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The modern mathematics treats "space" quite differently from the classical mathematics. The differences are listed below; their origin is explained afterwards.
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The [[Heisenberg Uncertainty Principle|Heisenberg uncertainty principle]] for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.


==Differences==
An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).
{| class="wikitable"
|-
! Classic
! Modern
|-
| a single space
| many spaces of various kinds
|-
| axioms are obvious implications of definitions
| axioms are conventional
|-
| theorems are absolute objective truth
| theorems are implications of the corresponding axioms
|}

Latest revision as of 02:25, 22 November 2023


The account of this former contributor was not re-activated after the server upgrade of March 2022.


The Heisenberg uncertainty principle for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.

An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).