What Actually Happens at the End of Greg Egan’s Quarantine?

Amazon

---

What Actually Happens at the End of Greg Egan’s Quarantine?

This post continues from yesterday's post, which looked at the interpretation of quantum mechanics assumed in Greg Egan's novel. Warning: it contains spoilers and really only makes sense if you have recently read the novel.

Greg Egan’s 1992 novel Quarantine begins as a cyberpunk detective story and ends ends with the deeper mystery of what it means for anything to happen at all.

In the late twenty-first century, the Solar System has been enclosed within an opaque Bubble, apparently erected by aliens to prevent human observers from collapsing the quantum state of the external universe.

Nick Stavrianos, a private investigator equipped with neural modifications, acquires an 'eigenstate mod' which allows his consciousness to remain distributed across alternative quantum outcomes - to 'smear'. This, it becomes apparent, is connected with the existence of the Bubble.

At the end of the book the capacity to 'smear' spreads through humanity. Reality erupts into miracles, nightmares and grotesque transformations. Then the disturbance apparently ends. Nick finds himself an anonymous refugee detained in a camp, wondering whether smeared humanity recoiled from what lay beyond the Bubble and collapsed itself back into a single world.

That is his first attempt at an explanation, but it is not the novel’s final one. In the closing pages Nick considers a more disturbing possibility: humanity never collapsed at all. The planet remains smeared, “one consciousness per eigenstate, branching out endlessly”. Blood still rains between the skyscrapers in some branches; children still conjure dancing flowers in others; every physically possible Heaven and Hell continues somewhere. The dreary camp in which Nick lies on his bunk is not the sole surviving reality. It is merely one component of an indefinitely branching superposition.

Egan does not quite confirm this in the text because the point is that the local Nick cannot know. A consciousness inside one eigenstate experiences a perfectly definite world. Nothing looks translucent, probabilistic or multiple. From Nick’s perspective there is one bunk, one darkness and one miserable future. The continued existence of innumerable other Nicks would leave no visible trace within his branch. This resembles the familiar Many-Worlds picture, in which every observer experiences one definite branch, although Egan’s mechanism is very far from the standard interpretation.

In this apparently anticlimactic ending, Nick has not returned from quantum chaos to ordinary reality. He has discovered that quantum chaos, viewed from inside one of its components, looks ordinary. Nick's final reflection, “It all adds up to normality,” is not just a consoling or resigned slogan; it states the novel’s final principle: however extravagant the underlying ontology, experience remains local and definite.

What about the Bubble? Is it there or not for Nick - can he see the stars? Surely this is evidence for the actual outcome of the novel - collapse or no collapse?

Just before the final apocalyptic climax, smeared humanity reaches beyond the Bubble, contacts the 'aliens' and the stars appear again: Nick sees them.

Nick initially assumes that the entity which was smeared-humanity then recoiled, or was driven back, and committed a kind of collective suicide by collapsing to one stable reality.

But later he reconsiders: if humanity remains smeared, there need be no single fact about whether the Bubble is removed or remains. Some eigenstates may contain visible stars; others may remain quarantined. The Bubble Makers themselves may be entangled with different versions of humanity. Asking whether “the Bubble has gone” may already impose a classical question upon a non-classical situation.

Nor is camp-Nick the uniquely authentic Nick. Every successor consciousness descends equally from the man who became smeared. The 'alien representative entity' Laura has already pointed out that each branch-Nick is a component of a higher smeared-consciousness which none of them individually comprehends, any more than a single neuron comprehends the entire mind.

The detective who narrated the story has ceased to be the privileged centre of it.

Egan has therefore not hidden one conventional ending behind the ambiguity. The ambiguity is the ending. Humanity most likely survives as a branching totality, while each human consciousness inhabits one apparently singular history. Nick cannot in general recover his dead wife in any way that would undo bereavement; infinity contains reunion, but does not make reunion uniquely real. Nick lies in darkness and cannot decide whether he is contemplating infinity or merely looking at the backs of his eyelids.

---

From Hilbert Space to the Standard Model (Gemini Flash 3.5/GPT5.5)

---

Structure, Symmetry, and the Appearance of Matter

To analyse the foundations of modern physics is to observe how the complex phenomenology of the material world can be systematically re-described in terms of formal mathematical constraints.

Rather than viewing the universe as a collection of independent material objects, contemporary quantum field theory and quantum gravity suggest a more austere ontology. We begin with a quantum state evolving within a highly structured Hilbert space governed by a specific Hamiltonian dynamics.

The transition from this abstract algebraic description to the familiar structures of the Standard Model is not a sequence of deductive inevitabilities, but a process of progressive restriction, where space, forces, and particles emerge as the stable solutions to structural and empirical constraints.

The first step in this reconstruction is the recovery of spacetime geometry. In classical physics, spacetime is the fixed background upon which quantum fields evolve. However, research in quantum gravity—most notably within the context of the holographic principle—suggests that semiclassical spacetime geometry may be reconstructed from the entanglement structure of the quantum state itself.

In certain highly controlled mathematical settings, such as the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, the spatial connectivity and metrical structure of the emergent geometry are directly related to the entanglement entropy of the underlying quantum degrees of freedom.

While extending this framework to a realistic, expanding de Sitter cosmology remains an open problem, these models suggest that aspects of semiclassical geometry, in special settings, can be reconstructed from quantum correlations.

Once a spacetime geometry is established, its kinematic symmetries impose rigid constraints on the types of fields that can exist within it. In flat or locally flat spacetime, these symmetries are described by the Poincaré group, which encompasses translations, rotations, and Lorentz boosts.

According to Wigner’s classification, the irreducible unitary representations of this group characterize the allowable properties of relativistic particle states, which are labeled by specific Casimir invariants: mass-squared and spin (or helicity).

Mass appears as the invariant associated with the four-momentum operator, whose components generate spacetime translations, while spin labels how the state transforms under spatial rotations. The connection between continuous symmetries and conserved quantities belongs to Noether; the classification of relativistic particle states belongs to Wigner. The kinematic furniture of the world is thus constrained by the geometry of the stage.

To account for the dynamic interactions between these fields, the framework incorporates internal gauge symmetries. The baseline assumption is that certain global internal transformations of matter fields are physically redundant or symmetry-preserving.

