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Friday, 31 August 2018

Deflating Quantum Mechanics: Pictures, Images & Analogies




The use of the words “deflating quantum mechanics” isn't meant in the sense of offering any challenge to quantum mechanics (QM) itself. Of course not. For a start, I'm not a physicist. (One would need to be a great physicist to challenge the fundamentals of quantum theory.) This piece, instead, is primarily aimed at the interpretations of QM by the layperson and indeed even by some physicists. In other words, quantum theory is fine by me. What I do have a problem with is commentators deliberately attempting to make QM even more (as it's often put) “weird” than it actually is. In addition, there's also of the problem of people focusing entirely on quantum weirdness.

More relevantly, it's argued that this quantum weirdness is largely brought about when people use images, pictures or analogies which are only applicable to the everyday world, and then applying them to the quantum realm. This - almost by definition - must surely be like pushing square shapes into round holes. In other words, it's bound to make QM weird/er.

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It would seem that one of the main positions advanced in this piece is partly contradicted by a well-known quote from Albert Einstein. Namely:

If I can't picture it, I can't understand it.”

So despite Einstein's words, it can also be said: 

If you can picture the phenomena of quantum mechanics, then you don't understand them. 

Werner Heisenberg, for example, argued that all the imagistic or analogical descriptions of QM are problematic. More precisely, he stated the following:

Progress in science has been bought at the expense of the possibility of making phenomena of nature immediately and directly comprehensible to our way of thought.”

In other words, in order to make the scientific 


“phenomena of nature immediately and directly comprehensible to our way of thought”, 

scientists have relied on images, pictures and analogies which simply don't do the (complete) job. On the other hand, when scientists don't use such analogies, pictures or images, then QM is incomprehensible to “our way of thought”.

There's a deep problem here - at least for laypersons!

So what if it's partly the overuse of imagery and analogies which makes QM seem so weird? Sure, QM is indeed weird. Nonetheless, using images, picture and analogies which are applicable to the macro-scale (then applying them to the micro-scale) can't help but make things weirder. On the other hand, without imagery and the requisite mathematics, how does any layperson or even physicist know that QM is weird at all?

It's not only laypersons who have problems with “picturing” the phenomena of QM - physicists do too. And since the failures (or limits) of the imagination have just been been stressed, here's the philosopher Ernan McMullin stating the following:

If we cannot quite imagine what they are, this is due to the distance of the microworld from the world in which our imaginations were formed, not to the existential shortcomings of electrons...”

Of course all this depends on what exactly is meant by the word “picturing” or “imagining”. It also depends on what's meant by the words “understanding quantum mechanics”. Sometimes the problem is also to do with the concepts we use to describe QM phenomena. In other words, it's not only about imagery.

Take a classic example: “wave-particle duality”.

Perhaps part of this problem is that the wave description isn't very apt in the first place. That is, waves at the subatomic level aren't like waves in the sea, in your bath or even like waves at all. (The graphic representations of the “peaks and troughs” of the interference pattern, for example, may not help.) This is why Erwin Schrodinger, for one, decided to call them “wave functions” instead of "waves". In other words, the wave description (even if only analogical) was never satisfactory to Schrodinger and indeed to many other physicists.

So what about particles?

The American philosopher Ernest Nagel once discussed the “puzzling characteristics” of particles. These puzzling characteristics were seen to have been “incompatible”. (The word “incompatible” isn't a synonym of “contradictory”.) More precisely, Nagel argued that 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”.

Since waves and particles have just been discussed, it's worth noting here what the astrophysicist and writer John Gribbin has to say on this. Gribbin ostensibly takes an extreme position on this part-rejection of analogies, images and pictures. 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 John 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 with words of warning (as can be seen in the quote above).

In fact we can even say that the very use of the words “particle” and “wave” may mean that Gribbin himself is 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?

Concepts

It's not only QM that's the problem here.

According to Freeman Dyson (who was talking about a “new theory [of] black holes”), the problem was that Stephen Hawking (at least at that point) was “still groping in the dark for concepts which will make his theory [of black holes] fully intelligible”.

All this depends on what Dyson meant by “concepts”. After all, he might have only been referring to mathematical concepts. In fact Dyson continued by saying that

[a]s usual when a profoundly original theory is born, the equations come first and a clear understanding of their physical meaning comes later”.

So not only is it the case that the mathematics isn't equal to the later images, pictures and analogies which people use for physical phenomena: at first the mathematics isn't even equal to anything “physical” at all. Or, more precisely, the maths isn't equal to the “physical meaning” which may - or will - “come later”.

This shouldn't be a surprise because mathematics itself is an abstract realm and numbers and equations (not their written symbols, etc.) are said (at least by some philosophers and physicists) to be “abstract objects”. Thus the equations Dyson referred to only became (as it were) concrete when given a “physical meaning” or when applied (in this case) to black holes.

