I just finished reading ** Beyond Weird: Why Everything You Thought You Knew About Quantum Physics Is Different** (2018) by science writer

**Philip Ball**. I like Ball a lot. He seems well grounded in physical reality, and I find his writing style generally transparent, clear, and precise.

As is often the case with physics books like these, the last chapter or three can get a bit speculative, even a bit vague, as the author looks forward to imagined future discoveries or, groundwork completed, now presents their own view. Which is fine with me so long as it’s well bracketed as speculation. I give Ball high marks all around.

The theme of the book is what Ball means by *“beyond weird.”*

Colloquially, someone might say (and they have), *“Oh, Wyrd, you’re acting beyond weird right now!”* By which they mean I don’t seem just weird to them but weird-magnified — weird-to-the-power-of — a weird too far.

Ball is punning this colloquial usage. He actually means it in the original sense of *going* beyond something. In this case, going beyond the simple acceptance of “weird quantum physics” to trying to understand what Mother Nature is really saying.

So this is a book about trying to figure out what quantum mechanics tells us about reality. Ball explores the various aspects of the quantum world that have earned its weirdness reputation: superposition, interference, and entanglement. A key question throughout is: what (if anything) divides the “classical” world from the quantum one?

**§**

In one of the last chapters, Ball mentions Jeffrey Bub (Univ. Maryland), who has some interesting quantum mechanics books himself. Bub is one of many theoretical physicists working on what’s called *quantum reconstruction*. The idea of which is to start with what we observe and try to build a completely different quantum theory — one that isn’t weird.

Or rather, since it seems the quantum world will always present a counter-intuitive side to us classical beings, a theory in which the mechanism of that weirdness is well understood and grounded.

I mention Bub because, as Ball puts it, *“Bub believes that non-commutativity is what distinguishes quantum from classical mechanics. This property, he says, is a feature of the way information is fundamentally structured in our universe.”* I like this notion a lot. It doesn’t necessarily explain anything, but it hits to the heart of the true difference.

Among other things, non-commutativity underlies the Heisenberg Uncertainty Principle and the wave-particle duality. The notion of commutativity is deeply embedded in quantum math.

Simply put, for a non-commutative system: **A×B ≠ B×A**

One illustration of this is that measuring a particle’s momentum *and then* its position gives different results from measuring its position *and then* its momentum. In quantum mechanics, in many cases, a measurement invalidates a previous related measurement (this is readily apparent in spin measurements).

This non-commutative relationship is true for all conjugate variables (such as position-momentum, time-energy, spin axes, and others). The notion is reified in what’s called a (mathematical) commutator.

In classical mechanics: **A×B = B×A**

One can measure the height, the width, the depth, the mass, the temperature, the electrical charge, the surface properties, and more; and these measurements can be done in any order. The results are the same regardless. The properties of classical objects don’t change upon being measured — they all commute.

That means we can measure (in any sequence) and know all these properties at once. Knowing the object’s height does not preclude knowing its width. In quantum mechanics we can never know *all* of an object’s properties.

Note that there are classical examples of operations that don’t commute. A common example is rotations of a cube. I like the example of getting dressed. First underwear then outerwear gives quite different results than putting underwear on last.

[For that matter, there are classical examples of spin ½ systems that take two full 360° rotations to return to their original state.]

**§**

The punchline, if there is one, is that many in this game wonder if it doesn’t all boil down to information. In their view the fundamental particle is an information bit of some kind (which aligns them with Wheeler’s “it from bit” view).

What’s interesting about this view (and I’m by no means sold) is that it accounts for a lot of the quantum “weirdness” we experience. The quantum world seems to be a world in which we’re only allowed to extract a certain amount of information. Knowing spin on one axis means we can’t know it on any other.

Ball illustrates with what I think is a compelling example:

Imagine a special version of Twenty Questions. I’ll present it the way Ball does, where you, dear reader, are the guesser or questioner. You’ve left the room, and the group has decided on how to puzzle you.

When you return, you begin asking questions: For example, *“Is it alive? Yes! Is it human? No! Is it animal? Yes! Four legs? Yes! Fur? No! Sharp teeth? No! […]”* Obviously the goal is to determine the secret with 20 questions (or less). Members of the group will alternate in answering.

