1862: Particle Properties - Revision history

42.book.addict at 16:57, 10 September 2025

2025-09-10T16:57:32Z

Natg19: /* Transcript */ cat

2025-02-08T01:31:31Z

‎Transcript: cat

172.68.225.161 at 02:25, 14 December 2024

2024-12-14T02:25:37Z

172.68.23.200: /* Explanation */ en dashes for negative signs

2024-08-04T07:23:03Z

‎Explanation: en dashes for negative signs

172.70.210.219: /* Explanation */ better description of spin from current comic explanation w/good video

2024-08-04T02:39:09Z

‎Explanation: better description of spin from current comic explanation w/good video

172.70.211.129: /* Explanation */ typo

2024-05-31T06:11:36Z

‎Explanation: typo

172.71.146.32: /* Explanation */ more correct

2024-05-30T07:55:56Z

‎Explanation: more correct

172.70.210.116: /* Explanation */ correct for non-maximally mixed states

2024-05-30T04:40:41Z

‎Explanation: correct for non-maximally mixed states

172.69.34.129: /* Explanation */ fix link

2024-05-30T04:21:05Z

‎Explanation: fix link

172.71.151.74: /* Explanation */ better usage

2024-05-30T04:17:15Z

‎Explanation: better usage

@@ Line 89: / Line 89: @@
 | Street value
 | [0,∞) in $
-| The value of a good or service (particles are usually not services{{fact}}) in non-retail, non-wholesale transactions between individuals.
+| The value of a good or service (particles are usually not services) in non-retail, non-wholesale transactions between individuals.
 |-
 | Entropy

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 |-
 | Spin number
-| (-∞,∞) (Intervals of ½)
+| (–∞,∞) (Intervals of ½)
 | {{w|Spin (physics)|Spin}} is a {{w|quantum number}} describing subatomic particles, named for the vaguely analogous but crucially distinct concept of {{w|angular momentum}} in classical physics. [https://www.youtube.com/watch?v=pYeRS5a3HbE&ab_channel=ScienceClicEnglish Quantum mechanical spin is ''not'' rotation, but rather how quickly the particle changes state when rotated.]
-Half-integer spin particles are classified as {{w|fermions}} and whole integer spin particles are {{w|bosons}}. Two fermions cannot have exactly the same state, an observation known as the {{w|Pauli exclusion principle}}. Thus, for fermions to exist in the same position, they must have opposite spins, of +½ and -½. It follows that a maximum of two fermions of the same flavor (e.g. two electrons) may exist in the same position.
+Half-integer spin particles are classified as {{w|fermions}} and whole integer spin particles are {{w|bosons}}. Two fermions cannot have exactly the same state, an observation known as the {{w|Pauli exclusion principle}}. Thus, for fermions to exist in the same position, they must have opposite spins, of +½ and –½. It follows that a maximum of two fermions of the same flavor (e.g. two electrons) may exist in the same position.
 |-
 | Flavor

@@ Line 31: / Line 31: @@
 | Spin number
 | (-∞,∞) (Intervals of ½)
-| {{w|Spin (physics)|Spin}} is an intrinsic property of particles, a relativistic form of angular momentum. The spin of a particle determines what statistics the particle follows, half odd integer spin particles are classified as fermions and integer spin particles are bosons.
+| {{w|Spin (physics)|Spin}} is a {{w|quantum number}} describing subatomic particles, named for the vaguely analogous but crucially distinct concept of {{w|angular momentum}} in classical physics. [https://www.youtube.com/watch?v=pYeRS5a3HbE&ab_channel=ScienceClicEnglish Quantum mechanical spin is ''not'' rotation, but rather how quickly the particle changes state when rotated.]
-Two fermions cannot have exactly the same state, an observation known as the Pauli exclusion principle. Thus, for fermions to exist in the same position, they must have opposite spins, of + ½ and - ½. It follows that a maximum of two fermions of the same flavor (e.g. two electrons) may exist in the same position.
+Half-integer spin particles are classified as {{w|fermions}} and whole integer spin particles are {{w|bosons}}. Two fermions cannot have exactly the same state, an observation known as the {{w|Pauli exclusion principle}}. Thus, for fermions to exist in the same position, they must have opposite spins, of +½ and -½. It follows that a maximum of two fermions of the same flavor (e.g. two electrons) may exist in the same position.
 |-
 | Flavor

