Quantum Mechanics (QM) is the fundamental theory of modern physics. Thus
far, it has successfully been used to describe all processes on scales smaller
than molecules. For systems on the scale of molecules, the complexity of
interacting processes hampers direct analysis using raw QM: however, analyses
via approximations plausible on the scales involved are consistent with the
view that all processes fit in with
QM. It has been
shown that the randomness inherent in quantum mechanics cannot be
explained away by any theory of hidden variables

– i.e. internal
mechanisms with deterministic behaviour, that we simply can't see. I am
persuaded that the entire universe is governed by quantum mechanical
processes. One stumbling block remains: we have no fully unified
understanding of General Relativity (i.e. gravity)
within QM. The theories which manage to combine the two, to greater or lesser
degrees, are known as Quantum Cosmology; the real goal of modern physics is to
build a Theory of Everything

, or Grand Unified Theory

–
i.e. a quantum theory which systematically and harmoniously accounts for
gravity along with all the fundamental particles (quarks, leptons and the
bosons that mediate their interactions) of the standard model of sub-atomic
physics.

Quantum mechanical discussions in this directory include:

- de Broglie's contribution
- Schrödinger's equation
- Analysis of the energy levels of atoms and my school-age model of the Hydrogen atom.
- The Hilbert space formalisation of quantum theory
- The position observable, considered in the context of a smooth manifold (i.e. a curved universe, as required for general relativity)
- Preliminary thoughts on Quantum Cosmology
- A rough outline of the standard model of particle physics

Some antique pages could do with clean-up, upgrades or possibly total rewrites:

- Some ruminations about the effects of observation
- Some related thoughts about the nature of the vacuum
- Initial doodle on collapsing superpositions, also known as the universe forking into many versions.
- A sketch of how colliding molecules can exchange internal energy in collisions.
- An incomplete account of the Kochen-Specker theorem and its proof.
- Initial notes on (conditional) quantum probability theory.
- A meander upon rational numbers and quantum mechanics.
- A scribbled fragment on diffraction.

- An analysis of balancing a US penny on its side.
- An
alleged
gravitomagnetic

effect detected at an ESA laboratory. - The transactional interpretation of Quantum Mechanics; and a hidden-time variant of it.
- Applying quantum mechanics to game theory changes the nature of even The Prisoners' Dilemma (article provides many fascinating links).
- Causaloid theory.
- Applying Quantum Information
- A relatively accessible account of Bell's Theorem and how naïve assumptions predict negative probabilities.
- An enlightening derivation of quantum mechanics from the elementary postulate that measurement is wont to change the system measured.
- A quantum solution to the
arrow-of-time dilemma: entropy can decrease, but only in a process which
destroys all evidence of its having happened; for all practical purposes, it
thus
*hasn't*happened ! - Sabine Hossenfelder on David Bohm's pilot wave interpretation of QM.
- On-going
pilot wave

investigations by fluid dynamicists hint at an alternate interpretation of quantum physics. Fortunately, we're all used to healthy heresy by now.

It is my belief that the notation in which modern physics is conducted is old, clunky and in need of revision. In particular, I believe that it is sufficiently clumsy that it is currently hampering the development of better models of the universe and impairing communication between researchers in different fields. (Donald Kennedy, editor of Science, wrote a piece with similar views, but the link is now broken.) This belief is, however, only a bunch of hot air until such time as I produce a notation in which it is actually easier to develop such models.

Consequently, while I study QM, I am exploring the mathematical notations
which can do what is required. One example of this is my analysis (dating
from 1995) of the position observable in QM, given
that position on a smooth manifold (the domain in which General Relativity
says we must work) is *not* a linear quantity (i.e. one to which one
can apply scaling and addition). This replaces the orthodox description of
observables, as Hermitian operators on a complex linear space S, with a
description as a measure

, on the space of values of the observable,
except that the measure

maps subsets of this space to projection
operators on S, rather than to real probabilities

; the projection
operators yielded by the measure all commute with one another; and the measure
can be used to integrate

any well-enough-behaved function f from the
observable's space of values to a fixed real linear space U, the integral
being a hermitian operator on S whose eigenvalues lie in U. In particular,
when the observable's space of values is linear, the identity on it can be
used as f and its integral is orthodoxy's hermitian operator.

If a body of given momentum, spin and charge lies entirely within some
region bounded by a Kerr event horizon matching those parameters, then we can
know nothing, in this outside world, about what is going on inside that
region. For a tiny thing like an electron, having it all inside such a tiny
region would entail a huge uncertainty of momentum, which was one of the
inputs to what region of space-time you examined. Still, it suggests a
low-level granularity beyond which one knows one is ignorant of the internals,
save only as to their momentum, spin and charge. When we come to stitch
together

charts of a region of space-time that is

an electron, we
can expect to get a full description of it without needing to use charts
smaller than chunks of would-be event tubes.

I picture an electron as a superposition of solutions to the field
equations, each amounting to a chart of a region of space-time that looks
like

an electron from the outside: all the charts in the superposition
give, internally, solutions of the field equations, and the surrounding
universe reads

them as agreeing on the spin, momentum and charge
within the same

charted region, at least to within the available
uncertainty of the relevant quantities. Such a view of an arbitrary portion
of space-time would make for interesting reading, too, I suspect.