Wednesday, 4 December 2019

Michio Kaku and Other Superstar Physicists on the Price of Bread



“It's okay to ask those questions [on “the meaning of life”, “destiny”, etc.], but one should not expect to get a wiser answer from a physicist.”

- Alan Guth (Quoted by Michio Kaku is his Parallel Worlds.)

"I deal with tough mathematical questions every day, but please don't ask me to help with Brexit."

- Stephen Hawking (After which he immediately offered his strong views on the reality of Brexit.)

i) Introduction
ii) Michio Kaku
iii) Stephen Hawking
iv) Conclusion

Why do far too many people simply assume that well-known physicists will have insightful things to say on almost (or literally) all other subjects? (I have in mind Michio Kaku, Brian Cox, Neil deGrasse Tyson, Sean Carroll, etc.) I noted this first with Albert Einstein, whose non-scientific words are quoted left, right and center. Yet much of what he said on politics and religion is fairly standard stuff. (Einstein's 'Why Socialism?' is often quoted – usually in Facebook memes.) And even when true or fairly insightful, the words would have probably been ignored if said by a layperson or even by an unknown physicist.

Thus we give the superstars of physics (if not physicists generally) leeway to comment on all sorts of stuff that's a million miles away from physics. This is like getting pop stars or actors to offer their profound insights on politics. It's also a case of a positive ad homimem, in that the man/women is automatically deemed to be saying insightful things simply because he/she is a famous actor, pop star... or physicist.

It needs to be noted, however, that I wouldn't class all “popular science” writers in this category. (I have in mind writers and physicists like Brian Greene, John Gribbin, Medium's Ethan Siegel, etc.) There is also, of course, a lot of snobbery about such books form academics and specialists. But my problem isn't the populism and clear writing style: it's the writers covering every subject under the sun.

In any case, I believe that this is primarily because physicists are seen as being the “brainiest” of all people – just behind brain surgeons. (Are brain surgeons brainy simply because they carry out surgery on the brain?) Many of them are indeed “brainy” and even highly imaginative. Yet, again, why does that give them a special insight into the price of bread or the meaning of life? Do psychologists, economists, etc. also have some insightful angles on quantum mechanics or wormholes? Such people could do, I suppose; though there's no reason to simply assume that they do.

So, sure, superstar physicists may have extremely insightful things to say on the price of bread or Hillary Clinton. But why should we assume that they do? What is it about theoretical physics that gives Michio Kaku, for example, an insight into the price of bread or the meaning of life?

Michio Kaku

Take Michio Kaku again. He's written and spoken on politics, God, consciousness, time travel, Donald Trump, environmental issues, fate, peace, social justice, biotechnology, the Internet, “play”, neuroscience, aliens, “the future of humanity”, “the world in 2030”, UFOs, déjà vu, Creationism, ad infinitum.

Even some of the issues that Kaku tackles which are indeed connected to cosmology and physics often seem a little esoteric, if not downright wacky. Thus Kaku has had a go at the whole lot: wormholes, teleportation, space travel, future civilisations, quantum computers, consciousness, etc.

Now for some of Kaku's published or broadcast words. Take this statement:

“I have nothing against investment banking, but it's like massaging money rather than creating money.”

That may be perfectly-correct economics. But why is Kaku commenting upon it?

What about this? -

“Leaders in China and India realize that science and technology lead to success and wealth. But many countries in the West graduate students into the unemployment line by teaching skills that were necessary to live in 1950.”

There's nothing necessarily wrong with this either; I just don't know why a theoretical physicist is saying it and having it published/broadcast. Then again, I suppose, someone could reply by saying:

Why shouldn't Michio Kaku comment on the price of bread and the meaning of life?

Now for this. -

“I think the 'Terminator' idea is a reasonable one - that is that one day the Internet becomes self-aware and simply says that humans are in the way.”

Here we can say that none of these statements are a result of Kaku's original research. Yet he rarely acknowledges the sources of these ideas. In other words, many theorists have commented on the possibility – or inevitability – of the Internet becoming “self-aware”.


