Noncommutative "time-asymmetric microcausality principle" to be tested by Shan Gao of a time-varying magnetic flux

 electrically charged particle is influenced by the [Solenoid] vector potential A in regions in which the magnetic field B=A is not-zero

Wolfram vid of Aharonov-Bohm Effect 

First, the solenoid is switched on at time t(on) during the electron’s interferometric passage
(0 < ton < T , where T is the interference completion time).  Second, the distance d between solenoid and electron path satisfies t(on) + d/c > T , so that classical retarded fields from the solenoid cannot reach the electron’s path before interference is complete. Third, and consequently, along the electron’s actual trajectory in spacetime up to time T , the classical retarded vector potential Aret(x, t) = 0. If no signal from the solenoid can reach the electron via retarded propagation before interference, should the solenoid have any effect on the interference pattern? Classical intuition and purely retarded descriptions of electrodynamics suggest the answer should be no. However, the standard in-out formalism of quantum electrodynamics (QED) makes a surprising prediction: a non-zero AB phase shift persists even under these conditions....for non-relativistic interferometers where d/c ≪ T , the solenoid must be switched
on very close to the interference completion time (t(on) > T − d/c), resulting in a phase shift
that is only a small fraction of the static AB value, typically of order (d/c)/T .

AI definition: 

 The "time-asymmetric microcausality principle" refers to a quantum field theory concept where operators at spacelike separation must commute (vanish commutator) to prevent faster-than-light signaling, enforcing relativistic causality; however, recent theoretical frameworks, like those using sedenionic algebra or noncommutative spacetime, propose modifying this principle, introducing fundamental time-asymmetry (e.g., via complex temporal steps) and non-commutativity, to build causality into spacetime itself, potentially resolving quantum gravity issues and explaining irreversible dynamics, moving beyond standard QFT's assumption of locality....

That's what AI explains above.   Here is the new Gao experiment

  the influence of a time-varying magnetic flux

 ....determined by the motion of the electron under the influence of the magnetic flux, not by the motion of the free electron. As we will see later, due to the existence of the
induced electric field, one beam will be accelerated and the other beam will
be decelerated, and thus the overlaping region will be in general different
from the overlaping region for the static case, although the meeting time T
are the same for both cases.

.... , the key is to realize that the AB phase shift (8) is precisely the phase shift for the time-dependent case, and in order to calculate the phase shift integral one must consider the motion of the electron around the solenoid.... it strongly suggests that the AB phase shift is
continuously generated during the traveling of the electron, not immediately generated when the electron beams overlap....This then supports a continuous, local potential explanation of the AB effect and disfavors a discontinuous, nonlocal field explanation of the AB effect.

 one can also generate a time-varying magnetic vector potential using a coherent light source 

 , the time-dependent case introduces an additional layer of complexity due to the dynamic angular velocity variations. This generalized AB effect highlights the interplay between time-dependent electromagnetic potentials and quantum mechanical phase accumulation, and in particular, it strongly suggests that the AB phase is locally and continuously generated via the action of gauge-dependent potentials.

Can the Future Influence the Past? A Delayed Aharonov-Bohm Test of Time-Symmetric QED

 https://www.academia.edu/145832302/Can_the_Future_Influence_the_Past_A_Delayed_Aharonov_Bohm_Test_of_Time_Symmetric_QED

 a solenoid is switched on during the interferometric journey such that its classical retarded field cannot reach the particle’s paths before interference is recorded—a situation we term the forward causal-disconnect condition.

....the advanced influence of the solenoid on the electron and the retarded influence of the electron on the solenoid..

