The Character of Physical Law by Richard P Feynman

Author:Richard P Feynman
Language: eng
Format: epub, mobi
ISBN: 9780141956114
Publisher: Penguin Books Ltd
Published: 1992-05-10T16:00:00+00:00

Figure 24

You can see that this is very much like the x and y business in space. If I stand facing an audience, then the two sides of the stage on which I stand are on a level with me. They have the same x, but different y. But if I turn round through 90°, and look at the same pair of walls, but from a different point of view, then one is in front of me and one is behind, they have different x′. So it is that the two events which from one point of view seem to be at the same time (same t), from another point of view can seem to be at different times (different t’). A generalization of the two-dimensional rotation that I spoke about was therefore made into space and time, so that time was added to space to make a four-dimensional world. It is not merely an artificial addition, like the explanation given in most of the popular books, which say ‘We add time to space, because you cannot only locate a point, you also have to say when’. That is true, but that would not make it real four-dimensional space-time; that just puts the two things together. Real space has, in a sense, the characteristic that its existence is independent of the particular point of view, and that looked at from different points of view a certain amount of ‘forward-backward’ can get mixed up with ‘left-right’. In an analogous way a certain amount of time ‘future-past’ can get mixed up with a certain amount of space. Space and time must be completely interlocked; after this discovery Minkowski said that ‘Space of itself and time of itself shall sink into mere shadows, and only a kind of union between them shall survive’.

I bring this particular example up in such detail because it is really the beginning of the study of symmetries in physical laws. It was Poincaré’s suggestion to make this analysis of what you can do to the equations and leave them alone. It was Poincaré’s attitude to pay attention to the symmetries of physical laws. The symmetries of translation in space, delay in time, and so on, were not very deep; but the symmetry of uniform velocity in a straight line is very interesting, and has all kinds of consequences. Furthermore, these consequences are extendable into laws that we do not know. For example, by guessing that this principle is true for the disintegration of a mu meson, we can state that we cannot use mu mesons to tell how fast we are going in a space ship either; and thus we know something at least about mu meson disintegration, even though we do not know why the mu meson disintegrates in the first place.

There are many other symmetries, some of them of a very different kind. I will just mention a few. One is that you can replace one atom by another of the same kind and it makes no difference to any phenomenon.

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