The generation now alive is perhaps the most important generation of humans ever to walk the Earth.”

Now that's as far from theoretical physics as you could go. However, I suppose there may be very tangential links to cosmology; though there can be tangential links between any x and any y – if you try hard enough to make them.

Stephen Hawking

Then there was Stephen Hawking, who has also talked about politics, religion and, of course, God. On the God front, you could argue that there's a strong physics-God link. But as for religion, that's not really so... surely?

Hawking commented on, and been extensively quoted commenting upon, the Iraq War, euthanasia, Brexit, nuclear weapons, animal testing, Donald Trump, the NHS, the Labour Party, etc. However, as far as I know, none of these issues appeared in his books or publications. Thus, if Hawking was asked a question on any x, then of course he had the right to answer it and offer his view. This is very different from a physicist superstar discussing the price of bread or the meaning of life in his books. In other words, Hawking and others can't help but answer the questions they're asked. And there's no reason they shouldn't answer them. After all, physicists are voters, members of society, human beings, etc.

Here's an example:

"I regard Corbyn as a disaster. His heart is in the right place and many of his policies are sound, but he has allowed himself to be portrayed as a left-wing extremist."

As already stated, this is fine because Hawking was simply responding to questions from the BBC.


"It is generally recognised that women are better than men at languages, personal relations and multi-tasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics."

At the risk of repeating myself, all the above may well be true (though many people may find it sexist or shocking). But I wouldn't think that a theoretical physicist and cosmologist would have anything interesting or special to say on women and mathematics/physics.

Conclusion

I would suggest a little more modesty from superstar physicists. However, since millions are buying their books, and the books tend to stray way beyond physics and cosmology, then why should the superstars stop? That is, these theoretical physicists create a niche in theoretical physics and then branch out... And the more they write and get published, the farther out they branch. Now this branching out isn't always unsuccessful. Indeed sometimes it may be insightful. However, why simply assume that all examples of this branching out will be insightful, let alone profound?

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Monday, 25 November 2019

Let's Eliminate All the Interpretations of Quantum Mechanics!



with John Gribbin

i) Introduction
ii) What is Interpretation?
iii) Shut up and calculate!
iv) Limits to John Gribbin's Pluralism
v) Only Maths?
vi) Waves and Particles
vii) Conclusion

This piece doesn't claim to offer a conclusive case for the elimination of all the interpretations of quantum mechanics (QM). It simply raises the possibility of elimination and then offers a few arguments in that direction.

The prime motive here is that, at least at present, there's no way of establishing which interpretation is the true/correct/etc. one. Secondly, the multiplicity of interpretations both confuses the issue and leads to scepticism towards many of them. Thirdly, some interpretations are so convoluted and wacky that laypersons and even physicists themselves have only aesthetic reasons to believe in them.

This is particularly true of the Many Worlds Interpretation. I can see no reason whatsoever for the layperson to accept it other than it can be taken to “explain the phenomena” (a phrase which is being used in contrast to Bas van Fraassen's "save the phenomena"). That is, in the way that panpsychism, idealism, Marxism, theism, etc. can all be taken to explain the phenomena. However, explaining phenomena is often very cheap and easy, even if it is neat and tidy. (Note Albert Einstein's rejection of David Bohm's theory.)

The first section introduces John Gribbin's position as well as a potted history of positions (which features Paul Dirac, Richard Feynman, etc.) which can be taken to lead towards a possible eliminitivism This section also deals with both the shut-up-and-calculate mantra and instrumentalism and how they can be taken to lead to eliminitivism. Then the simple question “What is Interpretation?” is asked. After that, Gribbin's pluralism is tackled and seen to be not very convincing (at least not from a philosophical point of view). The section “Only Maths?” is self-explanatory. Finally, the issue of wave-or-particles is discussed in the context of the elimination of interpretations of quantum mechanics.

What is Interpretation?