When this requirement is tightened to demand local gauge invariance—meaning the physics must remain invariant under transformations that vary independently at each point in spacetime—the standard derivative operator must be replaced by a covariant derivative.

This mathematical adjustment requires the introduction of a connection, which manifests physically as a gauge field.

The specific gauge groups of the Standard Model—SU(3) × SU(2) × U(1)—are not derived from first principles; they are empirically selected because they map with extraordinary accuracy to the observed strong, weak, and electromagnetic interactions.

Furthermore, the force-carrying bosons we observe are not all simple expressions of these primordial symmetries. While the gluons of the strong force remain massless, the fields of the electroweak sector undergo a profound reorganization. Through the Higgs mechanism and spontaneous symmetry breaking, the W and Z bosons acquire mass, while the photon emerges as the massless mixture of the original hypercharge and neutral weak gauge bosons, left uncompromised because the residual U(1) electromagnetic symmetry remains unbroken. 

Here, charge is properly understood as the representation label, together with the relevant generator eigenvalue, determining how a specific field transforms under the gauge group; the coupling constant sets the overall strength of that interaction factor.

The final stage in reconciling this field-theoretic description with our classical observations involves the mechanism of decoherence. The universe at the quantum level is defined by continuous, unitary evolution, which naturally generates vast superpositions of field configurations.

The appearance of definite, localised particles is an effect of environment-induced superselection, or einselection. When a microscopic system interacts with the wider environment, the trillions of unnoticeable degrees of freedom rapidly suppress the quantum interference between alternative states in the system's reduced density matrix.

Because many environmental interactions effectively monitor position, spatially localized states are often selected as robust pointer states. Within any interpretation of quantum mechanics that accommodates this process, the result is that the environment acts as a continuous filter, ensuring that the macroscopic world behaves, for all practical purposes, classically.

The journey from the abstract formalism of Hilbert space to the empirical reality of the Standard Model is therefore a demonstration of how formal constraints limit physical possibilities.

We assume a quantum state and dynamics; in certain models, their entanglement structure allows aspects of semiclassical spacetime to be reconstructed.

That geometry restricts allowable kinematics to specific combinations of mass and spin.

We apply local gauge constraints under empirically selected internal groups to define the forces and charges of the world, and we observe how environmental interaction restricts quantum superpositions into stable, classical outcomes.

The arbitrary parameters of the Standard Model remain unexplained, but the structural framework demonstrates how a world of apparent substance can be systematically organized by the rigorous application of mathematical symmetry.

---

Note: In response to my prompts, Gemini drafted the first essay. GPT5.5 then fairly savagely critiqued it and I added a few low-level thoughts. Gemini produced a second version which elicited milder criticisms from GPT5.5. The final draft from Gemini is as you see it here.

---

Block Time, Many Worlds, and the Persistence of Ordinariness

---

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.

---

Hyperion and the Decoherence of Worlds - (ChatGPT)

Hyperion and the Decoherence of Worlds

In a previous post, we explored how the Saturnian moon Hyperion—thanks to its chaotic rotation—provides a vivid case study for how classical unpredictability collides with quantum indeterminacy. But what stops us from encountering Hyperion in a state where it's simultaneously in multiple orientations? Why does it always appear to us as a moon tumbling this way or that, but never in some bewildering quantum blur?

The answer lies in decoherence. And in the context of the Many Worlds Interpretation (MWI), decoherence is not a marginal side effect—it’s the mechanism that gives structure and observational content to the branching wavefunction. Without decoherence, the wavefunction evolves but remains unstructured. With decoherence, the wavefunction evolves into effectively distinct classical histories.

1. Superposition: What It Is and Isn’t

A quantum system is said to be in a superposition when its state vector is a linear combination of eigenstates of some observable. For instance:

|ψ⟩ = α |A⟩ + β |B⟩

This is a statement about the system’s state in configuration space, not a claim about what one sees in any individual measurement. Upon observation, the system yields a single outcome—|A⟩ or |B⟩—with probabilities determined by the squared moduli of the coefficients. There is no such thing as “observing a superposition” in a single event.

Superposition is not a visual phenomenon, nor does it correspond to a macroscopic body appearing in multiple classical states at once. Rather, it is a mathematical descriptor of how the system's amplitudes are distributed across its configuration space.

2. Interference and Its Prerequisites

Interference is a physical phenomenon, not a formal one. It arises when different components of a quantum superposition recombine in such a way that their relative phases affect the probabilities of measurement outcomes. Interference can only be detected through statistical regularities in ensembles of measurements—such as the classic fringe patterns in a double-slit experiment with electrons.

A single electron does not interfere. Only an ensemble of identically prepared electrons, evolving through identical dynamics, can display interference effects.

For a system like Hyperion, there is no physical possibility of preparing an ensemble of identically initialised moons in the same quantum state. We cannot rerun the universe multiple times with Hyperion in the same chaotic quantum configuration. Consequently, even if Hyperion's quantum state becomes a superposition of orientations, there is no operational method by which interference effects between those orientations could be revealed.

3. Decoherence and the Emergence of Classicality

Hyperion is constantly interacting with its environment—sunlight, cosmic radiation, thermal photons, gravitational tides. These interactions cause decoherence: a process whereby phase coherence between components of the system’s wavefunction (expressed in a specific basis) is effectively destroyed by entanglement with environmental degrees of freedom.

(Here's a tutorial on the concept of density matrix, before you read further.)

This doesn’t collapse the wavefunction. Instead, it causes the system’s reduced density matrix to become diagonal in a preferred basis—typically one aligned with classical observables such as position or orientation. The states in this basis, called pointer states, are those that remain stable under environmental interactions. Because most interactions are local, the environment couples most strongly to position, making position eigenstates the natural classical basis.

In configuration space terms: decoherence suppresses the off-diagonal elements of the density matrix in the basis of classical configurations. This renders the quantum state a statistical mixture of distinguishable macroscopic states—each evolving independently. Hyperion’s rotational state, initially a quantum object, becomes a set of non-interfering classical alternatives, each entangled with a different environment.

4. Many Worlds Needs Decoherence

In the Many Worlds Interpretation, the universal wavefunction never collapses. All components persist. But without decoherence, there is no way to carve that wavefunction into meaningful branches—no structure of “worlds” that match the experienced classical order.

