Six Not-So-Easy Pieces - Einstein's Relativity, Symmetry, and Space-Time-Basic Books

Professor Hermann Weyl has given this defnition of symmetry: a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation

Not only Newton’s laws, but also the other laws of physics, so far as we know today, have the two properties which we call invariance (or symmetry) under translation of axes and rotation of axes

All quantities that have a direction, like a step in space, are called vectors

In fact, we can tell that the earth is rotating by using a so-called Foucault pendulum, without looking outside

The physical laws apparently cannot be reversible in time, because, as we know, all obvious phenomena are irreversible on a large scale: “The moving fnger writes, and having writ, moves on. ” So far as we can tell, this irreversibility is due to the very large number of particles involved, and if we could see the individual molecules, we would not be able to discern whether the machinery was working forwards or backwards

However, the only thing that life uses is L-alanine.(This is not exactly true. Here and there in living creatures there is a special use for D-alanine, but it is very rare

The reason we emphasize this is that people do not understand it when we say there is a neutron and also an antineutron, because they say, “A neutron is neutral, so how can it have the opposite charge?” The rule of the “anti” is not just that it has the opposite charge, it has a certain set of properties, the whole lot of which are opposite

if we bring a neutron and an antineutron together, they annihilate each other with a great explosion of energy being liberated, with various π-mesons, γ-rays, and whatnot

Now if we have antineutrons, antiprotons, and antielectrons, we can make antiatoms, in principle. They have not been made yet, but it is possible in principle

This gate is very elaborate, with lots of gables and beautiful carving and lots of columns and dragon heads and princes carved into the pillars, and so on. But when one looks closely he sees that in the elaborate and complex design along one of the pillars, one of the small design elements is carved upside down; otherwise the thing is completely

If one asks why this is, the story is that it was carved upside down so that the gods will not be jealous of the perfection of man. So they purposely put an error in there, so that the gods would not be jealous and get angry with human beings

We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the laws only nearly symmetrical so that we should not be jealous of His perfection

For over 200 years the equations of motion enunciated by Newton were believed to describe nature correctly, and the frst time that an error in these laws was discovered, the way to correct it was also discovered. Both the error and its correction were discovered by Einstein in 1905

Lorentz transformation.Einstein, following a suggestion originally made by Poincaré, then proposed that all the physical laws should be of such a kind that they remain unchanged under a Lorentz transformation. In other words, we should change, not the laws of electrodynamics, but the laws of mechanics. How shall we change Newton’s laws so that they will remain unchanged by the Lorentz transformation

Einstein, following a suggestion originally made by Poincaré, then proposed that all the physical laws should be of such a kind that they remain unchanged under a Lorentz transformation. In other words, we should change, not the laws of electrodynamics, but the laws of mechanics. How shall we change Newton’s laws so that they will remain unchanged by the Lorentz transformation

According to the principle of relativity, the laws of physical phenomena must be the same for a fixed observer as for an observer who has a uniform motion of translation relative to him, so that we have not, nor can we possibly have, any means of discerning whether or not we are carried along in such a motion.

In other words, whether or not a thing is measurable is not something to be decided a priori by thought alone, but something that can be decided only by experiment. Given the fact that the velocity of light is 186,000 mi/sec, one will fnd few philosophers who will calmly state that it is self-evident that if light goes 186,000 mi/sec inside a car, and the car is going 100,000 mi/sec, that the light also goes 186,000 mi/sec past an observer on the ground

So this idea of studying the patterns or operations under which the fundamental laws are not changed has proved to be a very useful one