To state the obvious: the interpretations of quantum mechanics are, well, interpretations. Thus it's hard to grasp what kind of standing (philosophical or scientific) a particular interpretation of quantum mechanics could (or should) actually have. Indeed the very word “interpretation” seem to deflate what it is that's being done – at least from a strictly scientific perspective. 

Does an interpretation become something else when it is proven or simply established to be true or correct? Do any interpreters of quantum mechanics believe that their own interpretations can be proven or shown to be true? What would that even mean?

When it comes to all interpretations of QM, the mathematical theory is taken as a given (or at least parts thereof). Thus the interpretation is something that's over and above the mathematical theory. (This is complicated by many laypersons' views on what exactly scientific theories are.)

In effect, the interpretation attempts to tie the mathematical theory to the world (or to reality). This is even the case when that (mind-independent) reality is rejected or simply seen as being philosophically problematic.

In the end, all interpretations ask and answer similar questions. Nonetheless, not all of these questions are to do with "what is real”. They can also be questions of measurement, determinism/what is random, and so on. Thus such questions aren't always about things – such as particles, waves, parallel worlds and so on.

Shut up and calculate!

John Gribbin (an astrophysicist who's been writing on quantum mechanics for over 40 years) has an interesting and radical position on the interpretations of quantum mechanics (QM). Thus, in this piece, I'll often bounce off Gribbin's words. However, although Gribbin doesn’t cite a case for the elimination of the interpretations of QM, he does strongly (for want of a better word) deflate them.

Following on from that, there's no reason why an eliminativist position on QM interpretations can't be advanced. By this I don't simply mean the instrumentalist, technological or “philistine” position which is best summed up by N. David Mermin's well-known quote, “Shut up and calculate.” Indeed it may even be possible to recruit both Paul Dirac and Richard Feynman to the eliminitivist cause.

Dirac, for example, once compared particles to the pieces of chess. He wrote:

I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it. The whole game of chess follows from this way of moving the various chessmen.”

To put it bluntly, Dirac's position seems to be eliminativist when it comes to particles. Yet if it is eliminativist, then why did he speak of “particles” at all? That's unless, of course, the word “particle” is simply shorthand for specific types of behaviour or movement. Yet this simply raises the question:

What is it that behaves or moves?

Richard Feynman also had a problem with seeing particles as particles. He hinted at the possibility that we have a wave-particle duality simply because there are no particles or waves in the first place. He wrote:

Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.”

Like Dirac, Feynman was emphasising behaviour, not particles or things.

From a purely scientific point of view, it's easy to agree with Mermin's well-known phrase which was quoted earlier. (Although he wasn't putting his own position.) So it's not a surprise that the science writer Philip Ball says that “[s]ome scientists feel the same way today”. Ball himself writes:

Quantum theory works. It allows us to calculate the shapes of molecules, the behaviour of semiconductor devices, the trajectories of light, with stunning accuracy.”

Thus the “theory works”; though “without our knowing what it's about”. And that, surely, wouldn't be such a bad thing if physicists also believed that there's no real (or available) answer to the what-is-it-about question. Perhaps some (or even many) physicists do believe that.

So what do the words, “What the maths mean”, mean? What does the maths describe? What is there beyond the maths (if anything)? Does the mathematics alone give us a full understanding?

Interestingly enough, Mermin also once quipped that

"new interpretations [of QM] appear every year. None ever disappear."

Now that's another reason to be sceptical of – or deflationary towards – the many interpretations of quantum mechanics.

One can also take a positive pragmatic (or instrumentalist) position on these many interpretations of quantum mechanics. Alternatively, one can take a pessimistic position on them. The theoretical physicist Steven Weinberg takes the latter option. He writes:

My own conclusion is that today there is no interpretation of quantum mechanics that does not have serious flaws. This view is not universally shared. Indeed, many physicists are satisfied with their own interpretation of quantum mechanics. But different physicists are satisfied with different interpretations. In my view, we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is only a good approximation.”

Now is Weinberg's position philosophical/ontological in nature? Is he saying that it's not all about prediction, experiment, observation, etc. – it's also about what is? In other words, is it a realist position on the interpretations of quantum mechanics?

