An Ontology of Nature with Local Causality, Parallel Lives, and Many Relative Worlds

Abstract

Parallel lives (PL) is an ontological model of nature in which quantum mechanics and special relativity are unified in a single universe with a single space-time. Point-like objects called lives are the only fundamental objects in this space-time, and they propagate at or below c, and interact with one another only locally at point-like events in space-time, very much like classical point particles. Lives are not alive in any sense, nor do they possess consciousness or any agency to make decisions—they are simply point objects which encode memory at events in space-time. The only causes and effects in the universe occur when lives meet locally, and thus the causal structure of interaction events in space-time is Lorentz invariant. Each life traces a continuous world-line through space-time, and experiences its own relative world, fully defined by the outcomes of past events along its world-line (never superpositions), which are encoded in its external memory. A quantum field comprises a continuum of lives throughout space-time, and familiar physical systems like particles each comprise a sub-continuum of the lives of the field. Each life carries a hidden internal memory containing a local relative wavefunction, which is a local piece of a pure universal wavefunction, but it is the relative wavefunctions in the local memories throughout space-time which are physically real in PL, and not the universal wavefunction in configuration space. Furthermore, while the universal wavefunction tracks the average behavior of the lives of a system, it fails to track their individual dynamics and trajectories. There is always a preferred separable basis, and for an irreducible physical system, each orthogonal term in this basis is a different relative world—each containing some fraction of the lives of the system. The relative wavefunctions in the lives’ internal memories govern which lives of different systems can meet during future local interactions, and thereby enforce entanglement correlations—including Bell inequality violations. These, and many other details, are explored here, but several aspects of this framework are not yet fleshed out, and work is ongoing.

Appendix

There are many details that one must become comfortable with before the elegance of this model becomes obvious, and toward this end, I have devised a classroom exercise for a group of students that will allow them to participate in a simulation of the local entanglement mechanism themselves, and violate a Bell inequality.

Some of the students in the exercise will acts as lives of different systems, while others will play the role of nature, and act as referees, who read and write from the memories of different students, and determine which lives can meet. In general, we will need the same number of students to acts as lives for every physical system we want to simulate, and we can keep the minimum total number small by restricting ourselves to only a few simple measurement settings—since each student technically represents an infinite number of lives, and we need to divide the lives into the right proportions. To simulate space-like separation, students cannot communicate directly during the exercise.

Each student who represents lives of a system will carry a notebook. The notebook contains a label for which system they belong to, like ‘qubit 1,’ and they also contain pages for internal memory, and other pages for external memory. Due to the initial interaction of the two systems, each student starts off with a pure quantum state $|\psi \rangle$ in their internal memory, which includes every system in the past interaction cone of the system. Furthermore, each student has one of the outcomes $|a\rangle ^1|b\rangle ^2$ of the interaction encoded in their external memory (which defines the preferred basis), along with a history of outcomes of past interactions for all other systems $|c\rangle ^o$ in the past interaction cone. The proportion of students in each of these relative worlds is $P(a,b,c) = |\langle \psi |a\rangle |b\rangle |c\rangle |^2$.

Now, suppose that system 1 interacts via unitary U with a new system 3, and the students of each system meet one-to-one. The referee now reads the internal memories $|\psi _1\rangle$ and $|\psi _3\rangle$ of an interacting pair of students from each system, and then updates them both to contain the relative state $|\psi '\rangle = U |\psi _1\rangle |\psi _3\rangle$. The interaction may also cause the preferred basis to change, and then each student encodes an outcome $|x\rangle ^1|y\rangle ^3$ in that basis into their external memory (which determines which relative world they experience), and the pair shake hands to signify their meeting event. Just as before, the proportion of students in each relative world is given by $P(x,y,z) = |\langle \psi |x\rangle |y\rangle |z\rangle |^2$, where again $|z\rangle ^o$ is the history state of other systems, which includes the outcome of the previous interaction between systems 1 and 2, and the referee pairs the students off according to these proportions.

When macro-scale systems meet, the interaction unitary is identity, and the preferred bases do not change, but their lives still synchronize their internal memories and encode the meeting into their external memories. These are the only rules we need in order to simulate a Bell experiment.

Let us consider one of the classic examples, developed by Wigner [75] and Mermin [76], of a Bell test involving a source which prepares two qubits in the singlet state $|\psi _0\rangle ^{1,2} = \big (|0\rangle ^1|1\rangle ^2 - |1\rangle ^1|0\rangle ^2 \big )/\sqrt{(}2)$, and sends one to Alice and one to Bob. We assume that we can ignore other systems in the interaction history of these two at the beginning of this experiment. At space-like separation, Alice and Bob randomly choose among the three equally spaced angles in the XZ-plane and measure the qubit along that axis. For this simulation we will need 16 students to act as lives, and 3 to acts as local referees. We will begin with this state already prepared, and let $\{|0\rangle ,|1\rangle \}$ be the preferred basis for both systems. Each qubit will have 8 students representing it, and this means that 4 students of qubit 1 are in state $|0\rangle ^1$ have a record in their external memory of meeting a student of qubit 2 in state $|1\rangle ^2$, and the other four are in state $|1\rangle ^1$ and met a student of qubit 2 in state $|0\rangle ^2$. All 16 of them have $|\psi _0\rangle ^{1,2}$ written in internal memory.

