Title text

Rutherford did say something like this but suggesting a barmaid instead of a six-year-old, while Hilbert suggested the first man on the street. Technically, if we assume the statement correct, then nobody has understood anything about science, ever. But I'd like to have my go at explaining Physics-y stuff as simply as I can, and, perhaps equally importantly, without too much of the "woaaah quantum mechanics is so weird, you just have to accept it like this even though it's completely non-intuitive" crap one often finds in science articles written for the laymen.

Saturday, January 10, 2015

To be or to not be

By popular demand,[citation needed] here's a place where I'll put down my very own understanding of Physics and discuss some of its (hopefully) interesting aspects. While I do hope that this be of interest to professionals, I imagine they might often find the content obvious. In fact I hope that they find it obvious, as opposed to, say, wrong. On the other hand, I do believe that some of my viewpoints are personal insights rather than canonically taught material (I guess they wouldn't be 'viewpoints' otherwise?), thus if a colleague finds them useful - great, and if they point out where and why I'm wrong - even better.

For the most part, however, my target audience is laymen with general interest in science. This is not only because I'm not afraid of criticism coming from that side, although I'm not. I've seen media articles getting away with all sorts of inconsistencies. And this is the reason why I'm setting out on a quest to straighten those out. Well, not really, or rather, I'm not really hoping I'll be able to do that. But I do think that a lot of the 'strange' aspects of Physics have been unnecessarily mystified - in some cases because of lack of better understanding, and in others - perhaps more often - because it just sounds cooler that way.

The champion theory in terms of mystification is of course Quantum Mechanics (QM), which is what the remainder of this post is about. Getting a good intuition of the quantum world is indeed quite tricky, which is I guess why it has come to serve as an excuse for scientists and laymen alike to discuss metaphysical phenomena like the soul, our place in the world, or telepathy, in a tone that sounds scientific but is most often not much. What's annoying is that I think it is possible to see the quantum world in an intuitive way, with a little bit of effort - and its 'strangeness' should not be taken for granted. The most important thing in this regard is to understand what is inside the theory and what is outside its scope - where, it turns out, a lot of the striking peculiarities hang out.

First, let me say that there are different interpretations of QM. An interpretation is the way one writes down the theory, starting from the assumptions and going all the way to predictions of experiments that we can carry out to test the theory. So the different interpretations should not be thought of as different theories because they all end up predicting the same results (the results of QM experiments), but they differ - sometimes significantly - on the philosophical level. The standard interpretation of QM is called the Copenhagen interpretation because of the place where its basis was developed, by scientists like Niels Bohr and Werner Heisenberg. This is the interpretation that is taught in school and university, and in fact it is so well-established that I was already doing my Master's degree when I realized it is not the only one. Thus, the rest of this discussion is in view of the Copenhagen guys' way of seeing the quantum world.

So, what goes in a physical theory? The first thing is the ontology of the theory, which according to wikipedia, '...deals with questions concerning what entities exist or can be said to exist...' In simpler terms the ontology is what your theory is about, what the object of your study is. For example, Newton's theory of gravity describes how massive objects attract each other, thus the ontology of the theory is 'massive objects'. The stuff in the ontology has the right of existing, of being in an absolute, a priori sense. Once we have the ontology, the rest of the theory is comprised by the laws that govern the system, and, importantly, that tell us how to observe stuff, because we would like our theory to be telling us something about the real world. Now, in Newton's gravity, being and being observed are pretty much the same thing: the laws determine where a massive particle is, and if we look for it, that's also where we are going to observe it. But it turns out that this is not the case in QM, and understanding the distinction between the objective being, and the subjective observation of being is the key to resolving some of the peculiarities.

The ontology of QM is the wave function. There is nothing else in there. The rest of the theory (within the Copenhagen interpretation) is the Schroedinger equation, which tells us how to compute the wave function of a system, and the measurement postulates, which tell us how to compute the outcome of an observation. So, very generally, there are two types of questions we can ask: 'what is the wave function?' and 'what do we expect to observe if we do such and such a measurement?'. Any other question would be outside the scope of the theory and so meaningless to ask - a bit like trying to divide by zero, or asking Newton's gravity how a charged object would move in an electric field.

If that doesn't sound at all simple - or important, maybe some practical examples will help. I'll cover some of the most common QM conundrums, always starting with a statement which one could sometimes hear, but which is wrong, then explaining why.

Wave-particle duality
Wrong statement: A quantum object is simultaneously a wave and a particle.
In fact: Remember our ontology: it is exclusively the wave-function. So the object is a wave (function). The particle nature comes second: it is only needed to explain outcomes of observations, like the fact that if we try to observe electrons, they appear at a very well-defined position, as if they're point-like particles hitting our detector. So quantum objects are fundamentally waves; we are only used to thinking of them as particles in some cases because of the way we are used to observing them.
Correct statement: A quantum object is a wave function, which in observations sometimes appears as a wave, but sometimes shows properties we associate with particles.

