Simon Saunders on the Nature of Time, Many-Worlds, and Bell’s Inequalities

Simon Saunders — Oxford philosopher of physics and a leading Everettian — moves from what time is (the block universe, and why physics has to strip out the felt sense of ‘now’ to get an adequate representation) to the Many-Worlds interpretation of quantum mechanics, the plurality of views that now travel under that name, and a locality-based derivation of the Born rule he calls finite frequentism.

Key ideas

1. Time is geometry, not flow. Saunders’ considered answer to ‘what is time’ is that it is the four-dimensional geometrical structure of spacetime, threaded together by dynamics — the block universe. Special relativity rules out a global present: there is no privileged three-dimensional ‘now’ shared by everyone, only a momentary reality centred on each observer. What that static picture cannot capture is the felt sense of passage — ‘what breathes fire into the equations’ — because awareness is inherently local in time in a way the representation is not.
2. The multiplicity of moments is the model for the multiplicity of worlds. Saunders draws a direct line from an everyday puzzle — that there have been thousands of past ‘yous’, each a complete person at the time, all equally real but not simultaneous — to the Everettian claim that branching quantum states are all equally actual. Just as we have learned to live with a block universe containing every past moment, an Everettian has to get comfortable with a multiplicity of branches containing every outcome.
3. The extended observer and the appearance of Bell non-locality. Two people in conversation, tightly correlated across branches, can be treated as a single ‘extended observer’ inhabiting a common Everettian branch, even though strictly each is in their own branch. Saunders links this correlation structure to why Bell-type experiments only appear to require non-local influence — a fuller argument he flags as needing much more space than this conversation allowed.
4. Not one Many-Worlds interpretation but several, and they conflict. Saunders distinguishes his own decoherent-histories-based reading of Everett — which he says was closely aligned with David Wallace’s until Wallace left Oxford around 2014 — from other pictures now marketed under the same ‘many worlds’ label. He singles out the idea that worlds correspond one-to-one with the discrete eigenspaces of the energy operator as, in his words, very different from anything he finds in Everett’s own writing.
5. Finite frequentism: deriving the Born rule from a locality postulate. Rather than assume the Born rule, Saunders derives it from a single physical postulate — that a physically allowed action on a system Y cannot change the probability of a disjoint system X, an extension of Bell-style locality to probability itself. Applied to unitary quantum mechanics, this postulate forces equal-amplitude branches to carry equal probability, but only up to an irreducible ‘grey zone’ of imprecision — probabilities come out as intervals, not sharp numbers, and the most extreme low-amplitude branches (his analogy: Boltzmann-brain-type scenarios) can never be pinned down by any finite analysis.

Content

What time is: the block universe and the view from nowhere

Asked to define time, Saunders opens with Feynman’s deflection — ‘time is how long you have to wait’ — and Augustine’s puzzle (unnamed but clearly invoked: perfectly obvious until you’re asked to explain it). His considered view is that time just is the geometrical structure of spacetime: a static four-dimensional block threaded by dynamics, in which every moment of every history is laid out at once, ‘like some extraordinary block of glass in which all of the myriads of threads weaving through it are each particles, objects, peoples.’

The argument for the block comes from special relativity: because there is no privileged frame of reference, there is no global three-dimensional present, only a momentary reality centred on each observer. Stitch all of those momentary presents together and the only public reality left is the block. But the block ‘doesn’t feel like time at all — it looks and feels like space.’ Stephen Hawking’s question — what breathes fire into the equations — names the gap: a static representation of a life’s worldline shows a person talking, gesturing, existing, but nothing in it explains the felt experience of passage. Saunders ties this to the localisation of awareness — consciousness is bound to a narrow temporal window (he cites the ‘~50 milliseconds’ specious present), and that locality, not the physics, is what generates the sense of flow. He notes the same structure recurs in quantum mechanics around probability: ‘something felt and missing in the theoretical representation when it comes to probability is rather parallel to the sense that something is missing in the representation of time.’

Kurt’s summary — that our phenomenology insists on a privileged now, a flow, and an open future against a fixed past, all three in tension with the block-universe model — Saunders accepts as an accurate statement of ‘the problem situation.’ Constructing an adequate physical representation requires ‘nullifying the personal perspective,’ which is straightforward for space (you can draw a map of a garden without marking where you stand in it) but not for time: you cannot mark a moment as ‘now’ in a block diagram without that choice being as arbitrary as marking an arbitrary point in the garden as ‘here’.

Why space doesn’t inherit time’s paradoxes

Pressed on why the space–time symmetry of relativity doesn’t transfer time’s puzzles onto space, Saunders locates the asymmetry in endurance. A three-dimensional space that persists — a garden, the surface of the rotating Earth — can be revisited: you can return to the same spatial point (defined by a system of approximately rigid bodies, not by absolute spacetime coordinates) again and again. There is no equivalent for time: you cannot revisit a moment along your own worldline. What underwrites the intuitive idea of an enduring three-dimensional space, translated into four-dimensional language, is a ‘congruence of timelike lines’ — one for each point of the space — running roughly parallel to one another with only slowly changing relations between them. Nothing comparable exists for a single timelike line taken on its own.

