# Determinism from periodic dynamics?

## Main Question or Discussion Point

Recently ( http://arxiv.org/abs/0903.3680 ) has been pointed out a relationship between QM and periodic dynamics, generalizing the old approach to QM due to de Broglie at.al. In particular it is claimed that imposing periodic boundary conditions to a field (on flat spacetime in the free case) one can obtain the following quantum behaviors in a deterministic way: Hilbert space; Schrodinger equation, Path integral interpretation, Commutation relation, Uncertainty relation, Black Body radiation, Double-slit experiment, Quantum harmonic oscillator and Superconductivity. Is this a new possible interpretation for QM, similar to the Bohmian one?

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I must admit that I'm new of this forum but, looking at the other threads, I think this
is the right place where to discuss the issue.

Since the paper is rather long I'll try to summarize a little the idea which is a consequence of the fact that Time can be defined only assuming periodicity or vice versa.

The action of a free scalar field defined in a time interval T allows
periodic solutions with periodicity T. The frequency of the free periodic fields fixes the energy of the quanta as usual.
The periodicity introduces a non-locality in
the theory which however has no hidden variables. Similarly to the KK theory
where there is a quantization of the mass spectrum, here there is a
quantization of the energy spectrum which depends on the inverse of the
period through the Planck constant. The dispersion relation of the
quantized spectrum is the correct one also for massive scalar fields
since the proper time acts like a "virtual extra dimension". This
implies that the periodicity varies with the energy through Lorentz
transformations or interactions so that special relativity and
causality hold.

Periodic fields are stationary waves and they trivially give rise to
Hilbert space.
the Schrodinger equation follows as the "square root" of the KG equation and in the
Hilbert space the time evolution operator is Markovian. From these
results already contained in the theory, it is immediate to derive the Feynman path integral, which is interpreted as a sum over all the periodic paths, as well as
Commutation relations and Uncertainty relations. These important links
to QM are derived in par.2 and par.3 which are the core of the paper.

As a consequence of the quantization of the energy spectrum the massless periodic fields avoid the UV catastrophe of the black body radiation whereas the
non-relativistic free particle and the double slit experiment emerge as
a consequence of the fact that in the non relativistic limit only the
first harmonic of the energy spectrum is relevant. The Quantum Harmonic
Oscillator is exactly solved due to the analogy with the
Bohr-Sommerfeld condition. An attempt to solve the interaction case
is done by describing periodic fields in a AdS metric, the result is similar to the AdS/CFT correspondence. In fact, as classical fields with periodic BCs in Minkowski metric should correspond to quantized free fields, periodic fields in a deformed metric should describe the quantization of interacting fields. The AdS/QCD correspondence comes from the fact that in the Bjorken model for quark-gluon plasma this deformation is exponential, giving a virtual warped metric.

The standard meter in Paris and the Cesium atom are the operative definition of space and time in physics. The real difference between the definition of time and space is that, whereas you can move in space and compare a meter measured here with a miter measured there, you cannot move in time and you cannot compare a length of a second measured now and the length of a second measured yesterday. The only way to avoid this problem is to assume periodicity of isolated system as a fundamental principle together with a constant speed of light.
As proved in arXiv:0903.3680 the assumption of periodicity as a fundamental principle yields the remarkable possibility of a coherent and deterministic view of SR and QM.

ZapperZ
Staff Emeritus
I must admit that I'm new of this forum but, looking at the other threads, I think this
is the right place where to discuss the issue.
Other than the BTSM and High Energy forums, practically all of the sources used in the other physics forums should either be established physics sources or peer-reviewed publications (there are exceptions). As far as I can tell, the manuscript you are citing is still not published.

I suggest we wait for a few months, and when it is published, we can go back to it.

Zz.

Redbelly98
Staff Emeritus
Homework Helper
The paper linked to in the OP has been published [Found. Phys. 41, p. 178-203 (2011)], and this thread is now open for discussion.

The idea is evolved in the meantime...

Title: Clockwork Quantum Universe

Essay Abstract: Besides the purely digital or analog interpretations of reality there is a third possible description which incorporates important aspects of both. This is the cyclic interpretation of reality. In this scenario every elementary system is described by classical fields embedded in cyclic space-time dimensions. We will address these cyclic fields as "de Broglie internal clocks". They constitute the deterministic gears of a consistent deterministic description of quantum relativistic physics, providing in addiction an appealing formulation of the notion of time.

http://fqxi.org/community/forum/topic/901