Decoherence solves this by defining the dynamical conditions under which different components of the wavefunction become mutually inaccessible. It ensures that each branch contains a consistent classical history, unpolluted by phase interference from others. In short: decoherence provides the effective disconnection that makes classical-looking worlds emerge from a fundamentally quantum substrate.

5. What We Don’t See

So when we say “we don’t see macroscopic superpositions,” we do not mean that there are such things which evade our detection, nor that a superposition is something you might glimpse like a ghost. What we mean—more precisely—is this:

We never observe interference effects between macroscopically distinct configurations, because we cannot prepare ensembles of systems like Hyperion in the same quantum state, and because environmental decoherence renders such interference physically inaccessible, even in principle.

The wavefunction may formally contain many such components—different orientations of Hyperion, for instance—but those components no longer interact. Their relative phases are scrambled into environmental degrees of freedom, never to return. In effect, the branches of the wavefunction become autonomous classical narratives.

6. Final Reflection

Hyperion is not both “this way” and “that way” until observed. Its quantum state evolves as a linear combination of possibilities, but decoherence ensures that these possibilities become mutually opaque long before any observation is made. There is no mystery in why we observe it in a single orientation. The mystery lies in how classicality emerges at all from the linear formalism of quantum mechanics—and decoherence is the key that makes that transition intelligible.

So the moon tumbles on, a chaotic fragment of ice and rock, participating silently in the cosmic branching of possibility. And yet, each time we train a telescope on it, we find a world that has—reliably and quietly—made up its mind.

The Chaotic Delocalisation of Hyperion - (ChatGPT)

The Quantum Weirdness of Hyperion

The Saturnian moon Hyperion is often cited as a natural example of quantum chaos, and it has played an interesting role in debates about the quantum-classical boundary—especially regarding decoherence and the role of the observer.

1. Classical Chaos in Hyperion's Rotation

Hyperion is a small, potato-shaped moon of Saturn. It rotates chaotically: that is, its axis of rotation wobbles so much that its orientation in space becomes unpredictable, because:

• It is non-spherical, so torques from Saturn’s gravity are complex and time-dependent.
• It is in an eccentric orbit, and experiences perturbations from other moons (notably Titan, with which it is in a 3:4 orbital resonance).

These features lead to chaotic tumbling: Hyperion’s rotational phase changes in a way that is exponentially sensitive to initial conditions—the hallmark of classical chaos.

This is a classic example of a "three-body problem" in celestial mechanics, where the interactions between Saturn, Titan, and Hyperion make it impossible to predict Hyperion's orientation more than a few months in advance. The system's "Lyapunov time" (the timescale over which small uncertainties in initial conditions become large, unpredictable differences) for Hyperion's rotation is about 30 days.

So far, all of this is standard Newtonian mechanics.

2. Quantum Analogue: Quantum Chaos

In quantum mechanics, the classical concept of chaos doesn’t apply straightforwardly. Schrödinger’s equation is linear and unitary; it doesn’t permit the divergence of trajectories in the classical sense. Nevertheless, we can still ask: what happens to the quantum state—the wavefunction—of a classically chaotic object like Hyperion?

In 1995, physicists Wojciech Zurek and Don Paz explored this question by modelling Hyperion as an isolated quantum system—neglecting environmental interactions for the sake of analysis.

3. The Argument: Delocalisation of the Wavefunction

In quantum mechanics, a system is described by a wavefunction that evolves deterministically over time. For macroscopic bodies like Hyperion, this wavefunction is typically sharply peaked in configuration space (that is, over classical variables like orientation), which allows us to approximate the system as behaving classically.

But for a chaotic system, Zurek showed that the wavefunction becomes delocalised in configuration space—though the underlying spreading is best understood via the system’s evolution in classical phase space.

Specifically:

• The wavefunction describing Hyperion’s rotational degree of freedom spreads exponentially over time.
• Within roughly 20 years (some estimates suggest even less), the quantum state becomes widely spread over many possible orientations.
• However, this spreading doesn’t lead to any observable interference, because the orientations become effectively non-overlapping in configuration space.

This is counterintuitive: the quantum state of Hyperion does not converge toward a classical trajectory but becomes a superposed, delocalised object. Yet we always observe Hyperion in a definite orientation.

4. The Role of Decoherence

The missing element is decoherence.

In reality, Hyperion is not isolated. It constantly interacts with its environment—sunlight, cosmic rays, thermal radiation, and so on. These interactions entangle the moon’s quantum state with vast numbers of environmental degrees of freedom.

Before continuing, you may wish to review this tutorial on the density matrix.

Decoherence causes the off-diagonal terms in Hyperion’s reduced density matrix (in the orientation basis) to rapidly vanish. In effect, the quantum coherence between different orientations becomes inaccessible—even in principle—because the environment has recorded “which orientation is which.”

This does not collapse the wavefunction or select a unique outcome. The total system—Hyperion plus environment—remains in a superposition of different orientation branches, each entangled with a corresponding environmental state. But from the perspective of any internal observer, each branch evolves as if the others do not exist.

So decoherence explains why Hyperion behaves as if it were in a definite orientation, even though its quantum state remains a superposition. It renders the alternatives mutually non-interfering.

5. Philosophical Bite: Many Worlds or Collapse?

What we make of this depends on how we interpret quantum mechanics:

• In the Many Worlds Interpretation (MWI), each decohered orientation corresponds to a separate branch of the universal wavefunction. All still exist. Decoherence tells us where the branches are.
• In collapse models, decoherence helps explain why collapse appears to occur in a specific basis—typically position or orientation—but collapse itself must still be postulated separately.

Either way, decoherence does not explain why one result occurs, but it does explain why we see stable classical behaviour, and why interference between macroscopically distinct outcomes never appears.

6. So, Is Hyperion in a Superposition?

Yes—prior to any observation, Hyperion remains in a quantum superposition of rotational states. Decoherence does not change this. It only ensures that these components are entangled with distinct environmental records and that their interference effects (if any) are physically unobservable.

This is not a superposition that could be revealed by measurement—because there’s no way to prepare an ensemble of Hyperions in the same quantum state, nor to recombine the branches. The superposition is real, but inaccessible.

