- Piscataway, New Jersey, United States
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Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In... more
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the ...
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In Bohmian mechanics the distribution |ψ|2 is regarded as the equilibrium distribution. We consider its uniqueness, finding that it is the unique equivariant distribution that is also a local functional of the wave function ψ.
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Recently Golshani and Akhavan 2001 J. Phys. A: Math. Gen. 34 5259 proposed an experiment that should be able to distinguish between standard quantum mechanics and Bohmian mechanics. It is our aim to show that the claims made by Golshani... more
Recently Golshani and Akhavan 2001 J. Phys. A: Math. Gen. 34 5259 proposed an experiment that should be able to distinguish between standard quantum mechanics and Bohmian mechanics. It is our aim to show that the claims made by Golshani and Akhavan are unwarranted.
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We re-examine Peres' statement ``opposite momenta lead to opposite directions''. It will be shown that Peres' statement is only valid in the large distance or large time limit. In the short distance or short time limit an additional... more
We re-examine Peres' statement ``opposite momenta lead to opposite directions''. It will be shown that Peres' statement is only valid in the large distance or large time limit. In the short distance or short time limit an additional deviation from perfect alignment occurs due to the uncertainty of the location of the source. This error contribution plays a major role in Popper's orginal experimental proposal. Peres' statement applies rather to the phenomenon of optical imaging, which was regarded by him as a verification of his statement. This is because this experiment can in a certain sense be seen as occurring in the large distance limit. We will also reconsider both experiments from the viewpoint of Bohmian mechanics. In Bohmian mechanics particles with exactly opposite momenta will move in opposite directions. In addition it will prove particularly usefull to use Bohmian mechanics because the Bohmian trajectories coincide with the conceptual trajectories drawn by Pittman et al. In this way Bohmian mechanics provides a theoretical basis for these conceptual trajectories.
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We re-examine Peres' statement “opposite momenta lead to opposite directions”. It will be shown that Peres' statement is only valid in the large distance or large time limit. In the short distance or short time limit an additional... more
We re-examine Peres' statement “opposite momenta lead to opposite directions”. It will be shown that Peres' statement is only valid in the large distance or large time limit. In the short distance or short time limit an additional deviation from perfect alignment occurs due to the uncertainty of the location of the source. This error contribution plays a major role in Popper's orginal experimental proposal. Peres' statement applies rather to the phenomenon of optical imaging, which was regarded by him as a verification of his statement. This is because this experiment can in a certain sense be seen as occurring in the large distance limit. We will also reconsider both experiments from the viewpoint of Bohmian mechanics. In Bohmian mechanics particles with perfectly opposite momenta will move in opposite directions. In addition it will prove particularly useful to use Bohmian mechanics because the Bohmian trajectories coincide with the conceptual trajectories drawn by Pittman et al. In this way Bohmian mechanics provides a theoretical basis for these conceptual trajectories.
Research Interests:
Recently Golshani and Akhavan 2001 J. Phys. A: Math. Gen. 34 5259 proposed an experiment that should be able to distinguish between standard quantum mechanics and Bohmian mechanics. It is our aim to show that the claims made by Golshani... more
Recently Golshani and Akhavan 2001 J. Phys. A: Math. Gen. 34 5259 proposed an experiment that should be able to distinguish between standard quantum mechanics and Bohmian mechanics. It is our aim to show that the claims made by Golshani and Akhavan are unwarranted.
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The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-(1/2) was dealt with by Holland. It appears that the... more
The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-(1/2) was dealt with by Holland. It appears that the uniqueness of boson paths can be enforced under well determined conditions. This in turn fixes the nonrelativistic particle equations of the nonrelativistic Schrödinger equation, which appear to correspond with the original definitions given by de Broglie and Bohm only in the spin-0 case. Similar to the spin-(1/2) case, there appears an additional spin-dependent term in the guidance equation in the spin-1 case. We also discuss the ambiguity associated with the introduction of an electromagnetic coupling in the Kemmer theory. We argue that when the minimal coupling is correctly introduced, then the current constructed from the energy-momentum tensor is no longer conserved. Hence this current cannot serve as a particle probability four-vector.
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In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by... more
In 1952 Bohm presented a theory about non-relativistic point-particles that move deterministically along trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm’s particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).