Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrödinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical interpretation is sufficient to predict all measurable results of classical mechanics. In the classical case, the wave function that satisfies a linear equation is positive, which is the main source of the fundamental difference between classical and quantum mechanics.
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
It has been well established that holographic dark energy (HDE) is a serious candidate for being the dark energy of the universe. Here we deal with models where the holographic bound for dark energy is not saturated for a large portion of the history of the universe. This is particularly compelling when the IR cut-off is set by the Hubble scale, since otherwise a transition from a decelerated to an accelerated era cannot be obtained for a spatially flat universe. We demonstrate using three generic but disparate dynamical models, two of them containing a variable Newton constant, that a transition between the two eras is always obtained for the IR cut-off in the form of the Hubble scale and the non-saturated HDE. We also give arguments for why such a choice for the dark energy is more consistent and favoured over the widely accepted saturated form.
Conventional relativistic quantum mechanics, based on the KleinGordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead to such predictions.
We consider a holographic dark energy model, in which both the cosmological-constant (CC) energy density ρ Λ and the Newton constant G N are varying quantities, to study the problem of setting an effective field-theory IR cutoff. Assuming that ordinary matter scales canonically, we show that the continuity equation univocally fixes the IR cutoff, provided a law of variation for either ρ Λ or G N is known. Previous considerations on holographic dark energy disfavor the Hubble parameter as a candidate for the IR cutoff (for spatially flat universes), since in this case the ratio of dark energy to dark matter is not allowed to vary, thus hindering a deceleration era of the universe for the redshifts z > ∼ 0.5. On the other hand, the future event horizon as a choice for the IR cutoff is being favored in the literature, although the 'coincidence problem' usually cannot be addressed in that case. We extend considerations to spatially curved universes, and show that with the Hubble parameter as a choice for the IR cutoff one always obtains a universe that never accelerates or a universe that accelerates all the time, thus making the transition from deceleration to acceleration impossible. Next, we apply the IR cutoff consistency procedure to a renormalization-group (RG) running CC model, in which the low-energy variation of the CC is due to quantum effects of particle fields having masses near the Planck scale. We show that bringing such a model (having the most general cosmology for running CC universes) in full accordance with holography amounts to having such an IR cutoff which scales as a square root of the Hubble parameter. We find that such a setup, in which the only undetermined input represents the true ground state of the vacuum, can give early deceleration as well as late time acceleration. The possibility of further improvement of the model is also briefly indicated.
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