Cutting a single photon in half leaves a state that takes many photons to describe

The photon count moves because the mirror is part of the definition of a photon. While the mirror is there it divides physical space in two, and the excitations that count as particles are excitations of the field in that divided space; take the mirror away and the excitations are of a different kind, so what counted as one particle before is not the same object after ^[7]. Rukan, Gulla and Skaar connect the two descriptions with a Bogoliubov transformation, the same mathematics that relates an incoming vacuum to outgoing thermal radiation in the standard account of why black holes must eventually decay ^[8]. Observer-dependence of particle number is not new here: what looks like a vacuum to a stationary observer can look like radiation to an accelerating one, known as the Unruh effect ^[13].

How fast the shutter opens changes the answer. With the reflector removed instantaneously, the expected number of photons in the final state comes out infinite, a result the trio treats as unphysical ^[9]. Remove the mirror slowly and the expectation value is finite ^[10]. A divergence that shows up only in the zero-time limit is the signature of an idealisation. The time profile of the cut, not just the fact of a cut, fixes the photon number.

That finite average is an average over many photon numbers. "There is a non-zero probability of observing any number of photons," Skaar said ^[11]. In the particle picture you would expect to find one forward-propagating photon or none. The calculation instead gives a classical mix and a quantum superposition of several ^[6].

Outside the transition region, nothing about the photon changes immediately ^[1]. An observer sitting out there cannot learn that the mirror moved until light from the event arrives ^[15]. The quantum state of the electromagnetic field does change when the mirror is removed, and the definition of a particle or a vacuum state is a very non-local concept ^[14].

Chopping a beam into pulses is a common technique in optical experiments, though physicsworld reports that what happens to a single photon under that operation had gone unexplored until now ^[12]. The calculation is a thought experiment built on an ideal mirror and an ideal shutter ^[5]. physicsworld does not report the width of the transition region or a figure for the expected photon count under gradual removal ^[16]. An experimenter chopping a single-photon pulse would need that width to know what fraction of the pulse sits where the one-photon label stops working ^[17].