http://arxiv.org/abs/1104.2822

A real ensemble interpretation of quantum mechanics

Lee Smolin

(Submitted on 14 Apr 2011)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the centre of masses of large macroscopic systems do satisfy Newton’s laws.

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What is a “beable”?

The term beable was proposed in (Bell 75) as a replacement in quantum physics of the traditional term observable.

http://ncatlab.org/nlab/show/beable

esselte said:

What is a “beable”?

Something which it is (physically) possible to be.

From ChrispenEvan’s link:

“The term beable was proposed in (Bell 75) as a replacement in quantum physics of the traditional term observable. While the latter is typically given a precise mathematical meaning which does express the way in which the physical system may be, the word “observable” alludes to the complicated and subtle issue of something (a quantum measurement device) or even somebody (a concious experimentor) “observing” these ways of the system to be. The point of the term “beable” is to help conceptually cleanly separate the being of quantum systems from whatever it means to observe them….

“In practice of theoretical physics most every time one writes “observable” it should, by this logic, rather be “beable”. While this might be reasonable, as a convention of conversation it has not been picked up.”

Hmm. Interesting. Never heard of it before.

Thanks.

Lee Smolin said:

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles.

It may be helpful to compare & contrast this view point with that of the Many Worlds interpretation (MWI) of QM.

Say we have an atom of a radioactive isotope with a half-life of one hour. In MWI we have an ensemble consisting of all the “copies” of this particular atom in all the different branch universes, and we say that at the end of an hour the atom will decay in half of the branches.

In Smolin’s approach, our ensemble is simply all of the other atoms of this isotope in our (Single World) universe, and certainly, half of those atoms will have decayed by the end of the hour. On the one hand, this seems more sensible than invoking the branch universes MWI, OTOH, it seems to imply some kind of non-local connection between all particles of a given type (whether fundamental or composite) throughout space and time. And it’s tricky to do that without breaking relativity, or using some kind of hidden variables, in violation of Bell’s Theorem . You can get around Bell’s Theorem by using non-local hidden variables, but to most physicists that smells like magic or God…

This approach isn’t exactly new; I pondered it myself in my early twenties, and IIRC, Smolin’s buddy David Deutsch has played with this idea. But maybe Smolin has done something more rigorous with it…

ICIINO, it is pronounced to rhyme with “seeable”, not “feeble”.

PM 2Ring said:

You can get around Bell’s Theorem by using non-local hidden variables, but to most physicists that smells like magic or God…

Don’t know why. It seems to me the simplest hypothesis that fits the evidence.

BTW, I hadn’t heard of beables either (and neither has the IE spell-chequer it seems).

Is it pronounced be-ables, or like Beatles?

The Rev Dodgson said:

BTW, I hadn’t heard of beables either (and neither has the IE spell-chequer it seems).

Is it pronounced be-ables, or like Beatles?

See my prev post

esselte said:

http://arxiv.org/abs/1104.2822

A real ensemble interpretation of quantum mechanics

Lee Smolin

(Submitted on 14 Apr 2011)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the centre of masses of large macroscopic systems do satisfy Newton’s laws.

—————————————————

What is a “beable”?

A Zaphod? as in “Beablebrox”?

bob(from black rock) said:

A Zaphod? as in “Beablebrox”?

Could be.

Hadn’t thought of him.