Quantum physics without probability?

[Johan0001]

Will we ever be able to describe the microscopic world , without using the notion of probability?
What are the boundaries and restrictions that require probability?
As technology , new particles, discoveries, dark matter etc materialize will we eventually be able to measure these discrete properties exactly as predicted. Or are we at a point where we are not allowed to know all the properties exactly , anymore, and probability is the end of the line.

your thoughts

 

[vanhees71]

According to quantum mechanics as known today, I think there is no way out of an inherently probabilistic behavior of nature. There are many debates about possible alternative interpretations of the quantum mechanical formalism, but so far these have lead to nothing useful for our understanding/description of nature. We know today from experiments, based on famous work by John Bell, that if there was a deterministic theory employing hidden variables, whose ignorance cause the need for probabilities in QT, leading to the same probabilistic results as quantum theory, it must be a non-local theory. This would be pretty complicated.

Of course, you can never know, whether QT will be proven wrong one day by (reproducible) observations, and maybe one will need another more refined description of nature, which might at the end be deterministic. Today, nothing like this is the case. Whenever quantum theory was put the experimental check, it was describing the observations perfectly, and these checks are among the most accurate measurements ever made (e.g., the violation of Bell's inequality predicted by quantum theory has been confirmed to an accuracy of more than 100 standard deviations. One example of such an experiment can be downloaded here:

http://arxiv.org/abs/quant-ph/9810003

 

[bhobba]

Will we ever be able to describe the microscopic world , without using the notion of probability?

Well we have this deep theorem called Gleason's theorem that shows if one part of QM is correct then probabilities are inevitable:
http://en.wikipedia.org/wiki/Gleason's_theorem

Its not impossible future progress will return determinism - but it looks highly doubtful.

Thanks
Bill

 

[tzimie]

... and there are hidden assumptions - "single history"
MWI is perfectly deterministic.

 

[Doc Al]

Even deterministic interpretations do not necessarily imply predictability. So probability remains essential to actually using the theory.

 

[DrChinese]

MWI is perfectly deterministic.

That's a stretch. There is certainly no explanation for the particular branch I am in right now other than to say every branch occurs.

Further: the normal use of the word "deterministic" implies there is but a single possible outcome for a specified set of initial conditions. That certainly does not occur in MWI.

 

[tzimie]

That's a stretch. There is certainly no explanation for the particular branch I am in right now other than to say every branch occurs.

Well, this is something about SSA or SIA (and BTW wiki claims SIA plays role in quantum cosmology). May be MWI is not complete without SIA, but it would mean that consciousness should be plugged in TOE on the axiomatic level.

But I am not sure if theory of consciousness belongs to any of the forum categories here. On the other side, I doubt it would be useful to discuss it with philosophers - too much blah bluh...

 

[bhobba]

... and there are hidden assumptions - "single history"
MWI is perfectly deterministic.

That's true - in MW probability is replaced by the issue of counterfactual definiteness, in that while completely deterministic you can't calculate which world will be experienced (that's the definition of couterfactual definiteness ie such is always calculable if it applies). One has to resort to some some kind of argument giving the likelihood of the world that will be experienced.

You haven't really avoided probabilities - simply given it a different basis.

Thanks
Bill

 

[DrChinese]

... while completely deterministic ...

How so? I do not follow this reasoning. How does the past lead to a specific future other than via the meaningless statement that every possibility occurs? In other words, what reasonable definition of determinism is involved in this labeling?

 

[bhobba]

How so? I do not follow this reasoning. How does the past lead to a specific future other than via the meaningless statement that every possibility occurs? In other words, what reasonable definition of determinism is involved in this labeling?

In MW you just have this very real universal wave-function and it evolves via the Schroedinger equation. Totally deterministic.

The interpretation is when you have decoherence the outcomes of the resultant mixed state are separate worlds. No collapse - nothing.

But which world will be experienced? The theory doesn't tell you that so one either postulates the Born Rule or you use some other argument like Gleason or the betting strategy of decision theory. Don't particularly like the betting strategy thing - its a bit too contrived for me - Gleason however is another matter.

Thanks
Bill

 

[bhobba]

There is certainly no explanation for the particular branch I am in right now other than to say every branch occurs.

This is a very common comment about MW.

There was a very long thread about it a while ago now:
https://www.physicsforums.com/threads/question-regarding-the-many-worlds-interpretation.706927/

MFB made some very pertinent points that actually changed my view.

