[Paper Review] Predictions of the hydrodynamic interpretation of quantum mechanics compared with quantum electrodynamics for low energy bremsstrahlung

Mark Davidson|ArXiv.org|Feb 6, 2003

Quantum Electrodynamics and Casimir Effect7 references3 citations

TL;DR

This paper compares the hydrodynamic interpretation of quantum mechanics with quantum electrodynamics (QED) in predicting low-energy bremsstrahlung radiation. It shows that the hydrodynamic model, which treats electromagnetic fields classically, predicts significantly reduced radiation when the force is localized within a region small compared to the electron's wave packet—unlike QED, which shows no such dependence. This difference offers a potential experimental test of the hydrodynamic interpretation.

ABSTRACT

It is shown that the hydrodynamic interpretation of a charged quantum particle leads to a different theoretical prediction for low energy bremsstrahlung than does quantum electrodynamics (QED). In the calculations, the electromagnetic fields are treated classically in the hydrodynamic case, but are quantized in QED. Calculations show the hydrodynamic model to have a different and more sensitive dependence on the size and shape of the radiating particle's wave packet then does QED. In particular it is shown that bremsstrahlung is sometimes greatly reduced when the force acting on the particle is localized to a volume small compared to the particle's wave packet. QED exhibits no such reduction. Therefore it is possible to test this effect experimentally. An experiment is proposed. It involves an electron microscope with a Wien filter for producing monochromatic beam electrons and an accurate energy measurement of the particle after passing through a local force field.

Motivation & Objective

• To investigate whether the hydrodynamic interpretation of quantum mechanics yields different predictions for low-energy bremsstrahlung than quantum electrodynamics (QED).
• To identify a measurable physical difference between the hydrodynamic model and QED in the context of bremsstrahlung emission.
• To propose a feasible experimental setup using electron microscopy and energy analysis to test the predicted discrepancy.
• To explore the implications of treating electromagnetic fields classically in the hydrodynamic approach versus quantized fields in QED.

Proposed method

• The hydrodynamic interpretation is applied to a charged particle undergoing acceleration in a localized force field, modeling the particle as a fluid with a probability density and velocity field.
• The electromagnetic fields are treated classically using Maxwell's equations, derived from the particle's probability density and current density.
• The bremsstrahlung power is calculated using the classical Larmor formula applied to the hydrodynamic probability current.
• The wave packet's spatial extent and shape are varied parametrically to assess their influence on radiation emission.
• The same physical scenario is analyzed using standard QED to compare radiation rates.
• An experimental proposal is developed using a Wien filter to produce monochromatic electron beams and precise energy measurements to detect differences in radiation loss.

Experimental results

Research questions

• RQ1 Does the hydrodynamic interpretation of quantum mechanics predict a different bremsstrahlung spectrum than QED for low-energy electron scattering?
• RQ2 How does the spatial extent and shape of the electron's wave packet affect radiation emission in the hydrodynamic model compared to QED?
• RQ3 Is there a regime in which localized forces lead to a significant suppression of bremsstrahlung in the hydrodynamic model but not in QED?
• RQ4 Can this difference be experimentally observed using current electron microscopy technology?
• RQ5 What is the role of classical electromagnetic fields in the hydrodynamic formulation compared to the quantized fields in QED?

Key findings

• The hydrodynamic model predicts a strong dependence of bremsstrahlung on the size and shape of the electron's wave packet, particularly when the force is localized within a region smaller than the wave packet.
• When the force is confined to a volume much smaller than the wave packet, bremsstrahlung is significantly reduced in the hydrodynamic model, even for low-energy processes.
• In contrast, QED shows no such reduction, indicating a fundamental difference in radiation prediction between the two frameworks.
• The discrepancy arises because the hydrodynamic model treats the electromagnetic field classically, leading to a non-uniform response to localized forces.
• The predicted suppression in radiation is most pronounced when the force acts over a spatial scale much smaller than the de Broglie wavelength of the electron.
• An experimental setup using a Wien filter and energy-resolved electron detection is proposed to test the predicted difference, offering a potential falsification test for the hydrodynamic interpretation.