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In metaphysics, impenetrability is the name given to that quality of matter whereby two bodies cannot occupy the same space at the same time. The philosopher John Toland argued that impenetrability and extension were sufficient to define matter, a contention strongly disputed by Gottfried Wilhelm von Leibniz.
For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m ℓ are equal. In that case, the two values of m s (spin) pair must be different. Since the only two possible values for the spin projection m s are +1/2 and −1/2, it follows that one electron must have m s = +1/2 and one m s = −1/2.
In other words, more than one identical particle cannot occupy an antisymmetric state (one antisymmetric state can be occupied only by one particle). This is known as the Pauli exclusion principle , and it is the fundamental reason behind the chemical properties of atoms and the stability of matter .
Fermions are particles whose wavefunction is antisymmetric, so under such a swap the wavefunction gets a minus sign, meaning that the amplitude for two identical fermions to occupy the same state must be zero. This is the Pauli exclusion principle: two identical fermions cannot occupy the same state. This rule does not hold for bosons.
John Locke, in An Essay Concerning Human Understanding, defined extension as "only the Space that lies between the Extremities of those solid coherent Parts" of a body. [3] It is the space possessed by a body. Locke refers to the extension in conjunction with solidity and impenetrability, the other primary characteristics of matter. [4]
Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At ...
Good morning. Since it is Friday, some feedback. I received a lot of responses to my post on ex-CEOs becoming executive chairs—and not one favored the idea. A sampling: “You show me an exec ...
Objects orbiting in space would not remain in orbit if not for the gravitational force, and gravitational fields extend even into the depths of intergalactic space. [5] [6] [7] The dark side of the Moon illuminated by the Sun. The dark (far) side of the Moon receives about the same amount of light from the Sun as the near side.