# Spin and Curvature of Space

• gorgos
In summary: In the model of preon theory, quarks and leptons are composed of more fundamental particles called preons. Therefore, protons and neutrons are still considered stable particles, as they are made up of other stable particles.

#### gorgos

According to contemporary ideas the spin of elementary particle is a certain mysterious inner moment of impulse for which it is impossible a somewhat real physical picture to create. The absence of spin visual picture, in opinion of a number of authors leaves the regrettable gap in quantum mechanics interpretation. On the other hand, there are highly developed geometrical disciplines which are difficult to apply to specific physical theories owing to the fact that it is not always possible to point out the
objects to which the geometrical notions could be corresponded.We point out to one interesting analogy which, in our view testifies to the geometrical interpretation of spin.

Let's recall that according Pauli principle the two identical
particles with half-integral spin (fermions) cannot be simultaneously in the same quantum state. The alternative of Pauli principle maintains that in one and the same quantum state any number of particles (bosons) with integral spin could be found (infinitely much in the limit). Thus, the two similar fermions can't be found in the same space point. For bosons the situation is quite
different.

The remarkable fact: when in one case in one and the same place of space one can't put more than one particle and in the other-infinitely much, which gives a hint that spin has a some-what geometrical sense. To speak in images the spin in one case creates very "tight", and in the other case - very "spacious" space. Why so? To this question we cannot now give an answer which speaks for necessity to find an answer in the geometrical notions.

That's why we proceed to the geometry and study some facts reminding us the situation with fermions and bosons.It is well-known that besides the Euclidean geometry there are other geometrical systems (Lobachevsky, Riemannian geometry).
According to Klein's interpretation, which is based on the
projective geometry, the Euclidean, Lobachevsky and Riemannian geometry’s are in the unified scheme. The most known indication toidentify the latter two geometry is: in the Riemannian geometry(elliptical) across given point can't draw a straight line which couldn't cross the given straight line (analogy with the fermion)and in the Lobachevsky geometry (hyperbolic) across every point the infinite set of straight lines is passing, not intersecting with the given hyperbolic straight line (the analogy with bosons).

The analogy yet proves nothing. But in this case this is the fact that requires close consideration, study and discussion.The suspicion arises that spin is the sign of elementary particle pointing out to its non-Euclidean nature. May be the zero curvature of our space develops from total positive and negative curvaturesof spaces created by fermions and bosons? Not this is a key tounderstand "the space-time foam", idea which was put forward by Wheeler and Hawking? Couldn't this approach help to solve the cosmological problems?

Yuri Danoyan

Fermions---antysymmetric wave function
Bosonы--symmetric wave function

Elliptic--pozitive curvature(symmetric)
Hyperbolic--negative curvature(antisymmetric)

Summary:

symmetry(mathematical)+antisymmetriy(physical)

antisymmetry( mathematical)+symmetry(physical)

Nfer x Mfer +NbosxMbos=0 ?
Nfer x{K>0}+Nbos x{k<0}=0 ?

gorgos said:
The analogy yet proves nothing.
True that nothing is proven, but it is interesting.
the two similar fermions can't be found in the same space point.
When you say similar, you must include spin and momentum. Two electrons with spin up can be in the same space point if they have different momenta.
Let's recall that according Pauli principle the two identical
particles with half-integral spin (fermions) cannot be simultaneously in the same quantum state. The alternative of Pauli principle maintains that in one and the same quantum state any number of particles (bosons) with integral spin could be found (infinitely much in the limit).
The link between spin and statistics is more rigorously understood in quantum field theory.

Supersymmetry is probably best suited for you purposes. It is the only extension the ordinary space-time symmetries to include fermion-boson symmetry. In superspace, you may give a more rigorous meaning to your intuitions.

See Gravitation of W.Misner,K.Thorn,J.Wheeler
Part IV, par.20 Conservation Laws for 4-Momentum and Angular Momentum
about connection between spin and curvature

Supersymmetry is probably best suited for you purposes

Best for me extended supersymmetry for n=3, cut by half, without graviton: 1 3 3 1, and 3 1 vice versa.

2. Only 3 elementary particles are stable with a half-integer spin (proton, electron, neutrino) and 1 is stable with an integer spin (photon),

gorgos said:
2. Only 3 elementary particles are stable with a half-integer spin (proton, electron, neutrino) and 1 is stable with an integer spin (photon),
But why do you include the proton in this list, which is not elementary ? A proton is made up of quarks. If you include the proton, then why don't you include the neutron ? Then why don't you include heavier nuclei !?

Nobody observed decay of proton.
Nobody observed free quarks.
Longevity of neutron only 17 min.
Heaviest nuclei not stable.

Last edited:
If you aren't prepared to accept the composite nature of protons, how do you explain the plethora of experimental data since we started doing the so-called "deep inelastic scattering" of protons?

The composite nature of protons not mean non-stable.

## 1. What is the difference between spin and curvature of space?

The spin of an object refers to its intrinsic angular momentum, or the amount of rotation it possesses. In contrast, curvature of space refers to the bending of space caused by the presence of mass or energy. While spin is an inherent property of all objects, curvature of space is a result of the effects of gravity.

## 2. How does the spin of an object affect its motion in space?

The spin of an object can affect its motion in space in several ways. For example, the spin of a planet causes it to have a slight bulge at the equator and results in its rotation. In quantum mechanics, the spin of a subatomic particle can influence its behavior and interactions with other particles.

## 3. What is the relationship between spin and angular momentum?

Spin is a type of angular momentum, which is a physical quantity that measures the amount of rotation an object possesses. However, spin is a different type of angular momentum than orbital angular momentum, which refers to the rotation of an object around an external axis. Spin is an intrinsic property of an object and does not require an external axis.

## 4. Can spin and curvature of space be observed or measured?

Yes, both spin and curvature of space can be observed and measured through various scientific experiments and observations. For example, the spin of a planet can be measured through its effects on its orbit and rotation. The curvature of space can be observed through the bending of light by massive objects, such as stars and galaxies.

## 5. How do spin and curvature of space relate to Einstein's theory of general relativity?

Einstein's theory of general relativity describes the relationship between matter and the geometry of space-time. The curvature of space is a key component of this theory, as it is caused by the presence of matter and energy. Spin is also accounted for in general relativity, as it is a form of energy that contributes to the overall curvature of space-time.

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