The physicist David Finkelstein also notes the problems with these different interpretations; though he doesn't really hint at any metaphysical concern. He tells us that “[q]uantum theory was split up into dialects” and that this was the case because “[d]ifferent people describe the same experiences in remarkably different languages”. Consequently, this pluralism may seem fine except for the fact that all “[t]his is confusing even to physicists”.

As hinted at above, the philosophical position called instrumentalism comes the closest to the position that rejecting all interpretations (or the need for interpretations) of quantum mechanics is a good idea. Yet it's still a philosophical position, if not an actual interpretation of quantum mechanics.

Having said that, interpretation is not even an issue for the many physicists and technologists in white coats. In quantum field theories, for example, the structures described are abstract (or purely mathematical). That is, they exist without any clear interpretations of the quantities which are part of the theory.

Yet, on the other hand, just as we can deflate QM interpretations, so we can also deflate the Technophile/Philistine Interpretation (as it were) of QM. For instance, Gribbin says that

"[j]ust how an electron, or a beam of electrons, get from A to B does not matter to an engineer designing, say, a TV set".

Put that way, it's hard to imagine any scientist not being interested in how electrons "get from A to B". Of course we may not be able to speak of the in between of A and B - and that's a recurrent theme in QM. (This is a position best highlighted by the relationalist - or interactionist - interpretation of QM; such as that offered by Lee Smolin and Carlo Rovelli.) Gribbin himself highlights the problem in this way:

"If you have a set of parameters describing the system in state A, you can calculate the probability that it will be in state B after a certain time. But there is nothing which tells you what is going on in between."

Yet to many quantum theorists there is (effectively/simply) no "in between"!

Finally and more relevantly, there may be a philosophical case that can be given for eliminativism when it comes to the interpretations of QM. And this is something the shut-up-and-calculate brigade never offered.

Limits to John Gribbin's Pluralism

Gribbin's actual position is one of the “complementarity” of all the different interpretations of QM. That is, no interpretation (or no set of classical physical concepts) can refer (at the same time) to a singular quantum system. This of course can be traced back to Niels Bohr's theoretical stance on both the wave and particle descriptions (see later section).

Prima facie, Gribbin's position seems to be one of relativism. Or, at the very least, one of conceptual pluralism. For example, Gribbin believes that

none of them [quantum mechanical interpretations] is anything other than a conceptual model designed to help our understanding of quantum phenomena”.

His primary reason for stating the above is that all the interpretations he considers “make the same predictions”. Sure, this is hardly an original point. People have been saying this about all the interpretations of quantum mechanics since at least the 1950s. Yet surely even if we see the essential limitations of these interpretations, and the fact that they don't offer us a complete picture, that doesn't also mean that all of them must be treated equally. That simply doesn't follow.

Take a murder that hasn't be solved and which has engendered numerous interpretations (or explanations). Does that mean that all interpretations should all be treated equally? Having said that, if they're all in the same ballpark (as, arguably, all/most QM interpretations are), then perhaps they are all equal.

Gribbin himself also believes that all interpretations of quantum mechanics are effectively in the same ballpark. Thus can we also argue that all the interpretations are in the same ballpark as purely metaphysical/ontological theories? Or, more simply, that they're all actually metaphysical/ontological theories? The fact that QM interpretations are about physical (or scientific) realities doesn't really seem to make any difference here. The fact is that they go beyond the maths, predictions, experiments, observations, etc. And that means that they're (almost by definition) philosophical in nature. (That's not necessarily a criticism.) However, can we say (as already stated) that the interpretations of QM are also in the same boat as, say, panpsychism, monism, idealism, theism, Marxism and whatnot? If they are, then the interpretations may never be able to smoothly bridge the gap between the mathematical theory and the interpretations.

As stated, Gribbin is a pluralist (as are many scientists and philosophers when it comes to scientific theories, concepts and models). Gribbin, in the following, again talks about the interpretations of quantum mechanics:

I stress, again, that all such interpretations are myths, crutches to help us imagine what is going on at the quantum level and to make testable predictions. They are not, any of them, uniquely 'the truth'; rather, they are all 'real', even where they disagree with one another.”