 This prediction exposes a fundamental tension between two postulates of quantum field theory: the time-symmetric structure of quantum amplitudes (encoded in the Feynman propagator) and the time-asymmetric principle of microcausality.

  positive result would constitute direct evidence for the operational role of
time-symmetric (advanced and retarded) interactions in QED amplitudes, challenging
purely retarded descriptions and conventional notions of causality

 The prediction of a non-zero phase shift under forward causal-disconnect conditions reveals a fundamental tension with the microcausality axiom of quantum field theory. Microcausality requires that local observables at spacelike separations commute:... thereby forbidding superluminal signaling and preserving relativistic causality

 While such dependencies do not enable superluminal signaling (the phase shift can only be read out after t(on), they challenge the conventional interpretation of microcausality as prohibiting any dependence, not just signaling-capable dependencies.
The tension is real and fundamental: standard QED with the Feynman propagator predicts observable consequences from spacelike-separated sources, while microcausality demands complete independence

 Conversely, the imaginary part (26), proportional to the Hadamard function, contributes
an exponential suppression factor exp(− Im Seff ) in the interference amplitude. This term
represents decoherence induced by vacuum fluctuations of the electromagnetic field.
Thus, the decomposition (23) physically separates the coherent unitary evolution (aris-
ing from causal photon exchange) from stochastic noise (arising from symmetric vacuum
correlations). This distinction is crucial for understanding how quantum electrodynamic
environments affect interference phenomena, including the AB effect in the presence of electromagnetic fluctuations....

 In a time-symmetric theory such as standard QED, however, an advanced influence from
the solenoid can still affect the electron....Thus, any advanced influence appears to the electron before the solenoid is switched on—a manifestation of the time-symmetric structure of the QED amplitude... the phase shift is a global quantum property that can be read out only after the solenoid has been switched on. No classical information can be transmitted faster than light.

 The delayed-switch AB experiment therefore provides a clear test of whether the time-symmetric structure of the QED amplitude—encoded in the Feynman propagator—or a purely retarded interaction governs the observable phase in a finite-time interference experiment...

 Since the observable phase shift ∆ϕ depends only on the real part of the effective action, ...it reflects the fundamental symmetry of the interaction in the real part of the amplitude: contribution from the electron influencing the solenoid is identical to that from the solenoid
influencing the electron....it means that the interaction between electron and solenoid is fundamentally symmetric in its real part: the
contribution from the electron influencing the solenoid is equal to that from the solenoid
influencing the electron. In the path-integral formulation, this symmetry reflects the fact
that quantum amplitudes sum over all possible histories, including those where influence
flows in either temporal direction.
Contrary to the simplified interpretation that the phase arises from either an advanced
influence of the solenoid on the electron or a retarded influence of the electron on the solenoid, the correct interpretation is that both contributions exist and together constitute the total observable phase. 

Just as I have argued - the future and the past overlapping causally. 

 Both processes are mediated by virtual photons propagating on the light cone. The forward causal-disconnect condition ensures that conventional retarded influence from solenoid to electron (Rps) is impossible, but the time-reversed advanced influence (Aps) and the electron-to-solenoid retarded influence (Rsp) remain possible and are, in fact, equal [but the retarded influence vanishes due to space separation].

 ............

 The conventional notion of causality—that only retarded influences from sources to probes are physical—is challenged by this result. Instead, quantum amplitudes incorporate influences in both temporal directions, and these contribute coherently to observable phases.
Importantly, this does not violate relativistic causality. No superluminal signaling is
possible because: First, the phase shift is a global, topological effect that can only be read
out after the solenoid has been switched on.

 Second, the commutator [Aμ(x), Aν (y)] vanishes for spacelike separations. Third, no classical information can be extracted from the phase before t(on).
The delayed-switch AB experiment therefore tests whether this time-symmetric structure
of QED manifests in observable interference patterns even when forward causal contact is
absent. A positive result would confirm that both advanced and retarded influences are
operationally significant in quantum theory.

 the observable AB phase in the delayed-switch experiment arises from the coherent sum of two physically distinct but mathematically equivalent processes, both of which are essential features of quantum electrodynamics.

