A novel perspective on relativistic transformation recently-proposed provides an insight into the very meaning of the principle of relativity. With this novel perspective and Bell's theorem, we argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between the two theories. A new theory of relativistic quantum mechanics is formulated upon this novel perspective. This new relativistic quantum mechanics is free from such anomalies as the negative probability density, the negative-energy states, Zitterbewegung, and the Klein paradox deep-rooted in the current relativistic quantum mechanics. Moreover, a remarkable result is found that a particle can not be confined within an infinite square well of width less than half of the Compton wavelength. As implications 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 by whatever interaction. Furthermore, we argue that the postulates of non-relativistic quantum statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of relativistic quantum statistics is formulated such that the probability distribution functions are the same as the three well-known probability distribution functions in non-relativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived by the new relativistic quantum statistics and the new relativistic quantum mechanics. This relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region. Yet, this relativistic speed distribution differs remarkably from Jüttner speed distribution in the high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic quantum statistics.
A novel perspective on relativistic transformation recently-proposed provides an insight into the very meaning of the principle of relativity. With this novel perspective and Bell's theorem, we argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between the two theories. A new theory of relativistic quantum mechanics is formulated upon this novel perspective. This new relativistic quantum mechanics is free from such anomalies as the negative probability density, the negative-energy states, Zitterbewegung, and the Klein paradox deep-rooted in the current relativistic quantum mechanics. Moreover, a remarkable result is found that a particle can not be confined within an infinite square well of width less than half of the Compton wavelength. As implications 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 by whatever interaction. Furthermore, we argue that the postulates of non-relativistic quantum statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of relativistic quantum statistics is formulated such that the probability distribution functions are the same as the three well-known probability distribution functions in non-relativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived by the new relativistic quantum statistics and the new relativistic quantum mechanics. This relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region. Yet, this relativistic speed distribution differs remarkably from Jüttner speed distribution in the high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic quantum statistics.
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 book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds systematically from the principle of relativity and postulates of quantum measurements to the renormalization in quantum electrodynamics. In the second part of the book "Quantum theory of particles" this traditional approach is reexamined. We find that formulas of special relativity should be modified to take into account particle interactions. We also suggest reinterpreting quantum field theory in the language of physical "dressed" particles. This formulation eliminates the need for renormalization and opens up a new way for studying dynamical and bound state properties of quantum interacting systems. The developed theory is applied to realistic physical objects and processes including the energy spectrum of the hydrogen atom, the decay law of moving unstable particles, and the electric field of relativistic electron beams. These results force us to take a fresh look at some core issues of modern particle theories, in particular, the Minkowski space-time unification, the role of quantum fields and renormalization as well as the alleged impossibility of action-at-a-distance. A new perspective on these issues is suggested. It can help to solve the old problem of theoretical physics -- a consistent unification of relativity and quantum mechanics.
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for the boson, neutral and charged, scalar and vector, including the photon, the electron. Uniqueness of this design has been proved. This is a relativistic invariant, describing the probability of the particle observation in points of space-time. The time is deprived of his role of a dynamic parameter of distribution and formally equalized with other coordinates. Also the meaning of the energy-momentum distribution is clarified. Conditions of such distributions observation are described. As applied to the quantum field these structures are transformed into new characteristics of particles distribution in space-time in addition to those for momentum states. Their operators for free fields are obtained. Under such model the Heisenberg's uncertainty relations are grounded for the relativistic particle; both particles and antiparticles turn out to be different states of a single particle; vacuum state of boson quantum field has zero energy.
A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.
Most of the applications of quantum mechanics are in the realm of the three phases of matters: gases, liquids and solids. In these cases a nonrelativistic quantum theory is sufficient. However, in principle, a strictly correct treatment should include relativity. For relativistic particles, that is, for particles travelling at speeds close to the speed of light, the nonrelativistic Schrödinger equation is not applicable. Oskar Klein and Walter Gordon1 proposed a relativistic wave equation for a free particle. Their equation fell into dispute because the probability density function is not positive definite, thereby preventing the probability interpretation.
Quantum mechanics, which describes the behaviour of matter and energy on very small scales, is one of the most successful theories in the history of science. Einstein's theory of special relativity, which describes the relationship between space and time, is likewise a highly successful and widely accepted theory. And yet there is a well-documented tension between the two theories, to the extent that it is still not clear that the two can ever be reconciled. This thesis is concerned with furthering the current understanding of the relationship between quantum mechanics and special relativity. In the first part of the thesis we study the behaviour of quantum information in relativistic spacetime. The field of quantum information arose from the realisation that quantum information has a number of crucial properties that distinguish it from classical information, such as the no-cloning property, quantum contextuality, and quantum discord. More recently, it has been realised that placing quantum information under relativistic constraints leads to the emergence of further unique features which are not exhibited by either non-relativistic quantum information or relativistic classical information; as part of this ongoing research programme we develop a new relativistic quantum `paradox' which puts pressure on conventional views about the spatiotemporal persistence of quantum states over time. We then study a new set of relativistic quantum protocols which involve the distribution of entangled states over spacetime, defining one task involving the distribution of the two halves of a known entangled state, and another task involving the distribution of the two halves of an unknown entangled state. The second part of the thesis deals with relativistic quantum cryptography, a field which first began attracting serious attention when it was realised that a cryptographic task known as `bit commitment,' can be implemented with perfect security under relativistic constraints. This result was highly significant, since it is provably impossible to implement bit commitment with perfect security in a purely classical or purely quantum context, and hence bit commitment is an ideal starting point for probing the power of relativistic quantum cryptography. In this thesis we propose several new relativistic quantum bit commitment protocols which have notable advantages over previously known protocols. We then move to a related task, a generalization of zero-knowledge proving which we refer to as knowledge-concealing evidencing of knowledge of a quantum state; we prove no-go theorems concerning the possibility of implementing this task with perfect security, and then set out a relativistic protocol for the task which is asymptotically secure as the dimension of the state in question becomes large. These results have interesting foundational significance above and beyond their applications in the field of cryptography, providing a new perspective on the connections between knowledge, realism and quantum states.