Diffraction Effects in Semiclassical Scattering Book

WARNING

If you kindly devote some of your time to reading this review, you may become frustrated. Because I am not referring directly to Chad's book very much. I am expressing thoughts that were triggered through my reading of his book, and I find these thoughts fascinating. Still, there is a link to the book, and you will find it in the middle of my blurb under the heading "A message to Chad".

The universe is making fun of me

So here's the problem: Particles do not exist - fields do. Fields do not exist - particles do.

This insight is not helping me. In fact, I find that it leaves me profoundly frustrated. Clearly, the universe is conspiring against me. It is thwarting all my efforts to grasp what is going on. My intuition is failing. The way I have thought about the world all my life is useless when trying to understand how the world works at a deeper level. I am in a quagmire, I am thrashing around, straining to grasp the branch of a tree in an attempt to steady myself, to lift myself onto solid ground.

The branch snaps, and I am being sucked down a little deeper into the pit.

But hold on. Perhaps the problem is that I am not expressing myself properly. Perhaps the universe is not out to upset me. Perhaps I am just not using the right words.

So let me try this again.

What is a particle?

My view of what a particle is has been shaped by an intellectual tradition that goes back to, indeed was started by, the Greek atomists of antiquity. As far as I know, Democritus is held to be the first philosopher who expounded an idea that matter is composed of indivisible entities called atoms. Although Plato thought the complexity of the universe could not be explained by the mere notion of atoms, his own idea of what we today call the "Platonic solids" shares with Democritus the notion that the world is composed of basic building blocks. Aristotle contradicted this idea by stating that the four elements (fire, water, earth, air) were continuous, but the idea of atomism survived the Middle Ages in the form of commentaries on Aristotle before experiencing a renaissance after the 16th century through thinkers such as Bacon, Gallileo, Hobbes, and, although in a slightly different form, Descartes.

So the idea that an elementary particle is a tiny billiard ball that interacts with others just as its macroscopic counterparts in a game of pool (or snookers) is deeply ingrained, and I cannot shake it. But the insights of quantum physics tell a story that is simply irreconcilable with this mental picture. For one thing, these particles do not have a well-defined position. Before we try to measure the position, there is a chance that we will find the particle here, there, and everywhere. And in the case of these 'particles', this is not just a phrase! The normal state of a particle is "superposition", a state in which it exists in different positions at once. Another thing that is vaguely unsettling is that a particle can be part of a system in which it gives up its individual existence. In the spooky phenomenon called "entanglement", two particles duplicate each other's properties but also the range of spacetime points at which they may be encountered by a measuring observer. So, does it still make sense to speak of entangled particles in the plural? Are there really 'two'? What happens to the ultra-fundamental human concept of countability when we deal with entangled states?

Well then. If a particle can be in different positions at once, and lose its haecceity (the characteristics that define a thing as a particular thing, also known in philosophical literature by the funny expression "thisness"), then we are really not dealing with tiny billiard balls at all, are we?

I am slowly approaching an insight here, I think. Maybe the universe is not playing a mischievous trick on me. Maybe language is. It makes no sense calling something a 'particle' that refuses to behave like objects that I associate with the word. So we really shouldn't. But what is it that 'particle physics' analyses? What do particle colliders collide? What do particle detectors detect?

Who knows. Language has developed to describe things that we need to talk about because they happen in a world accessible to our sensory toolkit. Quantum things do not. So we are left with metaphors. I have started to think about particles as a kind of non-local 'fog' that is spread out across the entire universe, with different densities at different, specific, spacetime locations. The particles detected by particle detectors are more like ripples in a field, or "excitations of the sensory material", as German philosopher and physicist Meinard Kuhlmann said in a recent article in Scientific American ("What is Real?", in Physics at the Limits, Scientific American Special Edition Winter 2015).

Ok then. Disturbances in a field. This is much better.

What is a field?

Only it isn't. Turns out we are running into very similar linguistic problems when we adopt the expression 'field' in the hope this would solve the issues. But it is a slightly different kind of problem. This problem is at the same time less and also more severe. It is less so because the mental image of a 'field' seems less ingrained in the collective psyche than that of a 'particle'. But the physical description of a 'quantum field' turns out to be even more elusive if we insist that we cannot use a purely mathematical description to capture it.

Anybody who was forced by their physics teacher at school to comment on the way that iron filings orientate when brought into proximity with a magnet knows what the classical interpretation of a field is. A classical field is a near-physical object in which every point has a uniquely measurable identity. I can measure the strength of a magnetic field in any one location. I can measure the force between a probe and the charge of an electric field at any point in the field.

