Feynman 4: Symmetry in Physical Law

This is the fourth of seven chapters in Richard Feynman's, The Character of Physical Law, a series of lectures he gave at Cornell in 1965. The previous three were:

• Gravitation as an example of physical law
• The relation of physics to math
• Great conservation laws

I didn't find this lecture as interesting or as clear. It's curious to me why the idea of symmetry seems at first glance to be rather boring. I suspect it is partly because I don't know much about it. But it is probably also because of some matter of my personality. I remember studying "translation" in high school, mapping one coordinate frame onto another. I remember it seeming very boring.

But the end of the lecture hinted at something interesting about symmetry. Apparently, the laws of conservation in the previous lecture relate in some way to the symmetries in this one.

1. The first part of the chapter explores several different kinds of symmetry in nature. He defines symmetry as being able to change something in some way and it looking exactly as before.

The ones he presents are:

• symmetry of translation (if you move everything over, it operates the same)
• translation of time (if you move stuff forward in time, the laws of nature operate the same)
• rotating things (if you turn everything a certain way, they operate the same)
• motion in a straight line (relative to your frame of reference, everything operates the same)
• atom replacement (you can replace one atom with another same atom and everything works the same)

There are some interesting twists and turns in his presentation of these, although sometimes he gets a little tedious with his "what ifs." Here were the "what ifs" I found most interesting:

• If the universe had a beginning, then the translation of time symmetry wouldn't work for the beginning of time, but usually scientists don't include that part of time in their discussion of such symmetry.
• Einstein's theory of relativity sets the speed of light as an absolute speed limit for the universe, so motion in a straight line only is symmetrical within a frame of reference, not from one frame of reference to another moving relative to it.

2. Then he presents some items of the universe that are not symmetrical.

• Change of scale. If you make something bigger, it does not operate the same way. If you took a matchbox cathedral and increased the scale to the size of an actual cathedral, it would collapse under its own weight. This relates to one of the random discussions on Big Bang Theory on whether a giant rat was possible. 
• Spinning is not symmetrical in the sense that you can tell if you are spinning (e.g., with a gyroscope). By contrast, you cannot tell if you are moving at constant velocity without looking outside your car.
• One of the most interesting apparent non-symmetries is reflection. I did a quick search to see if this non-symmetry still holds. From my brief look, it seems like it does. 

Feynman shows that reflection symmetry holds to a very large extent. There are some interesting twists. For example, apparently living organisms prefer "right-handed" molecules. Bacteria will eat all the sugar that comes from nature. But they will only eat half of the sugar that is artificially produced, even though it has the same chemical formula. (This is an argument, by the way, that all life is derivative on the same basic original life-structure--all life is "right-handed" on the molecular level, so to speak).

But when he gets down to the atomic level, apparently all electrons spin left. You can create a positron (positively charged electron) that spins right, but it isn't (if I understand correctly) an exact mirror. So on the subatomic level, symmetry doesn't hold. You can't create a right-handed electron.

3. So we arrive at the pay off of the chapter, which is a deep connection between symmetry and laws of conservation. He lines them up this way:

• symmetry of translation relates to conservation of momentum
• symmetry in time relations to the conservation of energy
• symmetry in rotation relates to the conservation of angular momentum

Interesting!