7. Final Thought: Quantum and Classical Chaos

Hyperion’s case illustrates that:

• Classical chaos amplifies quantum uncertainty by exponentially spreading the wavefunction in configuration space.
• Decoherence suppresses quantum interference, producing the appearance of classical spacetime behaviour.
• The interplay of these two effects is central to understanding how the classical world emerges from quantum mechanics.

It remains one of the clearest examples of where quantum theory touches the macroscopic world—not through spooky paradoxes, but through the subtle mathematics of entanglement, entropy, and environmental indifference. A tumbling moon becomes a case study in the fragility of classicality itself.

In the next post we dig deeper into the role of decoherence in all of this.

What is an Electron Really?

From ChatGPT

This summary, the result of a little prompt-dialogue between ChatGPT and myself, seems as good an account as any other, and is consistent with Matt Strassler's book, "Waves in an Impossible Sea" .

---

In the realm of classical physics, an electron is often conceived as a tiny, negatively charged particle orbiting the nucleus of an atom. However, modern physics, particularly Quantum Field Theory (QFT), offers a radically different perspective.

In QFT, an electron is not a point-like particle but rather a quantum excitation of an underlying entity known as the electron field. This field pervades all of space, and what we perceive as an electron is simply a localized disturbance or excitation within this field. This excitation carries certain properties—such as charge, spin, and mass—that we associate with the electron.

The electron's position is not definite until it is measured. Instead, the electron exists in a superposition of possible states, each corresponding to a different location. This superposition means that the electron doesn’t have a single, well-defined position but rather a range of probabilities (quantum amplitudes really) of being found in various locations.

When we incorporate the Many-Worlds Interpretation (MWI) of quantum mechanics, this notion takes on an even more intriguing aspect. According to the MWI, each possible position of the electron corresponds to a different “world” or branch of reality. 

In one world, the electron might be detected at a particular point, while in another world, it appears somewhere else. These different worlds coexist in a vast multiverse which constitutes reality, and the electron’s delocalization can be understood as it existing in multiple worlds simultaneously, with each world realizing a different outcome of its position. Note that in each specific world, the electron is still an 'excitation of the electron field', a 'wavicle' according to Strassler.

This is a difficult ontology to imagine or believe, but it's the best we can do today.

"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.

“Metaphorical Worlds Interpretation” (Chad Orzel)

Amazon link

I bought this a couple of weeks ago (Kindle) but it still sits in my stack. Soon!

Peter Woit has this post today, however, where he links to a piece by Chad Orzel.

Orzel thinks there is a better way to think about the "Many Worlds Interpretation":

"The problematic aspect here is that the wavefunction of the universe has everything in complicated superposition states, but when we select out a tiny piece of it as our system of interest, we often see that system only in single states, not a superposition of multiple states. The question that’s too often un-asked, though is: What measurement would you do to demonstrate that your system is really in a superposition?

The answer to this doesn’t need to be a procedure specific enough to actually do the experiment; a general outline would be sufficient. And, in fact, we have a couple of centuries of experience at doing exactly this: When we want to show that something has been in two states at the same time, we do an interference experiment. We put our system of interest in a superposition of two states, arrange for those two states to evolve at slightly different rates for some time, and then bring them back together and measure the final state.

If a superposition exists, there will be some oscillation in the probability of a given final state that depends on the differential evolution in the middle. This takes lots of forms– if the two states of the superposition correspond to passing through spatially separated slits, it’ll show up as an interference fringe pattern in space; if they’re two states of a cesium atom in an atomic clock, it’ll show up as a varying probability of ending up in one of those states as you adjust the frequency of your microwave oscillator.

In every case, though, you’re measuring a probability. And not even a Bayesian can accurately measure a probability from a single experiment. To get a good measurement of a probability of some outcome– let alone the variation in probability that is the signature of a superposition state– you need a large number of repeated measurements. And those measurements have to be made under the same conditions every time.

That’s the key feature that lets you carve out some parts of the giant wavefunction of the universe and choose to treat them as systems in definite states, while others need to be treated as full quantum superpositions. The vast majority of the universe that we’re bracketing off as “the environment” affects the measurement conditions, which changes the probabilities you’re measuring.

If the interaction with the environment is small, though, you can ensure that the conditions are close to identical for enough trials to unambiguously see the changing probabilities that show a superposition exists. That subpart of the universal wavefunction needs to be dealt with as a fully quantum system.

If the interaction with the environment is strong and poorly controlled, though, the conditions of your measurement change enough from one repetition to the next that you’re not really doing the same measurement multiple times. If you could know the full state of the environment for a given trial, you would predict one probability, but knowing the full state of the environment for the next trial would lead you to predict a different probability.

In the absence of that knowledge, adding together repeated results just gets you junk– you won’t see a clear dependence on the different evolution of the different states in the superposition, because it’s swamped by the unknown effect of the environment. If you can’t see the interference effect, that system “looks classical,” and you can treat it as having a definite state.

That process of interaction with the changing state of an unknown environment gets the name “decoherence,” and it’s what enables the bookkeeping trick that lets us split off pieces of the wavefunction and consider them in isolation. If the piece you’re interested in is big enough and interacts with the environment strongly enough, there’s no hope of doing the interference measurement that would show it’s in a superposition state. If you can’t do a measurement that would show the existence of the other piece(s) of the superposition, you can safely treat it as being in a single definite state.

It should be emphasized, though, that this is just bookkeeping, not a real separation between “copies of the universe,” or even copies of the system of interest. There’s only one universe, in an indescribably complex superposition, and we’re choosing to carve out a tiny piece of it, and describe it in a simplified way.

It’s not even true, strictly speaking, that the results of a given experiment for a particular object are unaffected by the presence of the other parts of the superposition for that specific object. If you could do the full probability calculation for the whole wavefunction, including all of “the environment,” the probability you would predict for that experiment would include a contribution from all the various states that are superposed. In the absence of that complete knowledge, though, you can get away with ignoring them, because you’ll never be able to repeat the measurements in the way you would need to see the influence.
...
Rather than “Many-Worlds Interpretation,” I’d go with “Metaphorical Worlds Interpretation,” to reflect the fact that all the different ways of cutting up the wavefunction into sub-parts are fundamentally a matter of convenience, a choice to talk about pieces of the wavefunction as if they were separate, because the whole is too vast to comprehend."

