Chapter 8: The Special Principle of Relativity

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A "symmetrical" object is one which can be viewed from different points of view and appear the . Nature is said to be symmetric under a transformation (change) if no experiment you could perform would allow you to tell whether the change had been made, i.e., because the laws of nature are unchanged by it. Knowledge of symmetry is useful in helping people to formulate the mathematical expressions of new physical laws because the useful symmetries that one can observe in nature can be coded into the mathematical laws, thus limiting the form that expressions for unknown laws can take. Examples of useful symmetries are: Could you detect a change in the world if all positive charges were suddenly changed to negative and all negative charges changed to positive? Could you detect a change in the world if the world were suddenly changed to its mirror image? Could you detect a change in the world if time were suddenly reverses? When we say "could you detect a change" we mean could you perform an experiment which shows that the laws of nature as understood in our real world are different in the changed world. "Position symmetry" means that nature is symmetric under changes in in space, i.e., that you could not detect a change in the laws of physics if everything were suddenly moved to a new position in space. As a consequence of this symmetry in the world, we believe that the of nature are the same everywhere in space. "Time symmetry" means that nature is symmetric under changes in time, i.e., that you could not detect a change in the laws of physics if everything were suddenly "moved" forward or backward in time. As a consequence, we believe that the laws of nature are the as they were in the remote past and will be in the future. "Motion symmetry" means that nature is symmetric under changes from one frame of reference to another that is moving relative to the first with (uniform, accelerated?) motion. It means that (uniform, accelerated?) motion is undetectable, i.e., that no experiment would reveal a change in the laws of physics just because it is done in a frame that is moving with uniform motion instead of one that is at rest. Motion symmetry is also called the "special principle of relativity." However, accelerated motion is (detectable, undetectable?) . The earth has two nonuniform (accelerated) motions that are, in principle, detectable: the earth spins on its axis and it revolves around the sun. In principle, these are both detectable motions, but sufficient time has to be allowed in the observations that the path of the accelerated motion deviates significantly from a (straight, curved?) line. But how do you know that the earth spins? How could you "prove" it to someone else? One observation that bears on the question is the observation that the stars revolve about the North Star at night. But, is it because the earth spins or because the stars themselves move? Why is one explanation considered "scientific" and the other not when both explain equally well what is actually seen? The Foucault Pendulum is also taken as evidence that the earth spins. At the North Pole, the Foucault Pendulum swing path seems to move to the side and complete a cycle in (number, how many?) hours. At the equator it would take forever. Science prefers the explanation of the spinning earth (rather than the moving stars) partly because it explains both the movement of the stars and the Foucault Pendulum with the same simple model. This is an example of the use of Occam's Razor in science. Stellar is one evidence that the earth revolves about the sun. Stellar parallax means that the relative positions of nearby seem to change slightly and then back again in rhythm with the earth's annual seasons. The observation of the motion of the planets also is evidence for revolution of the planets around the sun.

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