https://arxiv.org/pdf/2206.10918.pdf
Bohm was in particular fully aware of the necessity to develop
the pilot wave interpretation in configuration space and never questioned this peculiarity; de Broglie on the contrary has never been very enthusiastic about the idea of a dynamics in configuration space, and persistently tried to develop a pilot wave in real, 3D space, in the spirit of the semi-classical theory outlined here in section 1. Several clues indicate that, actually, de Broglie was always reluctant to recognize the long range implications of entanglement [18, 19], although he was the first in 1926 to recognize these implications at the level of the guidance
equation [12].
Do(es the influence of) empty waves survive in configuration
space? 2022
Thomas Durt
However, whenever we consider at least two photons, entanglement is likely to be present, and a classical description `a la Maxwell in the physical, 3-d space must be replaced by a description in the configuration space.
citing F. Selleri. Wave-Particle Duality: Recent Proposals for the Detection of Empty Waves
in Schommers, W. (eds) Quantum Theory and Pictures of Reality. Springer, Berlin,
Heidelberg, 1989:
In the same paper, F.Selleri wrote, about Einstein’s photon that ...A problem immediately coming to mind with Einstein’s philosophy is the following: If the localized particle carries all the energy and momentum, in which sense can the wave be considered real? This problem was felt so acutely by Einstein that he referred to these waves a Gespenterfelder (ghost fields): An object without energy and momentum is in fact unable to exert
a pressure when impinging on a material surface, which means that it does not have that quality that makes us call something real. Still, the equations of the quantum theory describe this wave as propagating in space and time.
The difficulties associated with the concept of an empty wave(...) have led many people to discard the idea as a scientific impossibility(...). It will be shown in the present chapter that the previous objection can be overcome because not only changes in energy and momentum can be observed, but modifications of probabilities as well. The last sentence also applies to the present paper.
In this approach, the Heisenberg uncertainty relations are not considered as an intrinsic limitation to the concept of trajectories but rather as a constraint relative to the statistical distributions of the position and the momentum of a quantum system. In the 50’s Bohm will tackle the measurement problem (still pretty much disregarded in 1926) and suggest a solution anticipating the concept of decoherence, developed later in the 1970s within the framework of open quantum systems [7]. The decoherence idea completes the theoretical construction prefigured by Broglie in 1926 and 1927 (during his presentation at the 1927 Solvay Conference [29] de Broglie gave a simplified version of his Double-Solution program [9], that constitutes the backbone of what is known today as the “pilot wave theory” [31, 32]) along the following lines:
-the particles are localized at all times in a spatial region much smaller than the support
of the Schr ̈odinger wave;
- the trajectories satisfy the guidance condition applied to the Schr ̈odinger pilot wave (Ψ
wave) (here expressed in the N particles case) according to which the 3N dimensional velocity obeys
at all times the statistical distribution of positions is governed by Born’s rule (that is
|Ψ(x1, y1, z1, x2, y2, z2, ..., xi, yi, zi, ..., xN , yN , zN , t)|2);
- any measurement is ultimately a measurement of position. This means among others that a detector will click if and only if the particle “is located inside” and/or “passes through” the detector. Already in his seminal paper of 1926 [12], de Broglie faced a serious problem: when one considers a composite quantum system (for example a pair of particles) described by a nonfactorizable Schr ̈odinger wave function (“entangled”, according to the term introduced by Schr ̈odinger in 1935), the interpretation leads to trajectories that, in agreement with equation (18), are not defined in our 3-dimensional physical space, but in configuration space (having dimension 3N for a system composed of N particles). de Broglie will never really overcome this problem and neither will he subscribe [18] to the view developed later by Bohm (in 1951) [13, 14] and highlighted by Bell (in 1964) [19], a view according to which quantum physics is an inherently non-local theory.
When Bohm updated the pilot wave interpretation in 1952 [13, 14], he was the first to reformulate the EPR paradox in terms of spin 1/2 particles, a result which played an essential role in the genesis of Bell’s inequalities as Bell recognized later. From this point of view, Bohm was the first (and not de Broglie) to appreciate and to fully recognize the non-local character of quantum correlations between entangled systems, which is manifest at the level of the guidance equation (18).
if empty waves are used to carry information, they are likely to suffer less from dissipation than their non-empty, corpuscular counterpart. A potential application would be long distance quantum communication, which justifies the theoretical bet made here concerning the possible existence of an “empty wave effect”.
https://link.springer.com/article/10.1007/s10701-022-00655-w
In de Broglie–Bohm theory, the past is connected with the future through particle trajectories and in the delayed choice experiment the particle swaps wave packets through the region of interference where the packets from each slit overlap; the particle received by a particular detector has actually passed through the slit it is not looking at.
But, Bohm argued, that if quantum non locality implies a preferred frame (in which the nonlocal connection could be described as instantaneous) this does not conflict with relativistic requirements provided that the preferred frame is not experimentally distinguishable.
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