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arXiv:2408.00046 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Measuring the speed of quantum particles without a round-trip under non-synchronized quantum clocks

Tomer Shushi

Published Jan 1, 2025• 0 citations
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Abstract

One of the main issues in measuring the speed of light when it only travels from one spatial position into another position, known as the one-way speed of light, is that the clocks belonging to each separated spatial position are not and, in principle, cannot be synchronized. Here, we show that it is possible, in principle, to measure the velocity of particles that travel at the speed of light without assuming a round-trip once we adopt a quantum mechanical description under two boundary conditions to the state of the quantum system followed by the two-state-vector formalism while assuming non-synchronized quantum clocks with unknown time dilation. The weak value of velocity can be measured for a test particle that has a clock that is not synchronized with the clock of the quantum particle. Following the proposed set-up, when the weak value of the velocity is known even without knowing the time states of the system, such a weak velocity is the two-way speed of light. We further explore some fundamental implications of the set-up. The proposed approach opens a new avenue toward measuring the velocities of quantum particles while overcoming relativistic issues regarding the synchronization of clocks.

DOI
10.1098/rspa.2024.0708

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One of the main issues in measuring the speed of light when it only travels from one spatial position into another position, known as the one-way speed of light, is that the clocks belonging to each separated spatial position are not and, in principle, cannot be synchronized. Here, we show that it is possible, in principle, to measure the velocity of particles that travel at the speed of light without assuming a round-trip once we adopt a quantum mechanical description under two boundary conditions to the state of the quantum system followed by the two-state-vector formalism while assuming non-synchronized quantum clocks with unknown time dilation. The weak value of velocity can be measured for a test particle that has a clock that is not synchronized with the clock of the quantum particle. Following the proposed set-up, when the weak value of the velocity is known even without knowing the time states of the system, such a weak velocity is the two-way speed of light. We further explore some fundamental implications of the set-up. The proposed approach opens a new avenue toward measuring the velocities of quantum particles while overcoming relativistic issues regarding the synchronization of clocks.
The conceptual foundations of the special and general theories of relativity differ greatly from those of quantum mechanics. Yet in all cases investigated so far, quantum mechanics seems to be consistent with the principles of relativity theory, when interpreted carefully. In this paper I report on a new investigation of this consistency using a model of a quantum clock to measure time intervals; a topic central to all metric theories of gravitation, and to cosmology. Results are presented for two important scenarios related to the foundations of relativity theory: the speed of light as a limiting velocity and the weak equivalence principle (WEP). These topics are investigated in the light of claims of superluminal propagation in quantum tunnelling and possible violations of WEP. Special attention is given to the role of highly non-classical states. I find that by using a definition of time intervals based on a precise model of a quantum clock, ambiguities are avoided and, at least in the scenarios investigated, there is consistency with the theory of relativity, albeit with some subtleties.
Measuring velocities requires the synchronization of spatially-separated clocks. Because this synchronization must precede the determination of velocities, no system of clock synchronization--such as that based on Einstein's presumption of light-speed isotropy--can ever be founded on an experimentally-validated velocity. I argue that this very old observation, which lingers in the philosophical literature under the heading ``Conventionality of Synchronization,'' suggests an explanation of why ``spooky'' quantum correlations can transfer no information at any speed, superluminal or otherwise. This work constitutes the first application of the Conventionality doctrine outside of Relativity itself.
The concept of position and its measurement are fundamental to modern navigation technology as well as to theoretical physics. Nevertheless, a consistent notion of position has not been found in modern physics because of apparent inconsistencies between quantum mechanics and relativity. In quantum mechanics the probability distribution for a particle's position is determined by its wave function. A wave function strictly localized in space describes a particle within that locality, and nowhere else. But the quantum equations of motion predict the function will disperse, after any length of time at all, to occupy all space. Therefore the theoretical prediction is that, shortly after detection in a laboratory, a particle may be found anywhere in the universe, including regions requiring faster-than-light travel to reach. This contradicts the theory of relativity, which precludes a body traveling faster than the speed of light. The conflict arises from unexamined assumptions regarding the time of the measurement event and the time of the system under measurement. The prevailing view in physics is that time is only a parameter, having a definite value, describing dynamic changes in physical systems. This view endures even though quantum mechanics recognizes position as a quantum variable with inherent uncertainty, and relativity indicates that time should be placed on the same footing as position. But if time is recognized as a quantum variable with inherent uncertainty, the conceptual problems with position are resolved. The particle has finite probability of being in the past (or future) of the observer, while the quantum mechanical operator describing the position measurement contains a term which extrapolates from the intrinsic time of the particle to the time of the observer. Being potentially well in the past of the measurement event, the particle has time to travel to remote regions without exceeding the speed of light, and the conflict with relativity is resolved. A relativistic quantum theory can therefore be constructed incorporating a well-defined concept of position.
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of these effects as physical constraints. Here, we propose to rebuild Special Relativity from quantum mechanical considerations. This is done by dropping one of its fundamental postulates: the universality of the speed of light. Lorentz transformations are obtained by a quantum mechanism. We use the fact that quantum states depend on the Galilean reference frame where they are defined. In other words, quantum states outside an observer's Galilean reference frame are distorted. Then, we show in a theorem the existence of time-dependent observables that are sensible to this distortion in such a way that their expectation value is a Lorentz-covariant function of time. We then postulate this mechanism as the source of the phenomena of Special Relativity. As a corollary of the main theorem, we show the existence of a Lorentz covariant momentum and mass operators which yield the relativistic momentum and mass. In this theory, the fundamental limit of the speed of light imposes a transparency condition for faster-than-light particles: they are allowed but they are not observable. The transparency effect could explain dark matter in a more general theory following this quantum formalism.
Since Einstein stated the constancy of the speed of light to be a mere “stipulation … to arrive at a definition of simultaneity”, theorists argued that it could be possible for the speed of light to differ in different directions since there are many anisotropies like the amount of matter vs antimatter. However, this assumption has not been confirmed yet. No experiment has been proposed that measures the one-way speed of light; all experiments to date measure the round-trip speed of light. The experiment proposed in this paper seeks to measure the one-way speed of light by using an entanglement-controlled stopwatch while remaining blind (during the experiment) on whether the speed of light is isotropic or anisotropic, thereby answering the century-long question.
In a rod of length AB =L= L=L, rotating uniformly, any two spatially separated points along the rod are connected in a way that shows analogies with the quantum entanglement of the spin of particles. This ”classical entanglement” reflects the simultaneity preset in the system, which can be used for syncing two distant clocks, one at A and the other at B. Since it differs from Einstein synchronization, this procedure can be adopted for testing the one-way light speed and Lorentz invariance. Applications to optical Sagnac effects confirm that a consistent interpretation requires the adoption of absolute versus relative simultaneity.