Superposition states
Wrong statement: In QM, a particle can be in two places at the same time.
In fact: There is no 'particle' in our ontology. There is only the wave function, which is the only thing that can be such and such. The question 'what is the position of the particle' is not among the questions that can be answered by the theory, since the only questions about being we can ask are about the wave function. Now, it is true that there is a wave function which corresponds to a particle being observed at a given position with a probability 1. It is also true that we can take such a function, which places the particle at position A, and another one which places the particle at a different position B, sum them up, and get a valid wave function which would correspond to observing the particle at either A or B with probability 1/2 each. But we will always observe the particle in exactly one of the two positions. Before that, the particle is not at two places at the same time. The only thing that is is the wave function, which is what it is, duh. One of my biggest pet peeves is when scientists who should know better make wrong statements regarding superposition, which are always hugely misleading for the public.

Uncertainty principle
Wrong statement: In QM, a particle cannot be in a well-defined position with a well-defined velocity.
Correct statement: We cannot simultaneously observe the exact position and the exact velocity of a quantum object.
The key is, as usual, in what is allowed to be.

Wrong statement: QM states that the world is intrinsically non-deterministic.
In fact: The wave function evolves in a deterministic way, as given by the Schroedinger equation. The outcomes of measurements are, however, indeed probabilistic. So the universe - the wave function - follows well-defined laws, but our observation of it has some in-built randomness. It is by the way very commonly said that Einstein could not accept this and that he famously said, 'I don't believe God plays dice'. This is, again, not exactly true. Even if Einstein had some difficulty accepting probabilistic outcomes of measurements, at some point he was willing to live with it. His much more important objection against QM was its apparent non-locality, which is a vast topic and to a large extent still an open question (but I won't discuss it in this post).
Correct statement: In QM, what is is deterministic, what is observed is probabilistic.

By the way, Einstein's full quote actually goes, "I don't believe God plays dice since the intervention."

Schroedinger's cat
Wrong statement: The cat in Schroedinger's thought experiment is simultaneously dead and alive.
In fact: The cat will be observed either dead or alive, with probability 1/2. Outside of that the cat is not being a cat, but instead is a quantum object (composed of a huge number of quantum objects, but that doesn't matter) which is a wave function in a superposition state, see above.

Bottom line: everything in the quantum universe is a wave function, and nothing else can be anything. Once we accept this, it is not the reality which is strange, it is only the outcomes of measurements which appear so. I realize all this might not be a very satisfying explanation. For example, it's hard to accept that the cat is in fact not a cat but a wave function, and we're only observing it (in the most literal sense: by looking at it) to be a cat. But I do think that if everybody kept in mind the important distinction between the physical reality and the results of its observation, and hence between valid statements and those which are wrong simply because they are meaningless within the scope of the theory, the world would be a better place.

By the way, all this is not, like, 'just my opinion'. I mean, I cannot go as far as to say that everything written here is correct and whoever disagrees is an idiot, but I guarantee that the 'wrong statements' above are wrong, and I'm willing to argue to the death with anybody about this. Also, Bohr himself supposedly often emphasized that the answer to most 'paradoxes' of QM lies in the fact that people are asking questions they are not allowed to ask. So, you know... I like to think that even he would agree with this post, if he could see it.

Perhaps you don't see an important difference between the correct and the wrong statements above. Perhaps you do, but it seems to you that I substituted one 'strangeness' with another. Or everything is clear? Whichever the case, all this is just scratching the surface. Everything that is in italics within this post deserves a post on its own, and will get one in due time.

So... stay tuned!

Edit: It's become clear to me that I shouldn't be talking so freely about 'ontology'. Here, by 'ontology' I mean whatever the theory is about, the 'reality' of the theory. There is a deeper philosophical question which is whether what the theory is about is also what constitutes the reality we live in, or whether reality is something else that just behaves in a way that's predicted by what the theory is about. The two points of view are called 'ontological' and 'epistemological', respectively, where now 'ontology' refers to the actual, physical reality. This debate is still widely open when it comes to the Copenhagen interpretation. Honestly, to me this question is a dead end: I can't even conceive of a way one could begin to resolve it. Thus, it was never my intention to go into these purely philosophical matters - in fact, I wanted to keep philosophy to the minimum and only talk about what is found within the well-defined framework of the 'standard' Quantum Mechanics. The main goal of the text, to summarize it in one sentence, is to explain that there is no objective 'being' in QM apart from the being of the wave function and the being of results of measurements. 

No comments:

Post a Comment