From the multiplicity of moments to the multiplicity of worlds

Saunders builds the bridge to Everett through contingency. Ordinary life is already saturated with a felt multiplicity of possibilities we mostly manage not to think about — the bus that might hit you, the lottery you might win — and we are, he says, ‘extremely adept’ at weighting them, using an inbuilt Aristotelian common-sense theory of causation and probability. The Everettian move is to take that same multiplicity — the branching structure generated by the unitary evolution of the quantum state — and treat it not merely as representing possibilities but as representing actuality, with no further postulate required: ‘that negotiation from an Everettian point of view is exactly an understanding of branching structure. And branching structure from an Everettian point of view is the source of the many worlds.’

He illustrates what a branch actually is with two examples from Everett’s own 1957 work. A superposition of two large masses in different classical configurations does not describe one contradictory object in two places; tracking the quantum states across the superposition, each ‘story’ obeys its own approximate classical equations of motion, recovering ordinary Newtonian trajectories inside each branch. And the electromagnetic field carrying two simultaneous beams of light, or thousands of overlapping mobile-phone conversations, is not one signal ‘saying two things at once’ — ‘it is not a beam of light in a superposition pointing in two different directions. It is two beams of light — I think it would be a madman who would deny that on being pressed.’ Multiplicity, on this reading, was present in Everett from the start; it did not require the word ‘worlds’ to be true to his thesis.

The extended observer and Bell non-locality

Asked whether it is more correct to speak of ‘the branch you are in’ than ‘the branch we are in,’ given that any two observers’ branches will eventually diverge, Saunders concedes the literal point — ‘I am just in my Everettian branch, you are in your Everettian branch’ — but argues that because the two branches are tightly correlated (a conversation exchanges, in his estimate, thousands of bits a minute), it is coherent to treat the pair as a single extended observer inhabiting a common branch, so long as neither party is probing localised quantum systems that would reveal the divergence.

He then connects this correlation structure directly to Bell: if the two of you were to run quantum experiments on entangled systems from opposite sides of the Atlantic, ‘we would maybe find some interesting — from a branching-structure point of view — some very interesting aspects to it that underly the appearance, at least, of Bell non-locality.’ This is the episode’s most direct statement of the claim previewed in the introduction — that Bell violations are evidence for Everett rather than evidence against locality — but Saunders does not develop it further here; running short on time, both he and Kurt defer the detailed unpacking to a future conversation.

Not one Many-Worlds interpretation

Saunders is candid about disagreeing with other prominent Everettians. His own reading grew out of decoherent-histories theory and, he says, was closely harmonised with David Wallace’s until Wallace left Oxford around 2014. He is critical of pictures that emerged afterwards without engaging decoherence theory at all — singling out the idea that worlds correspond one-to-one with the discrete eigenspaces of the energy operator as ‘very different from anything that I have gathered from Everett.’ (He does not name whose view this is.) He is equally sceptical of readings that deny Everett himself was committed to many worlds at all, calling that interpretation implausible even while welcoming it as legitimate open inquiry. What unifies the genuinely Everettian camp, on his account, is not agreement on what a ‘world’ is but a shared refusal to add anything to unitary quantum mechanics beyond the bare formalism.

Finite frequentism: deriving the Born rule from locality

Saunders’ current work on the Born rule problem — how to justify treating squared amplitudes as probabilities — proceeds by decomposing the universal quantum state into microstates of equal amplitude and counting, for a given projection operator (a proposition or property), what fraction of microstates say ‘yes’ and what fraction say ‘no’. Because at least one microstate will typically be indeterminate for any given projector (a Schrödinger-cat state relative to that property), this yields not a point probability but an interval — a lower bound from the ‘yes’ microstates and an upper bound excluding the ‘no’ microstates, with a residual ‘grey zone’ in between. The narrower the interval, the more informative the probability; a maximally uninformative case spans the whole of [0, 1].

The derivation itself rests on a single postulate, framed as an extension of locality: ‘you cannot change the probability of X by an action on Y when Y is disjoint from X, and the action preserves disjointness throughout.’ Under unitary quantum mechanics — where all physical changes are unitary — this postulate forces equal-amplitude states to receive equal probability, which is the Born rule. Saunders stresses that low-amplitude, Born-rule-violating branches (the kind that would show up as anomalous experimental statistics) always fall inside the irreducible grey zone: no finite decomposition of the state can assign them a definite probability at all, which he compares to the Boltzmann-brain problem — ‘you will not even see the probability’ for the pathological scenario, because it cannot be captured in any finite analysis.

Related

• Simon Saunders — speaker; Oxford philosopher of physics and Everettian
• Curt Jaimungal — host
• Many-Worlds Interpretation — the interpretation Saunders defends, in a decoherence-based reading he distinguishes from other Everettians’
• Quantum Measurement Problem — the problem the block-universe/passage-of-time discussion parallels via the missing ‘actuality’ in quantum probability
• Consciousness — the localisation of awareness in time, and the extended-observer treatment of two correlated Everettian branches