This is heavy stuff. Of course what's true of quantum interpretations (or “myths”) isn't also true when it comes to mathematical theories. (The above is certainly problematic for string theory, for example, for the simple reason that Gribbin talks about such theories/interpretations making - unique - “testable predictions”.)

Despite all the above, Gribbin happily acknowledges that the quantum interpreters believe that their interpretations are true. He writes:

"[T]he interpreters and their followers will each tell you that their own favoured interpretation is the one true faith, and all those who follow other faiths are heretics."

And that passage comes straight after Gribbin tells us that

"[a]t the level of equations, none of these interpretations is better than any other".

Thus, logically, "none of the interpretations is worse than any of the others, mathematically speaking". Though all this hinges on precisely how we're to take the phrases "at the level of equations" and "mathematically speaking". That, of course, is the main issue of this piece.

Gribbin also gets all psychological or aesthetic when he concludes (as the very end of a book) that we

are free to choose whichever one gives you most comfort, and ignore the rest”.

Again, there may well be an argument that all interpretations are superfluous when it comes to predictions, technology, etc. However, that certainly doesn't mean that all interpretations are “equally good”. They may be equally good in the sense that they don't make the slightest bit of difference when it comes to to mathematical theory, predictions and (quantum) technology; though are they equally good in literally every respect?

Gribbin also talks in terms of what he calls a “physical model” of “mathematical concepts”. He writes (in his Schrodinger's Kittens and the Search for Reality) that “a strong operational axiom” tells us that

literally every version of mathematical concepts has a physical model somewhere, and the clever physicist should be advised to deliberately and routinely seek out, as part of his activity, physical models of already discovered mathematical structures”.

Yet even in Gribbin's case, it's still clear that a “mathematical concept” comes first and only then is a “physical model” found to square with it.

Only Maths?

Do mathematical physicists require (or need) Gribbin's “conceptual models” or any interpretations of QM? It depends. It depends on what they’re doing and what they want.

One way of interpreting Gribbin's remarks is that only those who know the mathematics can bypass QM interpretations altogether. Thus are all these interpretations the result of commentators (or laypersons) having a mathematical deficit? That can't be true for the simple reason that many well-known QM interpreters have also been adept mathematicians and mathematical physicists. (Not all have taken the eliminitivist position of Paul Dirac – see later section.) Thus if the maths literally gives us everything, then why did all these people feel the need to interpret QM in the first place? For a start, they aren't simply telling stories to assuage the layperson. Yes, they also believe that their own interpretations are true/accurate/etc.

In addition, it may not be the case that knowing all (or much of) the maths of QM (as, say, Richard Feynman did) automatically brings you closer to the truth when it comes to interpretations. For example, say that I acquire literally all the mathematical knowledge which is used and known by all the believers in the Many Worlds Interpretation of QM. Would I then automatically see that this interpretation is the only true one? There will still be a leap from the mathematics to the interpretation. That is, the links between the mathematics and the interpretation will neither be (entirely) mathematical nor (entirely) logical. Indeed it can be argued that they can't be (entirely) scientific either.

On the other hand, Stephen Hawking’s question as to “what breathes fire into the equations will always hover over the heads of the physicists who don't endorse an interpretation. The science writer Kitty Ferguson (in her The Fire in the Equations) offers a possible Platonist answer to Hawking's question by saying that “it might be that the equations are the fire”. Alternatively, could Hawking himself have been “suggesting that the laws have a life or creative force of their own?”. Again, is it that the “equations are the fire”?

If the maths is “only” a tool for predictions, experiments and suchlike, then the maths alone can't possibly answer all the questions raised by QM interpreters.

The physicist John Archibald Wheeler also provided a powerful riposte to such Platonism (as it were) in physics. We're told that Wheeler used to write arcane equations on the blackboard and stand back and say to his students:

Now I'll clap my hands and a universe will spring into existence.”

