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arXiv:1212.6508

Quantum temporal probabilities in tunneling systems: II. No faster-than-light signals are possible in tunneling

Charis Anastopoulos, Ntina Savvidou

Published Dec 28, 2012• 0 citations
arXivHTMLPDF

Abstract

In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between particles and waves. To this end, we employ a new method for constructing probabilities associated to quantum time measurements that provides an explicit link between the tunneling time of particles and the associated quantum fields. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. Our results suggest that direct measurements of the transit time in tunneling could provide a new testing ground for the predictions of quantum theory versus local hidden-variables theories.

DOI
10.48550/arxiv.1212.6508

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In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between particles and waves. To this end, we employ a new method for constructing probabilities associated to quantum time measurements that provides an explicit link between the tunneling time of particles and the associated quantum fields. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. Our results suggest that direct measurements of the transit time in tunneling could provide a new testing ground for the predictions of quantum theory versus local hidden-variables theories.
A simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier. The model has the advantage of yielding sensible results for energy eigenstates and does not require the use of time-dependent wave packets. Although the treatment does not forbid superluminal tunneling velocities, there is no implication of faster-than-light signaling because only the transit duration is measurable, not the absolute time of transit. A comparison is given with the weak-measurement post-selection calculations of Steinberg.
Abstract Particles cannot travel faster than the speed of light, nor can information. Nonetheless, this assumption has been frequently questioned over the years. This includes radical proposals like tachyons that can be observed in particle accelerators to more subtle ideas like studying superluminal causation to find classical explanations for quantum correlations. Most recently, it has been argued (Dragan and Ekert 2020 New J. Phys. 22 033038) that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. A consequence of this resolution is that different observers no longer agree whether a particle is incoming or outgoing or in a superposition of the two. We further find a similar apparent paradox for the entropy and/or temperature under superluminal Lorentz boosts and resolve it in an analogous fashion. Finally, we discuss Bell experiments under superluminal quantum reference frame transformations, showing that the involved probabilities still remain conserved. By applying the toolbox of quantum reference frames, we start charting an unexplored territory of superpositions between sub-and-superluminal quantum observers which gives rise to new conceptual questions.
While particles cannot travel faster than the speed of light, nor can information, this assumption has over the years been frequently questioned. Most recently, it has been argued [New J. Phys. 22, 033038 (2020)] that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. We also discuss Bell experiments under superluminal quantum reference frame transformations, showing that involved probabilities remain conserved.
We exploit the analogy between tunnelling across a potential barrier and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly 'superluminal' behaviur of the tunnelling particle in the barrier. We demonstrate that 'superluminality' occurs when the value of the duration τττ spent in the barrier is uncertain, whereas when τττ is known accurately, no 'superluminal' behaviur is observed. In all cases only subluminal durations contribute to the transmission, which precludes faster-than-light information transfer, as shown by a recent experiment.
Since 1992 experimental evidence of superluminal (faster than light, FTL) signals are causing much excitement in the physical community and in the media. Superluminal signal velocity and zero time tunneling was first observed in an analog tunneling experiment with microwaves. Recently, the conjectured zero time of electron was claimed to be observed in ionizing helium. The FTL signal velocity was reproduced with infrared light and with various tunneling barriers in several laboratories worldwide. Remarkable, it was shown that the tunneling time is a universal quantity for elastic and for electromagnetic fields. Many theoretical physicists predicted this FTL nature of the tunneling process. However, even with this background many members of the physics community did not accept the superluminal signal velocity interpretation of the experimental results and they also ignored the universal tunneling time. The predicted and measured zero tunneling time was taken as a fantastic nonsense. A brief explanation of the misleading theoretical approaches against FTL signals due to the tunneling process is presented eventually.
We solve numerically the time-dependent Dirac equation for a quantum wave packet tunneling through a potential barrier. We analyze the spatial probability distribution of the transmitted wave packet in the context of the possibility of effectively superluminal peak and front velocities of the electron during tunneling. Both the Dirac and Schr\"odinger theories predict superluminal tunneling speeds. However, in contrast to the Dirac theory the Schr\"odinger equation allows a possible violation of causality. Based on an analysis of the tunneling process in full temporal and spatial resolution, we introduce an instantaneous tunneling speed that can be computed inside the potential barrier.