Related papers: The Quantum-Classical Transition: The Fate of the …
We construct physical semi-classical states annihilated by the Hamiltonian constraint operator in the framework of loop quantum cosmology as a method of systematically determining the regime and validity of the semi-classical limit of the…
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural…
The origin of cosmic structure is widely regarded as quantum, yet the Universe today appears classical. Standard lore attributes this to a "quantum-to-classical" transition on super-horizon scales during inflation. Gravity plays a central…
Quantum speed limits set an upper bound to the rate at which a quantum system can evolve. Adopting a phase-space approach we explore quantum speed limits across the quantum to classical transition and identify equivalent bounds in the…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle…
If quantum mechanics were to be applicable to macroscopic objects, classical mechanics would have to be a limiting case of quantum mechanics. Then the category Set that packages classical mechanics has to be in some sense a 'limiting case'…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
One of the most important problems in Physics is how to reconcile Quantum Mechanics with General Relativity. Some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favor of a more…
After a revision of the main features of the structure of the Dirac electron a plausible definition of elementary particle is stated. It is shown that this definition leads in the classical case to a picture which produces a very clear…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…