Time & Probability: Relativistic Bohmian Mechanics

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In summary, the paper discusses the generalization of Bohmian mechanics to a relativistic theory without preferred foliation. This introduces the concept of spacetime probability, which is conserved in a scalar time. This concept is also seen in classical statistical mechanics of relativistic particles, where it is identified with proper time along particle trajectories. The paper proposes that only massive particles have Bohmian trajectories, and analysis of macroscopic measuring apparatus made up of massive particles aligns with the predictions of standard quantum theory.
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http://arxiv.org/abs/1309.0400v2
Time and probability: From classical mechanics to relativistic Bohmian mechanics
H. Nikolic
(Submitted on 2 Sep 2013 (v1), last revised 30 Sep 2013 (this version, v2))
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears naturally in classical statistical mechanics of relativistic particles, with scalar time being identified with the proper time along particle trajectories. The conceptual understanding of relativistic Bohmian mechanics is significantly enriched by this classical insight. In particular, the analogy between classical and Bohmian mechanics suggests the interpretation of Bohmian scalar time as a quantum proper time different from the classical one, the two being related by a nonlocal scale factor calculated from the wave function. In many cases of practical interest, including the macroscopic measuring apparatus, the fundamental spacetime probability explains the more familiar space probability as an emergent approximate description. Requiring that the quantum proper time in the classical limit should reduce to the classical proper time, we propose that only massive particles have Bohmian trajectories. An analysis of the macroscopic measuring apparatus made up of massive particles restores agreement with the predictions of standard quantum theory.
 
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I'm still reading the paper, but since I know the author hangs out here, I hope he wouldn't mind me asking some questions before I've hardly started :)

If "only massive particles have Bohmian trajectories", what would be the interpretation of the photon trajectories that lie behind the conception of this experiment? http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/
 

1. What is Relativistic Bohmian Mechanics?

Relativistic Bohmian Mechanics is a quantum theory that extends the principles of Bohmian Mechanics to include relativistic effects. It proposes that particles have definite positions and trajectories, but their behavior is influenced by a wave function that describes the probability of finding the particle at a certain location. This theory aims to resolve some of the paradoxes and inconsistencies present in traditional quantum mechanics.

2. How does Relativistic Bohmian Mechanics explain time?

In Relativistic Bohmian Mechanics, time is treated as an absolute and objective quantity. It is not considered a subjective experience or an emergent phenomenon, but rather a fundamental aspect of reality. The theory proposes that time is continuous and that the evolution of the universe is determined by the interaction between the particle positions and the wave function.

3. What is the role of probability in Relativistic Bohmian Mechanics?

In this theory, probability is an inherent property of particles and their wave function. It is not a result of our lack of knowledge or understanding, but rather a fundamental aspect of the universe. The wave function determines the probability of finding a particle at a certain location, and this probability is influenced by the particle's position and the wave function's evolution in time.

4. Can Relativistic Bohmian Mechanics be tested or proven?

Like any scientific theory, Relativistic Bohmian Mechanics can be tested through experiments and observations. However, due to its complex nature, it may be challenging to design experiments that can conclusively prove or disprove its validity. Nevertheless, there have been several experiments that support this theory, such as the delayed-choice quantum eraser experiment.

5. How does Relativistic Bohmian Mechanics relate to other theories of time and probability?

Relativistic Bohmian Mechanics is a unique theory that differs from other theories of time and probability, such as the Copenhagen interpretation or the Many-Worlds theory. It offers a different perspective on the nature of reality and provides a potential solution to some of the paradoxes and limitations of traditional quantum mechanics. However, it is still a subject of ongoing research and debate within the scientific community.

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