High School Can Classical Physics Transform into Quantum Physics in Modified Space-Time?

[bayakiv]

TL;DR

Can space be made to rotate in time?

Formally, this means that all timelike lines in Minkowski space are mapped onto helical lines of an infinite cylinder. Can it be argued that in such a modified space-time, classical physics inevitably turns into quantum physics?

 

[phinds]

Can space be made to rotate in time?

You can play whatever games you like with math but physically, what does this even MEAN?

 

[bayakiv]

Physically, this means that a classical particle makes a rotation in a modified space-time, the angle of which is measured by the action of this particle, and therefore, in the case of small values of the action, the classical particle acquires quantum properties.

 

[Vanadium 50]

PF Rules do not permit discussion of personal theories. However, there is a persistent belief that the way one makes progress is theoretical physics is merely a matter of getting the words in the right order. Nothing could be further from the truth.

If you can't make a quantitative prediction, you don't really have a theory.

 

[bayakiv]

I don't understand what personal theory means in this case. The idea presented goes back to Yuri Rumer https://en.wikipedia.org/wiki/Yuri_Rumer. My merit is that I managed to pack the space into a sphere, but we are not discussing this here. As for the predictions, they appear (in the form of the generalized Schrödinger equation) only after complete compactification, which we do not discuss here. That is why I proposed to limit ourselves to the problem of the cause of the emergence of quantum physics from classical.

 

[Botsina]

Do you mean what if the time dimension were compact, (so the spacetime would be R^n x T^1) or that space is anti-de Sitter (which includes closed timelike curves)? In either case you seem to be asking does time travel cause classical systems to behave like quantum systems. At the very least you would have to assume in addition that any physical fields were continuous and there was background noise so that paradoxes (and instabilities) would generate the exponentially large treelike structure needed to encode an exponentially large Hilbert space.

 

[bayakiv]

As for the question of the origin of the compact component of time, let me draw your attention to the thread https://www.physicsforums.com/threads/geometry-of-matrix-dirac-algebra.994329/ from where you can understand that a closed action is associated with the rotation of a seven-dimensional sphere. If it is not very clear, then it is worth explaining (I will add a post later) that the time cylinder and the Clifford torus of space are generated by the vacuum flow of matter, and the Clifford algebra is generated by the free motions of the Clifford torus. The corresponding Lie algebra is generated by 28 rotations of an 8-dimensional Euclidean space and 6 pseudorotations of a doublet of Minkowski spaces.

I did not understand the statement of the statement of fields and the exponential growth of Hilbert space.

 

[bayakiv]

The corresponding Lie algebra is generated by 28 rotations of an 8-dimensional Euclidean space and 6 pseudorotations of a doublet of Minkowski spaces.

It is not true. Really, using paired rotations, one can get Lie algebras $sl_n (\mathbb{C})$. In fact, let
$$\begin{equation}
\begin{split}
& I_{ij} = \left(1_{2i-1, \,2j-1} - 1_{2j-1, \,2i-1}\right) + \left(1_{2i, \,2j} - 1_{2j, \,2i}\right)\\
& J_{ij} = \left(1_{2i-1, \,2j-1} + 1_{2j-1, \,2i-1}\right) + \left(1_{2i, \,2j} + 1_{2j, \,2i}\right) \\
\end{split}
\end{equation}$$
where $i<j$ and $i,j = 1,\ldots,n$, and
$$\begin{equation}
D_{ii} = \left(1_{2i-1, \,2i-1} - 1_{2n-1, \,2n-1}\right) + \left(1_{2i, \,2i} - 1_{2n, \,2n}\right)
\end{equation}$$
where $i = 1,\ldots,n-1$, and
$$\begin{equation}
I = \sum\limits_{1}^{n}\left(1_{2i-1, \,2i}-1_{2i, \,2i-1}\right)
\end{equation}$$
Then the set $\left\{I_{ij},J_{ij},D_{ii},II_{ij},IJ_{ij},ID_{ii}\right\}$ is linearly independent basis for the algebra $sl_n(\mathbb{C})$ and the set $\left\{I_{ij},IJ_{ij},ID_{ii}\right\}$ forms a basis of the algebra $su(n)$, and $\left\{sl_n(\mathbb{C})\right\} = \left\{su(n)\right\} + I\left\{su(n)\right\}$. The Lie algebra $sl_n (\mathbb{C})$ is implemented as the proper motions of the torus $T^{n}=S^1 \times\cdots\times S^1$ over Villarso circles (due to paired rotations of the torus in a $2n$ - dimensional Euclidean space) and as the motions of this torus over the surface of the hypersphere of a $2n$-dimensional space with a neutral metric.

However, it seems that the isomorphic $sl_4 (\mathbb{C})$ Clifford algebra can also be realized as geometric algebras of the doublet (a direct sum) of Minkowski spaces with signatures (1,3) and (3,1). To confirm it is enough to refer to the Dirac representation.

 

[bayakiv]

To gain experience with links to articles in peer-reviewed journals and to develop the thread, I will try to link to the article " Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena " by Igor V. Bayak

• doi:10.7546/jgsp-38-2015-1-23
• http://www.bio21.bas.bg/jgsp/jgsp_files/vol38/volume38cont.html