Block Time, Many Worlds, and the Persistence of Ordinariness

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Block Time, Many Worlds, and Why Tomorrow Resembles Yesterday - Mostly

If we combine two ideas that are often kept in separate conceptual boxes - the block universe of eternalism, and the Everettian “many worlds” account of quantum uncertainty - a question naturally follows. If the universe is a fixed four-dimensional whole, and if quantum events constantly branch reality into a plurality of decoherent futures, why doesn’t the world look, at the large scale, like a riot of amplified randomness?

Why does the past, looking backwards from here, present itself as overwhelmingly law-governed and almost pedestrian in its Newtonian-style determinism? And if that is what the past looks like, shouldn’t we expect the future, in almost all respects, to have the same look and feel despite its underlying quantum indeterminacy?

On the surface, this seems like a tension. “Many worlds” is habitually sold with a kind of metaphysical euphoria: infinite branching, limitless divergence, cosmic roulette. Yet our lived-history has never felt like roulette.

Most days contain no miracles, no macroscopic quantum surprises, no sudden turn of events caused by a radioactive atom choosing left rather than right. The planets keep their appointments; bridges don’t randomly fail because of a quantum coin-flip; people mostly continue being the sorts of people they were last week. Looking back, the macro-past seems more like a classical trajectory with occasional noise than like a random walk whose steps were decided by quantum dice.

The first thing to say is that, in Everett, the deep story is deterministic anyway - just not in the way we are used to. The universal wavefunction evolves unitarily: nothing “collapses”. There is no fundamental stochastic law picking a single outcome. The branching is not indeterminism in the global dynamics; it is the proliferation of effectively non-interfering sectors. What feels like chance from inside a branch is not a God’s-eye randomness but a self-location problem: which decohered continuation will I find myself in? From 'outside', the entire branching structure is fixed; from within, one experiences merely uncertainty about one’s address inside it.

That already blunts the popular intuition that “many worlds” ought to generate a future that is macroscopically erratic. Branching is constant, but meaningful divergence is not. Most quantum events do not amplify into macroscopic differences; they thermalise, cancel, or remain trapped in degrees of freedom that never climb the ladder of scale. Decoherence does not inject chaos into the classical world; it does almost the opposite. It explains why quasi-classical “pointer states” are stable, why macroscopic objects persist, why a chair remains a chair, why the classical description becomes such a good effective theory for large aggregates. The world looks classical because, for most practical purposes, it is.

It is worth stating an underappreciated symmetry here: what we now call “the past” was once, from some deeper-past vantage point, the future. The difference between “past” and “future” is not that one is ontologically settled while the other is metaphysically open; it is that we are embedded - instance by instance - at particular locations in the block.

In a block universe, every event is future-ward relative to earlier slices and past-ward relative to later ones. So if the world’s quantum branching had a natural tendency to erupt into large-scale caprice, we would already see that eruption when we look backwards - because the macro-history we inhabit has already run the gauntlet of being “the future” for countless earlier observers. The fact that it still reads, at human scale, as orderly is evidence that the branching is mostly hidden by the same structural constraints that will hide it tomorrow.

There is also the brute constraint of low-entropy initial conditions — the Past Hypothesis in its various guises. The universe’s special beginning does not merely explain the arrow of time; it also massively limits which macroscopic histories carry significant weight.

Wild, spectacularly diverging macroscopic histories exist as mathematical possibilities inside the universal wavefunction, but most of them are thin as mist in Born measure. The block is thick where the classical narrative is thick: regularities, stable structures, robust thermodynamic flows. The “tree” branches constantly, but almost all of the branch weight is clustered in futures that differ only in microscopic details and wash out at human scales.

So the rephrased answer is this: the reason the past looks largely deterministic is not that quantum randomness never happened, but that it almost never mattered at the scale we care about.

The macro-world is an emergent attractor: it is what you get when you coarse-grain a quantum substrate under decoherence and thermodynamics. And if that is what happened in the past, then in a block universe the future is not poised to suddenly become a carnival of amplified quantum accidents. The future block is “already there” in the same sense the past is already there - with branching built in, but with most branches differing only in trivial microscopic ways.

None of this denies that amplification can happen - it can: evolutionary contingency, threshold phenomena in neurobiology, chaotic systems near bifurcation points, rare catastrophic events. But even there, the range of viable macrostates is narrow, selection effects prune hard, and the world remains governed by constraints and regularities rather than by caprice. 

Everett does not imply a future that is wildly branching in any humanly vivid way.