Peter Woit likes this story. What do you think?

---

What is decoherence? Read this.

The Copenhagen ontology

Scott Aaronson has an interesting post on his personal interpretation of quantum mechanics (he's probably a 'none-of-the-above' but with a revealed preference for the MWI).

He is, however, particularly scathing about the so-called 'Copenhagen Interpretation'.

"As for Copenhagen, I’ve described it as “shut-up and calculate except without ever shutting up about it”!  I regard Bohr’s writings on the subject as barely comprehensible, and Copenhagen as less of an interpretation than a self-conscious anti-interpretation: a studied refusal to offer any account of the actual constituents of the world, and—most of all—an insistence that if you insist on such an account, then that just proves that you cling naïvely to a classical worldview, and haven’t grasped the enormity of the quantum revolution."

This seems spot on.

---

'You may not be interested in ontology, but ontology is interested in you.'

What happens when a convinced adherent to the Copenhagen Interpretation is asked straight out:

"... what constitutes the "act of measurement" in a world without sentient beings? In such a world (even in a world with sentient beings) there are just physical systems with atoms and molecules all under the rule of Schrödinger's equation. So when does "collapse" occur?

When can it be decided that a measurement has been made if there are no sentient beings?

If everything is made up of particles, and the particles are under the governance of Schrödinger's equation and unitary evolution, when do "measurement" and "collapse" occur? In a world without sentient beings, what would "when the new data arrives" refer to?"

Luboš Motl answers commentator Ricky's question above (in comment 16 here):

""The conceptually right [way] to describe a world without sentient beings is that an unspecified and unknown initial wave function evolves unitarily according to Schrödinger's equation and never collapses because it's only measurements that may collapse and there are none in your theory. The complete "diffusion" of the wave function (into the linear superposition of dead and alive cats and all objects, small and big, in the most general superpositions of all conceivable states) may be said to be a problem - but another problem is that the initial state is totally unknown, too.

"It makes no sense to say that the initial wave function is a particular thing because one may only say that the wave function is a particular thing [if] something is [a] measurement - if a sentient being becomes aware of the result of some measurement. This is not happening in a universe without sentient beings. So there's no specific science to discuss in a universe without sentient beings at all. The laws may still be the same as they are in our world but they won't be applied in any particular situation because there are no particular situations or particular special wave functions in a world where no one ever measures anything.

"Einstein asked whether there is any Moon over there if no one looks. In practice, classical physics is a good enough approximation, so one may assume that the Moon is pretty much there even before observers look etc. But conceptually, if you care about similar objects for which the quantum effects are strong, the right answer is that the Moon just isn't at any particular location and has no other particular properties if no one looks. The wave function isn't a real object of any type. Its amplitudes can't be measured in a single repetition of the situation. It is only a template storing information allowing to predict probabilities of things that actually can be measured - the observables."

The arch-exponent of Copenhagenism appears to believe that the universe is really some unitary evolution in Hilbert space, presumably with space-time somehow emergent. Because ontology.

MWI, plus entanglement leads to GR, maybe?

In this video Sean Carroll lectures at Kings College on the 'Many-Worlds Interpretation' of quantum theory and his attempts, with collaborators, to conceptualise general relativistic spacetime as an emergent phenomenon due to entanglement.

Apparently the degree of entanglement between distinct vacuum states falls off as the distance between them. But perhaps this can be inverted, so that the concept of distance could be seen as an emergent proxy for the degree of entanglement.

The 50 minute lecture is 'aimed at undergraduates who haven't necessarily yet taken a quantum mechanics course'. If you are such, Carroll's talk will be as compelling as a presentation on Summa Theologica from Thomas Aquinas.

On the other hand, a passable familiarity with Hilbert space, quantum superposition and the Schrödinger equation plus a hand-wavy feel for QFT and Einstein's field equations will allow you to properly appreciate Carroll's approach to physics (and would make you a physics graduate).

In a nutshell, it's believe in the maths. Once you appreciate the ubiquity of superposition (ie, it's everywhere) you're kind of committed to the reality - in some sense - of Hilbert space. The observed phenomena simply can't be explained by theories which restrict themselves to our classical-looking 4D spacetime.

Carroll's talk is not technical in argumentation, he mentions rather than uses the theoretical apparatus of modern physics. That does put the burden of getting his drift wholly on the theoretical preparation of the listener of course.

In the final part of his lecture, he describes the research programme which seeks to obtain geometry from entanglement in quantum field theories via entropy and then, through considerations of energy, to reconstruct the GR field equations as the classical limit.

He seems encouraged, though this is work-in-progress.

The quantum-theoretic block universe

Eternalism is not hard to justify.

Yesterday I contemplated my situation and concluded: "This is real, this is now."

Today, when I recollect that scene, I'm inclined to think it was indeed real, and shows the reality of the past (which has not flickered out of existence but is .. elsewhere).

Yesterday, I also thought, "Tomorrow, I will be writing a post."

Today, here I am doing it. For yesterday's me, that shows the reality of the future.

As Frank Sinatra observed, "You can't have one without the other."

---

For greater conviction, we can appeal to special relativity. As I wrote in a piece for sciencefiction.com,

"Brian Greene in ‘The Fabric of the Cosmos’ (page 134) considers an alien in a galaxy ten billion light years away, at the edge of the visible universe. Simply by ambulating towards or away from us at 10 mph, the alien’s view of what is happening ‘right now’ on earth swings from 149 years in the past to 149 years in the future."

Still, the block universe is classical and therefore inaccurate. It's necessary to move to quantum theory where, as usual, one needs to take the red pill.

Theoretical physicist Jeremy Bernstein on 'A Quantum Past'.

"In FAPP (For All Practical Purposes) language we have a quantum mechanical system described by a wave function ψ(t), I am  only interested in the time variable.

The wave function obeys a Schrödinger equation with a Hamiltonian H. The formal solution to this equation is ψ(t) = exp(iHt)ψ(0). Throughout I am setting ћ = 1. Thus to recover Ψ(0) from ψ(t) all we have to do is to multiply by exp(-iHt).

