# Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics

## Abstract

**:**

## 1. The Incoherence Problem

Ignorance: In order to make propositions such as “the probability that event E happens is p” meaningful in a deterministic universe, we must be ignorant of some facts about E.

## 2. Personal Identity and Ontological Structure

Dennett’s criterion: A macro-object is a pattern, and the existence of a pattern as a real thing depends on the usefulness—in particular, the explanatory power and predictive reliability—of theories which admit that pattern in their ontology [22] (p. 93).

There is a concept of transtemporal identity for patterns, but again it is only approximate. To say that a pattern ${P}_{2}$ at time ${t}_{2}$ is the same pattern as some pattern ${P}_{1}$ at time ${t}_{1}$ is to say something like “${P}_{2}$ is causally determined largely by ${P}_{1}$ and there is a continuous sequence of gradually changing patterns between them”—but this concept will not be fundamental or exact and may sometimes break down [22] (pp. 95–96).

## 3. The Lewisian Account of Personal Identity

## 4. Saunders and Wallace’s Lewisian Solution to the Incoherence Problem and Its Objections

In particular, I cannot wonder further whether my use of the pronoun ‘she’ when pointing at the observer picks out she↑ or she↓; since she↑ and she↓ coincide at the moment, I am pointing at both of them [11] (p. 6). (P. Lewis’s use of “she↑” and “she↓” is the same as the use of “Aristotle0↑” or “Aristotle0↓” in this paper.)

But HydraUP and HydraDOWN cannot each indexically refer to her own body via an utterance of ‘This is my body’ which has a single token sited in a single body-stage at time T prior to branching, because that single body-stage is common to the world-tube bodies of both HydraUP and HydraDOWN [12] (p. 311). (Tappenden’s use of “HydraUP” and “HydraDOWN” is the same as the use of “Aristotle0↑” or “Aristotle0↓” in this paper.)

## 5. Two Versions of the Solution

_{3}and (Aristotle0↓)

_{3}before the branching, and both of them supervene $|\mathrm{Aristotle}0\u27e9$. Namely, there is only one singular physical body as Aristotle before branching, but there are multiple mental states, or some other three-dimensional entities, that supervene $|\mathrm{Aristotle}0\u27e9$. (The requirement that there is only one physical body as Aristotle before the branching can be relinquished if we introduce multiple qualitatively identical “worlds” or multiple physical states before the branching, with each mind of Aristotle situated in a distinct world. I shall discuss this approach in Section 6 and Section 7. However, the claim that there are multiple mental states as Aristotle before the branching, which is more essential, shall remain unchanged. The term “three-dimensional” might be a bit perplexing when applied to a mental state. In this context, I am employing the term “three-dimensional” in a broad sense for the sake of convenience, aligning it with the terminology of three-dimensionalism and four-dimensionalism. A three-dimensional person-stage is momentary, while a four-dimensional person is not. From an eternalist perspective, one might uphold that there exists an overarching mental state for a person throughout all time, with their momentary mental states serving as partial “sub-states” of this ultimate mental state. I do not know who exactly upholds this view, but it is important to make a distinction here. In this paper, I call a mental state three-dimensional in the sense that it is momentary.) By having two or more minds that think before branching, which are qualitatively identical but numerically different, the objection presented in the previous paragraph can be resolved. Before the branching, neither thinking can tell which mental state it belongs to, as both share the same contents. But there are some further facts, though they might be unobservable in principle, that can determine which mental state it belongs to.

_{3}is uncertain whether (Aristotle0↑)

_{3}will be Aristotle↑ or Aristotle↓, and similarly, (Aristotle0↓)

_{3}is uncertain whether (Aristotle0↓)

_{3}will be Aristotle↑ or Aristotle↓.

## 6. The Problem of Supervenience

_{3}” and “(Aristotle0↓)

_{3}”, and replacing “personal identity relation” with “I-relation”. This notation shift is purely for convenience and does not imply the adoption of either the three-dimensionalism view or the four-dimensionalism view of personal identity.

Supervenience: The personal identity relations in a possible universe w′ are the same as the personal identity relations in a possible universe w, if w and w′ are physically identical. (In simple terms, personal identity in a universe supervenes its physical state. In the terminology of EQM, the term “universe” refers to the entirety of physical existences described by the formulation of Quantum Mechanics. On the other hand, the term “world” is used to denote a specific branch in the universe under decoherence. Therefore, in this paper, I use the term “possible universe” instead of “possible world”.)

## 7. The Divergence View

Then the two histories are exactly similar up to and including the penultimate projection operator, but differ on the final projection operator—they agree at all times up to t_{n−1}, but differ at t_{n}. The point at issue between the diverging and branching interpretations is whether the entities represented by the projection operators ${\widehat{P}}_{{\mathsf{\alpha}}_{0}}\dots {\widehat{P}}_{{\mathsf{\alpha}}_{\mathrm{n}-1}}$ in ${\mathrm{C}}_{\underset{\_}{\mathsf{\alpha}}}$ are numerically identical to the entities represented by the projection operators ${\widehat{P}}_{{{\mathsf{\alpha}}^{\prime}}_{0}}\dots {\widehat{P}}_{{{\mathsf{\alpha}}^{\prime}}_{\mathrm{n}-1}}$ in ${\mathrm{C}}_{\underset{\_}{\mathsf{\alpha}}\prime}$, or whether they are (numerically distinct) qualitative duplicates. Numerically identical entities give us overlapping worlds; qualitative duplicates give us diverging worlds [20] (p. 73).

That is, if one includes the global wave function in the state description of the worlds, then each world might be thought of as being described by a particular hidden-variable theory, where the preferred basis selects the always determinate physical quantity (the hidden variable), the local state of each world at a time gives the value of this quantity in that world, and the connection rule (together with the linear dynamics) determines, in so far as it is determined, how the quantity evolves in each world: A many-threads theory is ultimately just a hidden-variable theory where one simultaneously considers all physically possible worlds [33] (pp. 183–184). (It seems to me that Wilson does not pay much attention to Barrett’s alarm in Wilson’s writings. Wilson only cites Barrett once in [35] without mentioning this point. I am grateful to Shan Gao who reminds me of Barrett’s writing.)

## 8. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Lu, Z.
Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics. *Quantum Rep.* **2023**, *5*, 584-596.
https://doi.org/10.3390/quantum5030038

**AMA Style**

Lu Z.
Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics. *Quantum Reports*. 2023; 5(3):584-596.
https://doi.org/10.3390/quantum5030038

**Chicago/Turabian Style**

Lu, Zhonghao.
2023. "Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics" *Quantum Reports* 5, no. 3: 584-596.
https://doi.org/10.3390/quantum5030038