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"Something Deeply Hidden" - some thoughts

Amazon link

The title is a quote from Einstein, revealed at the end of the book. Carroll is on Einstein's side in the great Einstein-Bohr debates on the meaning and completeness of quantum theory. Sort of.

Carroll writes well, mostly. He's a fluent author and has the surpassing virtue of conceptual clarity. This is a book about concepts: conceptual analysis and what the equations are telling us. This works well at the beginning where he covers the material in a typical undergraduate course, falters later when he discusses quantum field theory, and stutters at the end, where he sketches the research program of deriving spacetime from Hilbert space.

Who is this book for? Not the layperson - it's too unfamiliar, too conceptually abstract and dense. It's for people who know quantum mechanics - the mathematics and the calculations - people who understand the machinery but, like everyone else, struggle to understand what it's telling us about the universe itself. The math he doesn't mention underpins the concepts he's keen to articulate and talk around.

He's persuasive on the many-worlds interpretation, mostly because it seems plausible to start with the wave-function of the universe-as-a-holistic-entity. He's at pains to point out that the MWI is really no more than that: austere quantum theory.

He's excellent on how decoherence works, giving a clear conceptual overview. You have to have covered superpositions and entangled states in your QM course - and to have thought about it - to really grasp what he's saying, though. He writes like it's pretty clear but it isn't.

Should one walk away from this book an Everettian?  Carroll makes a very strong case for this over all the other interpretations - his critiques sometimes feel like shooting fish in a barrel. He's convincing that we should conceptualise QM as if the MWI were true.

But is the universe really a state vector in a high-dimensional Hilbert space? With our familiar classical-looking spacetime something emergent? A reality emergent from entropic-entanglement (hence locality and metric) and then local sampling of that so-structured Hilbert space?

No-one knows. It might be nice .. but the research isn't in.

And then there are the lacunae. The genesis of the standard model is nowhere mentioned. It may all be quantum fields - but how did we get separate quantum fields for all the different fermions and bosons?

My conclusion: every physics undergraduate should read this book. All the questions they have about how quantum theory is put together (the map of the territory in fact) and how it all relates to the universe we experience are honestly discussed here. They won't find those issues addressed in class or in their textbooks.

They will also appreciate how much we still don't understand about the fundamentals of the theory and about reality itself. Quantum gravity is still, most likely, the holy grail. But in the absence of meaningful experiments (the collider plans don't really help) solid progress is likely to remain stalled.

Can Everett worlds ever merge?

This post follows up an issue from my review of "The Many Worlds of Hugh Everett III", by Peter Byrne. From the Everett FAQ site.

"Assuming that we have a reversible machine intelligence to hand then the experiment consists of the machine making three reversible measurements of the spin of an electron (or polarisation of a photon).

(1) First it measures the spin along the z-axis. It records either spin "up" or spin "down" and notes this in its memory. This measurement acts just to prepare the electron in a definite state.

(2) Second it measures the spin along the x-axis and records either spin "left" or spin "right" and notes this in its memory. The machine now reverses the entire x-axis measurement - which must be possible, since physics is effectively reversible, if we can describe the measuring process physically - including reversibly erasing its memory of the second measurement.

(3) Third the machine takes a spin measurement along the z-axis. Again the machine makes a note of the result.

According to the Copenhagen interpretation the original (1) and final (3) z-axis spin measurements have only a 50% chance of agreeing because the intervention of the x-axis measurement by the conscious observer (the machine) caused the collapse of the electron's wavefunction.

According to many-worlds the first and third measurements will always agree, because there was no intermediate wavefunction collapse. The machine was split into two states or different worlds, by the second measurement; one where it observed the electron with spin "left"; one where it observed the electron with spin "right".

Hence when the machine reversed the second measurement these two worlds merged back together, restoring the original state of the electron 100% of the time.

Only by accepting the existence of the other Everett-worlds is this 100% restoration explicable."

Many Worlds: whence and what?

Where does the idea of the "Many Worlds Interpretation of Quantum Mechanics" actually come from? Everettians claim that it's simply a matter of taking the formalism seriously, in its own terms, as David Wallace explains from his paper: "A prolegomenon to the ontology of the Everett interpretation".

"To see how that works, let’s suppose we have a measurement device represented by a pointer, that can be in three states: pointing left, pointing right, and pointing nowhere. And suppose the measurement is set up so that if the electron is measured in position x the pointer moves so that it points left, and if it is measured in position y, it moves so that it points right. We can certainly find a state space suitable for such a pointer, and indeed can find wave-packet states φ_L (for the pointer pointing left), φ_R (for it pointing right), and φ₀ (for it pointing nowhere). The idea of these states, as with the electron, is that φ_L (say) is a state such that, if we measure where the pointer is — with the naked eye, or otherwise — we’re pretty much guaranteed to get the result that it’s in the pointing-left position.

