The compatibility of special relativity and Quantum Mechanics has been questioned by several authors. The origin of this tension can be traced back mainly to the introduction of the measurement processes and the corresponding wave function reduction, which play a crucial role in Quantum Mechanics. We approach this problem within a recent proposal for a model of Quantum Mechanics, where the measurement is explicitly described as a specific stochastic process. This implements ordinary Quantum Mechanics, where measurement and reduction are treated as phenomenological events of unknown origin without any physical justification. To state clearly the question, we first discuss and establish the effect of a Lorentz transformation on a generic wave function in space-time. This allows to formulate the relativistic version of the model. We then consider few thought experiments in order to analyze to what extent Quantum Mechanics follows relativistic invariance and find the specific critical points where non invariance possibly occurs. The relevance of this analysis on the experimental observations is also discussed.
The compatibility of special relativity and Quantum Mechanics has been questioned by several authors. The origin of this tension can be traced back mainly to the introduction of the measurement processes and the corresponding wave function reduction, which play a crucial role in Quantum Mechanics. We approach this problem within a recent proposal for a model of Quantum Mechanics, where the measurement is explicitly described as a specific stochastic process. This implements ordinary Quantum Mechanics, where measurement and reduction are treated as phenomenological events of unknown origin without any physical justification. To state clearly the question, we first discuss and establish the effect of a Lorentz transformation on a generic wave function in space-time. This allows to formulate the relativistic version of the model. We then consider few thought experiments in order to analyze to what extent Quantum Mechanics follows relativistic invariance and find the specific critical points where non invariance possibly occurs. The relevance of this analysis on the experimental observations is also discussed.
A Lorentz invariant model for gravity-induced quantum state reduction is presented, which is mainly developed from Penrose's argument that the time translation operator in a superposition of macroscopic states is ill-defined. The problem to define a Lorentz invariant stochastic dynamics for the wave-function is solved by assuming that the stochastic time flow is running orthogonal to the deterministic, unitary time evolution inside the four-dimensional space-time, which makes the direction of causality independent from the chosen reference frame. This new view allows to accept Bell's position on the implication of quantum non-locality on relativity, without having to give up the Lorentz invariance of the specified dynamics. It is shown that it is possible to formulate on the basis of this new view a meaningful physical model. The model is also checked for possible higher order effects, which provide new starting points for experimental research.
The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. On the basis of a detailed analysis of Bell's concept of local causality, which is violated in quantum theory, we argue that this is a subtle, as well as an important effort. A central requirement appearing in relativistic quantum mechanics, namely local commutativity, is analyzed in detail and possible justifications are given and discussed. The complexity of the implications of wave function reduction in connection with Minkowski space-time are illustrated by a quantum mechanical measurement procedure which was proposed by Aharonov and Albert. This procedure and its relativistic implications are explicitly analyzed and discussed in terms of state evolution. This analysis shows that the usual notion of state evolution fails in relativistic quantum theory. Two possible solutions of this problem are given. In particular, it is shown that also a theory with a distinguished foliation of space-time into space-like leafs - accounting for nonlocality - makes the right predictions for the Aharonov-Albert experiment. We will repeatedly encounter that an analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory, but that the actual events in space time, which are predicted and described by the theory, are crucial. Relativistic versions of quantum mechanical theories which precisely describe actual processes in space-time are briefly described and discussed in the appendix.
We argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between those two theories. A new relativistic transformation recently-proposed renders physical laws form-invariant via transformation of physical quantities, instead of space-time coordinates. This new perspective on relativistic transformation provides an insight into the very meaning of the principle of relativity. The principle of relativity means that the same physical laws hold in all inertial frames, rather than their mathematical formulas are Lorentz-covariant under the Lorentz transformation of space-time coordinates. The space-time concept underlying this new relativistic transformation is Newtonian absolute space and absolute time. With this new perspective, quantum theory becomes compatible with the principle of relativity. A new theory of relativistic quantum mechanics is formulated. The new relativistic quantum mechanics thus obtained maintains the essentials of non-relativistic quantum mechanics, for instance, the statistical single-particle interpretation. Studies on standard problems in quantum mechanics, square step and barrier potential, show that the new relativistic quantum mechanics is free from such anomalies as the negative probability density, Zitterbewegung and the Klein paradox bedeviling the current relativistic quantum mechanics. Furthermore, a remarkable result is found as applying the new relativistic quantum mechanics to study the problems of square potential well --- a particle can not be confined within an infinite square well of width less than half of the Compton wavelength of the particle. As implications of this finding in nuclear physics, there is a lower bound on the size of atomic nucleus. Neither an electron, nor a positron, can be confined inside the nucleus.
This paper presents a conceptual framework for reinterpreting the Lorentz transformation through the lens of quantum mechanics. By treating spacetime as a quantum structure, the author explores the eigenvalue nature of the speed of light (±c) and derives relativistic effects from the probabilistic superposition of lightlike intervals. Key highlights: - **Quantum Spacetime:** Proposes that space and time are not independent backgrounds but emerge from the quantum states of spacetime quanta. - **Derivation of Lorentz Transformation:** Demonstrates how the transformation arises from the statistical correlation of quantum states rather than classical kinematics. - **Philosophical Implications:** Offers a novel perspective on the ontology of motion, suggesting that reference frames are representations of quantum states. This work aims to provide an intuitive understanding of special relativity and stimulate discussion on the quantum nature of spacetime.
Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.
This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity.