Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different

by Philip Ball

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we have no problem saying that the tennis ball was travelling at 100 mph and then I measured it. The tennis ball had the pre-existing property of a speed of 100 mph, which I could determine by measurement. We would never think of saying that it was travelling at 100 mph because I measured it. That wouldn’t make any sense. In quantum theory, we do have to make statements like that. And then we can’t help asking what it means. That’s when the arguments start.

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The wavefunction is not a description of the entity we call an electron. It is a prescription for what to expect when we make measurements on that entity.

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all suggestions that the wavefunction is ‘real’ are predicated on the assumption that there is after all some deeper picture in which particles have concrete, objective properties regardless of whether or not we measure them (or even can measure them). This picture is commonly called a realist view. There is no reason to think that it is a valid way to think about the world, and a fair bit of evidence implying that it is not.

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Take radioactive decay. Some radioactive atoms will decay by emitting an electron from inside the nucleus: this electron is, for historical reasons, called a beta particle, but it’s just a common-or-garden electron. Atomic nuclei don’t exactly contain electrons – we saw that these orbit outside the nucleus. But they do contain particles called neutrons, which may spontaneously decay into an electron, which gets spat out, and a proton, which stays in the nucleus.*1 Beta decay of carbon-14, one of the natural forms of carbon atoms, is the process used for radiocarbon dating, and it transforms the carbon atom to a nitrogen atom. Beta decay is a quantum process, so the probability of the neutron decaying is described by a wavefunction. (It’s actually a kind of quantum tunnelling process: the electron tunnels out of the nucleus, where it would otherwise be bound by electrical attraction.) All the wavefunction can tell you is the probability that the decay will occur – not when that will happen. Take any specific atom of carbon-14, and its decay could happen tomorrow, or in 1,000 years. And there’s nothing, nothing, you can do to figure out which it will be, for all the carbon-14 atoms look alike. However, once you know the probability of beta decay, you can estimate when, from a sample of a billion or so atoms, exactly half of them will have decayed. This

in an antenatal class with ten other expectant mothers with the same due date, you can’t be sure exactly when any one of the babies will be born but you can make a pretty good estimate of the date by which 50% of them are likely to have been born. The bigger the sample, the better the estimate. For radioactivity, this time taken for half of the atoms in a sample to decay depends on the detailed specifics of the type of nucleus in question, and is called the half-life. For carbon-14, the half-life is 5,730 years, which is just right for estimating ages of objects derived from living things over the past several centuries or millennia.

But for radioactive decay, there is nothing you can monitor to explain why a particular atom decayed when it did. There is nothing we can call a reason. OK, so atomic nuclei are pretty hard to peer into. But that’s not the root of the problem. It’s that we simply can’t, for quantum processes, talk about a historical progression of events that led to a given outcome.

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You can ‘fire’ a photon from a laser at some initial time, and then at some later time you are highly likely to detect it at another position just as though it went there along a straight-line path from the laser at the speed of light. It seems the ‘reason’ you detected it at B is that it left A and reached B along the most direct path. What’s wrong with that tidy story of cause and effect? Sometimes there really is no harm in telling it as if it happens that way. But we must try as hard as we can to keep that ‘as if’ in sight.

What do we mean by ‘is’? Is an electron a particle or a wave? It can, in different circumstances, display the characteristics of either – or even a bit of both. But as for what an electron ‘is’, all we can talk about for sure is what we can see and measure, not what causes those observations. We must say that wave–particle duality is not a property of quantum objects but a feature often invoked (to questionable benefit) in our descriptions of them. They don’t have ‘split personalities’. The same applies to the much-vaunted notion that quantum particles can be in two places at once – or more generally, in two states at once. This, too, is not really true, but again I wouldn’t go so far as to say it is wrong. We are suspended in language. From the human perspective, it certainly looks as though quantum objects can possess two different, even contradictory, values of some property at once. But the human perspective is the wrong one for understanding quantum mechanics. Nonetheless, it’s all we have.

