The logical consistency of a description of quantum theory in the context of general relativity, which includes minimal coupling principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will argue from this standpoint and use an argument that claims the incompleteness of the general relativistic description of gravitation, which emerges as a consequence of the gravitationally induced phases of the so-called flavor-oscillation clocks, that the postulates of quantum theory are logically incompatible with the usual minimal coupling principle. It will be shown that this inconsistency could emerge from the fact that the required geometrical information to calculate the probability of finding a particle at any point of the respective manifold does not lie in a region with finite volume. Then we put forth a new quantum minimal coupling principle in terms of a restricted path integral, and along the ideas of this model not only the propagator of a free particle is calculated but also the conditions under which we recover Feynman's case for a free particle are deduced. The effect on diatomic interstellar molecules is also calculated. The already existing relation between restricted path integral formalism and decoherence model will enable us to connect the issue of a quantum minimal coupling principle with the collapse of the wave function. From this last remark we will claim that the geometrical structure of the involved manifold acts as, always present, a measuring device on a quantum particle. In other words, in this proposal we connect the issue of a quantum minimal coupling principle with a claim which states that gravity could be one of the physical entities which results in the collapse of the wave function.
The logical consistency of a description of quantum theory in the context of general relativity, which includes minimal coupling principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will argue from this standpoint and use an argument that claims the incompleteness of the general relativistic description of gravitation, which emerges as a consequence of the gravitationally induced phases of the so-called flavor-oscillation clocks, that the postulates of quantum theory are logically incompatible with the usual minimal coupling principle. It will be shown that this inconsistency could emerge from the fact that the required geometrical information to calculate the probability of finding a particle at any point of the respective manifold does not lie in a region with finite volume. Then we put forth a new quantum minimal coupling principle in terms of a restricted path integral, and along the ideas of this model not only the propagator of a free particle is calculated but also the conditions under which we recover Feynman's case for a free particle are deduced. The effect on diatomic interstellar molecules is also calculated. The already existing relation between restricted path integral formalism and decoherence model will enable us to connect the issue of a quantum minimal coupling principle with the collapse of the wave function. From this last remark we will claim that the geometrical structure of the involved manifold acts as, always present, a measuring device on a quantum particle. In other words, in this proposal we connect the issue of a quantum minimal coupling principle with a claim which states that gravity could be one of the physical entities which results in the collapse of the wave function.
The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an example, the case of a particle whose coordinates are being monitored. Employing the so-called restricted path integral formalism, it will be shown that the measuring process could always contain information concerning the gravitational field. In other words, it seems that with the presence of a measuring process the equivalence principle may, in some cases, break down. The relation between the breakdown of the equivalence principle, at quantum level, and the fact that the gravitational field could always act as a decoherence environment, is also analyzed. The phenomena of quantum beats of quantum optics will allow us to consider the possibility that the experimental corroboration of the equivalence principle at quantum level could be taken as an indirect evidence in favor of the quantization of the gravitational field, i.e. the quantum properties of this field avoid the violation of the equivalence principle.
The relation between Einstein equivalence principle and a continuous quantum measurement is analyzed in the context of the recently proposed flavor-oscillation clocks, an idea pioneered by Ahluwalia and Burgard (Gen. Rel. Grav.29, 681(E) (1997)). We will calculate the measurement outputs if a flavor-oscillation clock, which is immersed in a gravitational field, is subject to a continuous quantum measurement. Afterwards, resorting to the weak equivalence principle, we obtain the corresponding quantities in a freely falling reference frame. Finally, comparing this last result with the measurement outputs that would appear in a Minkowskian space–time it will be found that they do not coincide, in other words, we have a violation of Einstein equivalence principle. This violation appears in two different forms, namely: (i) the oscillation frequency in a freely falling reference frame does not match with the case predicted by general relativity, a feature previously obtained by Ahluwalia; (ii) the probability distribution of the measurement outputs, obtained by an observer in a freely falling reference frame, does not coincide with the results that would appear in the case of a Minkowskian space–time. Concerning this last difference, the probability distribution differs in two directions. Firstly, the maximum, as function of the energy of the system (that emerges if we calculate first the probability distribution in the original curved manifold and then, resorting to the weak equivalence principle, we find the corresponding expression in a freely falling reference frame) is shifted with respect to the case in which the system is in a Minkowskian space–time. Secondly, the magnitude of this maximum is not equal to the respective quantity predicted by general relativity. In other words, we obtain two new theoretical results that predict a violation of Einstein equivalence principle, and that could be measured.
“Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using the Dirac–Pauli representation of free Dirac equation to search for the clues. In particular, we study how the double-slit diffraction experiment, when only one Dirac particle (‘say’ electron) at a time is in the apparatus, could test a gravitizing QT proposal in which the wavefunction collapse emerges on the detector screen from the Dirac–Pauli representation, as an objective process, resolving the measurement problem of QT.” [1] We found that the Dirac–Pauli representation is inherently a unified theory embodying a gravitizing QT proposal that Dirac–Pauli representation as wave nature is manifestation of inertial mass and the Foldy-Wouthuysen representation as particle nature is manifestation of gravitational mass such that the fact, that same physics is involved in these two representations, is simply the validity and exhibition of the principle of equivalence, of GR, in QT. [1] Richard Howl et al 2019 New J. Phys. 21 043047 DOI 10.1088/1367-2630/ab104a
It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's "checker-board" trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum "coordinates". This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.
A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation of a given classical mechanics. Instead, our approach to quantum mechanics is modelled on a statement that is close in spirit to the equivalence principle of general relativity, thus bearing a strong resemblance with the equivalence principle of quantum mechanics formulated by Faraggi-Matone.
Given the classical dynamics of a non-relativistic particle in terms of a Hamiltonian or an action, it is relatively straightforward to obtain the non-relativistic quantum mechanics (NRQM) of the system. These standard procedures, based on either the Hamiltonian or the path integral, however, do not work in the case of a relativistic particle. As a result we do not have a single-particle description of relativistic quantum mechanics (RQM). Instead, the correct approach requires a transmutation of dynamical variables from the position and momentum of a single particle to a field and its canonical momentum. Particles, along with antiparticles , reappear in a very nontrivial manner as the excitations of the field. The fact that one needs to adopt completely different languages to describe a relativistic and non-relativistic free particle implies that obtaining the NRQM limit of QFT is conceptually nontrivial. I examine this limit in several approaches (like, for e.g., Hamiltonian dynamics, Lagrangian and Hamiltonian path integrals, field theoretic description etc.) and identify the precise issues which arise when one attempts to obtain the NRQM from QFT in each of these approaches. The dichotomy of NRQM and QFT does not originate just from the square root in the Hamiltonian or from the demand of Lorentz invariance, as is sometimes claimed. The real difficulty has its origin in the necessary existence of antiparticles to ensure a particular notion of relativistic causality. Because of these conceptual issues, it turns out that one cannot , in fact, obtain some of the popular descriptions of NRQM by any sensible limiting procedure applied to QFT. To obtain NRQM from QFT in a seamless manner, it is necessary to work with NRQM expressed in a language closer to that of QFT. This fact has several implications, especially for the operational notion of space coordinates in quantum theory. A close examination of these issues, which arise when quantum theory is combined with special relativity, could offer insights in the context of attempts to combine quantum theory with general relativity.