Charge acceleration without radiation

TL;DR

The paper questions the conventional notion that acceleration inevitably produces radiation in quantum regimes, demonstrating that a charge can be accelerated without radiating by leveraging the Aharonov-Bohm effect and dynamical nonlocality. By creating a superposition of spatially separated wavepackets and imprinting a relative AB phase, the momentum distribution shifts (acceleration) without local forces or emitted radiation, with the AB phase given by $\alpha = q\Phi$. Crucially, the momentum moments satisfy $\langle p^n \rangle_{\alpha} = \langle p^n \rangle_0$ for all integers $n$, while the distribution changes due to modular variables, illustrating nonlocal control of momentum. These results suggest a need to revise the classical radiation paradigm and hint that similar nonlocal mechanisms could apply to other forms of radiation across physics.

Abstract

The existence of electromagnetic radiation - radio-waves, microwaves, light, x-rays and so on - is one of the most important physical phenomena, and our ability to manipulate them is one of the most significant technological achievement of humankind. Underlying this ability is our understanding of how radiation is produced: whenever an electric charge is accelerated, it radiates. Or, at least, this is how it has been hitherto universally thought. Here we prove that quantum mechanically electric charges can be accelerated without radiating. The physical setup leading to this behavior is relatively simple (once one knows what to do) but its reasons are deep: it relies on the fact that quantum mechanically particles can be accelerated even when no forces act on them, via the Aharonov-Bohm effect. As we argue, the effect presented here is just them tip of an iceberg - it implies the need to reconsider the basic understanding of radiation. Finally, it seems clear that the effect goes far beyond electromagnetism and applies to any kind of radiation.

Figures (8)

• Figure 1: An electron starts in a wavepacket aligned above the x-axis, and moves downwards in the z-direction.
• Figure 2: An electron moves past a solenoid with flux $\Phi$ which is oriented along the y-axis. We use the singular gauge for the vector potential ${\bf A}$, taking it to be non-zero only along the half-plane with $z=0$ and $x>0$.
• Figure 3: The electron moves past the right of the solenoid. It crosses the singular line of the vector potential, acquiring an overall phase in our gauge.
• Figure 4: The electron, in the superposition $\frac{1}{\sqrt{2}}(\Psi_L + \Psi_R)$, moves past the solnoid. The momentum distribution changes, without radiation.
• Figure 5: An infinite parallel plate capacitor, $C$, is placed between the left and right wavepackets of an electron in the superposition $\frac{1}{\sqrt{2}}(\Psi_L + \Psi_R)$. The capacitor is charged and discharged, which results in a relative phase between the two wavepackets but no radiation, similar to the action of the solenoid.