Given state spaces for the electron and for the pointer, quantum theory gives us a recipe to construct a state space (the so-called “tensor product space”) for the combined system of electron-plus-pointer. If φ is any state for the electron alone, and ψ any state of the pointer alone, there is then a combined state φ ⊗ ψ of both together, which gives the same experimental predictions as φ for measurements of the electron and the same experimental predictions as ψ for measurements of the pointer.

If the measurement device works as intended, the dynamics of measurement must look something like this:

ψ_x ⊗ φ₀  =>  ψ_x ⊗ φ_L

ψ_y ⊗ φ₀  =>  ψ_x ⊗ φ_R

In other words, if the electron starts off in a state such that its position is always found to be x, the pointer must reliably end up in a state such that its position is always found to be on the left (and similarly for y). But now, the linearity of the dynamics causes trouble: what if we measure the electron’s position when it is in the mysterious state αψ_x + βψ_y? The dynamics in this case have to give

( αψ_x + βψ_y) ⊗ φ₀  =>   αψ_x ⊗ φ_L + βψ_y ⊗ φ_R

So now there seems to be a contradiction between our measurement algorithm and the actual physical process of measurement. The algorithm tells us that the measurement should give x a fraction |α |² of the time and y the rest of the time, and hence that the pointer should point left a fraction |α |² of the time and right the rest of the time. But the actual physical process never gives ‘left’ or ‘right’ as pointer states at all, and is not indeterministic at all: instead, it deterministically gives the strange, indefinite state

αψ_x ⊗ φ_L + βψ_y ⊗ φ_R,

in which the pointer seems to be pointing left and pointing right at the same time.

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The immediate question one asks about the Everett interpretation — why do we only see one pointer, if actually there are two? — can be resolved by remembering that you too, dear reader, are a physical system, and if χ _L and χ _R are, respectively, states in your state space representing you seeing a pointer pointing left and you seeing it pointing right, then the same linearity argument used above predicts that the state of (you-plus-pointer-plus-electron), once you look at the pointer, will be

αψ_x ⊗ φ_L ⊗ χ_L + βψ_y ⊗ φ_R⊗ χ_R

In other words, you will be in a state of seeing left and seeing right at the same time, and this state (according to the Everett interpretation) should also be understood as telling us that there are two yous, one seeing the pointer pointing left and one seeing it pointing right.

Notice — crucially — that although the state above is the sum of two macroscopically very different state, in each term in the sum the results of the two measurements are correlated (in each term the electron has a particular position, the pointer records it as having that position, and you observe the pointer as so recording it.)

Once a system gets above a certain size, it cannot help being measured constantly — by chance collisions with the atmosphere and with sunlight, if by nothing else. In doing so, the multiplicity spreads to more and more systems, while the correlations in each term in the state remain. In due course, the state (schematically) evolves into something like

α (Whole planet is as if electron was found in position x) + β (Whole planet is as if electron was found in position y).

When this, too, is understood as representing both states of affairs simultaneously, the “many-worlds” label for the Everett interpretation starts to sound apposite."

Notice that we are doing nothing more here than taking the superposition seriously. But what kinds of mathematical (and physical) entities correspond to taking all the elements of the superposition as being concurrently 'present'? This is not at all obvious, and as I read Wallace's book and many papers, it seems that the Everettian community finds this stuff pretty opaque too. Sometimes, as above, each superposition branch is claimed to look like the 3 + 1 dimensional space-time which we appear to inhabit; other times the micro-physics underlying the world of appearances seems decidedly weird! Crudely: the quantum state lives in high-dimensional Hilbert space - and the world we inhabit doesn't.

And don't mention the g-word!

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Gravity. A workable theory of quantum gravity might be strange in the micro-physics (i.e. at extremely small length scales - or in areas of extreme field strength) so that our placid large-scale experience of reality is once again emergent.

Dreamers and Doers

Sean Carroll has a guest post by Chip Sebens on the Many-Interacting-Worlds Approach to Quantum Mechanics. Here's the first part of it.

