A Groundwork for Perspectival Quantum Mechanics

Abstract

There has recently been a renewed focus on ‘perspectival’ quantum theories.

which simultaneously maintain the existence of single measurement outcomes

and the universality of unitary evolution. At the same time, these theories have

come under attack with results by Frauchiger and Renner, Baumann and Wolf,

and others. This dissertation aims to respond to a number of these attacks by

providing a groundwork for these types of theories.

To lay this groundwork I focus on encapsulated measurements, which involve

an isolated observer and a superobserver (who measures the observer). I

first distinguish between invasive and non-invasive measurements. Each leads to

a possible inconsistency: In non-invasive measurements, the observer is certain

of the superobserver’s measurement outcome while the superobserver’s physics

predicts multiple possible outcomes. In invasive measurements the superobserver

can be certain of his measurement outcome while the observer predicts

non-zero probabilities for all possible outcomes.

I argue that in the case of non-invasive measurements, the perspectivalist

avoids diffculty by denying that the observer’s result has any impact on

the physics experienced by the superobserver. Consistency is then maintained

between them by looking to the unitary evolution of the superobserver’s measurement.

This response leads to a detailed discussion about the metaphysical

commitments of the perspectival approach. Here I argue the perspectivalist must

accept one surprising result – there is a significant divorce of fundamental ontological

states from physical dynamics.

Turning to invasive measurements, I argue that the concern here is entirely

misplaced. Arguments that raise worries about invasive measurements assume

the observer should describe herself to be in a quantum state of having observed

her measurement outcome when predicting the superobserver’s measurement

results. I argue that this is incorrect. Rather, I explain that it is impossible for

any observer to know her quantum state and so she should never describe herself

as being in any quantum state at all, let alone use such a description to make

predictions about a superobserver’s measurement.

To conclude, I explain how the perspectivalist responds to concerns raised

about entanglement and the possibility of action at a distance. Combining this

with the results above brings into focus how the perspectivalist may develop a

consistent, single-world picture of quantum mechanics.