This ‘two (or more) states at once’ is called a superposition. The terminology conjures up the image of a ghostly double exposure. But strictly speaking a superposition should be considered only as an abstract mathematical thing.

What observable superposition of large buckyballs

The wavefunction is an expression that makes the ‘equals’ sign in the Schrödinger equation true.*2 In general there is not just one of these solutions; there are many, just as another solution to x2 = 4 is x = –2. That’s why there’s a whole bunch of energy states for an electron in a box, or in an atom.

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But photons can also be created in superpositions of polarization states: say, an up–down vertical polarization combined with a side-to-side horizontal polarization.

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Bohr asserted that instead the entire experiment is the phenomenon that we must understand. Whether we have one slit open or both of them, or whether we have a particle detector lurking in one slit or not, are not experiments that explore different manifestations of the same underlying phenomena. They are different phenomena. No wonder we get seemingly contradictory outcomes, because we are looking at different things.

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in the view of Bohr and Wheeler, there are no fundamental quantum phenomena about which we have any right to speak until we measure them. To the question ‘What was happening to the photon between its emission from the laser and its detection?’, we can’t simply reply ‘I don’t know, I wasn’t looking.’ We have to say ‘Because I wasn’t looking, that question has no meaning.’

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Wheeler’s less spooky but no less perplexing way:

"No phenomenon is a phenomenon until it is a an observed phenomenon."

One objection is that the particle trajectories it predicts are bizarre and at odds with any ever observed. Others say that the paths only look that way, because the non-locality of the quantum potential gives us an unreliable view:

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The problem with the collapse of the wavefunction is that, as we saw, quantum mechanics contains no prescription for it – it has to be added by hand.

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There’s no obvious reason why the ‘collapse’ term in the revamped GRW Schrödinger equation shouldn’t just happen to be tuned to give us microscopic quantumness on the one hand and macroscopic classicality on the other. What’s more of a problem is that there is absolutely no evidence that such an effect exists.

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Well, in QBism you can. Here, all quantum mechanics refers to are beliefs about outcomes – beliefs that are individual to each observer. Those beliefs do not become realized as facts until they impinge on the consciousness of the observer – and so the facts are specific to every observer (although different observers can find themselves agreeing on the same facts). This notion takes its cue from standard Bayesian probability theory,

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Quantum mechanics generally assumes that quantum states exist in some meaningful sense, and that the math tells us what we can know about those states. But in QBism there are no objective states. Rather, according to Chris Fuchs, ‘quantum states represent observers’ personal information, expectations and degrees of belief’.

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This feels like another sleight of hand. Worse, it makes the world even more intangible and unspeakable than the strictest Copenhagen Interpretation. Everything that Bohr prohibited about the quantum world – imagining some objective reality beyond what we can measure – now applies to the classical world too.

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QBism, then, embraces the notorious ‘observer effect’ in quantum mechanics in a particularly subtle way. It makes quantum mechanics the theory needed to make sense specifically of that situation in which decision-making agents like us interact with some tiny fragment of the universe that captures our attention.

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Specifically, we must accept that events exist and that they happen with a particular probability: as Einstein might have put it, that God plays dice but that the dice eventually come to rest with one face uppermost. Then, quantum-mechanical predictions of probabilities are as good as it gets.

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quantization doesn’t exactly mean, as is often implied, that quantum quantities are obliged to take certain values and no others. The quantization is not so much a property of the system we are studying; it is a property of measurements we make on it.

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Heisenberg’s Uncertainty Principle is not exactly a constraint on how precisely we can make a measurement of some quantum property. Rather, it constrains how precisely the property we want to know about exists at all. It might have been better christened the Unknowability Principle – better still, the Unbeability Principle – although doubtless that would have spawned a mysticism of its own.