At first you notice the answer come quickly, but as the game wears on, it seems to take each person longer and longer to answer. Which is weird, right?

Finally you guess, *“It’s an elephant?”* At first there’s no reaction, you notice some exchanged glances (and are now really wondering what’s up), and then everyone starts laughing and agreeing that, yes, it was an elephant.

What you learn later is that elephant wasn’t the secret. *No* object was. Instead, the first answers (especially the very first) are essentially random, except that each answer must be consistent with previous answers. There must be *some* object those answers identify.

This is why the game takes longer and longer. The person responding to the question has to find an object that fits all the properties so far named, and give an answer that fits the new question. (People don’t confer during this, each is on their own to come up with an appropriate reply.)

This, Ball suggests, is similar to how the quantum world appears to us.

We can ask questions and get answers (and the more information we gather, the more effort those answers do take), but it is a mistake to think there was ever a *specific* answer to begin with.

Effectively, *measurement* weaves reality over time.

(Note that asking questions doesn’t imply a mind or experiment. That infamous cat is being constantly questioned by its environment and its own body: Are you alive or dead? In fact the questioning goes on at an *extremely* high rate.)

**§**

What I’m maybe a bit askance at is, far from seeking a physical grounding, an axiomatic (and so far undefined) “bit particle” is exactly the sort of speculative physics I shun.

That said, maybe there simply isn’t any physical grounding for the quantum reality without some new basic axiom.

(It would have to be new, since what we see as elementary particles, such as the electron, photon, and quark, would have to contain multiple information bits. That said, I have long wondered about the ontology of an invisibly small elementary “particle” with multiple properties, even if *some* of them are *mutually* unknowable. String theory was attractive for providing that ontology.)

**§ §**

One thing I appreciated a lot about this book is that Ball resists the temptation to cover either the basics or quantum mechanics or its very interesting history (and hence the temptation).

But if I have to read about Planck discovering the quantum one more time…

**§**

This book delivered big time on what I wanted: a recent overview of leading edge quantum physics.

It’s an interpretation-free overview in the sense that Ball is generally agnostic about interpretations given this is a book very much about different interpretations. One of Ball’s key points is that he doesn’t like any of them and, per the idea of reconstruction, would scrap them all.

Also per reconstruction, apparently I’m a fan, since I’ve long wondered if QM went down a very successful, *but basically wrong*, path. (The canonical example is Epicycles.)

Ball does single out the *“shut up and calculate”* flavor of the Copenhagen Interpretation as, albeit is very successful, an unacceptable, and ultimately untenable, position. That we can’t just *accept* quantum weirdness is the point of the book.

A notable exception to his agnosticism is the MWI, which Ball devotes an entire chapter deconstructing. He and I see eye-to-eye on this. The MWI is an attractive brainstorm idea, but it seems to lead to an incoherent view. In narrowing the view exclusively to the Schrödinger equation, it becomes *too* simple to rationally account for our observations. Further, it’s actually *giving in* to quantum weirdness, not solving it.

(I would prefer to avoid *debating* the MWI here. (Mention as context is fine.) Let’s try to focus on established (by experiment and math) physics and the information ideas Ball raises. I have a post planned, *MWI: Objections* (or maybe just *MWI: Questions*) to summarize issues I’ve accumulated in recent discussion, reading, and thought. We can debate there, if desired.)

**§ §**

Some interesting bits from the book:

Speaking of the notorious wave-function “collapse” Ball dismisses the Copenhagen approach that makes it axiomatic while noting Bohr saw it as “emblematic” of the quantum-classical divide. Ball asserts that the collapse is just a name we give the process that turns quantum states into observations. He goes on to say (emphasis his):

Wavefunction collapse is then a

generator of knowledge: it is not so much a process thatgives us the answers, but is the process by whichanswers are created. The outcome of that process can’t, in general, be predicted with certainty, but quantum mechanics gives us a method for calculating the probabilities of particular outcomes. That’s all we can ask for.

From the POV of our mathematics and our observations, that seems to be the case. At least, so far.

I highlighted that paragraph and added the note: *“Reality weaves itself each moment.”* I like the notion that the universe it constantly measuring itself. When we isolate a tiny system, that measuring stops and the underlying quantum reality emerges.

Ball illustrates the quantum-classical divide with a great metaphor:

The quantum-classical transition is then like an ocean crossing between two continents: drawing a border somewhere in the open sea is an arbitrary exercise, but the continents are undeniably distinct.