Haven’t we then recovered the past? What is all the fuss about? The problem is that there is more to life than the wave function. There are the “observables” which represent what we really want to know about the system. These observables are described by Hermitian operators A. B. C and so on. We can expand ψ in a sum over the orthonormal eigenfunctions of any of these operators. The coefficients in the expansion are related to the probabilities that in a measurement the system will be found to have one of these eigenvalues. This is “Born’s rule” and in FAPP it must be assumed.

To find which of these eigenvalues the system actually has, we must perform a measurement. Stripped to its essence the apparatus that produces this measurement projects out from the sum of eigenfunctions one of them.

After the measurement the rest of the terms in the sum disappear. Using the term of art, the wave function “collapses”. It is at this point that we lose our capacity to reconstruct the past.

Projection operators are singular. They do not have inverses. All the king’s horses and all the king’s men cannot put the wave function back together again.

It was von Neumann in the early 1930’s who first noted that in FAPP mechanics there were two kinds of processes. There were processes that could be described by a Schrödinger equation and there were measurements which could not. He did not, as far as I know, comment on what this implied for retrodiction.

A case in point is an electron described by a spherically symmetric Schrödinger wave. If this electron strikes a detector is does so at a place - a spot. After this happens all trace of the spherically symmetric wave function vanishes.

I have certainly not made a careful search of the literature but among the founding fathers of FAPP I can come up with only two references that deal with the matter of the quantum past.

One is Heisenberg and the other is a paper by Einstein, Richard Tolman, and Boris Podolsky, “Knowledge of Past and Future in Quantum Mechanics” which they wrote in 1931 when Einstein was spending time at CalTech."

Bernstein talks about these two references, and then discusses where he thinks the problem resides, and what is to be done.

"It seems to me that any interpretation of the quantum theory that addresses this [the problem of wavefunction collapse] must have the feature that measurements are simply just another interaction like the rest.

Von Neumann’s notion that there were two classes of interactions one whose time evolution could be described by a Schrödinger equation and one of which couldn’t, has to be abandoned.

I will discuss two proposals for doing this each of which has its adherents and its detractors. On the one hand I am going to discuss what I will call “Bohmian mechanics” a term which David Bohm, who invented this approach , apparently did not like. As far as he was concerned, he was just doing quantum mechanics but in a different way. However nearly everyone else calls it Bohmian mechanics - so will I.

On the other hand, I am going to discuss the “decoherent history” interpretation which Murray Gell-Mann and Jim Hartle have done the most on. Sometimes this is called the “many worlds” interpretation, but not by them. I think that the term “many worlds” is misleading. As far as we know there is one world, the one we live in."

I'm not a fan of “Bohmian mechanics” and insofar as any quantum ontology works for me, it has to be "Many Worlds" (Sean Carroll explains why).

So I'll skip over Bernstein's description of Bohm's view of the quantum past and quote his take on “decoherent histories”.

"In the "Many Histories Interpretation" what indeed is history?

At first sight this might seem to be obvious. All we have to do is to run the chain backwards.

Yes this gives one history but there are others, possibly very many others. The reason is that if all we know is the present state vector there are many paths by which we could have arrived there depending on which initial state vector we started from. We have no way of knowing this from the data we have at hand.

Let us take an example discussed by Hartle - the Schrödinger cat (I can’t resist noting that when I spent an afternoon with Schrödinger in his apartment in Vienna there was no cat). In any event this unfortunate feline is put in a box that contains a capsule of poison gas and a sample of uranium. The capsule is triggered so that if the uranium has an alpha decay, the alpha sets off the trigger and the unfortunate feline expires.

After a time interval we open the box and happily the cat is alive. It could, according to the many history approach have arrived at this state in two ways. The initial state might have been a cat alive state or it might have been a coherent sum of a cat alive and a cat dead state. From the presence of the living cat we cannot decide.

The vision of the past given by the decoherent history interpretation and the Bohmian seems radically different. In Bohmian mechanics we could in principle follow all the cat molecules backwards in time and arrive at one and only one past.

I don’t know how you feel, but the ambiguity of the past makes me queasy. It might be entertaining to imagine that in an alternate past my grandmother who was born in a Polish stetl could have been Eleanor Roosevelt.

I readily accept that these pasts to not communicate but there seem to be too many of them from the point of view of economy. A trip to a barber wielding Occam’s razor seems warranted.

In any case when it comes to quantum pasts, as Duke Ellington taught us, “Things ain’t what they used to be.”

Perhaps Bernstein wrote this short paper just for that final joke at the end?

To summarise, if you take quantum theory seriously and you take eternalism (the block universe) seriously, then it seems that the past is as indeterminate as the future.

---

How does this relate to the 'low entropy in the past' idea used to explain the 'arrow of time'?

Since quantum theory is consistent with the second law of thermodynamics, a picture emerges of backwards branching towards (superpositions of) Big Bang variants.

My ex-colleague Roy said as much in this comment, on an earlier post devoted to the MWI. See here for more.

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."

'The Many Worlds of Hugh Everett III' - Peter Byrne

Amazon Link

I finally got round to reading Peter Byrne's biography of Hugh Everett III.

It's a good book, weaving between three themes: Everett's thesis on the 'Many Worlds Interpretation'; his career as a cold-war nuclear strategist for the Pentagon; and his curiously unconventional personal life (swinger, incipient alcoholic, heavy smoker, womaniser, cynic, libertarian, genius).

The 'Many-Worlds' work was his proudest achievement, although he never published a word on quantum mechanics after his thesis paper. The physics establishment ignored the concept for two decades, while individuals around Bohr were poisonously hostile.

The historical treatment works well, showing how the controversies reflected ongoing preoccupations and progress in the community. Cosmology, quantum gravity and decoherence were later catalysts for renewed interest, as was quantum computing (David Deutsch a key visionary here).

Everett's ideas were continually misunderstood, often wilfully. His concept of 'splitting universes' whenever a 'measurement' is made is actually a topological statement that the universe (multiverse) is a network (not a tree, which would fail time-reversibility) consisting of a non-denumerable infinity of evolving universes, each like our presently observed one, linked by 'measuring events'.

