## Quantum Hyperspheres?

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### Quantum Hyperspheres?

Browsing this fascinating site, I have come across many speculations on higher dimensions and quantum matters and particle spins that may relate to something I have been working on for some years. I would like to outline it here to see if forum members can either find faults in the reasoning or ways forward with it. I welcome criticism or collaboration with equal enthusiasm.

1) The following paper makes the case that the entire universe has the geometry of a Glome type hypersphere or 3-sphere.
(see https://www.specularium.org/hypersphere-cosmology)

2) Quantum physics appears incomplete to say the least, and quantum field theory looks like an increasingly tortuous conceptual mess of ad-hoc hypotheses and questionable maths.

3) If a hyperspherical geometry applies to the entire universe then perhaps it also applies to the quanta and fields which compose it.
The Quantum Hypersphere idea starts with a model of the neutrino, the seemingly simplest of the matter quanta or fermions.

A four-dimensional object can rotate in two different planes simultaneously. See a doubly rotating tesseract/hypercube here: -
https://en.wikipedia.org/wiki/Rotations ... dean_space
This gives a visualisable picture of such a double rotation.

If we imagine the ‘inside out’ rotation as occurring in the wz plane with z also representing the direction of propagation, then the xy rotation corresponds to the ‘roll’ around the z axis.

If the double rotation is not isoclinic but has xy rotating at only half the rate of wz then perhaps this accounts for the spin ½ spinor.

Reversing the direction of the propagation z axis also reverses the direction of the xy spin. Thus, a neutrino coming from the opposite direction appears as an antineutrino and we get the observed parity violation, i.e. no right handed neutrinos or left handed antineutrinos.

I hope to show that all fermions have a basic neutrino ‘skeleton’. Electrons and nuclear particles can have extra spins* as well that do not reverse with inversion of the z axis of spatial propagation, thus allowing for both right- and left-handed electrons and positrons for example.

(* I suspect this involves extra dimensions, possibly imaginary time dimensions which may have a pseudo-spatial Minkowski signature.)

Anyway, I look forward to your comments on the basic idea of spinors from a non-isoclinic double rotation in four spatial dimensions.

Regards, Pete.
Peter J Carroll
Mononian

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Joined: Wed May 05, 2021 3:47 pm

### Re: Quantum Hyperspheres?

Are you assuming that neutrinos move at lightspeed? If not, then what's the "direction of propagation" of a neutrino at rest?

What happens when a particle slowly accelerates from -z to 0 to +z velocity? Does it instantaneously change from left-handed to right-handed?
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
mr_e_man
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Joined: Tue Sep 18, 2018 4:10 am

### Re: Quantum Hyperspheres?

Do any observations show neutrinos moving at anything less than lightspeed?

I understand that a lightspeed particle should have no mass but that neutrino oscillation implies that they may have mass, and so an apparent contradiction appears.

A photon reflected from a mirror changes its handedness and I would expect a neutrino to do the same, however, what could act as a neutrino mirror?
Peter J Carroll
Mononian

Posts: 5
Joined: Wed May 05, 2021 3:47 pm

### Re: Quantum Hyperspheres?

Neutrino mirror! Never thought of that.

Okay, say neutrinos move at lightspeed. But what about an electron accelerating in a uniform electric field from -z to 0 to +z velocity?

Peter J Carroll wrote:Electrons and nuclear particles can have extra spins* as well that do not reverse with inversion of the z axis of spatial propagation, thus allowing for both right- and left-handed electrons and positrons for example.

Are you saying here that its handedness stays the same?

What would distinguish a left- from a right-handed electron at rest, when both have the same direction of spin?
ΓΔΘΛΞΠΣΦΨΩ αβγδεζηθϑικλμνξοπρϱσςτυϕφχψωϖ °±∓½⅓⅔¼¾×÷†‡• ⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎
ℕℤℚℝℂ∂¬∀∃∅∆∇∈∉∋∌∏∑ ∗∘∙√∛∜∝∞∧∨∩∪∫≅≈≟≠≡≤≥⊂⊃⊆⊇ ⊕⊖⊗⊘⊙⌈⌉⌊⌋⌜⌝⌞⌟〈〉⟨⟩
mr_e_man
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Joined: Tue Sep 18, 2018 4:10 am

### Re: Quantum Hyperspheres?

The 4D spinor model proposed for the neutrino implies that it behaves as a Majorana rather than a Dirac fermion, and thus it acts as its own antiparticle.

The electrons correspond to abstract Dirac bi-spinors and I seek to give this description a geometric meaning in extra dimensions of some sort.

A particle moving at lightspeed always has its chiral spin axis in the direction of propagation, so its helicity corresponds to its chirality.

At sub-lightspeed the direction of a particle’s spin axis does not have to align with the direction of propagation, and as the Stern-Gerlach experiment implies it seems to either tumble around randomly or exist in a superposition of states between impositions of measurement.

Can we in principle ever bring an electron to rest and measure its spin without disturbing its state of rest?
Peter J Carroll
Mononian

Posts: 5
Joined: Wed May 05, 2021 3:47 pm

### Re: Quantum Hyperspheres?

Neutrino Spin and Electron Spinors.PNG

Hopefully I have just discovered how to add a diagram, apologies for the delay.

Taking some inspiration from these papers https://physicsdetective.com/articles/a ... particles/

(do participants here give them any credibility?)

It would seem that a simple twist propagating at lightspeed may suffice for a description of the neutrino and the antineutrino, although each then becomes the antiparticle of itself if they meet head on.

It would seem that we could describe electrons as bi-spinors composed of a wz and an xy rotaion with the magnetic and electric aspects of their electromagnetic charge arising from their wz and xy spins respectively. Electrons only have to have wz spins precisely parallel to their direction of propagation if they travel close to lightspeed. The geometry of electrons would thus correspond to a doubly rotating fat spindle torus that 'looks' spherical and has a similar topology to a hypersphere.

In this model quanta do not appear as point particles but as spins in the fabric of spacetime that have a frame dragging effect.

Do participants see any mileage in this approach?
Peter J Carroll
Mononian

Posts: 5
Joined: Wed May 05, 2021 3:47 pm