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arXiv:2308.02942 · Symmetry

Observing Ghost Entanglement Beyond Scattering Amplitudes in Quantum Electrodynamics

Chiara Marletto, Vlatko Vedral

Published Dec 18, 2025• 1 citation
arXivHTMLPDF

Abstract

A fully local quantum account of the interactions experienced between charges requires us to use all four modes of the electromagnetic vector potential in the Lorenz gauge. However, it is frequently stated that only the two transverse modes of the vector potential are “real” in that they contain photons that can actually be detected. The photons present in the other two modes, the scalar and the longitudinal, are considered unobservable and are referred to as “virtual particles” or “ghosts”. Here we argue that this view, which is rooted in standard quantum electrodynamics, is a consequence of assuming that charges are always dressed in such modes and that naked charges do not have an independent existence. In particular, we present a thought experiment where, assuming that naked charges can be independently manipulated, one can then measure the entanglement generated between a charge and the scalar modes. This entanglement is a direct function of the number of photons present in the scalar field. Our conclusion, therefore, is that the scalar quantum variables, under this assumption, would be as “real” as the transverse ones, where reality is defined by their ability to affect the charge. A striking consequence of this is that there is a critical value of charge beyond which we cannot detect its spatial superposition by local means.

DOI
10.3390/sym17122179

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A fully local quantum account of the interactions experienced between charges requires us to use all four modes of the electromagnetic vector potential in the Lorenz gauge. However, it is frequently stated that only the two transverse modes of the vector potential are “real” in that they contain photons that can actually be detected. The photons present in the other two modes, the scalar and the longitudinal, are considered unobservable and are referred to as “virtual particles” or “ghosts”. Here we argue that this view, which is rooted in standard quantum electrodynamics, is a consequence of assuming that charges are always dressed in such modes and that naked charges do not have an independent existence. In particular, we present a thought experiment where, assuming that naked charges can be independently manipulated, one can then measure the entanglement generated between a charge and the scalar modes. This entanglement is a direct function of the number of photons present in the scalar field. Our conclusion, therefore, is that the scalar quantum variables, under this assumption, would be as “real” as the transverse ones, where reality is defined by their ability to affect the charge. A striking consequence of this is that there is a critical value of charge beyond which we cannot detect its spatial superposition by local means.
The covariant quantization of the electromagnetic field in the Lorentz gauge gives rise to longitudinal and scalar photons in addition to the usual transverse photons. It is shown here that the exchange of longitudinal and scalar photons can produce entanglement between two distant atoms or harmonic oscillators. The form of the entangled states produced in this way is very different from that obtained in the Coulomb gauge, where the longitudinal and scalar photons do not exist. A generalized gauge transformation is used to show that all physically observable effects are the same in the two gauges, despite the differences in the form of the entangled states. An approach of this kind may be useful for a covariant description of the dynamics of quantum information processing.
The Aharonov--Bohm (AB) phase for a closed interferometric loop is widely regarded as gauge invariant. This conclusion is usually obtained by treating the electromagnetic source as a fixed background that is unaffected by the test charge. We investigate whether this conclusion remains valid when backreaction is included within the standard gauge-fixed formulation of quantum electrodynamics (QED). Our analysis indicates that, when the interfering branches become entangled with distinct electromagnetic field configurations, changes of the gauge-fixing condition can induce a non-vanishing shift of the total phase. This result gives rise to an apparent paradox: the total phase predicted by the QED formalism appears gauge dependent, whereas experiments robustly exhibit a definite interference shift. We examine two possible resolutions of this paradox. The standard approach attributes the observed interference only to a gauge-invariant component of the total phase and treats the remaining gauge-dependent contribution as physically irrelevant. We argue, however, that the QED formalism itself predicts the total phase governing the interference outcome and does not provide a dynamical prescription that extracts a gauge-invariant component while discarding the remaining terms. We then explore an alternative perspective in which the electromagnetic potential AμA_\muAμ​ is regarded as a physical field whose configuration is determined by the Lorenz condition together with appropriate causal and boundary conditions. From this viewpoint, the total phase can be interpreted as a well-defined physical quantity within the QED formalism. We conclude by discussing a possible experimental test based on direct measurements of open-path relative phases, which may help clarify the ontological status of electromagnetic potentials.
