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Def Symmetry/Weyl: a thing is symmetrical, if it can be subjected to a certain operation and it then appears as exactly the same as before.
Symmetry/Physics/Laws/Feynman: For example, if we move a machine, it will still work.
Translation in space - translation in time - rotation around a fixed angle - constant speed in a straight line (Lorentz transformation) - time reversal - reflection of space - exchange of the same atoms or particles - quantum mechanical phase
Matter antimatter (charge conjugation).
Asymmetry/Scale/Scale Change/Feynman: in the case of scale changes, the physical laws are not symmetrical!
Question: will an apparatus which is re-built five times larger work in the same way? - No!
E.g. The light wavelength, e.g. emitted by sodium atoms in a container, is the same when the volume quintuples. It is not made five times longer by that
Consequently, the ratio of the wavelength to the size of the emitter changes.
E.g. Cathedral made of matches: if it were built on a real scale, it would collapse, because enlarged matches are not strong enough.
We might think that it is enough to take a larger earth (because of the same gravitation). But then it would become even worse!
Symmetry/Law/Conservation Law/Quantum Mechanics: in quantum mechanics there is a corresponding conservation law for every symmetry! This is a very profound fact.
The fact that the laws of translation are symmetrical in time means, in quantum mechanics, that the energy is conserved.
Invariance in rotation corresponds to the conservation of the angular momentum. (In quantum mechanics).
Symmetry/reflection of Space/Right/Left/Direction/Space Direction/Feynman: a clock whose every part was mirror symmetrical, would run the same way.
If this was correct, however, it would be impossible to distinguish between "right" and "left" by any physical phenomenon, just as it is impossible to define an absolute speed by a physical phenomenon.
The empirical world, of course, need not be symmetrical. We can define the direction in geography.
But it does not seem to violate the physical laws that everything is changed from right to left.
E.g. right/left: If you wanted to find out where "right" is, a good method would be to buy a screw in a hardware store. Most have legal threads. It's just a lot more likely. (Convention).
E.g. right/left: next possibility: Light turns its polarization plane when it penetrates sugar water. So we can define "right-turning".
But not with artificially made sugar, only with that from living creatures! (>Monod, molecular structure, right-turning/left-turning).
Feynman: it looks as if the phenomena of life (with much more frequent molecules in a certain direction) allow the distinction between left/right.
But that is not the case!
The Schrödinger equation tells us that molecules rotating right and left behave the same physically. Nevertheless, there is only one direction in life!
Conservation Law: there is no preservation of the number of right-sided molecules. Once started, evolution has increased their number and we can further multiply them.
We can assume that the phenomena of life do not violate symmetry but, on the contrary, demonstrate the universal nature and the ultimate origin of all living creatures.
Mirror Symmetry: is fulfilled by the laws of: electricity, gravitation, magnetism, nuclear forces.
They cannot be used to define right/left!
But there is a violation of symmetry in nature: the weak decay (beta decay): (1954): there is a particle, a certain cobalt isotope, which decays into three π mesons, and another one that decays into two.
Def South Pole: can only be defined by cobalt isotopes: it is such that the electrons in a beta decay prefer to lead away from it.
This is the only way to explain right/left unambiguously to the Martian: he gets building instructions for a beta decay in a cooled system.
Parity/Law of Violation of Parity Conservation/Asymmetry/Symmetry/Feynman: only unsymmetrical law in nature: the violation only occurs with these very slow reactions: the particles that bear a spin (electron, neutrino, etc.) come out with a left-tending spin. The law combines the polar vector of a speed and the axial vector of a rotational momentum, stating that the rotational momentum is more likely to be opposite to the velocity than being parallel to it.
Symmetry/Nature/Feynman: where does it come from? We don't know.
Vom Wesen physikalischer Gesetze München 1993
Vorlesungen über Physik I München 2001