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Absolute Space-Time and Measurement

Salim Yasmineh

Published Feb 28, 2020• 0 citations
OpenAlex

Abstract

The concept of simultaneity is relative in special relativity whereas, it seems to have a definite meaning in quantum mechanics. We propose to use the invariant space-time interval introduced by special relativity as a benchmark for constructing an absolute notion of space-time. We also propose to illustrate that when no measurement is conducted on a quantum system its wave function lives as a wave in the absolute space-time but, when a measurement is to be conducted, we must switch to an ordinary observable frame of reference where the quantum system lives as a particle.

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The concept of simultaneity is relative in special relativity whereas, it seems to have a definite meaning in quantum mechanics. We propose to use the invariant space-time interval introduced by special relativity as a benchmark for constructing an absolute notion of space-time. We also propose to illustrate that when no measurement is conducted on a quantum system its wave function lives as a wave in the absolute space-time but, when a measurement is to be conducted, we must switch to an ordinary observable frame of reference where the quantum system lives as a particle.
Abstract The concept of simultaneity is relative in special relativity whereas, it seems to have a definite meaning in quantum mechanics. On the other hand, theory and experiments in quantum mechanics have revealed the existence of non-local causal relations. We propose to use the invariant space-time interval introduced by special relativity as a benchmark for constructing a spacetime framework presenting a notion of an invariant time. We suggest that a physical system creates a non-local field within the spacetime framework and that the wavefunction of the physical system is an ontological entity that represents this non-local field. We propose to explain measurement and entanglement by using de Broglie Bohm theory in the context of the constructed spacetime framework.
In Newtonian physics, the equation of motion is invariant when the direction of time (t→−t) is flipped. However, in quantum physics, flipping the direction of time changes the sign of the Schrödinger equation. An anti-unitary operator is needed to restore time reversal in quantum physics, but this is at the cost of not having a consistent definition of time reversal applicable to all fundamental theories. On the other hand, a quantum system composed of a pair of entangled particles behaves in such a manner that when the state of one particle is measured, the second particle ‘simultaneously’ acquires a determinate state. A notion of absolute simultaneity seems to be inferred by quantum mechanics, even though it is forbidden by the postulates of relativity. We aim to point out that the above two problems can be overcome if the wavefunction is defined with respect to proper time, which in fact is the real physical time instead of ordinary time.
We provide strong evidence for single-electron spatial dynamics with a macroscopic discontinuity. The dynamics is observed in an electron quantum phase consisted of macroscopic quantum orbits similar to those responsible for the integer quantum Hall effect. The dynamics is consistent with the standard QM that predicts a "cloud-like" behavior of electron in quantum orbits regardless of their lengthscale. Sinse the dynamics is beyond the relativistic paradigm of movement, it may well be nonlocal. It thereby can be the basis for a quantum concept of absolute simultaneity, which now rests not on the meaningless notion of infinite speed but on empirically-tested quantum effect. This concept revives the Bell-Popper idea to replace the current "kinematic" version of relativity by the "dynamic" version by Lorentz and Poincare with a revival of the classical view of space and time where the problem of preferred reference frame now can be solved without to involve the vague notion "aether". We argue that the concept of quantum absolute simultaneity opens the door to a realistic interpretation of standard QM through a deeper insight of what is called "reality" and ultimately to a harmony between quantum and relativity theories.
The developments of special relativity and quantum mechanics marked beginning of modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity---the space-time interval---whose value all inertial observers agree upon. This reveals, so to speak, a genuine fact of universe, a relativistic invariant. On other hand, since dawn of quantum mechanics, there is no consensus on what theory is all about. The situation is admittedly subtler: quantum theory is grounded on a complex vector space and very notions of and reference frame are controversial. Here we construct a theoretical framework within which a given combination of quantum resources is shown to be a Galilean invariant. To this end, we postulate a principle of relational symmetry between the observer and the observed and employ notion of quantum reference frame. Unitary transformations then follow that allow us to perceive physical resources seen from viewpoint of any quantum system. Interestingly, we find that one needs more than quantum coherence and quantum correlations to prove quantum resources covariance. Finally, we show that notion of physical reality implied by quantum mechanics is not absolute.
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.
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 with the help of 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 in general, we first discuss and establish the effect of a Lorentz transformation on a generic wave function in space-time. Alongside the analysis we 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 analysis can shade light to the interpretation of the existing experimental observations.