Which reflects what I’ve been saying for a while now. The divide isn’t a hard line, but due to many contributing factors. (Which we may someday be able to fully understand.)

**§ §**

There are many other bits just too meaty to share here (as my word count approaches 1800). There is much to be said about entanglement, for instance.

In particular, entanglement with regard to experiments testing Bell’s Inequality. These turn on notions of inseparable states and quantum non-locality. I have some issues with Ball’s Bell’s analogy — and I’ve had issues with other analogies, too; it seems a difficult experiment to explain clearly.

The topic is more than deserving of its own post, and I’ve long been planning to explore and post about those experiments.

There is also more to be said about how the classical world emerges from the quantum one. That, too, is a topic big enough to handle in future posts.

Stay beyond weird, my friends! Go forth and spread beauty and light.

∇

December 22nd, 2020 at 11:07 am

There’s a relevant bit of text due to Bohr that I saved from somewhere:

“In every phenomenon the interaction between the object and the apparatus comprises at least one quantum. But the description of the phenomenon must use classical notions in which the quantum of action does not occur. Hence, the interaction cannot be analysed in this description. On the other hand, the classical character of the description allows us to speak in terms of the object itself. Instead of saying: “the interaction between a particle and a photographic plate has resulted in a black spot in a certain place on the plate,” we are allowed to forgo mentioning the apparatus and say: “the particle has been found in this place.” The experimental context, rather than changing or disturbing pre-existing properties of the object, defines what can meaningfully be said about the object.”

This is somewhat linked to what Ball talks about a lot (and I didn’t really get into in the post), that our (classical) perceptions and language just aren’t sufficient to the task of understanding or describing quantum mechanics. Any possible experience we have of the quantum world is necessarily classical, so of course we have no way to think about it or describe it. (Other than with mathematics, which appears to describe it very well.)

Bohr’s statement goes even further in pointing out we literally have no way to access the quantum world. Any instrument we use is necessarily classical. Ball’s main point is that we can only know what we can (classically) measure.

December 22nd, 2020 at 7:01 pm

We can consider the oddities of two-slit experiments in light of this notion of information.

For instance, the oddity that the interference pattern goes away when we extract information about the particle’s path from the system. In doing so we exhaust the information (the phase coherence) responsible for the interference.

Extracting the “particle” information means there’s no “wave” information available.

December 22nd, 2020 at 7:42 pm

After reading

Beyond Weird, I decided to re-readThrough Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality(2018) by Anil Ananthaswamy.I mentioned it briefly in my post, Time and Two Doors, but that post mainly covered Carlo Rovelli’s book,

The Order of Time. I didn’t talk about Ananthaswamy’s book much, because, as I recall, I didn’t find much meat on its bone. Other than it being about two-slit experiments, I didn’t take away much from it.But having hit an inflection point in my QM learning curve, I thought I’d give it another try. Maybe there are things I didn’t notice the first time…

December 27th, 2020 at 8:08 am

Finished it. Don’t know I got much more out of it; it’s pretty general, and I was hoping for more details. That was largely my reaction the first time; I was hoping for more detail. But it does connect with stuff I’ve read since, so it was worth reading again.

I didn’t get much into the book when I first posted about it (that post was mainly about the Rovelli book and time). I might need to do another post more in detail about the two-slit experiment.

December 23rd, 2020 at 11:55 am

(Except that QM doesn’t take longer and longer for answers.) But this doesn’t strike me as weird at all. Annoying, I suppose. Of course asking questions is going to affect the responders, whether dealing with a group of humans or an object. The humans have to

hearyour question – which affects them, even outside of this particular game. The objects, well, you have to bounce light or sound or something off of them.If this is how Ball takes us beyond weird, I think he succeeds.

December 23rd, 2020 at 2:22 pm

Yeah, it’s not like nature has to figure out the answer. The time thing might be there more to make the game make sense — to highlight how each player is refining the set of possible answers.

