rocket’s measurements. Where does this whole problem of simultaneity come from? The answer is the second postulate of Einstein’s Theory of Special Relativity. It states that the speed of light must be the same for all observers, no matter how they are moving. Oddly enough, that’s what does it! In order for everyone to measure light as traveling at the same rate, we run into problems with defining when things happen at the same time. The demonstration of this involves some math, and I will leave this for you to read about later if you would like to go into this in more depth. For some more details, just about any college introductory textbook will have at least a chapter on relativity that can get you started. One you might try is “Physics Matters” by Trefil and Hazen, which is a conceptual physics book without much math. Another book, one that goes over the experimental verification of Einstein’s Theories, Special and General, is “Was Einstein Right?” by Clifford Will. Well, James, I hope I have answered your question. If you would like some more information, please let us know. Sincerely, Jim Guinn
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