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To get a good probability of finding the particle in a small region of space from a wave-like probability distribution, we can combine waves of different wavelengths such that they interfere constructively (page 66) in just that region but destructively everywhere else. This localized wave is called a wave packet. To increase the localization and get a more tightly defined position for the particle, we must add more waves. But the wavelength determines the particle’s momentum. So the more waves there are, the more possibilities there are for a measurement of momentum.

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It suggests that ‘quantum uncertainty’ isn’t a sort of resolution limit, like the point at which objects in a microscope look blurry, but is to some degree chosen by the experimenter. This fits well with the emerging view of quantum theory as, at root, a theory about information and how to access it.

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in any experimental run, there are four possibilities for this correlation. Yet Alice and Bob only ever measure two of them: each chooses to set the angle of the magnets to either this value or that one. If we’d measured either of the other two options instead, we can be certain that we’d get a value of ±1 too. But we didn’t measure them!

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the problem is that we’re assuming we can say something meaningful about a quantity that we don’t measure. But in the Copenhagen Interpretation, we can only make meaningful statements about things that we do measure. As Asher Peres has put it, ‘Unperformed experiments have no results.’ It is the inability to speak meaningfully about a quantity we don’t measure that allows quantum mechanics to violate Bell’s bounds.

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First, we’d better confront that ‘paradox’. If indeed the properties of particles are indeterminate until one is measured, it does look as if there is instantaneous communication between them in an EPR experiment. The unobserved particle seems to ‘know’ at once which spin or polarization the measurement on the other particle has produced, and to then adopt the opposite orientation. Contrary to what Einstein thought, however, that is not really ‘action’, it is not ‘spooky’, and it doesn’t exactly involve ‘distance’. Neither does it violate special relativity. What relativity says is that events at one place may not exert a causal influence on events at another place faster than the time it takes for light to pass between them.

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Einstein and his colleagues made the perfectly reasonable assumption of locality: that the properties of a particle are localized on that particle, and what happens here can’t affect what happens there without some way of transmitting the effects across the intervening space. It seems so self-evident that it hardly appears to be an assumption at all. But this locality is just what quantum entanglement undermines – which is why ‘spooky action at a distance’ is precisely the wrong way to look at it. We can’t regard particle A and particle B in the EPR experiment as separate entities, even though they are separated in space. As far as quantum mechanics is concerned, entanglement makes them both parts of a single object.

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In some simple models of a quantum universe, a phenomenon that looks like gravity emerges spontaneously from the mere existence of entanglement. Physicist Juan Maldacena has shown that a model of an entangled quantum universe with only two dimensions of space and lacking any force of gravity at all mimics the same kind of physics seen in a three-dimensional model of an ‘empty’ universe filled with the kind of spacetime fabric necessary for a general-relativistic description of gravity. That’s a mouthful, but what it amounts to is that taking away entanglement in the 2D model is equivalent to unweaving spacetime in the 3D case.

Holographic universe

But in quantum mechanics, even when you ask the same question (‘How many black and white balls are there?’), the answer you get may depend on how the measurement is done.

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This essence, whatever it is, defies any local realist description of the quantum world: one in which objects have specific, well-defined features that are intrinsic to the object itself.

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This spreading is the very thing that destroys the manifestation of a superposition in the original quantum system. Because the superposition is now a shared property of the system and its environment – because the quantum system has lost its integrity and exists in a shared state with all the other particles – we can’t any longer ‘see’ the superposition just by looking at the little part of it.

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The researchers could control the rate of decoherence in these molecular beams by altering the pressure of the gas inside the apparatus: the more gas molecules there are, the more the fullerene molecules collide with them and lose their coherence. As expected, the contrast between the bright and dark interference bands became ever fainter as more methane gas was let into the chamber. This decay of interference reflects the erasure of ‘quantumness’ in the matter waves due to decoherence.

