Difference between revisions of "Statistical Physics"
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==Planck== | ==Planck== | ||
| − | From the beginning of Boltzmann's statistical approach Planck, among many others, rejected the Boltzmann's statistical approach. Bot, in the end, not Boltzmann and Planck had to accept what the math was telling them. Some time the system will do unexpected things. This was a an unwelcome outcome for logical minds.<ref name=baggott>Jim Baggot ''Quantum Cook Cookbook'' Oxford (2020) ISBN = 9780198827863</ref> | + | From the beginning of Boltzmann's statistical approach Planck, among many others, rejected the Boltzmann's statistical approach. Bot, in the end, not Boltzmann and Planck had to accept what the math was telling them. Some time the system will do unexpected things. This was a an unwelcome outcome for logical minds.<ref name=baggott>Jim Baggot ''Quantum Cook Cookbook'' Oxford (2020) ISBN = 9780198827863</ref> This rear-guard action against any statistical solution continues even to this day. Almost no one seems to like the possibility that everything that happens, from the very lowest event, is up to chance. |
==Consequences== | ==Consequences== | ||
Revision as of 15:52, 6 June 2023
Full Title
Context
- From the time of Gauss probability was used in experimental physics to estimate error bound in experiments. But the assumption was that the underlying physical laws were absolute and admitted to no variability.
- Bernoulli, Clausius and Maxwell developed the idea that motions of atoms in a gas could be used to explain heat and the idea of entropy which can never decrease in closed systems.
Boltzmann
The starting idea for classical statistics is the Hamiltonian phase space of 6N dimensions where N is the number of particles. So each particle has its own unique 3 position and 3 momentum values which are tracked over time. See the wiki page on Identical Particle for details on this concept.
Planck
From the beginning of Boltzmann's statistical approach Planck, among many others, rejected the Boltzmann's statistical approach. Bot, in the end, not Boltzmann and Planck had to accept what the math was telling them. Some time the system will do unexpected things. This was a an unwelcome outcome for logical minds.[1] This rear-guard action against any statistical solution continues even to this day. Almost no one seems to like the possibility that everything that happens, from the very lowest event, is up to chance.
Consequences
Statistical analysis become necessary when dealing with particles that were too numerous to track individually. It turns out the the very success of Newtonian physics and the calculus was to assume that differences could be made small enough that calculations could be easily performed. When the reality of particles that were not continuous because part of the study of physics, then Statistical Physics became necessary. We find that in Quantum Mechanics probability and statistics becomes the only way to make any sort of predictions at all. Richard Feynman that his to say about the uncertainty implicit in a statistical approach. "The uncertainty principle “protects” quantum mechanics. Heisenberg recognized that if it were possible to measure the momentum and the position simultaneously with a greater accuracy, the quantum mechanics would collapse. So he proposed that it must be impossible. Then people sat down and tried to figure out ways of doing it, and nobody could figure out a way to measure the position and the momentum of anything—a screen, an electron, a billiard ball, anything—with any greater accuracy. Quantum mechanics maintains its perilous but still correct existence."[2]
References
- ↑ Jim Baggot Quantum Cook Cookbook Oxford (2020) ISBN = 9780198827863
- ↑ Richard Feynman Quantum Behavior (1965) https://www.feynmanlectures.caltech.edu/III_01.html