 A natural suspicion is that the advanced and retarded components of the Feynman propaga-
tor might cancel in the delayed-switch configuration, yielding a vanishing phase. However,
this does not occur.

 integrating out the electromagnetic field yields the effective action whose real part governs the relative phase between interfering histories. ...in the forward causal-disconnect regime the retarded contribution vanishes due to spacelike separation, while the advanced contribution remains nonzero. Crucially,
the two contributions are additive rather than subtractive; there is no antisymmetry or sign
difference that could produce cancellation. The symmetrized structure of the propagator
therefore enforces a nonvanishing result.

... a finite spacetime region remains in which the two particle currents differ. It is precisely this region that contributes to the phase. Since there is no corresponding region with opposite sign or symmetry to cancel it, the remaining contribution survives. The nonzero phase is therefore not an artifact of incomplete path subtraction but rather persists because the cancellation has been properly implemented....

 While individual path phases are gauge dependent, the observable interference phase—
defined as the relative phase between two complete histories—is gauge invariant. In the
effective-action formulation, gauge invariance is ensured by current conservation, which re-
moves all longitudinal components of the propagator. The surviving contribution depends
only on the transverse, physical degrees of freedom.

  the present calculation does not rely on artificial truncation of time integrals. All
integrals may be taken over infinite spacetime, with the finite result emerging solely from
the cancellation of common path contributions.
More generally, in–out amplitudes are routinely used to analyze time-dependent processes, including radiation emission and vacuum polarization. There exists no principle
within QED requiring interaction terms to vanish for spacelike-separated, finite-duration
couplings at the level of amplitudes.

 The factor of 1/2 in the effective action arises precisely to prevent double counting when
integrating out a Gaussian field. Removing either contribution by hand would violate the
symmetry of the Green’s function and spoil the recovery of known results, including the
static Aharonov–Bohm phase. The decomposition into advanced and retarded terms is a
mathematical identity, not a sum over independent physical processes.

 The in–out formalism computes transition amplitudes between asymptotic states, whereas experimentally accessible quantities are expectation values of observables at finite times

 So as quantum physics professor Basil J. Hiley emphasized - the quantum potential is the transition amplitude and this is noncommutative! 

 The in–out framework permits time-symmetric correlations at the level of amplitudes, whereas the in–in framework enforces microcausality at the level of expectation values.

 The effect thus provides a sharp diagnostic of the conceptual foundations of QED, isolating the interplay between time-symmetric amplitudes and time-asymmetric causality conditions.

 contributes to the quantum amplitude but does not correspond to a classical advanced field that could be directly measured locally. Second, the phase shift is a global, topological effect—a consequence of the electron’s wave function acquiring a phase proportional to the flux enclosed, even when the local field is zero....this phase is gauge-invariant (it depends
only on the closed-line integral ∮ A · dl) but is not associated with any local, measurable
field strength.

 if the advanced influence were a classical advanced field (i.e., a solution of Maxwell’s
equations with sources in the future), it would be locally detectable and could in principle
transmit information backward in time, violating relativistic causality. However, the Feyn-
man propagator’s advanced component, when used in the scattering amplitude, does not
allow such signaling because: the commutator [Aμ(x), Aν (y)] vanishes for spacelike separation; the phase is read out only after the solenoid has been switched on, with no information about the solenoid’s state extractable before t(on); and the effect is coherent and non-local—it modifies the interference pattern but cannot be used to send a superluminal message.

  The advanced contribution corresponds to those histories in which a virtual photon connects the electron to the solenoid in a time-reversed manner. Such histories are not “real” in the classical sense but are an essential part of the quantum superposition that yields the observable phase.

https://inspirehep.net/literature/778987 

... prove that, in the case of space-space noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality.

 https://arxiv.org/pdf/0802.0997

 The relations (1) are not covariant under the Lorentz transformations, and noncommutative QFT is usually treated as a specific form of field theory with a nonlocal interaction breaking the Lorentz symmetry to a subgroup. In the Lagrangian formalism, the theory is defined by replacing the ordinary product of fields in the interaction terms of the actions with the Moyal ⋆-product.......⋆ denotes now a star multiplication of field operators at different spacetime points...the star commutator fails
to vanish even in the spacelike wedge and completely violates causality. 