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specifically, decoherence-inducing interactions with the environment simply transform a pointer state into an identical-looking state. Recall that the coherence of quantum states is a question of whether the phases of their wavefunctions – the positions of the peaks and troughs, you might say – are aligned. But pointer states are special states for which shifts of phases caused by interaction and entanglement with the environment make no difference. The state still looks the same after the shift. Crudely you can think of it rather like the difference between a circle and a square. You can rotate the circle by any angle you wish and it looks the same, but not so for the square. This implies that the environment doesn’t just squash quantumness indiscriminately: it selects particular states and trashes others, a process Zurek calls environment-induced superselection or ‘einselection’. The survivors are the pointer states, which are detectable. Superpositions of pointer states do not have this stability, and so they are not ‘einselected’.

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What I’m saying is that decoherence imprints information about an object onto its environment. A measurement on that object then amounts to harvesting this information from its environment.

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Decoherence results from a transfer of quantum information: when one object becomes entangled with another, information about each object is no longer confined to the object itself. The role of decoherence in measurement, then, is not simply to destroy quantum interference and make objects become more classical the more strongly they’re wired into their environment. It creates a kind of ‘replica’ of the object itself – or rather, of the pointer states of that object – in the environment. It is this replica or imprint that eventually produces a reading in our classical measuring apparatus.

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We destroy quantumness in proportion to the amount of information we import from the system into its environment. Zurek and his colleague Bill Wootters have shown that, in a double-slit experiment, it is possible to obtain some information about which path a photon took without losing all the quantum interference. While you’re not totally certain which path it took, but have reason to think one is more likely than the other, some interference remains. And it turns out that you can get a surprising amount of path information without making the photon completely ‘particle-like’ and losing all interference. You can become 90% certain about which path while still keeping about half of the contrast of light and dark in the interference bands. (But if you try to get the last 10% of certainty, you’ll lose that contrast altogether.)

****** "observation" involves extracting information from the environment

Quantum Darwinism creates a precise framework for this seemingly (but not genuinely) obvious and mundane fact: it says that the states we can measure are ones that are able not just to imprint themselves in many replicas in the environment, but specifically to do so in many different parts of the environment – so that we can find them out without having to look everywhere. The states we can measure are the ones that are most easily found out. There’s a bizarre corollary to this picture. In general, when we measure a property of a quantum system by probing its ‘replica’ in the environment, we destroy that replica (by entangling it with the measurement apparatus). Might we then potentially ‘use up’ all the available copies by repeated measurement, so that the state can’t any longer be observed? Yes we can: too much measurement will ultimately make the state seem to vanish.

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What it says is that if we keep poking at a system to find out about it, eventually we’ll perturb it into another state.

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It is the gathering of information that alters the picture. Measurement erases the information that the environment holds about what is measured.

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You can equivalently think of quantum discord as measuring how much a system is unavoidably disrupted – by ‘destroying’ superpositions or entanglement say – when information about it is gathered by measurement. It’s a measure of the ineluctable cost of measurement: how far there is to fall from the misty, elusive quantum heights to the terra firma of the classical valley. For classical systems, the discord is zero. If it is greater than zero, the system has some quantumness to it.

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Measurement now means ‘strong interaction with the environment’: strong enough, that is, to enable the quantum state to be deduced in principle from the imprint it has left, regardless of whether we actually make that deduction or not.

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computation – is. The rest is a question of building software and interfaces that turn these bits into symbols glowing on the screen, or ink sprayed onto paper, or whatever it takes for us to be able to communicate with the machine and vice versa.

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qubits can access a vast range of states, that vastness expanding rapidly as the number of qubits increases. Because of this widening of options, you can manipulate information much more efficiently in an array of qubits than in an array of classical bits.

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Charles Bennett suggested a more catchy name: quantum teleportation.

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Entanglement means that computational steps somehow ‘count for more’ on a quantum computer. Thanks to quantum non-locality, by making an intervention here you seem able to influence what goes on there. And so by doing one thing to the qubits, you get a whole lot more for free.

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