And since they are the smartest physicists both of the last century this must be true I guess.
Dirac unified Heisenberg’s matrix mechanics with Schrödinger wave mechanics
The first formulation of QM was done by heisenberg using matrix mechanics. This was quite complicated. Schrödinger then formuled his wave mechanics. This was easier. Dirac unified them by using his dirac notation.
The natural numbers
Connection between entropy, chance and principle of least action
The Principle of Least Action serves as the foundation for Newton’s laws. It can be derived from the path integral formulation in quantum mechanics (QM). Path integrals, resembling expressions such as ∫e^ix
, bear a resemblance to the integrals in statistical mechanics, specifically those of the form ∫e^(-βH).
These integrals, ∫e^(-βH), find their origin in the concept of entropy (S), where S is defined as k lnω. Here, k represents the Boltzmann constant, and ω denotes the multiplicity of quantum states. Thus, the intricate connection between the Principle of Least Action, quantum mechanics, and statistical mechanics unveils a rich tapestry of mathematical relationships within the realm of physical laws.
And another interesting connection is that general relativity can be derived from statisticla mechanical considerations.
More appropriate speed of a wave equation c=λf=…
Fermi gas and black holes
Looks like hawking radiation and the fermi surface an event horizon
Why are electrons identical to another?
Quantum particles are fundamentally identical and indistinguishable because there exists a reference frame where both particles appear as just a single particle. There world lines can be connected in a reference frame.
Why words are defective
You cannot name every real number, it is impossible. So there are more things in the world than words.
What is probability?
I think the world is deterministic and that chance is a measure of degree of missing information. Thus entropy (which quantifies missing information) is more fundamental than chance.
Effect of antidepressants on REM sleep
Nearly all antidepressants cause increased REM latency and reduce total REM sleep time.
If you prevent REM sleep in a patient with depression the mood becomes better. Interesting maybe it is one of the ways antidepressants work.