quantum mechanics - How do we show that no hidden variable theories can replace QM?

I've always hit two big stumbling blocks in conceiving of the proof or disproof of hidden variable theories as being even valid idea, let alone an answerable question... I feel I must be misunderstanding some very fundamental things.

1. 
   

   Quantum mechanics is deterministic, ignoring the bit where we take our complex number and fudge it into a probability.

   
   


2. 
   

   We use computers to make calculations to provide the predictions of quantum mechanics - how is this not itself a hidden variable theory?

   
   

From what I understand the famous Bell theorem and work around it doesn't disprove hidden variable theories, just one specific flavour of them, and even then I am not convinced. I feel like I must be missing something again, because this result seems to me in no way profound... although it certainly fits into the picture of the EPR 'paradox' and is a good demonstration of the validity of QM.

I guess the crux of my problem is that this 'area' really addresses wave function collapse and the problems it causes, but I don't see the need for some collapse mechanism to begin with... again I feel like I am missing something really fundamental.

Apologies if this is a bad question. I have had a look around and there are similar questions, but I don't feel that either of my points are addressed...

Answer

Jherico, I see that you are keen in finding answers to your questions, or putting your views across for a debate, and this is really good. This is what science is all about. I think your questions deserve attention and proper debate.

Here is an effort from my side to help dilute some of the misunderstanding through the comments section of this forum.

(1) Your opening statement “Quantum mechanics is deterministic …”

The deterministic nature of QM is only in relation to the inherent structure of Schrodinger equation, which gives us the ability to predict the *probability for an event to take place. We can only predetermine probabilities, and this does not make QM deterministic in any way. Even if we had the most accurate Hamiltonian or Lagrangian (whatever we want to call it) we would still be calculating probabilities.

The probabilistic nature of QM is related to the fact that nature always has numerous options available to choose from, when she does something and, amazingly she picks just the right amount from each option and does a perfect job out of it!! ADMIRABLE + FASCINATING!!

(2) “We use computers …”

This has been answered by @Lubos Motl very well. I will only add the following: The use of computers to solve the complex problems in the quantum world is not a compromise over the richness of subtleties of QM. The algorithms used are of purely mathematical nature and only help us with the finding solutions to the complex mathematics involved in our problems. The hidden variables you are referring to probably relate to errors propagating and accumulating, and therefore might obscure the accuracy of the answers we obtain. But that is a purely computational problem and has nothing to do with the hidden variables physicists are referring to when they talk about hidden variables.

I hope I have cleared up some of the misunderstanding, and please do keep in touch with physics. You will find it is one of the most fulfilling enterprises undertaken by mankind.

Some discussion on Bell’s inequalities can be found in several places in this forum, but if you wish more detail you could try this book:

Speakable and Unspeakable in Quantum Mechanics (Any new edition)

Cambridge University Press

John S Bell;