Identical Quantum Particles as Potential Parts

Abstract

The mathematical rules used to handle systems of identical quantum particles bring into question whether the elementary constituents of matter, such as electrons, have the fundamental characteristics of persistence and reidentifiability that are usually attributed to classical particles. However, despite considerable philosophical debate, the metaphysical profile of these entities remains elusive. Previous debates have taken the mathematical rules, and the language in which these are usually couched, as a starting point. Here, we argue that this methodology is inherently limited, and develop a new conception of identical particles based on a recent mathematical reconstruction of these rules. Using this reconstruction, we demonstrate that the special behaviour of identical particles originates in the confluence of identicality and the active nature of the quantum measurements. We propose that identical particles are appropriately viewed as potential parts of a whole, and show how this leads to striking consequences such as restricted transtemporal identity.

Figures (5)

• Figure 1: Reidentification of classical particles. An ideal experimenter records a pattern of flashes at closely-separated times, $t$ and $t + \Delta t$, which are assumed to be generated by persistent particles. (a) If the experimenter cannot assume that the particles move continuously (or via small 'jumps'), he cannot reidentify them---he is unable to say 'this flash at $t$ is generated by the same particle as that flash at $t + \Delta t$', despite knowing (from the assumption of persistent particles) that the same particle is responsible for one of the flashes at $t$ and one of the flashes at $t + \Delta t$. (b) If the particles move continuously (or via small 'jumps'), then approximate reidentification becomes possible. If the particles move continuously (as posited by classical physics), the precision of such reidentification can theoretically be increased indefinitely by reducing the size of $\Delta t$, and tends to exactness in the limit at $\Delta t \rightarrow 0$.
• Figure 2: Reidentifying interacting classical particles. (a) Nonidentical particles can be reidentified by measuring their state-independent properties (mass, charge) before and after the interaction; tracking within the interaction region is unnecessary. (b) Reidentification of identical particles requires that they be tracked sufficiently precisely as they pass through the arena of interaction.
• Figure 3: Reidentification and measurement of a particle's state-independent properties in a bubble chamber. A bubble chamber image is parsed into distinct 'tracks', each of which is assumed to be due to a specific particle. The inset (bottom left) indicates that a track in fact consists of a sequence of discrete bubbles. The particles move in helical trajectories due to an applied magnetic field, which enables calculation of the particles' charge to mass ratio. (Image courtesy of Brookhaven National Laboratory).
• Figure 4: Persistence and nonpersistence models of flash-data. Two flashes are registered at time $t_1$ and at time $t_2$. Two different object-models of this data are possible. (a) The persistence model posits that each flash is the momentary appearance of a persistent object ('particle'). Hence, according to the persistence model, two possible transitions are compatible with the flash data, only one of which occurred. (b) The nonpersistence model posits that both flashes at each time are the momentary appearance of a single holistic object.
• Figure 5: Synthesis of persistence and nonpersistence models. An ideal experimenter registers two flashes at $t_1$ and two flashes at $t_2$. Two models---a persistence model and a nonpersistence model---of this data are constructed, described in the Feynman formalism, and then synthesized by the operational indistinguishability postulate (OIP).