Brief introduction to Quantum Foundations

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Brief Introduction to quantum foundations

Shivnag 
IISc, Bangalore

In this post, I shall attempt to briefly examine some of the foundational issues of quantum mechanics (which I will abbreviate as QM for convenience). I think it is a good idea to remind the well-experienced practitioners of QM every now and then the fact that they don't really understand what they are working with. That is, this post serves to remind us of the fact that QM is, at its heart, quite messed up. On a more pragmatic note, with all the talk about entanglement-this and entanglement-that (every guy on the street who has heard the word “quantum” has probably heard of it attached to the word “entanglement”), it is perhaps a good idea to understand what exactly entanglement is and what's the big deal about it. If you do wish to pursue these issues in more details, you inevitably arrive at the doorstep of quantum computation and quantum information, but that's for a later day (and a later post). So, let's get started!

Setting the Stage

First off, what are the features of quantum mechanics you found most annoying when learning about it in your sophomore (or was it junior) year? Most of us would agree that it was rather unsettling to see that QM answers to questions like “What precise outcome do we observe when we make a measurement?” by giving a set of possible outcomes and telling us the likelihood of each outcome. That is, if you were to perform the same experiment a million times under identical conditions, you could use QM to conclude how many of those times you'd get outcome A or outcome B, or you might be able to say that outcome C is ruled out because it is not in the set of allowed outcomes predicted by QM. While this is progress in itself, it begs the question, “Why can't I predict the precise outcome of any one experiment?” The first thing that we are told in our QM courses is that the problem is qualitatively different from say, the problem with predicting whether you get heads or tails on a coin toss. In principle, you could predict the outcome of a toss if you knew the exact mass distribution of the coin, the exact angular velocity with which it is flipped, the exact pressure distribution of air molecules which create drag on the coin etc. In addition to knowing every last detail about the coin, its surroundings and how you toss it, you'd need to have a computer powerful enough to process all that information (and preferably do it before the coin landed back in your hand). Needless to say, we'll not be discarding our method of using coin tosses to decide who bats first anytime soon. However, what's important is that it can be done.

However, we are told that the situation is different in QM. That is, it isn't a technological limitation that is preventing us from predicting the outcome of a single run of an experiment. The uncertainty is built into the physical laws. That is, no matter how powerful a computer you build, you'll not be able to predict the outcome of a quantum measurement precisely. Naturally, the first question that comes to mind is, “How are we sure that QM is the whole story?” And I am not posing this question in any deep, philosophical sense (that's for later). The most pedestrian objection one can have to this line of thought is, “Isn't it possible that QM is not capable of understanding some interaction (or missing something else) and that's the reason why it fails to predict precise outcomes?” Or one may wonder, “Maybe nature has some additional variables that need to be measured and fed into our mathematical machinery to get precise predictions?” Both these questions are important, and both bothered physicists and philosophers alike over the past century. Also, if the answer to either question is a yes, then that would mean that QM is incomplete or worse, wrong. The latter is unlikely because we have verified the predictions of QM countless times in numerous situations. You are doing it right now as you read this - for instance, QM provides the theoretical framework for understanding and working with the semiconductor electronics which power your computer. However, it surely can be incomplete, and one school of thought is to try and probe (no pun intended!) the question of how measurement works in quantum mechanics. This might not be as futile a venture as people these days make it to be. After all, Einstein arrived at special relativity, by examining the question of how you measure distances and times (that's what led him to conclude that simultaneity is not an absolute concept). The same could be true for quantum mechanics too, because the truth is, we don't have a good idea as to what exactly constitutes a measurement in quantum mechanics.

I will try to make some progress in this direction by trying answer the two questions I posed above. I will start with the second one - that is, the question of whether there are variables in Nature which haven't been observed and which, if observed, could eliminate the uncertainties in quantum mechanics. In fact, Einstein & co. believed that this was indeed the case and the great lengths they went to in order to prove their point is the stuff of legends. The argument that Nature has hidden variables that we have not (or cannot) observe go by the rather unimaginative name of “hidden variable theories”. I will examine their argument in the next post and see how (if at all) this argument can be verified.