@@ Line 97: / Line 97: @@
 In classical thermodynamics, entropy is a macroscopic property describing the disorder or randomness of a system with many particles. However, in statistical mechanics and quantum mechanics, the concept of entropy can also be applied to single particles under certain conditions. If the particle's position is not precisely known and can be described by a probability distribution, this contributes to entropy. Similarly, if the particle's momentum is uncertain and described probabilistically, this also contributes to entropy. A single quantum particle in a pure state (e.g., an electron in a specific atomic orbital) has zero entropy. This is because there is no uncertainty about the state of the system. If the single particle's state is described by a density matrix representing a mixed state (a probabilistic mixture of several possible states), the Von Neumann entropy can quantify the degree of uncertainty or mixedness of the state.
-Imagine two identical balloons filled with the same gas and heated from two opposite sides with identical heat sources, creating symmetric temperature gradients in both; because the distribution of temperatures is the same, the Gibbs statistical thermodynamic entropy 𝑆 of the gas molecule particles in each balloon will be the same. In contrast, if one balloon is heated by a low-power heat source and another from by an otherwise identical high-power heat source, the balloon next to the high-power heat source will have a steeper temperature gradient, increasing the number of [https://www.sciencedirect.com/topics/mathematics/accessible-microstates accessible] {{w|Microstate|microstates}}, so the Gibbs entropy 𝑆<sub>low power</sub> < 𝑆<sub>high power</sub>. Now consider electrons in two atoms excited by absorbing identical photons to a mixed state; if the mixed states have the same probabilities for different energy levels, their Von Neumann quantum entropy 𝑆 values will be the same. Conversely, if one atom has electrons excited to a {{w|Purity_(quantum_mechanics)|pure state}} and another to a mixed state by photons of different energies, the mixed state will have higher entropy due to greater uncertainty, i.e., 𝑆<sub>pure</sub> = 0 and 0 < 𝑆<sub>mixed</sub> ≤ ln(2).
+Imagine two identical balloons filled with the same gas and heated from two opposite sides with identical heat sources, creating symmetric temperature gradients in both; because the distribution of temperatures is the same, the Gibbs statistical thermodynamic entropy 𝑆 of the gas molecule particles in each balloon will be the same. In contrast, if one balloon is heated by a low-power heat source and another by an otherwise identical high-power heat source, the balloon next to the high-power heat source will have a steeper temperature gradient, increasing the number of [https://www.sciencedirect.com/topics/mathematics/accessible-microstates accessible] {{w|Microstate|microstates}}, so the Gibbs entropy 𝑆<sub>low power</sub> < 𝑆<sub>high power</sub>. Now consider electrons in two atoms excited by absorbing identical photons to a mixed state; if the mixed states have the same probabilities for different energy levels, their Von Neumann quantum entropy 𝑆 values will be the same. Conversely, if one atom has electrons excited to a {{w|Purity_(quantum_mechanics)|pure state}} and another to a mixed state by photons of different energies, the mixed state will have higher entropy due to greater uncertainty, i.e., 𝑆<sub>pure</sub> = 0 and 0 < 𝑆<sub>mixed</sub> ≤ ln(2).
 Please see also [[2318: Dynamic Entropy]].

@@ Line 79: / Line 79: @@
 | Proof
 | [0,200]
-| This refers to {{w|alcohol proof}}, which is the measure of the amount of ethanol in a beverage by volume. In the United States, 100 proof correspond to 50% alcohol, so the proof of a beverage is two times the percentage of ethanol, so the maximum value is at most 200, and usually around 190 because of e.g. the formation of hydrates.
+| This refers to {{w|alcohol proof}}, which is the measure of the amount of ethanol in a beverage by volume. In the United States, 100 proof correspond to 50% alcohol, so the proof of a beverage is two times the percentage of ethanol, so the maximum value is at most 200.
 |-
 | Heat