So is the maths simply a tool which doesn't tell us what is? Sure, the “what is the case?” question may end up being bogus (i.e., from an anti-realist or instrumentalist point of view). Nonetheless, surely there must always be something beyond the maths and therefore beyond the predictions, the technological applications, etc. of QM.

A sharp and to-the-point anti-Platonist (as it were) position is also put by the science writer, Philip Ball. He writes:

... equations purportedly about physical reality are, without interpretation, just marks on paper”.

In other words, what exactly (as Hawking put it above) “breathes fire into the equations [to] make a world”?

The Philip Ball quote above also highlights two other problems:

i) The fact that we can make mistakes about physical reality.
ii) That even if the equations are about physical reality, then they're not one and the same as the physical reality.

Ontic structural realists (in the philosophy of physics), on the other hand, would say that this distinction (i.e., between maths and the world) hardly makes sense when it comes to physics generally - and it doesn't make any sense at all when it comes to quantum physics. Nonetheless, surely there's still a distinction to be made here.

Waves and Particles

Niels Bohr made it clear that only mathematics gives us a true picture of the quantum realm. He wrote:

"We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.”

This, again, is a roundabout of saying that only the mathematics is adequate when it comes to describing sub-atomic phenomena. Thus, by this definition, the words “particle” and “wave” simply can't do the full job. Yes, they can do part of the job; though not the full job. Indeed it's not just the word “particle” that's problematic, thinking of particles as things is too. Bohr wote:

"Isolated material particles are abstractions, their properties being definable and observable only through their interaction with other systems."

In other words, it can't possibly be about the world “as it is in itself”. Every statement we make about the world comes with a lot of contingent baggage. There is of course a causal set of relations to any x – though those very same relations can be described in an indefinite number of ways.

At the most basic level, “seeing” a subatomic x as a particle or as a wave is an act of interpretation. So is seeing them as both (i.e., within different experimental contexts), as Louis de Broglie and many other did. Finally, seeing x as neither a wave nor a particle may also involve interpretation.

In more general terms, Bohr argued that the reality behind our measurements and experiments is that there is neither a particle nor a wave. But we must still talk about something (his "poetry"). However, that something isn't necessarily a thing as such (this is grammar speaking here). And we give that x (which doesn't need to be a thing, only a something) the name “wave” or “particle”.

So when de Broglie argued (in 1924) that that every moving particle (yes, particle) can be equally described as either a wave or a particle, that may well be because this x is neither a wave nor a particle. Nonetheless, describing x as a wave or a particle still helps both physicists and laypersons.

In more detail and to go back to the 1920s. Erwin Schrodinger was committed to waves. Werner Heisenberg and Paul Dirac to particles. (Heisenberg dealt with pure numbers in the form of arrays – i.e., matrices). In the end and in a strong sense, all this didn't matter because Dirac went on to show/prove that the wave and particle interpretations are equivalent. That is, equivalent when it came to the maths, experiments, predictions and, later, technology.

In actual fact, we can go back to J.J. Thomson, when he showed that electrons are particles. Then, 30 or so years later, his son, George Thomson, showed that electrons are waves.

The American philosopher Ernest Nagel (in his 'The Cognitive Status of Theories') had a different (though related) take on particles and waves. Firstly he discussed their “puzzling characteristics”. These puzzling characteristics seem to be “incompatible”. (Though the word “incompatible” isn't a synonym of “contradictory”.) More precisely, electrons are “construed to have features which make it appropriate to think of them as a system of waves”. Yet, “on the other hand”, electrons “also have traits which lead us to think of them as particles”. They're deemed to be particles because each one has “spatial location and a velocity”. However, “no determinate position and velocity can in principle be assigned simultaneously to any of them”. It's here that Nagel appears to deflate quantum mechanics. He does so by saying that

many physicists have therefore concluded that quantum theory cannot be viewed as a statement about an 'objectively existing' domain of things and processes... On the contrary, the theory must be regarded simply as a conceptual schema or a policy for guiding and coordinating experiments”.

