Understanding Randomness in Quantum Mechanics (QM)

[Descartz2000]

Can anyone give a really solid definition of 'random' as it relates to QM? It seems I am never quite sure what the researcher or writer is referencing when randomness is discussed, unless the terms are defined with clarity. However, it seems the terms are not often clarified.

 

[malawi_glenn]

same as in mathematical theory of probability and statstics.

 

[QuantumBend]

Can anyone give a really solid definition of 'random' as it relates to QM? It seems I am never quite sure what the researcher or writer is referencing when randomness is discussed, unless the terms are defined with clarity. However, it seems the terms are not often clarified.

You need this: Random Number is when NOT possible say next number with mathematics.
Here is Random Number: 127 and 287

 

[ueit]

You need this: Random Number is when NOT possible say next number with mathematics.
Here is Random Number: 127 and 287

Well, 287 = 127 + 160. Your example is wrong.

Generally, randomness implies a lack of pattern. However, for any finite sequence it impossible to prove that.

 

[QuantumBend]

finite sequence it impossible to prove that.

My number random NOT infinity = 127, 23, 834. Infinity is hotel problem - no good. Quantum has random and prooved.

 

[atyy]

Randomness in QM means that the outcome of individual experiments cannot be predicted. Only the average outcome of many, many experiments can be predicted.

There are some exceptions. For example, if 1000 identical particles are prepared in identical energy eigenstates, you can measure the energy of each particle, and you will get the same answer for all of them. But this is not true for all experiments. If instead of measuring energy, you can measure the position of each particle, you will find a different position for each particle.

 

[QuantumBend]

Randomness in QM means that the outcome of individual experiments cannot be predicted. Only the average outcome of many, many experiments can be predicted.

OK, I give you random number - 7, I know this. Why say you NOT? - no good.

 

[Tac-Tics]

Can anyone give a really solid definition of 'random' as it relates to QM? It seems I am never quite sure what the researcher or writer is referencing when randomness is discussed, unless the terms are defined with clarity. However, it seems the terms are not often clarified.

In QM, random just means that no one has yet found a theory that predicts the outcome of any particular experiment. To go a step further, most people believe such a theory cannot be found. In fact, the existence of such a theory would probably cause problems with relativity.

 

[Naty1]

Feynmann used to say "Shut up and calculate" since calculational methodologies were agreed upon, their meaning/interpretation by the people doing the calculations was not...and I think you may be in that foggy land.

Wikipedia says
http://en.wikipedia.org/wiki/Quantum_superposition

Quantum mechanics has the exact same rules for multiplying and adding numbers associated with (classical probability) events, except that the quantities are complex numbers called amplitudes instead of positive real numbers called probabilities.

The principle of superposition states that if the world can be in any configuration, any possible arrangement of particles or fields, and if the world could also be in another configuration, then the world can also be in a state which is a superposition of the two, where the amount of each configuration that is in the superposition is specified by a complex number.

So while I can't give a good answer to the original question, (solid definition of "random" the idea that quantum randomness is simply a reflection traditional "randomness" seems overly simplistic.

Also, I'm not sure where randomness and uncertainty intersect but there are a number of experimental results that are hindered by the latter: http://en.wikipedia.org/wiki/Quantum_uncertainty#Other_uncertainty_principles

So it would seem that while probability distributions would be calculated in a standard manner, the functions would not necessarily provide identically classical results...

Here's an interesting article: Quantum randomness may not be random (a minority view)
http://www.newscientist.com/article/mg19726485.700

And a different take:

Whenever a mathematical proposition is undecidable
within the axioms encoded in the state, the measurement associated with the proposition gives random outcomes. Our results support the view that quantum randomness is irreducible and a manifestation of mathematical undecidability.

http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.4542v1.pdf

Finally, Charles Seife in DECODING THE UNIVERSE, 2006 looks at physics from an information theory perspective...he notes

quantum information is much more pwoerful than ordinary information...a quantum bit has additional properties that are unavailable to the classical 1's and 0's...quantum objects can be two things at once...

and I can't find the quote but he says information based approaches to QM is beginning to unlock some of its mysteries...
and don't forget about entanglement...that ain't "random".

 

[csprof2000]

I'm not sure there is a rigorous definition of a random number... if you were to rigorously define it, you would be able to calculate it, and then it would by definition not be "random", no?

I think the right way to think about it is to talk about probability density functions and combinatorics. Maybe "random number" is just a colloquial and intuitive way of talking about perceived uncertainty? In mathematics, at least mainstream mathematics, you can't really have uncertainty per se. Who knows... maybe this is the wrong way to think about it.

 

[Fra]

I think the usual introduction of QM contains two points where it's easy to feel that a missing understanding exists.

1) One of the spirits of QM, is to focus on what you can measure. And unless you are able to perfectly predict the next measurement, then the idea is to instead predict the expectation. Ie. to predict how the measurements are expected to the distributed if you are about to repeat the experiment many times.

The obvious problem here is the that abstraction of picturing a statistical ensemble of a particular event really isn't very rigourour from the point of view of reasoning. There are many problems with this. First is the issues how you can duplicate one event, and know the conditions are the same. And even if you could do that, to repeat an experiment many times isn't enough, to find the exact probability distribution you need to repeat it an infinite of times, and how long time would such an experiment take. Also how can you store all the data from an infinite experiment series? Sometimes this "idealisation" is certainly good enough, but if you use such an abstraction at a very fundamental and general level of the theory, then it's easy to have objections IMHO.

If you try to consider that the abstraction of the ensemble really must be constructed by the observer, and supposed that the observer in this case is a small particle, then I think it's reasonable to expect that the limited capacity of such an observer, severly constrains the construction of this ensemble both complexity wise and time-wise (ie. computation wise, if you picture the universe a bit like a computer).

If such a suspicion proves to be valid (yet to be seen of course) then this reasoning will cause revisions of the entire probabiltiy abstraction used in quantum mechanics. It's not that it will go away, but I rather execpt the probability spaces themselves to become more observer attached(subjective) and also dynamical. At that point i would personally also expect that the notion of "randomness" becomes relative to the observer. IE. what appears to be a random sequence to one observer, could well seem non-random to another. The missing logic here is to see how this can be consistent, and still reproduce all the predictions of QM we have learned is right.

One could probably imagine that the "complexity" of the random-generator determines the degrees of randomness, and that an observers less complex(massive??) than the generator would simply be computation-wise, unable to with certainty distinguish the sequence from a random sequence.

This is the direction of progress I personally expect to come up.

2) The other thing is how the expectations and probabilities are combined, and calculated. Ie. the quantum logic vs classical logic. This is currently what's usually understood in the shut up and calculate way. But I expect that eventually there will be a more solid understanding of this.

Edit: When you think about this for awhile, you may start to think that the two points are connected. IE, could the revision of the notion of the probability abstraction, require also a revision of the "classical logic" and thus yield quantum logic - I think so. Hopefully this will also at some poing be more understood.

/Fredrik

 

[Descartz2000]

Thanks Naty1, I read the article on the minority view of the advances of Bohm's view. Very interesting. I had not read this article, but when I have read about the implicate and explicate order before from Bohm, his view always seemed to be a better fit for me rather than the Copenhagen view. I don't see how truly random variables can account for behavior. I have always thought for an event to be truly random, implies it is not accounted for by the larger Universe nor any of it's processes. If the building blocks of the Universe are truly random, how can we come to understand the order and patterns we see in micro and macro events?