So here we have a disjunction between mathematics and reality/nature that's only brought together when the mathematics is given a physical meaning or when applied to reality. However, even then it can be said that the disjunction still exists in a strong way. This means that whereas many scientists stress the unity of maths and physical reality, the opposite (as with string theory!) can also be stressed.

So we can still ask this question:

Freeman Dyson talked about the concepts which will make the theories of physics fully intelligible... but fully intelligible to whom?

Was it to himself and Stephen Hawking? To other physicists generally? Or to laypersons?

Scales and Levels

Richard Feynman once wrote (when talking about an electron taking “many paths” at the same time) the following:

[Quantum mechanics] describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is – absurd.”

Perhaps when Feynman used the words “common sense”, that common sense position may primarily be a result of attempting to think of (or visualise) what happens at the quantum-mechanical scale in the same way in which one thinks of (or visualises) what happens at the everyday scale.

Feynman himself singled one such scale: the scale of the atom. He said that

if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple”.

We also have this from the nuclear physicist Kenneth W. Ford:

For example, to picture the nucleus, whose size is about 10-4 to 10-5 of the size of the atom, one may imagine the atom expanded to, say, 10,000 feet or nearly two miles... A golf ball in the middle of New York International Airport is about as lonely as the proton at the center of the hydrogen atom.”

Think also the extra dimensions of string theory. Only four of string theory's extra dimensions are observable. (That's if you can literally observe macro-object-free spacial or time dimensions.)

Even if extra dimensions do exist, they may still be (or are) incredibly small; as well as “compacted”. Thus the very idea of extra dimensions bears little relation to those portrayed in horror and science-fiction films. Indeed, way back in 1926, the extra dimension suggested by Oskar Klein was thought be curled up and too small to be detectable. Thus only something equally small could (as it were) live in this extra dimension.

And strings themselves are fantastically smaller than protons, neutrons and electrons. Let Freeman Dyson explain by going even further with superstrings:

First, the entire universe. Second. The planet Earth. Third, the nucleus of an atom. Fourth, a superstring. The step in size from each of these things to the next is roughly the same.The Earth is than the visible universe by about twenty powers of ten. An atomic nucleus is smaller than the Earth by twenty powers of ten. And a superstring is smaller than a nucleus by twenty powers of ten. That gives you a rough measure of how far we have to go in the domain of the small before we reach superstrings.”

In any case, things at different scales (or things of different types) display remarkably different kinds of behaviour.

Take fleas, which can jump 100 times their own height. Take the bacteria that survive below freezing point. And on the moon, astronauts can float. However, these examples are still in a different logical space to the things which occur at the quantum scale. At the QM scale, some things are deemed to be "paradoxical" and even "logically contradictory". Nothing a flea or astronaut does can be described that way.

So when we're talking about the subatomic scale, things are almost bound to be fundamentally different. And when we get down to the scales tackled by string theory, then you'd hardly expect the kind of things you experience in your local pub.

Scales and Superposition

There's a big problem with this emphasis on the importance of scales when it comes to QM. This means that it will need to be said why it is that these scales (i.e., the micro and macro scales) should make such a profound difference to things.

Take superposition.

It's often argued that superposition is only applicable at the micro-scale. It's also argued that it “cancels out” at the macro-scale. More technically, it's said that when there are many superpositions at the quantum level, then when such superpositions are taken together, they produce a macro-state that is “definite”. That is, such a “probabilistic collapse” would result in a definite statistical process at the macro-level.

Nonetheless, this very-neat division also needs to be explained: it has been rejected.

Put simply, there are good reasons to expect superpositions at the macro-level too. Indeed there are “interpretations” (for example, Hugh Everett's) which state that superpositions do occur at the macro-level: it's just that we only experience one such state of each superposition.

We can also take Professor Brian Greene's general point about this far-too-neat micro/macro division:

It's not as though the universe comes equipped with a line in the sand separating things that are properly described by quantum mechanics from things properly described by general relativity. Dividing the universe into two separate realms seems both artificial and clumsy.”

This position seems to back up a point Roger Penrose has made about how different levels of description (which, he argues, are brought about by the effect of “measurement” or observation) determine Greene's “line in the sand” between the quantum realm and the “classical” realm. In Penrose's own words:

Since randomness comes in, quantum theory is called probabilistic. But randomness only comes in when you go from the quantum to the classical level. If you stay down at the quantum level, there's no randomness. It's only when you magnify something up, and you do what people call 'make a measurement'. This consists of taking a small-scale quantum effect and magnifying it out to a level where you can see it. It's only in that process of magnification that probabilities come in.”

Thus Penrose particularly notes how randomness is a consequence of observing quantum phenomena at the “classical level”. Nonetheless, this can still be deemed to be an epistemic problem, rather than an ontological one. That is, the probabilities (or randomness) arise not from the ontology of the quantum world, but from our epistemic access to it.

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