We study the entanglement between an electron and the photon it scatters, resolved in real space and time. Starting from nonrelativistic QED in Fermi's oscillator representation, we write Fock's coupled equations for components with fixed photon number in the photon configuration space, in the length gauge, where the photon is created around the atom through a nonlocal kernel. Truncated at one photon, the equations are solved numerically without the rotating-wave approximation for a one-dimensional model atom in a waveguide with a single transverse mode and enhanced coupling. The atom is driven by a short, off-resonant laser pulse, with the electron and photon represented on real-space grids. The global electron-photon entanglement is largely transient. It peaks during the pulse and decreases as the polarized electron cloud returns to the core, leaving a state close to a product of the electron state and a superposition of the field vacuum with a single scattered photon. Local entanglement, obtained from walkers sampled across both photon-number components, exhibits opposite spatial patterns for the two particles. The electron entropy is smallest at the nucleus and maps the local strength of the dipole coupling, whereas the photon entropy is largest near the atom, where photons are created and absorbed, and smaller in the outgoing wave packets.
The problem of the relation between the Ahronov-Bohm effect and traditional postulates of electrodynamics, which claim that only electric and magnetic fields are observable, is resolved by denial of the statement about validity of the Maxwell equations for microscopic fields. We proceed from the idea that the Maxwell equations, as the generalization of experimental data, are valid only for averaged values. We show that microscopic electrodynamics should be based on postulation of the d'Alembert equations for four-vector of the electromagnetic field potential. The Lorentz condition is valid only for the averages and provides the implementation of the Maxwell equations for averages. This concept eliminates the problem of electromagnetic field quantization and provides the correctness of all known results of quantum electrodynamics. Therefore, the "virtuality" of the longitudinal and scalar photons has a formal mathematical character, conditioned by the Maxwell equations for averaged fields. The longitudinal and scalar photons provide not only the Coulomb interaction of charged particles, but also allow the electrical Aharonov-Bohm effect.
We propose that quantum entanglement occurs because the fundamental particles, such as electrons, quarks, and photons, simultaneously experience both the 4th real spatial dimension in R4 as well as the time dimension in (3 + 1)-D spacetime. Consequently, the entangled particles can never become separated in the 4th spatial dimension no matter how far they have moved apart in the other 3 spatial dimensions. Because the quark and lepton families represent specific different discrete symmetry binary subgroups of SU(2), we can establish that the quantum states of the fundamental particles are defined in 4 spatial dimensions, so there is then no need for a spacetime communication from one detector (or particle) to inform the other detector (or particle) of the physical state of the first detected entangled particle. A clever experiment needs to determine whether the fundamental particles actually experience a 4th spatial dimension, and if so, whether they experience the 4th spatial dimension as the time dimension simultaneously. Apparently, if a Casimir-like test reveals that virtual particles have a non-zero mass, there are claims that a 4th spatial dimension does not exist.
Abstract If we reject the ‘spooky’ action at a distance that seems to be required in the Copenhagen interpretation of quantum theory, and which is highlighted by the EPR thought experiment, we must accept the EPR argument that the theory is somehow incomplete. In essence, this involves the rejection of the first postulate of quantum theory: the state of a quantum mechanical system is not completely described by the wave function or state vector.Einstein had hinted at a statistical interpretation. In his opinion, the squares of the wave functions or state vectors of quantum theory represented statistical probabilities obtained by averaging over a large number of real particles. The Copenhagen interpretation of the EPR experiment insists that the reality of the physical states that can be measured is defined by the nature of the interaction between two quantum particles and the nature of the experimental arrangement. A completely deterministic, locally real version of quantum theory demands that the physical states of the particles be established at the moment of their interaction and that the particles separate as individually real entities in those physical states. The physical states of the particles are prescribed by the physics of their interaction and independent of how we choose to set up the measuring instrument, and so no reference to the nature of the latter is necessary, except to define how the independently real particles interact with it. The instrument thus probes an observer-independent reality.