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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.
Any number of identical bosons can occupy the same quantum state, such as photons produced by a laser, or atoms found in a Bose–Einstein condensate. A more rigorous statement is: under the exchange of two identical particles, the total (many-particle) wave function is antisymmetric for fermions and symmetric for bosons.
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 ...
An executive chair leads to corporate confusion: ‘Two people cannot occupy the same space and make the same decisions’ Alan Murray, Nicholas Gordon September 8, 2023 at 12:21 AM
A common or traditional definition of matter is "anything that has mass and volume (occupies space)". [31] [32] For example, a car would be said to be made of matter, as it has mass and volume (occupies space). The observation that matter occupies space goes back to antiquity.