I believe the entire game sequence is analogous to a single measurement (making the time aspect even less relevant). The analogy also doesn’t say much (at least not directly) about the notion of a

limitedamount of information we can get from a system. I like that part of the information view.I also like the idea that reality, in some sense, doesn’t fully exist until we measure it (or until

somethingmeasures it). It’s almost idealism, but doesn’t actually involve ideas (or brains having them).As you say, the questioned are definitely affected, and I think that might be part of the metaphor. Our questions affect raw reality such that it presents a valid (classical) answer (which is the only kind of answer we can understand). Each question affects the group, picking a path through possible answers. It’s kind of a neat analogy.

I think it’s a successful book, too. We’ve had a theory for 100 years that works great but which no one truly understands. It’s in conflict with our other really great theory, and in many ways quantum mechanics is kind of an ugly patchwork once you factor in the standard model. It seems to beg for something better.

(As Ball points out, having a theory that requires

interpretationis strange. Newtonian mechanics, plate tectonics, cosmology, chemistry, there’s no “You are here” sign and no need tointerpretanything. The theory is exactly what the theory is about. It all argues that QM is blind men and an elephant. We’re just not seeing the elephant yet.)December 24th, 2020 at 10:04 am

Offline a friend asked some questions about this post. They were such good questions I though it was worth sharing them here:

“Does complementarity imply it is impossible to learn the full quantum state of a system?”Yes. We can never learn everything about a system described by a wave-function, only properties we choose to measure, and those measurements prevent

everknowing the results of other measurements we could have made.A simple example is measuring spin. We must choose the axis on which to measure it, and that axis can be any angle we like. Say we choose 25° and get an UP result (the only other result we could have gotten is DOWN — under the MWI we did also get that result).

But even if we knew the spin on some other axis before, now we don’t. We can

onlysay the system is spin-UP relative to the 25° axis.If we repeat the measurement on the 25° axis, we’ll get the same result, UP. The system is in a known state, and we can repeat the measurement and (generally) get the same result 100% of the time. If we now measure spin on a different axis, we’ll get a random result that is correlated with the previous result

depending on the angle we choose to use.If the

differencein angle is 0° the correlation is 100%. If the difference in angle is 180°, the correlation is still 100%, but we get the opposite result (DOWN). If the difference is 90° the correlation is 0% — the outcome is completely random.For angles between 0° and 90° the correlation isn’t linear, but follows quantum rules. It’s these off-angle measurements that Bell’s tests use. The 0° and 90° correlations can match classical hidden variable theories (so do measurements at 45°, which give 50% correlation). But other angles have different math between classical and quantum theories. Experiments confirm the quantum correlation math.

[Mathematically, consider photon polarization, which is spin in photons. The probability of a photon with known polarization passing through a filter depends on the angle of the filter. At 0° (relative to the known polarization), the odds are 100%. At 90°, the odds are 0%. At 45° it’s 50%. The probability at these angles matches a classical linear slope. As such, the classical expectation for a filter at 22.5° would seem to be 75% (halfway between 100% and 50%). But in the quantum world the probability is calculated by

cos(θ)^{2}=85.36%, so the quantum world allows more photons to pass, which is what Bell’s experiments test.]“Does it depend on the QM interpretation?”Not as far as I know. Even in the MWI, one is restricted to knowing what is available in one’s branch. I’m not sure, even considered across branches, all information can be extracted from a system.

For instance, in spin measurements, a branch occurs in which both UP and DOWN measurements occur, but in both those branches information about spin on other axis has been lost.

One can imagine a version of MWI in which

allpossible measurements occur (the everything that can happen does happen view). But one would still need to access across branches, so I’m not sure it isn’t the case the answer is simply no. 🙂“Given a system isolated from the environment (except for our ability to probe it), given a deterministic view, can the future state of the system be predicted?”Yes! That exactly what qubits are and exactly what quantum computing is.

December 28th, 2020 at 7:06 pm

Something I read that tickled me:

“Quantum mechanics is the operating system. The classical world is the simulation it runs.”Kind of a cool way to put it. Wish I could remember where I read it.

December 28th, 2020 at 7:20 pm

I saw this formula in a lecture about spin:

It’s the probability of a down measurement at arbitrary angle θ given the initial state:

Which will be important when it comes to experiments testing Bell’s Inequality.

December 31st, 2020 at 7:59 am

[…] very much enjoyed Jim Baggott’s book about fairy tale physics as well as Philip Ball’s book about quantum mechanics interpretations. Both books concerned ideas I’ve been reading about and pondering for a while now. Quantum […]