Three major issues continue to puzzle researchers. Everett believed he had derived the Born probability rule from his topology: many physicists disagree. The dispute seems highly technical.

Then there is the problem of the 'preferred basis', which reflects that the concept of superposition is itself basis-dependent, so that the act of splitting seems both arbitrary and non-consistent from point to point on the multiverse network (Everett thought this a non-issue as the act of measurement itself presupposes a basis).

Finally, and a point not brought out by the book, the state vector evolves (via the Schrödinger equation) in Hilbert space, not our familiar four-dimensional spacetime. Yet the Everettian multiverse seems to be a network of spacetime universes. How do we get from the ontology of Hilbert space to that of ordinary spacetime? This seems to be an active research question.

Peter Byrne's book has the usual problems of pop-sci. It's conceptually too remote for a purely lay reader while too imprecise for someone who knows some quantum mechanics (the failure to differentiate spacetime and configuration space, for example).

There are the odd errors of authorial comprehension - Byrne does not appear to understand computer science and his explanation of the Halting Problem is just wrong.

Finally, it's hard to write about the people doing the math and computer simulations for thermonuclear warfare, optimal counterforce strategies and assured destruction without taking some moral stance - but it's just parochial judging those guys, including Everett, from the 'superior' standpoint of an impeccable pacifistic-liberal. Biting the hand that fed you, methinks.

If you want to get a handle on the strange birth and tortuous development of the MWI, you couldn't do better than read this book. And as a bonus you get a voyeuristic tour of scarily-dysfunctional Everettian family life as well.

---

Sean Carroll has a good defence of the MWI.

---

If you have a graduate level of understanding of quantum mechanics, here is your next step.

Amazon link

The definitive introduction to Everettian quantum mechanics.

---

Update: In the comments you will see a discussion as to whether it is really true that worlds can merge as well as split. Splitting occurs via the thermodynamically-irreversible process of decoherence and thus is overwhelmingly the likely thing to happen. Yet under very special circumstances, distinct worlds can merge. This is highlighted in my follow-up post.

Reality and the MWI

From "Many Worlds? An Introduction" by Simon Saunders.

“As Popper once said, physics has always been in crisis, but there was a special kind of crisis that set in with quantum mechanics. For despite all its obvious empirical success and fecundity, the theory was based on rules or prescriptions that seemed inherently contradictory. There never was any real agreement on these matters among the founding fathers of the theory.
...
“In what sense are the rules of quantum mechanics contradictory? They break down into two parts. One is the unitary formalism, notably the Schrödinger equation, governing the evolution of the quantum state. It is deterministic and encodes spacetime and dynamical symmetries.

“Whether for a particle system or a system of fields, the Schrödinger equation is linear: the sum of two solutions to the equation is also a solution (the superposition principle). This gives the solution space of the Schrödinger equation the structure of a vector space (Hilbert space).

“However, there are also rules for another kind of dynamical evolution for the state, which is - well, none of the above. These rules govern the collapse of the wavefunction. They are indeterministic and non-linear, respecting none of the spacetime or dynamical symmetries. And unlike the unitary evolution, there is no obvious route to investigating the collapse process empirically.

“Understanding state collapse, and its relationship to the unitary formalism, is the measurement problem of quantum mechanics. There are other conceptual questions in physics, but few if any of them are genuinely paradoxical. None, for their depth, breadth, and longevity, can hold a candle to the measurement problem.

“Why not say that the collapse is simply irreducible, ‘the quantum jump’, something primitive, inevitable in a theory which is fundamentally a theory of chance? Because it isn’t only the collapse process itself that is under-specified: the time of the collapse, within relatively wide limits, is undefined, and the criteria for the kind of collapse, linking the set of possible outcomes of the experiment to the wavefunction, are strange.

“They either refer to another theory entirely - classical mechanics - or worse, they refer to our ‘intentions’, to the ‘purpose’ of the experiment.

“They are the measurement postulates - (‘probability postulates’ would be better, as this is the only place where probabilities enter into quantum mechanics). One is the Born rule, assigning probabilities (as determined by the quantum state) to macroscopic outcomes; the other is the projection postulate, assigning a new microscopic state to the system measured, depending on the macroscopic outcome.

“True, the latter is only needed when the measurement apparatus is functioning as a state-preparation device, but there is no doubt that something happens to the microscopic system on triggering a macroscopic outcome.

“Whether or not the projection postulate is needed in a particular experiment, the Born rule is essential. It provides the link between the possible macroscopic outcomes and the antecedent state of the microscopic system. As such it is usually specified by giving a choice of vector basis - a set of orthogonal unit vectors in the state space - whereupon the state is written as a superposition of these. The modulus square of the amplitude of each term in the superposition, thus defined, is the probability of the associated macroscopic outcome.

“But what dictates the choice of basis? What determines the time at which this outcome happens? How does the measurement apparatus interact with the microscopic system to produce these effects? From the point of view of the realist the answer seems obvious. The apparatus itself should be modelled in quantum mechanics, then its interaction with the microscopic system can be studied dynamically. But if this description is entirely quantum mechanical, if the dynamics is unitary, it is deterministic. Probabilities only enter the conventional theory explicitly with the measurement postulates. The straightforwardly physicalistic strategy seems bound to fail. How are realists to make sense of this?

“The various solutions that have been proposed down the years run into scores, but they fall into two broadly recognizable classes. One concludes that the wavefunction describes not the microscopic system itself, but our knowledge of it, or the information we have available of it (perhaps ‘ideal’ or ‘maximal’ knowledge or information). No wonder modelling the apparatus in the wavefunction is no solution: that only shifts the problem further back, ultimately to ‘the observer’ and to questions about the mind, or consciousness, or information - all ultimately philosophical questions.

“Anti-realists welcome this conclusion; according to them, we neglect our special status as the knowing subject at our peril. But from a realist point of view this just leaves open the question of what the goings-on at the microscopic level, thus revealed, actually are. By all means constrain the spatiotemporal description (by the uncertainty relations or information-theoretic analogues), but still some spatiotemporal description must be found, down to the length-scales of cells and complex molecules at least, even if not all the way to atomic processes.

“That leads to the demand for equations for variables that do not involve the wavefunction, or, if none is to be had in quantum mechanics, to something entirely new, glimpsed hitherto only with regard to its statistical behaviour. This was essentially Einstein’s settled view on the matter.

