CharacterOfPhysicalLaw

The Character of Physical Law (Richard Feynman)

Very good. Quick read. Learned something about conserved quantities and that relativity implies local conservation laws.
The reason for the law of inertia is unknown.
The relative strength of EM to gravity between two electrons is 10⁴². Amazingly enough its the same ratio as between the size of a proton and the observable universe.
Mathematics is not just another language. It is a language plus reasoning. It is a tool for reasoning, a way of going from one set of statements to another. This can be very useful in physics.
The minimum principle (principle of least action) is a consequence of QM. The best laws we know are a combination of local laws and the minimization principle.

The correct laws of physics are expressible in many equivalent ways. If you modify them, you tend to reduce the number of ways in which the laws can be written (mysterious)

With the current laws, it takes a computer an infinite number of steps to figure out what goes on in an arbitrarily tiny amount of space and time. How can all that be going on in such a tiny space? What should it take an infinite amount of time to figure out what one tiny piece of space/time is going to do?
The closing and opening of switches in a computer is quite different from what is happening in nature (JA: Math is useful because its a good emulator?)
Symmetry is much more important in QM than in classical physics, bc QM often deals with very simple systems (and identical particles!)

The fact that all the molecules in living things have exactly the same kind of handedness is probably one of the deepest demonstrations of the uniformity of the ancestry of life, right back to the completely molecular level.
QM implies deep connection between conservation laws and symmetries. If we assume the laws are given by a minimum principle (true via QM) then b/c you are at the lowest point taking a step doesn't make much of a difference. If we move the path over it doesn't affect the action to first order, the total action on path ACDB (pg 99) is the same as on the original path AB. However the action on AB is the same as on CD if there is a space translation symmetry. This implies that small step from A->C is the same as the step from D->B at the end => there is a quantity that does not change as time goes on.
Against Boltzmann Brains: If the universe were a fluctuation the prediction would be that if we looked at a place were we have not looked before we should see a disordered mess. Eg: we would not expect to see hot stars and cold space, in regions we haven't looked yet. The success of all "historical sciences" (history, astronomy, geology, etc) indicates that we did not come from a fluctuation, but from a condition that was more separated and organized. This is needed to understand the irreversibility of nature.

The philosophy around a theory may change radically when there is only a very tiny change in the theory. eg: the change in philosophy needed in gravity to predict Mercury's orbit. In order to get something that gives a slightly different result, you need a completely different theory (Not true anymore with EFTs?)