Quaternionic foundations of Quantum Mechanics and spin 1⧸2 visualization

This is a talk I gave at the Hypercomplex Seminar in 2023 on Quaternion Quantum Mechanics (based on the work of Marek Danielewski), using an elastic solid model of the universe.
It includes visualiziations and explanations of spin 1/2.
• Chantal Roth, Quaterni...

[@FractalWoman]

Hey Chantal. I just posted a link to this video in my community section. Hopefully this will get it some views.

[@barrypickford1443]

I saw this movement on a DMT trip. It’s actually pretty common to see complex geometries and seemingly impossible movements.

[@leonlee8524]

Yeah. Theres a reason those who meditate and cultures steeped in mysticism and practices do too. There's something fundamental about it that exists on all scales, or most at least. I fkin love it

[@VSears-Vortex]

the Torus solution would definitely be exciting to a large group of people, studying Rodin/Vortex coils.

[@frun]

So the Lie groups of the Standard model U(1)xSu(2)xSu(3) are basically deformations of material.

[@Achrononmaster]

@3:10 "wavefunction monism" is a non-starter. Massive violation of causality, but worse... massive gauge redundancy. Any mathematical model with a gauge redundancy is nonphysical, you remove the redundancy to obtain the physically relevant degrees of freedom. In the case of Hilbert space QM, removing the redundancy you get just particles, but with non-Markov and indivisible transition probabilities (q.v. Jacob Barandes). The indivisible stochasticity could be explained perhaps by Planck scale wormhole topology (or any similar bipartite structure, which yields a nonclassical generalized probability theory). So the wavefunction is more likely epistemic. Also, from a geometric algebra perspective (superior to quaternions, the ℍ are embedded as a subalgebra of the spacetime algebra) the spinor is a rotation & dilation instruction. Instructions are not physical ontology.

[@Achrononmaster]

Instead, I suggest you look at taking 4D spacetime itself as the "aether". Particles are then topological geons, so your "solitons" if you prefer, but they can be viewed as particles, which is the more sensible model. Since topological solitons propagate and can be coupled by wormhole bridges you may also treat them a little bit like waves, provided you are not measuring them. (Entanglement is equivalent to superposition in the context of a GPT (bipartite generalized measurement framework).)

[@dip4fish]

Quaternions are a subalgebra of Clifford Cl(3)

[@Achrononmaster]

based comment bro.

[@3zdayz]

1) Euler Angles aren't really where you're coming from, what you represented was axis-angle or Euler Axis which is a different thing to Euler Angles. Euler Angles are built as composites of rotation matrices - they work best when dealing with motors that have fixed mounting points, but not so much for the angular torque applied to a rocket in a more general direction. There is a system that is Euler Axis or Rotation vectors that is separate from Euler Angles; and grouping them together is a fair diservice, and actually somewhat of a reach as to why axis-angle is worse to work with than quaternions.... especially when your quaternions are time varying and you're really re-exponentiating the Log-0 Quaternions into Quaternations with the sin(theta*t);cos(theta*t)... and then you have the natural axis. YOu can use Rodrigues composite rotation formula for the equation to work with the axis part alone, and then you don't even lose where you are; it is possible that the same quaternion can be interpreted in two different ways, especially where a negative direction axis shows up. 2) Late in the show he was asking about wave speed relative to the emitter - and, as expected, jumped right into 'relative to the observer'. The motion of the observer an affect the observed speed of light, but the emitter emits a photon at a place and the wave has a velocity independent of the emitter (though there can/will be frequency shift, because a wave is emitter over time, and the maximum propagation speed is C, (which is actually why there's a doppler shift), and a wave will be compressed/elongated depending on where you're observing the result from.... 3) Space isn't compressed and more dense where there's more gravity; quite the opposite really. a) if it were compressed, there there would be an opposite time dilation where clocks would run faster, since it takes less space to cover to make the same signal... quite the opposite of travelling at a velocity. b) If space were compressed and drawn inward, then there would be an arc behind a black hole that is blacked out rather than being able to see the ring immediately from the other side - not to mention other things from actually directly behind the black hole. c) I've come to think of the random gittering of the particles - the so called intrinsic momentum, then (hypothetically) the waves and jitter will want to be in space that is less confining, and will in their random motions find a gradient towards a gravity well where space is LESS DENSE, and they will have more space to move in... the net aggregate force generally moves towards gravity... this would be partially why it's a weak 'force'... the space around a planet isn't actually stretched that much - the time dilation from a place in a gravity well is the same as the time dilation from travelling at the escape velocity from that point in the well... there's even a direct ratio of how much the space is stretched.... 4) rotation a rotation ( if you have an axis-angle, for something that is spinning, it would be a rotation, and applying it to some points you can get an orientation) then for the rotation, a torque on that rotation that rotates the rotation requires 720 degrees to get back to exactly the origin state of the initial rotation. It rotates from pi+x,axis to pi-x,-axis and then back, the first rotation is 2p, but the resulting rotation is a conjugate of sorts to the original that makes it rotate to the same orientation in 1 full tick. I have this STFRPhysics project on github that I played with all of this.... and have some demos to show where the intersections are for like rotation curves around the right, up and forward axises... I can draw the full rotation loops and the intersect at the 0 where they start, and 2pi rotation around on the other side of the origin... there's a lot of ways of looking at the relation could be x and 2pi-x or pi+x and pi-x, when rotating things, the effective range is actually generally around the 1pi rotation of the north pole rotated to the south pole, which is really sort of where the pi base comes from... Euler Axis vectors are additive too - and can be used with subtraction to find corrections; but addition applies when you have a bunch of toques measured in axis-angle that apply at the same moment they can all be added before being applied to the rotation. So there's toque, rotation and orientation; orientation is the result of applying a rotation to some points, and is a final representation - it's how the coffee cup looks - even though there might be a different rotation vector that gets it to exactly that location....

[@Achrononmaster]

There is no such thing as "compressing space". That'd just be a conformal gauging (remapping of coordinates, so unphysical). A bunch of masses or energy pulses can be compressed: as measured, say, by a network of a null ray affine parameters between them.

[@3zdayz]

@@Achrononmaster the gravitational waves aren't longitudinal compression waves?