“The only other serious alternative (to realists) is quantum state realism, the view that the quantum state is physically real, changing in time according to the unitary equations and, somehow, also in accordance with the measurement postulates.

“How so? Here differences in views set in. Some advocate that the Schrödinger equation itself must be changed (so as to give, in the right circumstances, collapse as a fundamental process). They are for a collapse theory.

“Others argue that the Schrödinger equation can be left alone if only it is supplemented by additional equations, governing ‘hidden’ variables. These, despite their name, constitute the real ontology, the stuff of tables and chairs and so forth, but their behaviour is governed by the wavefunction. This is the pilot-wave theory.

“Collapse in a theory like this is only ‘effective’, as reflecting the sudden irrelevance (in the right circumstances) of some part of the wavefunction in its influence on these variables. And once irrelevant in this way, always irrelevant: such parts of the wavefunction can simply be discarded. This explains the appearance of collapse.

“But for others again, no such additional variables are needed. The collapse is indeed only ‘effective’, but that reflects, not a change in the influence of one part of the quantum state on some hidden or ‘real’ ontology, but rather the change in dynamical influence of one part of the wavefunction over another - the decoherence of one part from the other.

“The result is a branching structure to the wavefunction, and again, collapse only in a phenomenological, effective sense. But then, if our world is just one of these branches, all these branches must be worlds. Thus the many worlds theory - worlds not spatially, but dynamically separated.”

Saunders' introductory chapter from the book, "Many Worlds?" underlines the central puzzle of quantum mechanics. What would reality have to be like to make the theory of quantum mechanics so incredibly accurate?

Realists driven to the 'Many Worlds Interpretation' can still make no sense of it (Sean Carroll is a consistent defender, though). As Saunders observes on page 20,

“How does talk of macroscopic objects so much as get off the ground? What is the deep-down ontology in the Everett interpretation? It can’t just be wavefunction [...]; it is simply unintelligible to hold that a function on a high-dimensional space represents something physically real, unless and until we are told what it is a function of  - of what inhabits that space, what the elements of the function’s domain are.

“If they are particle configurations, then there had better be particle configurations, in which case not only the wavefunction is real.”

And so I have bought "The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family" by Peter Byrne.

Is quantum suicide allowed?

So here is my dilemma. I'm still reading "The Hollow Man" by Dan Simmons to Clare. The story starts with hero Jeremy losing his beloved wife Gail to the agonies of cancer. The hero and his wife are telepathic. (We are prepared thus far to suspend disbelief).

In one thread of the story, Jeremy falls apart in grief and descends into a hobo-existence (this is set in America) - there is a purposeful analogy to Dante. In the other thread, we get flashbacks to Jeremy's research as a mathematician, full of gobbledegook about personality/consciousness as hologram, the Schrödinger equation and populist quantum theory. It's the data dump from hell, riddled with spurious guff. This I don't read to Clare.

In the end, you sort of know that Jeremy and Gail are going to get reunited, but how can this be? The answer is a variant of quantum suicide. My question: do I dare read this to Clare; does it pass the suspension of disbelief test?

I can get away with the idea of a quantum superposition. Most people know that, for example, a particle's position can't be definitely localised - we say its wave function is spread out. This is equivalent to saying that it's in a superposition of location states. It's basic quantum mechanics, experimentally observed and not the least bit speculative.

We can also have discrete rather than continuous superpositions: the best known is Schrödinger's famous cat. This is also legitimate science though the fine details remain unresolved.

Now to quantum suicide (Wikipedia article). It's like you replace the cat and the radiation-triggered cyanide is replaced by a gun. You decide to shoot yourself. Now, there is some probability that the gun will misfire due to some unlikely outcome of events down at the quantum level. So the time-evolution of you with the gun evolves into a superposition like this:

|You and gun not fired>  =>  a|you-alive and gun-misfired> + b|you-dead and gun-fired>

a and b are coefficients expressing the relative amplitudes of these two states, with |b| expected to be enormously larger than |a| for a reasonably reliable gun.

In the standard interpretation of quantum mechanics, this simply means that you'll most likely end up dead: end of story. The superposition quantum state 'collapses' to the

 |you-dead and gun-fired>

state with probability |b|² (or maybe you got lucky with probability |a|²) once somebody notices (these days we invoke decoherence).

But in the many-worlds interpretation there are no collapses. All states of a superposition are realised in separate versions of the universe. Since you have no consciousness when you're dead, your continuing sense of self will continue to exist in the universe with this state:

|you-alive and gun-misfired>

Immortality!

Quite a lot of physicists believe in the many-worlds interpretation: it seems the only way to make objective sense of quantum mechanics and to remove the subjective role of a 'collapse-inducing' observer. But would Clare, my proxy for 'the person in the street', believe it for the purposes of a plot denouement?

I don't think so. And that's why Dan Simmons novel just doesn't work and I continue with the challenging work of real-time editing!

A long read

Clare and Nigel in Greece: 2007

A pointless holiday snap: we were travelling with the Andante archaeological travel company visiting Athens, Delphi, Corinth, Sparta and the site of the ancient Olympics at Olympia.

Terry Pratchett's humour doesn't really agree with me, although I respect his evident intelligence, wisdom and all-round national treasure status blah, blah, blah. I had therefore avoided "The Long X" sequence, X ∈ {Earth, War, Mars, ..., ...} on the grounds of anticipated boredom. Co-authorship with Stephen Baxter, big science and poor characterisation, did nothing to mitigate my fears.

A visit to the library and I weakened, bringing home {Earth, Mars}. The critics are right: nothing much happens for hundreds of pages. I quite like the idea of a countable (possibly countably-infinite) number of parallel universes accessible by 'stepping' -  a Euclidean fifth large dimension. That seems to have been where their joint imagination ran out.

But could the universe be even stranger? It would be soooo cool if the spacetime of our common-sense reality were an emergent property of some high-dimensional Hilbert space. Now wouldn't that be something!*

---

* I don't pretend to understand this paper, but I like the authors' aim:

" ... a new approach to the problem of unification of quantum theory with general relativity theory. Its key idea is to “general relativise quantum theory” instead of “quantising general relativity” ...".