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"In Newtonian physics objects always have definite locations. They are never in two places at once. To determine how an object will move one simply needs to add up the various forces acting on it and from these calculate the object’s acceleration. This framework is generally taken to be inadequate for explaining the quantum behavior of subatomic particles like electrons and protons. We are told that quantum theory requires us to revise this classical picture of the world, but what picture of reality is supposed to take its place is unclear. There is little consensus on many foundational questions: Is quantum randomness fundamental or a result of our ignorance? Do electrons have well-defined properties before measurement? Is the Schrödinger equation always obeyed? Are there parallel universes?

"Some of us feel that the theory is understood well enough to be getting on with. Even though we might not know what electrons are up to when no one is looking, we know how to apply the theory to make predictions for the results of experiments. Much progress has been made―observe the wonder of the standard model―without answering these foundational questions. Perhaps one day with insight gained from new physics we can return to these basic questions. I will call those with such a mindset the doers. Richard Feynman was a doer:

“It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, ‘But how can it be like that?’ which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. … I think I can safely say that nobody understands quantum mechanics. … Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

-Feynman, The Character of Physical Law (chapter 6, pg. 129)

"In contrast to the doers, there are the dreamers. Dreamers, although they may often use the theory without worrying about its foundations, are unsatisfied with standard presentations of quantum mechanics. They want to know “how it can be like that” and have offered a variety of alternative ways of filling in the details. Doers denigrate the dreamers for being unproductive, getting lost “down the drain.” Dreamers criticize the doers for giving up on one of the central goals of physics, understanding nature, to focus exclusively on another, controlling it. But even by the lights of the doer’s primary mission―being able to make accurate predictions for a wide variety of experiments―there are reasons to dream:

“Suppose you have two theories, A and B, which look completely different psychologically, with different ideas in them and so on, but that all consequences that are computed from each are exactly the same, and both agree with experiment. … how are we going to decide which one is right? There is no way by science, because they both agree with experiment to the same extent. … However, for psychological reasons, in order to guess new theories, these two things may be very far from equivalent, because one gives a man different ideas from the other. By putting the theory in a certain kind of framework you get an idea of what to change. … Therefore psychologically we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics.”

-Feynman, The Character of Physical Law (chapter 7, pg. 168)

"In the spirit of finding alternative versions of quantum mechanics―whether they agree exactly or only approximately on experimental consequences―let me describe an exciting new option which has recently been proposed by Hall, Deckert, and Wiseman (in Physical Review X) and myself (forthcoming in Philosophy of Science), receiving media attention in: Nature, New Scientist, Cosmos, Huffington Post, Huffington Post Blog, FQXi podcast… Somewhat similar ideas have been put forward by Böstrom, Schiff and Poirier, and Tipler.

"The new approach seeks to take seriously quantum theory’s hydrodynamic formulation which was developed by Erwin Madelung in the 1920s. Although the proposal is distinct from the many-worlds interpretation, it also involves the postulation of parallel universes. The proposed multiverse picture is not the quantum mechanics of college textbooks, but just because the theory looks so “completely different psychologically” it might aid the development of new physics or new calculational techniques (even if this radical picture of reality ultimately turns out to be incorrect)."

Click here for the rest of it.

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The essential mystery of quantum mechanics is that the theory is built around the dynamics of a thing called the wave function (hence wave mechanics), conventionally labelled ψ. The value of the wave function at each point in space and time is given by the solution to the Schrödinger equation (with appropriate boundary conditions): you imagine the ψ wave flowing around obstacles, through slits, and interfering with itself. The trouble is, the wave function is (apparently) not a 'real entity'. For one thing its values are complex, not real (all observables are real numbers); for another, in its multi-particle mode, the wave function lives in an arbitrarily high-dimension space called configuration space, not our conventional 3 + 1 dimensional space-time.

The wave function, as mentioned, is not itself observable. But if you square the value of the wave function (e.g. in a region of space at a point in time) you get the probability of observing the attribute-value of your interest (e.g. the probability of finding the particle in that region at that time).

The theory is incredibly accurate in giving you the correct probabilities; but it does not tell you what reality is actually doing. About that, quantum mechanics is not just silent - it informs you that your prior beliefs about the world consisting of well-defined particles with defined positions and momenta cannot be true (Bell's theorem).

Gulp!

The doers get on and calculate .. and design the modern technological world; the dreamers wonder whether there is completely non-obvious way to reconstruct the world of appearances ('reality') such that (relativistic) quantum mechanics turns out to be true in that structure of reality.

To date, no-one ever quite succeeded. Maybe Chip Sebens is onto something; maybe the Everett many-worlds formulation of quantum mechanics (still a work-in-progress) can be made to work.

It is my birthday tomorrow (I've reached binary one million) and I expect a present which will shed further light on these perplexing issues.