The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This approach is based on the assumption that quantum theory represents a theory being constitutive for human knowledge. Physical objects are characterized by the information one can gain from them being contained in the quantum state they are described by. Since every Hilbert space can be represented as a tensor product of two dimensional Hilbert spaces, one is led to the ur objects. According to this approach relativistic quantum fields and thus the existence of a Minkowski space-time are the consequence of an iteration of a quantization of binary alternatives. In the original formulation there was only obtained a description of quantum fields on a flat Minkowski space-time. In this work there is made the attempt to incorporate general relativity and to describe the gravitational field within this approach. Thus the existence of a (3+1)-dimensional space-time in the sense of general relativity is assumed to be a consequence of quantum theory interpreted in an abstract sense.
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This approach is based on the assumption that quantum theory represents a theory being constitutive for human knowledge. Physical objects are characterized by the information one can gain from them being contained in the quantum state they are described by. Since every Hilbert space can be represented as a tensor product of two dimensional Hilbert spaces, one is led to the ur objects. According to this approach relativistic quantum fields and thus the existence of a Minkowski space-time are the consequence of an iteration of a quantization of binary alternatives. In the original formulation there was only obtained a description of quantum fields on a flat Minkowski space-time. In this work there is made the attempt to incorporate general relativity and to describe the gravitational field within this approach. Thus the existence of a (3+1)-dimensional space-time in the sense of general relativity is assumed to be a consequence of quantum theory interpreted in an abstract sense.
The quantum theory of Ur-alternatives of Carl Friedrich von Weizsaecker tries to constitute general quantum theory based on the concept of logical alternatives in time. Based on this interpretation of quantum theory the existence of free objects in space, their symmetry properties and their interactions shall be inferred. The alternatives are represented by binary alternatives, which are called Ur-alternatives because of their logically fundamental character. Through Ur-alternatives as elementary quantum theoretical units of information the Copernican revolution with respect to the question of space is realized in a consequent way. This means that not the objects of nature are in a given space, but the existence of space arises as a kind of indirect representation of relations between abstract quantum theoretical objects. The Ur-alternatives do not exist in a given physical reality, but the existence of space is constituted by Ur-alternatives at all. Such a concept of reality is implicitly contained within the uncertainty relation and can be seen especially in the EPR-paradoxon. It is shown in this thesis in a mathematical consistent way that a state in the tensor space of many Ur-alternatives can directly be mapped into a real three dimensional space which means that together with the dynamics a representation in a (3+1)-dimensional space-time becomes possible. By considering the G2 an approach for the incorporation of the internal symmetries can be suggested. Furthermore the Ur-alternatives enable the constitution of a concept of interaction, which is based on quantum theoretical entanglement. By using this concept it is tried to obtain a purely quantum theoretical description of electromagnetism and gravity. This corresponds to a much more principle and in a radical sense background independent way of quantization.
Ever since quantum mechanics was first developed, it has been unclear what it really tells us about reality. A novel framework, based on 5 axioms, is presented here which offers an interpretation of quantum mechanics unlike any considered thus far: It is postulated that physical objects can exist in one of two distinct modes, based on whether they have an intrinsic actual spacetime history or not. If they do, their mode of existence is actual and they can be described by classical physics. If they do not, then their mode of existence is called actualizable and they must be described in terms of an equal-weight superposition of all possible actualizable (not actual) histories. The distinction is based on an axiom according to which there exists a limit in which spacetime reduces to a one-dimension reduced version, called areatime, and that objects which merely actualizably exist in spacetime actually exist in areatime. The operational comparison of the passage of time for such objects to the passage of time for a spacetime observer is postulated to be made possible by what is called an angular dual bilateral symmetry. This symmetry can be decomposed into the superposition of two imaginary phase angles of opposite sign. To mathematically describe the spacetime manifestation of objects which actually exist in areatime, each actualizable spacetime history is associated with an actualizable path, which in turn is associated with the imaginary phases. For a single free particle, the complex exponent is identified with a term proportional to its relativistic action, thus recovering the path integral formulation of quantum mechanics. Although based on some highly unfamiliar ideas, this framework appears to render at least some of the usual mysteries connected with quantum mechanics amenable to simple conceptual understanding. It also appears to connect the foundations of quantum theory to the foundation of the special theory of relativity while clarifying its relationship to the general theory of relativity and yields a testable prediction about a type of experiment, as yet unperformed, which under the current paradigm is utterly unexpected, namely, that the gravitational field of radiation is zero. The paper concludes with some speculations about how the theory may be extended to a metatheory of nature.(Note the paper was edited on 3-October-2011 to remove one sentence on page 7)
Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements-the principles of relativity and light speed invariance-are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.
Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements—the principles of relativity and light speed invariance—are used to derive the mathematical structure of Minkowski space–time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.
It is made the attempt to explain why there exists a division between internal symmetries referring to quantum numbers and external symmetries referring to space-time within the description of relativistic quantum field theories. It is hold the attitude that the symmetries of quantum theory are the origin of both sorts of symmetries in nature. Since all quantum states can be represented as a tensor product of two dimensional quantum objects, called ur objects, which can be interpreted as quantum bits of information, described by spinors reflecting already the symmetry properties of space-time, it seems to be possible to justify such an attitude. According to this, space-time symmetries can be considered as a consequence of a representation of quantum states by quantum bits. Internal symmetries are assumed to refer to relations of such fundamental objects, which are contained within the state of one single particle, with respect to each other. In this sense the existence of space-time symmetries, the existence of internal symmetries and their division could obtain a derivation from quantum theory interpreted as a theory of information.
Abstract Quantum mechanics and relativity are extraordinarily successful mathematical theories, yet their conventional physical interpretations rely on substantially different conceptual frameworks. The Theory of Space (TS) proposes a fourth dimension defined by the Planck-related interval, with interpreted as a longitudinal dimension associated with energy (cτ), rather than as the conventional Minkowski spacetime interval. This fourth dimension does not coexist continuously with the observable three spatial dimensions as a conventional four-dimensional manifold. Instead, TS proposes an oscillatory existence between observable 3D presence and a non-observable fourth-dimensional phase. Through this oscillation, the quantum system undergoes repeated dimensional projection into observable 3D, with individual eigenstates manifested probabilistically while the underlying quantum state continues to evolve. Within this framework, phenomena including measurement, the Born rule, the arrow of time, entropy, entanglement, tunneling, and Bell-type correlations acquire a common physical interpretation. Heisenberg uncertainty and non-commutativity are interpreted as consequences of physical parameters associated with different phases of the dimensional oscillation and therefore not simultaneously manifested within the same 3D instance. TS further distinguishes between the quantum system’s spatial component and its compact physical entity. Their coexistence within the complete system provides a proposed physical basis for quantum interference and phase-dependent phenomena, including the double-slit experiment and the path-integral description of quantum evolution. As an extension of the model, TS proposes that the periodic displacement and replacement of quantum space generate a pulsed inward spatial flow. This mechanism provides a possible basis for a quantized gravitational interaction and suggests that gravitational energy may be represented by a positive contribution. Related developments, including spiral spatial flows, follow naturally from the same dimensional-oscillation mechanism. The Theory of Space therefore seeks to provide a common conceptual framework for quantum, relativistic, and gravitational phenomena without replacing the established mathematical equations that successfully reproduce experimental observations. The present work develops this framework and invites critical examination of its assumptions, physical implications, and potential experimental consequences. Keywords: relativity; Lorentz transformation; quantum superposition; quantum superposition; collapse; entanglement; quantum gravity