Statistical Physics - Revision history

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‎Consequences

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‎Planck

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‎Planck

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‎Bose-Einstein

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‎Fermi-Dirac

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 ==Full Title==
-[[Complexity]] does not permit the exact determination of all states for even so much as a single atom larger than one proton and one elsectron.
+* [[Complexity]] does not permit the exact determination of all states for even so much as a single atom larger than one proton and one electron.
 ==Context==

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 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 became part of the study of physics, then [[Statistical Physics]] became necessary to understand physical reality. 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 accurate existence."<ref>Richard Feynman ''Quantum Behavior'' (1965) https://www.feynmanlectures.caltech.edu/III_01.html</ref>
-By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer, a physicist at Chapman University, said, but “it’s not a description of reality.”<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
+By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer, a physicist at Chapman University, said, but “it’s not a description of reality.”  This “orthodox” presentation of quantum mechanics raises profound questions. What does ψ, the Schrödinger Euqation, with all the possibilities it describes? Is it a physical thing that exists in the world? Or is it a mathematical representation of our incomplete knowledge of the future, something that exists only on our blackboards and in our minds?<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
 ==References==
 [[Category: Physics]]

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 ==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 became part of the study of physics, then [[Statistical Physics]] became necessary to understand physical reality. 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 accurate mexistence."<ref>Richard Feynman ''Quantum Behavior'' (1965) https://www.feynmanlectures.caltech.edu/III_01.html</ref>
+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 became part of the study of physics, then [[Statistical Physics]] became necessary to understand physical reality. 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 accurate existence."<ref>Richard Feynman ''Quantum Behavior'' (1965) https://www.feynmanlectures.caltech.edu/III_01.html</ref>
-By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer, a physicist at Chapman University, told me over Zoom the week before the conference, but “it’s not a description of reality.”<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
+By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer, a physicist at Chapman University, said, but “it’s not a description of reality.”<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
 ==References==
 [[Category: Physics]]

@@ Line 41: / Line 41: @@
 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 became part of the study of physics, then [[Statistical Physics]] became necessary to understand physical reality. 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 accurate mexistence."<ref>Richard Feynman ''Quantum Behavior'' (1965) https://www.feynmanlectures.caltech.edu/III_01.html</ref>
-By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer(opens a new tab), a physicist at Chapman University, told me over Zoom the week before the conference, but “it’s not a description of reality.”<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
+By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer, a physicist at Chapman University, told me over Zoom the week before the conference, but “it’s not a description of reality.”<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
 ==References==
 [[Category: Physics]]

@@ Line 41: / Line 41: @@
 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 became part of the study of physics, then [[Statistical Physics]] became necessary to understand physical reality. 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 accurate mexistence."<ref>Richard Feynman ''Quantum Behavior'' (1965) https://www.feynmanlectures.caltech.edu/III_01.html</ref>
-By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
+By the early 1930s, it was becoming clear that quantum mechanics, in either the wave version or the matrix version, does not deal with particles in specific positions moving in specific directions. It predicts many possible future outcomes and says nothing about a singular, fixed reality. Do an experiment over and over, and the theory says only what percentage of the time you’ll measure one result versus another. It was a shocking retreat from what physicists were allowed to think about — one that Schrödinger and Einstein never accepted. “You are suddenly speaking of what we know about nature and no longer about what nature really does,” Heisenberg recalled Einstein telling him.  “It’s our most fundamental description of reality,” Matt Leifer(opens a new tab), a physicist at Chapman University, told me over Zoom the week before the conference, but “it’s not a description of reality.”<ref>Charlie Wood, '' ‘It’s a Mess’: A Brain-Bending Trip to Quantum Theory’s 100th Birthday Party'' Quanta Mag. 2025-07 https://www.quantamagazine.org/its-a-mess-a-brain-bending-trip-to-quantum-theorys-100th-birthday-party-20250808/?mc_cid=5e37a88898&mc_eid=ffe1625684</ref>
 ==References==
 [[Category: Physics]]

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 ==Planck==
-From the beginning of Boltzmann's statistical approach Planck, among many others, rejected the Boltzmann's statistical approach. But, in the end, both Boltzmann and Planck had to accept what the math was telling them. Some time any complex physical 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.
+From the beginning of Boltzmann's statistical approach Planck, among many others, rejected the Boltzmann's statistical approach. But, in the end, both Boltzmann and Planck had to accept what the math was telling them. Some time any complex physical system will do unexpected things. This was a an unwelcome outcome for logical minds.<ref name=baggott>Jim Baggot ''The Quantum Cookbook: Mathematical Recipes for the Foundations of Quantum Mechanics'' 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.
 When Planck tried to solve the problem of black-body radiation, where the then current theories predicted that the amount of radiation should continuously increase as the frequency increased, his result looked a lot like Boltzmann's solution for the distribution of heat in an ideal gas. This was not the solution that Plank expected, but he finally had to accept that a statistical solution was required, but with a difference. In Planck's solution he took the unexpected step of treating the quanta of energy as indistinguishable from every other quanta of energy with the same energy level. When he did that he arrived at his famous formula E =  h&nu;.

← Older revision		Revision as of 05:33, 28 June 2023
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−	Wave number, a unit of frequency, often used in atomic, molecular, and nuclear spectroscopy, equal to the true frequency divided by the speed of the wave and thus equal to the number of waves in a unit distance. In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ: thus ν = c/λ. ~~A typical~~	+	Wave number, a unit of frequency, often used in atomic, molecular, and nuclear spectroscopy, equal to the true frequency divided by the speed of the wave and thus equal to the number of waves in a unit distance. In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ: thus ν = c/λ.

	==Fermi-Dirac==		==Fermi-Dirac==

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   E = &Sigma; N<sub>s</sub> h&nu;<sub>s</sub>. Sum over all states.
 The values N<sub>s</sub> will exactly determine the total energy in the same manner as Feynman was able to use the sum of all paths (see below) to determine the total probably of each possible event for a particle in motion.
 ==Fermi-Dirac==