Abstract
In a series of essays, beginning with this article, we are going to develop a new formulation of microphenomena based on the principles of reality and causality. The new theory provides us with a new depiction of microphenomena assuming a unified concept of information, matter and energy. So, we suppose that in a definite microphysical context (including other interacting particles), each particle is enfolded by a probability field whose existence is contingent on the existence of the particle, but it can locally affect the physical status of the particle in a context-dependent manner. The dynamics of the whole particle-field system obeys deterministic equations in a manner such that when the particle is subjected to a conservative force, the field also experiences a conservative complex force, the form of which is determined by the dynamics of the particle. So, the field is endowed with a given amount of energy, but its value is contingent on the physical conditions the particle is subjected to. Based on the energy balance of the particle and its associated field, we argue why the field has a probabilistic objective nature. The basic elements of this new formulation, its application for some stationary states and its nonlinear generalization for conservative systems are discussed here.
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References
A Shafiee, On a new formulation of micro-phenomena: Quantum paradoxes and the relativistic generalization, quant-ph/arXiv:0810.1033
A Shafiee, A Massoudi and M Bahrami, On a new formulation of micro-phenomena: The double-slit experiment, quant-ph/arXiv:0810.1034
A Einstein, B Podolsky and N Rosen, Phys. Rev. 41, 777 (1935)
This indeed happens in the tunnelling effect which is explained in [1].
Two adjacent points which satisfy the relation ds 2 = c 2dt 2 − dq 2 (c is the velocity of light) can be connected by a light signal. This introduces a unified concept of spacetime in microworld which could be considered as a geometric relation for other applications.
An objective probability interpretation, here, means that there exist real, observer-independent properties attached to the very concept of probability, beyond the mere subjective knowledge one can gain from a stochastic examination. In our approach, the probability fields are another facet of a unified reality in which objective physical notions like matter, energy and motion are involved. So, while we might be ignorent of some of these properties (e.g., the energy of the field) at a given level of examination, their real existence would have effectively outward appearances somewhere in practice (see, e.g., §4).
Here, in general, we analyse the many-body problem in the centre-of-mass frame, where the total momentum of the particles is assumed to be zero and therefore the kinetic energy of the system only includes the motion of particles relative to the centre-of-mass.
D W Belousek, Foundations of Science 8, 109 (2003)
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The original EPR proposal, however, is a special case in which the context-dependency plays no role. For more explanation, see [1].
More accurately, the Bohr radius is defined as \(a_{0}={\hbar ^{2}}/{ m_{e}e^{\prime 2}}=0.52918\) Å. Considering μ ≃ m e , the two definitions coincide.
Whenever the particle is subjected to a conservative force, the energy of the whole PF system will be conserved too. This is because, when the energy of the particle is conserved, its associated field also experiences a conservative force (see, e.g, the relation (28)). Then, the energy of the whole system should also be conserved as is illustrated in the time-independent Schrödinger equation.
In fact, usually, the stationary fields are either real functions or they can be made real. An exception, however, is free particle’s state. Yet, for a free particle, one can deduce from relation (5) that f F = 0. So, this case is of no concern for what we discuss in this section.
By the term Hermitian, we mean that for every physical observable B, we should have \(\langle B\rangle =\langle B\rangle ^{\ast }\).
A D Polyanin and V F Zaitsev, Handbook of exact solutions for ordinary differential equations, 2nd edn (CRC Press, Florida, 2003) pp. 64–66
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SHAFIEE, A. On a new formulation of microphenomena: Basic principles, stationary fields and beyond. Pramana - J Phys 76, 843–873 (2011). https://doi.org/10.1007/s12043-011-0092-5
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DOI: https://doi.org/10.1007/s12043-011-0092-5