Heisenberg uncertainty principle
There is plenty of information on the topic on the web. So just links for now.
It makes for the volume of atoms not collapsing down any further
and for the energy and strength of covalent bonds
for just two very fundamental consequences.
A principle of math not just physics
Interestingly the uncertaintly principle is not just a principle of physics but also a principle of math.
Taking the Fourier transform of a Gauss curve one gets back a Gauss curve in reciprocal space.
The smaller the Gauss curve in one space the bigger it gets in the other and vice-versa.
Physics just attaches the physical unit of action to it.
And the see-saw can have more than two sides with
complete sets of commuting observables.
Canonical conjugate pairs make for see-saws
- (angular)position <=°=> (angular)momentum
- energy <=°=> time
This also relates to Noether's theorem
where thee is a pairing between continuous symmetries and conserved quantities
according to the canonical conjugate pairs
- conserved momentum <=> symmetry in position
- conserved energy <=> symmetry in time
Further related are generating functions (and symplectic geometry).
Wild connection over to to computer science and programming
Wildly generating functions also appears in
the without context odd/absurd seeming idea of taking derivatives of data-structures.
with the particular concrete instance of zippers data-structures as sort of Taylor series decomposition.
for tree data-structures that are useful for operation on such tree data-structures.
The odd/absurd idea of taking derivatives of data-structures naturally comes form
the discovery of the 1:1:1 mapping between:
mathematical logic – type theory – category theory
(which is known as the Curry-Howard-Lambeck isomorphism)
And then filling in the mutual holes.
This is a fascinating discovery process.
A prime example of "discovered rather than invented".
Enough digression.
(wiki-TODO: Make more clear how generating functions relate to both sides.)
Related
Perhaps somewhat controversial takes on the probability interpretations here:
External links
- https://en.wikipedia.org/wiki/Uncertainty_principle
- https://en.wikipedia.org/wiki/Exchange_interaction
- https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables
- https://en.wikipedia.org/wiki/Action_(physics) … not to confuse with entropy though there are strong links
- https://en.wikipedia.org/wiki/Noether%27s_theorem
- https://en.wikipedia.org/wiki/Generating_function
- https://en.wikipedia.org/wiki/Symplectic_geometry
Looking more closely at one observable of a "complete set of commuting observables"
then one or more of the others need to blur further out to compensate for that.
The minimal phase space volume of the Planck quantum cannot be further compressed.