Its basically the Baysian view of hypothesis testing. You have some process that while perfectly deterministic leaves some things up in the air. One then uses the Bayesian idea of updating the degree of belief.

Thanks
Bill

 

[bhobba]

But I am not sure if theory of consciousness belongs to any of the forum categories here.

Its got nothing to do with conciousness even though I tend to use words like what world would be experienced.

Dr Chinese has raised a very common issue with MW.

I have been though it many times - eg see that long thread I linked to above.

It won't be the last time it needs working through - nor do I think it will really resolve anything - but that's fine - its a legit issue.

Thanks
Bill

 

[Demystifier]

Well we have this deep theorem called Gleason's theorem that shows if one part of QM is correct then probabilities are inevitable:
http://en.wikipedia.org/wiki/Gleason's_theorem

The Gleason theorem does not say that probabilities are inevitable. Essentially, it says that if the quantum state defines a probability, then it is given by the Born rule. But it does not prove that quantum state must define a probability in the first place.

 

[tzimie]

Its basically the Baysian view of hypothesis testing. You have some process that while perfectly deterministic leaves some things up in the air. One then uses the Bayesian idea of updating the degree of belief.

Let me ask you, what is your answer to the Sleeping beauty problem? 1/2 or 1/3?
it came to my mind that it could be important because of the extreme degree of the "unfair sampling" of the reality we observe.

Regarding Baysian view, in infinite Universe there is no difference between Baysian and Frequentist views: Baysian probabilities just define how often we find that particular state.

 

[bhobba]

The Sleeping Beauty problem is a puzzle in probability theory and formal epistemology in which an ideally rational epistemic agent is to be woken once or twice according to the toss of a coin, and asked her degree of belief for the coin having come up heads.

My solution is its un-decidable because I attach the Kolmogorov axioms to probability so degrees of belief don't come into it.

As you probably suspect I am not enamoured with MW either - don't like conscious agent belief coming into anything. Although I am forced to admit its the most natural way of looking at Bayesian hypothesis testing.

Thanks
Bill

 

[bhobba]

The Gleason theorem does not say that probabilities are inevitable. Essentially, it says that if the quantum state defines a probability, then it is given by the Born rule. But it does not prove that quantum state must define a probability in the first place.

Yes - yes. Well said and true.

Gleason needs a number of assumptions to apply it and probabilistic outcomes is just one - the strong principle of superposition and non-contextuality are others.

But the argument of the MW guys is because the theory is ambivalent to which world you will experience probabilities is all you can have. In that long link I gave MFB argues its basically Bayesian hypothesis testing which after thinking about it I agreed with and think it's the best way of looking at it.

Thanks
Bill

 

[DrChinese]

In MW you just have this very real universal wave-function and it evolves via the Schroedinger equation. Totally deterministic.

The interpretation is when you have decoherence the outcomes of the resultant mixed state are separate worlds. No collapse - nothing.

But which world will be experienced?

I appreciate the argument, but to me* that is not determinism. Either there is no prediction as to which branch I am in upon collapse, or there are predictions that every branch exists (which is contradicted by failure to observe them). Either way, it is just words to say that counts as determinism. To me, this is what I call a "non-realistic" interpretation.*At least not in this branch. :)

 

[stevendaryl]

In MW you just have this very real universal wave-function and it evolves via the Schroedinger equation. Totally deterministic.

But probabilities are still involved in comparing theory to experiment, since the results of our experiments are nondeterministic from the point of view of the observer. That there might be a "bigger picture" that is deterministic doesn't change the fact that we observe is not this bigger picture, but an unpredictable part of it.

 

[bhobba]

I appreciate the argument, but to me* that is not determinism. Either there is no prediction as to which branch I am in upon collapse, or there are predictions that every branch exists (which is contradicted by failure to observe them). Either way, it is just words to say that counts as determinism. To me, this is what I call a "non-realistic" interpretation.

As I suspected you know the issues well.

All I can say is they are really hashed out in that long thread.

My view is that the Bayesian view of hypothesis testing cracks it.

I do have other issues with it such as the exponential dilution of the wave-function.

Thanks
Bill

 

[bhobba]

But probabilities are still involved in comparing theory to experiment

Of course. Its just viewed differently - as the objective confidence level of a rational agent.

Thanks
Bill