Now, the 8 students of qubit 1 walk over to Alice, and the 8 students of qubit 2 to Bob. For simplicity, we let setting 1 be the already-preferred basis, and settings 2 and 3 be, $\left\{ \frac{\sqrt{3}}{2}|0\rangle + \frac{1}{2}|1\rangle , \frac{1}{2}|0\rangle - \frac{\sqrt{3}}{2} |1\rangle \right\}$, and $\left\{ \frac{\sqrt{3}}{2}|0\rangle - \frac{1}{2}|1\rangle , \frac{1}{2}|0\rangle + \frac{\sqrt{3}}{2} |1\rangle \right\}$, respectively. We will let Alice begin in the ready state $|R\rangle ^A$, and the interaction unitary is then $U^{1,A} = |s_1\rangle ^A |s_1\rangle ^1 \langle R|^A \langle s_1|^1 + |s_2\rangle ^A |s_2\rangle ^1 \langle R|^A \langle s_2|^1 +$ (terms with $\langle R_\bot |^A$), where $|s_1\rangle$ and $|s_2\rangle$ are the basis states of the measurement setting, and similar for Bob’s $U^{2,B}$.

If Alice chooses setting 1, then 4 of her students meet a student of qubit 1 already in state $|0\rangle ^1$ and experience outcome $|0\rangle ^A$, and the other 4 meet a student already in state $|1\rangle ^1$ and experience outcome $|1\rangle ^A$. Using $P(s_1^1, s_1^A, h^2)$, we see that if Alice measures either setting 2 or 3, then three students of qubit 1 which were previously in the relative world $|0\rangle ^1$ now enter relative world $|s_2\rangle ^1$ and meet students of Alice in state $|s_2\rangle ^A$, one student of qubit 1 which was previously in the relative world $|0\rangle ^1$ now enters relative world $|s_1\rangle ^1$ and meets a student of Alice in state $|s_1\rangle ^A$, three students of qubit 1 which were previously in the relative world $|1\rangle ^1$ now enter relative world $|s_1\rangle ^1$ and meet students of Alice in state $|s_1\rangle ^A$, and one student of qubit 1 which was previously in the relative world $|1\rangle ^1$ now enters relative world $|s_2\rangle ^1$ and meets a student of Alice in state $|s_2\rangle ^A$.

For any setting, the referee then writes the outcomes in the external memory of the students of both Alice and qubit 1, and the state $|\psi ^{1,2,A} \rangle = U^{1,A}|\psi _0\rangle ^{1,2}|R\rangle ^A$ in their internal memories. To save on students during the measurement interaction, the same 8 students playing lives of qubit 1 now also play lives of Alice, and after the interaction they continue as lives of Alice.

The situation is symmetrically identical for Bob, so after the measurement, his 8 students will now have $|\psi ^{1,2,B}\rangle = U^{2,B}|\psi _0\rangle ^{1,2}|R\rangle ^B$ written in their internal memories.

Now Alice’s 8 students and Bob’s 8 students reunite. When two systems meet, their internal memories synchronize by accumulating all states and coupling unitaries from both of their past internal memories. When students of Alice and Bob meet, their internal memories synchronize to $|\psi \rangle ^{1,2,A,B} = U^{1,A} U^{2,B}|\psi _0\rangle ^{1,2}|R\rangle ^A |R\rangle ^B$, and their preferred bases remain the same, so the proportion of students in each relative world who meet is given by $P(s_a, s_b, h) = |\langle \psi |^{1,2,A,B} | s_a\rangle ^A | s_b\rangle ^B |h\rangle ^{1,2}|^2 = |\langle \psi _0|^{1,2} | s_a\rangle ^1 | s_b\rangle ^2 |^2$ , where $s_a$ is the ath outcome of Alice’s measurement, and $s_b$ is the bth outcome of the Bob’s measurement, and $|h\rangle ^{1,2}$ is the most recent external memory state of qubits 1 and 2 within the history h. The proportion of lives that meet with each pair of specific histories is determined using Eq. 3.

If Alice and Bob measured the same setting, then four students of Alice who got $|s_1\rangle ^A$ each meet a student of Bob who got $|s_2\rangle ^B$, and four students of Alice who got $|s_2\rangle ^A$ each meet a student of Bob who got $|s_1\rangle ^B$. If they measured different settings, then three of Alice’s students who got $|s_1\rangle ^A$ each meet a student of Bob who got $|s_1\rangle ^B$, one of Alice’s students who got $|s_1\rangle ^A$ meets a student of Bob who got $|s_2\rangle ^B$, three of Alice’s students who got $|s_2\rangle ^A$ each meet a student of Bob who got $|s_2\rangle ^B$, and one of Alice’s students who got $|s_2\rangle ^A$ meets a student of Bob who got $|s_1\rangle ^B$. In any case, it is easy to see that the entanglement correlations of the initial state $|\psi _0\rangle ^{1,2}$ have been obeyed for the entire group of students.

Then, by repeating the exercise many times, an individual student will experience Born rule statistics and thus a violation of a Bell inequality, even though everything was done obeying explicit local causality.