Spin and Curvature of Space

[Yuri Danoyan]

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?

 

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)

Edited July 26, 2008 by Yuri Danoyan
multiple post merged

[foodchain]

The idea I get from this is that some differentiation comes from how you put the Pauli exclusion principal. Such as the geometry as I think you are putting it exists from how this occurs or is observed? So an analogy would be because such has this geometry is why impact between objects can exist for instance, sort of like or exactly like an electron in a way? Such as with that if memory serves you have to obey the Pauli exclusion principal and or the hund rule when filling in atomic orbital right?

 

So what I think with this in regards to QM does not put it as some magical force if you want. Rather if QM is continuous but non linear how would it obey itself in time for whatever the definition of time is.

 

That’s why I think it has to hold some properties in common with the concept that is natural selection, in that variance has to hold true in same fashion to simply exist, plus I do not think you could model for a reality that states something that physically exists cant, so I always aim to include evolution somehow anyways. So I would think that momentum and position have to hold a physical basis, I mean classical physics calls for such right, and of course I think such is in relativity right? Yet as with QM both of those theories suffer some kind of limit or shortfall in say ability to predict natural behavior or is it physical behavior?

[Yuri Danoyan]

See my thread about space and time...

http://www.scienceforums.net/forum/showthread.php?t=34427

 

Eventually we can speak about space separately from timeю

[Yuri Danoyan]

"I rather suspect that the simple ideas of geometry, extended down into infinitely small space, are wrong"

 

R.P. Feynman, The Character of Physical Law (The M.I.T. Press, 1990), p. 166.

 

Why Richard Feynman didn't wrote about traditional space - time.Only about space?

 

"I rather suspect that the simple ideas of geometry, extended down into infinitely small space, are wrong"

 

R.P. Feynman, The Character of Physical Law (The M.I.T. Press, 1990), p. 166.

 

Why Richard Feynman didn't wrote about traditional 4-dimensional space-time .Only about space?

 

According to Klein's interpretation, which is based on the

projective geometry, the Euclidean, Lobachevsky and Riemannian geometry’s are in the unified scheme.

Interesting that Dirac used projective geometry as power tool for his derivations.

Edited August 17, 2008 by Yuri Danoyan