PARALLEL BLOCK UNIVERSES
The mathematics of quantum mechanics evolved through attempts to explain what were, according to the classical physics of the time, counterintuitive observations such as the array of discrete wavelengths emitted by excited atoms (in technical language, quantized atomic spectra) or the discrete spins of electrons revealed by the experiment of Stern and Gerlach (see Quantum Spin Filter page).
In 1930 the loose ends of these attempts were woven together in a beautiful synthesis by Paul Dirac, a bizarre but brilliant, probably autistic, physicist, who had already, in 1928, merged quantum mechanics with special relativity to produce his famous Dirac equation. This in turn led him to propose the existence of an anti-particle to the electron (which we now call the positron).
(While Dirac was still a doctoral student at Cambridge, his supervisor had sent him an early paper of Heisenberg’s matrix approach to quantum theory. Dirac was suddenly struck by a deep connection that he saw between this approach and the mathematics of classical physics, and he developed this into a new and fundamental structure of quantum mechanics. This formed the basis of a paper published in 1926 for which he received his doctorate. Later, in 1930, he published his celebrated Principles of Quantum Mechanics which remains a standard textbook to this day: I still have my 1970 edition that I bought as an undergraduate.)
Dirac’s work was criticized by John von Neumann who was uneasy about what he saw as Dirac’s rather cavalier use of a mathematical tool that he, Dirac, had invented to make his work easier to understand. (In fact, this tool, the Dirac delta function, was later given mathematical legitimacy.) Von Neumann finally settled the issue of the mathematical equivalence of matrix and wave theory which, he had noted, Schrödinger had already attempted but had not entirely succeeded in doing. It meant that the two approaches could be relied on ultimately to produce the same answers to physical problems. He went on to write his own treatise on quantum mechanics, setting Dirac’s work in a mathematically more rigorous framework, called Mathematical Foundations of Quantum Mechanics.
There is a certain beauty in this mathematics (I took great pleasure in simply handling my copy of Dirac’s beautifully bound book, hefting it in my palm, fondling its creamy pages and synesthetically equating its weight to the grand significance of the equations printed on its leaves). But it is still legitimate to ask: what does this mathematics actually mean?
The mathematics of quantum mechanics is open to a wide range of interpretations. A concrete example is Dirac’s so-called “ket” vector. Bohr and his followers regarded the ket vector as one possible state of a property of a system out of a (possibly infinite) number of such possible states. Everett, on the other hand, regarded it as a real state, not just a possibility. The point is that both Bohr’s view and Everett’s view use the very same mathematics, although the corresponding interpretations of the mathematics are wildly different.
Crucially, Everett’s interpretation, summarized in the Many Worlds page, avoids the problematic collapse of the wave function. As we have seen, this is ruled out by special relativity. However, that very same theory, special relativity, also rules out Everett’s interpretation for a different reason.
In the Block Universe page, I showed how the relativity of apparently simultaneous events can mean that, if Bob is moving towards Alice, then a time interval which is in Alice’s future can already be in Bob’s past. Ultimately, this means that all events in the universe are fixed in the fabric of spacetime. In particular, it means that the “shape” of our universe’s spacetime – its topology, if you like – is like a block – and, in particular, it does not branch.
So, if we thought of the trunk, AB in Figure 1, as being our universe before Alice and Bob make their measurements, then the branching higher up has the wrong topology according to special relativity.
One of the main results of my first arXiv paper is that there is a solution to this problem that retains the principal advantage of the Many-Worlds interpretation (that it avoids wave-function collapse) while observing the requirement of a block-universe topology. I have illustrated this solution in Figure 2.
Figure 2 is essentially a copy of Figure 7 of the Many Worlds page, which showed how the detailed branching topology of the Many Worlds interpretation depends upon the viewpoint of the observer. However, in Figure 2, I have divided the branches into separate strips or filaments, with each filament corresponding to a particular experimental result.
I have highlighted one filament in grey. This is the one where Alice observes spin-up (with her spin-filter set at 0°) while Bob detects spin-down (with his spin-filter set to observe spin-up at 120°). As we saw in the Quantum Entanglement page, the probability for that to happen is ⅛. So that filament represents a block universe with that particular outcome for the entanglement experiment.
There is no discrepancy in the fact that, in the top-left picture, the block universe is in the branch where Alice has found spin-up and Bob’s result is as yet unknown whereas, in the bottom-right picture, the block universe is in the branch where Bob has found spin-down and Alice’s result is as yet unknown. That simply refers to the two different viewpoints – Alice’s and Bob’s – within the same block universe. The block universe permits different perspectives just as the two Minkowski diagrams in Figures 3 and 4 of the Causality and Special Relativity page show how Alice and Bob, who are moving relative to each other, see events in the same block universe happening in a different order.
I have drawn Figure 3 to highlight the difference between the Many-Worlds model and the multiverse of parallel, block universes. I have labelled the latter as the “Plexus model” because, as we shall see, the Plexus is the mathematical structure that contains our multiverse, as well as all other possible mathematical structures. Of course, there are many more block universes in our multiverse than the eight shown: the picture is illustrative only. I shall discuss this later.
In the Plexus model, quantum uncertainty emerges naturally. In each of the eight universes shown, there is an identical version of you, complete with all the same memories and histories. I have shown the eight universes at the moment of the entanglement experiment.
In three of these universes, you see both Alice and Bob measure spin-up, in three of them, you see both Alice and Bob measure spin-down, in one you see Alice measure spin-up while Bob measures spin-down, and in one you see Alice measure spin-down while Bob measures spin-up.
Quantum probabilities arise because any given version of you is three times more likely to see Alice’s and Bob’s spin-direction results agree than disagree, which, of course, is what quantum mechanics predicts for this entanglement experiment. I shall discuss the implications of the parallel block-universe model for quantum probability in greater detail in the page called The Origin of Quantum Probability.
Click here to go to [11] the Origin of Quantum Probability page