Not so for a quantum field. Quantum fields are non-local, and their quantities are not assigned to any specific points in space-time. Instead, their values are determined by a mathematical idea called the 'state vector'. The state vector can be formulated as a direct consequence of the superposition state of the 'particles' that give rise to the quantum field. In a baffling feat, 'particles' exist in all their allowed states simultaneously, like a schizophrenic who manages to act out all his different personalities at once. Accordingly, the state vector is a sort of probability-weighted average of all the allowed states of a 'particle'.

Language as we know it simply fails to do justice to these phenomena. We have not developed any words that would allow us to capture these dynamics, simply because we never had any need to.

A message to Chad

So perhaps we should not try. I feel that quantum physics, just as relativity theory, cannot be understood at a satisfactory intellectual level by reference to concepts we know. I am aware that in my own review, I have done the same, and introduced the metaphors of 'fog' and 'schizophrenic' to capture the behaviour of particles. But of course, while these words may help me to visualise what a state vector is a bit better, they may confuse others even more.

Metaphors are not helpful in getting to grips with non-empirical subjects! So, Chad, would you please stop with the dog and the squirrels. I thought you explained the physics well, and I liked your book for these explanations, but I found myself skipping over the animal-metaphors very early on. I know that dog of yours is a brain-box, but I must confess I liked your book despite its unique selling point, rather than because of it.

How shall we think about the world, then?

Still. There is something that still leaves me unsatisfied. I am perfectly happy, on one level, to learn the maths required and think about 'particles' as state-vectors, and of their propagation as 'probability-waves', but there is something still missing. I still want to develop an intuitive understanding of these processes, I am not entirely content to leave them consigned to the realm of abstract mathematics.

So what do we do? Help may be at hand in the form of a new branch of philosophical thought, unhelpfully, and I would even argue incorrectly, called 'trope ontology'. The first part of this weird expression is just a neologism for the expression 'property', and the second part refers to the philosophy of 'existence' (but, I would argue, the use of this expression is misleading, as the classical interpretation of ontology is exactly reversed in this new philosophy).

The idea of this revised way of thinking about reality is to reverse the relationship between an object and its properties - and then get rid of the object. Meinard Kuhlmann, one proponent of this way of thinking, gives the example of a ball in the article I referenced earlier - I am going to go beyond what Meinard said, but my thoughts on this subject rest on his idea:

Consider a simple object, say a red, squishy ball. An adult recognises the object as a ball first, and then identifies properties attached to the object - round, spherical, squishy, red. An infant would not do this. An infant would recognise the properties first: there's something bright, it is squishy to the touch, and it feels the same way whichever way I hold it. Later on, the infant learns to refer to this bundle of properties by using a shortcut phonetic code. This code is the word 'ball'. Through usage, the infant will then learn to replace the bundle of properties with the linguistic label. At that point, the transition will be complete - the ball will have properties, the bundle of properties will no longer exist independently of its physical carrier, as they used to do in the observer's infancy.

But if we thought of objects as abstract bundles of properties, we would find it easier to intuit the world of quantum dynamics. What we used to call a 'particle' is a collection of properties. These properties do not need a physical carrier to exist meaningfully, and as they do not, neither do they need a linguistic label that fixes a mental picture that robs them of this free existence. The properties are mass, charge, and spin, and also position and momentum.

So it seems that the new and alien world of quantum physics may provide more than a deeper understanding of nature. If understood well, it may re-define our relationship with language itself, and remind us that words are simply shortcuts that we use to define bundles of properties. If we managed to understand this fact consciously, we would enhance our ability to grasp the dynamics around us on a philosophically deeper level than ever before. We would be able to recognise the limitations of language, and in so doing re-define somewhat the idea that we and 'reality' are somehow disparate entities. The study of quantum physics, combined with a conscious re-definition of how we perceive reality, may lead us again to the insight that a conscious intellect is the 'unverse observing itself', and even cross Wittgenstein's barrier that language is the final obstacle to reality.

Why Four Stars?

Well. For some time while I was reading the book, I was in two minds about my rating. In fact, I was in five minds, one for each potential rating for the book. I existed in a state of superposition of five allowable states at once, and the state vector describing this phenomenon is:

|Rating> = a(1) |*> + a(2) |**> + a(3) |***> + a(4) |****> + a(5) |*****>

The amplitudes 'a(t)' of the states '|Stars>' are complex numbers normalised so that the sum of their squared moduli is unity (equals one). The amplitudes a1 to a5 in my state vector are 1/8; 1/4; 1/2; 1/sqrt(2); sqrt(11)/8. When I measured my state, I found that the outcome was "4 stars" with highest probability of 50%.