The formalism of the quantum theory leads to results that agree with experiment with great accuracy and covers an extremely wide range of phenomena. As yet there are no experimental indications of any domain in which it might break down. Nevertheless, there still remain a number of basic questions concerning its fundamental significance which are obscure and confused. Thus for example one of the leading physicists of our time.

M. Gell-Mann has said “Quantum mechanics, that mysterious, confusing discipline, which none of us really understands but which we know how to use”.

Just what the points are that are not clear will be specified in detail throughout this book, especial- ly in chapters 6, 7, 8 and 14. We can however outline a few of them here in a preliminary way.

1. Though the quantum theory treats statistical ensembles in a satisfactory way, we are unable to describe individual quantum processes without bringing in unsatisfactory assumptions, such as the collapse of the wave function.

2. There is by now the well-known nonlocality that has been brought out by Bell in connection with the EPR experiment,

3. There is the mysterious ‘wave-particle duality’ in the properties of matter that is demonstrated in a quantum interference experiment.

4. Above all, there is the inability to give a clear notion of what the reality of a quantum system could be.`

All that is clear about the quantum theory is that it contains an algorithm for computing the probabilites of experimental results. But it gives no physical account of individual quantum processes. Indeed, without the measuring instruments in which the predicted results appear, the equations of the quantum theory would be just pure mathematics that would have no physical meaning at all. And thus quantum theory merely gives us (generally statistical) knowledge of how our instruments will function. And from this we can make inferences that contribute to our knowledge, for example, of how to carry out various technical processes. That is to say, it seems, as indeed Bohr and Heisenberg have implied, that quantum theory is concerned only with our knowledge of reality and especially of how to predict and control the behaviour of this reality, at least as far as this may be possible. Or to put it in more philosophical terms, it may be said that quantum theory is primarily directed towards epistemology which is the study that focuses on the question of how we obtain our knowledge (and possibly on what we can do with it).

It follows from this that quantum mechanics can say little or nothing about reality itself. In philosophical terminology, it does not give what can be called an ontology for a quantum system. Ontology is concerned primarily with that which is and only secondarily with how we obtain our knowledge about this (in the sense, for example, that the process of observation would be treated as an interaction between the observed system and the observing apparatus regarded as existing together in a way that does not depend significantly on whether these are known or not).