Argument for quantum indeterminism

[alpha358]

If any application of probability and statistics doesn't imply that particular proces doesn't have deterministic laws, then how quantum physicists come up with an idea that determinism is false ?

P.S.
I am second year bachelor student of applied physics and I will have quantum physics course next year.

 

[mfb]

I don't think I get all those negations.
Experiments show that determinism does not work together with other reasonable things, like locality and causality.

 

[alpha358]

I don't think I get all those negations.
Experiments show that determinism does not work together with other reasonable things, like locality and causality.

If we can't find deterministic laws at some scale this doesn't mean that world is indeterministic. Is there any formal proof of indeterminism ?

 

[mfb]

Bell's theorem
Kochen–Specker theorem
You cannot prove indeterminism, but you can prove that it does not work together with other features you would like to have in a theory.

There are deterministic interpretations/variants of quantum mechanics like the De Broglie–Bohm theory, but they do not have other features like locality.

 

[alpha358]

So we are in interesting situation when neither indeterminism nor determinism can be proved ? Than why does some physicists in the media say that Einstein was wrong about God playing dice ?

 

[Nugatory]

If we can't find deterministic laws at some scale this doesn't mean that world is indeterministic. Is there any formal proof of indeterminism ?

The mathematical formalism of quantum mechanics is non-deterministic but, as you say, that doesn't prove that the world is really non-deterministic, it just means that this particular theory refuses to give us non-probabilistic answers.

However, if you google around for "Bell's Theorem" (and you could do worse than our own DrChinese's page at http://www.drchinese.com/Bells_Theorem.htm) you will find a very convincing argument: Any theory that is both local and deterministic must in some cases make different predictions than quantum mechanics; and these predictions have been tested experimentally and the results agree with QM, disagree with the local realistic prediction.

Note the qualifier "non-local" above. It is possible to construct deterministic theories that match the quantum mechanical predictions as long as they are non-local. There is also superdeterminism, but as it is carefully defnined to be indistinguishable from the nondeterminism that we observe in Bell-type experiments it doesn't much advance the discussion).

Disclaimer: I am playing a bit fast and loose here with words like "realistic" and "deterministic". The above is, IMO, a fair answer to your question, but if you want to seriously dig into the philosophical issues here (google for "interpretations of quantum mechanics") you'll want to be more rigorous in your terminology.

 

[Naty1]

The following quote is from Roger Penrose celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England...An interesting insight into quantum/classical relationships:

..Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrödinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrödinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity...

 

[alpha358]

Thank you for your time and effort, I will study quantum physics soon and very carefuly (checking what is really proved). Now I see that we don't have formal proof of indeterminism.
I am interested in truth no matter how it looks like - deterministic or not.

 

[bhobba]

Bell's theorem
Kochen–Specker theorem
You cannot prove indeterminism, but you can prove that it does not work together with other features you would like to have in a theory.

There are deterministic interpretations/variants of quantum mechanics like the De Broglie–Bohm theory, but they do not have other features like locality.

That's it.

But just to give a slightly different take another way of looking at it is via Gleasons theorem (Kochen-Sprecker is a simple corollary to that theorem):
http://en.wikipedia.org/wiki/Gleason's_theorem

You can't define a measure of 0 and 1 on a vector space which means you can't have determinism in the formalism of QM - it inherently is a probabilistic theory. There is an out - contextuality - ie what you measure is dependent on whatever else you are measuring at the same time.

Don't be too worried if you don't understand it right now - you will be able to grasp it better when your math and physics is a bit more advanced. Just take it that your question is quite deep and there is an answer - namely the formalism - with a bit of an out - implies it must be probabilistic - but you need to have a bit more of a background in math than you probably have right now to understand it.

But in case you have the background check out:
http://kof.physto.se/theses/helena-master.pdf

Thanks
Bill