 There is an essential distinction between the cases of a space-space and time-space noncommutativity. If the time coordinate is involved in noncommutativity, then a string theoretical interpretation
of the field theory comes up against the problem of nonunitarity [2] and inconsistency
with the conventional Hamiltonian evolution [3]. A consistent Hamiltonian framework
for the scalar field theory with time-space noncommutativity has been proposed in [4].
The definition given there leads to an perturbatively unitary S-matrix and is interesting
by itself, even though its relationship with string theory is unclear. Field theories with
only space noncommutativity (that is θ0ν = 0) avoid the problems with unitarity, and
models of this form attract the most notice because they describe a low energy limit
of string theory in certain backgrounds. However, its causal structure is different from
that of the standard QFT because the light cone is changed to a light wedge respecting
the residual Lorentz symmetry [5, 6, 7].

 .............

  the causality principle and the spectral condition into conflict.

 the vacuum expectation values of ⋆-products of field operators at different spacetime
points...there is no agreement regarding the physical interpretation of
the ⋆-product of quantum fields at different spacetime points.... the spectral condition comes into conflict with causality as is evident from the foregoing.

 Here we have proof that time-frequency noncommutativity is nonlocal and violates causality.

 https://arxiv.org/html/2512.18603v1

The two obstructions are logically distinct—noncommutativity concerns the algebraic structure of common causes, while covariance concerns their transformation properties under spacetime symmetries.

Redhead [16] argued that no-signalling resolves the tension between Bell nonlocality and relativity; our result shows this resolution is incomplete,...Bell nonlocality requires genuinely nonlocal beables or preferred foliations; our theorem formalizes this claim by showing that restoring Bell locality requires breaking covariance.

This is the causal explanation requirement: correlations arise from common causes in the past, not from future influences or direct spacelike connections.

A retrocausal model with $\lambda$ depending on future boundary conditions violates this requirement by construction: $\lambda$ is not localized in the past. Such a model may reproduce quantum statistics, but it does not provide a past-causal explanation of correlations.

 Retrocausality trades temporal asymmetry (past causes) for the ability to satisfy Bell factorization. But this trade-off is precisely what the covariance obstruction forbids in a different guise: any time-asymmetric structure (whether past-oriented causation or retrocausal dependence on specific future boundaries) must be specified relative to a foliation, breaking covariance.

 pregeometric” approaches where spacetime itself emerges from more fundamental quantum structures. In such frameworks—tensor networks, quantum information-theoretic reconstructions, or algebraic approaches—the correlations encoded in entanglement are primary, and classical spacetime geometry is derivative.

 The obstruction is logically independent of Hofer-Szabó’s noncommutativity obstruction: even permitting noncommuting common causes, covariance alone prevents Bell-local hidden variable models.

 The obstruction suggests that in any theory of quantum gravity with full diffeomorphism invariance, Bell correlations between spacelike-separated regions cannot admit classical causal explanations—a feature rather than a bug if spacetime geometry is emergent from entanglement....the choice of reference frame is not merely conventional but physically consequential for causal explanations.

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.73.045014 

 The commutator of ∶  𝜙⁡(𝑥) ⋆𝜙⁡(𝑥)   ∶ with ∂𝑦𝜇   ∶  𝜙⁡(𝑦) ⋆𝜙⁡(𝑦)   ∶ fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which 𝜃0⁢𝑖 =0. The failure to obey microcausality for these sample observables implies that this form of noncommutative field theory fails to obey microcausality in general.

 Quantum field theory on noncommutative spacetime stands as an intermediate
framework between string theory and the usual quantum theory of fields. ...field theory on noncommutative spacetime becomes a particular form of nonlocal field theory, with the nonlocality expressed in terms of the Moyal phases that occur in the star product.