It's also the case that the words “particle” and “wave” carry far too much baggage. After all, the original wave-particle experiments had water waves in mind. Is that a good thing when it comes to talk about happenings at the subatomic level? Yes, it is if it helps us get of grip of things. The same goes for the word “particle”. So there are a host of good reasons as to why x should be seen as a particle. Yet there are also a host of equally good reasons as to why we shouldn't see it as a particle.

Gribbin himself takes an equally radical position on particles and waves. He writes:

In the world of the very small, where particle and wave aspects of reality are equally significant, things do not behave in any way that we can understand from our experience of the everyday world...all pictures are false, and there is no physical analogy we can make to understand what goes on inside atoms. Atoms behave like atoms, nothing else.”

It can of course be said that even if it's correct that

all pictures are false, and there is no physical analogy we can make to understand what goes on inside atoms”

then it may still be the case that (at least for laypersons) that's all we've got. Indeed without the mathematics, all we have are pictures, images and analogies. So we'd better make do with all that. And surely Gribbin isn't arguing that pictures, images and analogies serve no purpose. Indeed he can't be arguing that because his books make extensive use of them. Having said that, all Gribbin's pictures, images and analogies do come along with words of warning (as can be seen in the quotes above).

In fact we can even say that the very use of the words “particle” and “wave” may mean that Gribbin himself is also using pictures or images and/or being analogical. That is, if “in the world of the very small” it's the case that

things do not behave in any way that we can understand from our experience of the everyday world”

then why is Gribbin using the words “particle” and “wave” in the first place?

Conclusion

One thing is certainly the case: without the maths, we'd have almost (or literally) nothing to "say" about the quantum world – real or otherwise. When it comes to QM, the usual means of ownership aren't available to us. That is, we can't observe, feel, smell or (often) even imagine the quantum world. Thus the maths is all we've got. This is excellently expressed in the following passage from John Horgan:

[M]athematics helps physicists definite what is otherwise undefinable. A quark is a purely mathematical construct. It has no meaning apart from its mathematical definition. The properties of quarks – charm, colour, strangeness – are mathematical properties that have no analogue in the macroscopic world we inhabit.”

If maths is all we've got, then it's not really a surprise that many physicists (i.e., the more philosophical ones) have said that quantum mechanics doesn't really “say anything about the real world”. Or, at the very least, everything that's said about the quantum world is said by the maths. Thus, all the imagery, picture painting, analogies, etc. aren't really about the quantum world – they're simply the crutches we use in order to get a grip of that world.

So when it's said that Richard Feynman, for example, could only do “quantum theory” (i.e., the maths), then that's not a surprise. That's because the maths may be all we've got. And when we stray beyond the maths into “interpretation”, then we (perhaps by definition) can't help but get things wrong... Or at least this is one sceptical scenario we must consider.

Again, it's not a surprise that Feynman didn't “know what the maths means”. That may be because the phrase “what the maths means” is (almost) meaningless. At the very least, there's a hint that we can't go beyond the maths. Yet it's still the case that so many philosophers, and somewhat less physicists, believe that the maths is only second-best to something far deeper – the interpretation (or ontology) of quantum mechanics.

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Afterthought

In many respects it can be argued that certain interpretations of quantum mechanics aren't really interpretations at all. Or, at the very least, they're less interpretational than their rivals. The Copenhagen Interpretation and QBism (quantum Bayesianism), for example, are good examples. The very fact that there are strong anti-realist or verificationist factors to these positions surely limits the need for interpretation.

Take the electron's journey from A to B mentioned in the piece above. To quote John Gribbin again:



"Just how an electron, or a beam of electrons, get from A to B does not matter to an engineer designing, say, a TV set… If you have a set of parameters describing the system in state A, you can calculate the probability that it will be in state B after a certain time. But there is nothing which tells you what is going on in between."

If Niels Bohr, John Gribbin, QBists, etc. all deny that in between (or simply play it down), then surely there's little room left for interpretation.