Consistent Histories (What's the catch?)

eloheim · Aug 18, 2012

I know this is a very general question, but I'm hoping someone well-versed in quantum theory is willing to provide an (appropriately general) answer.

Whilst investigating unrelated matters today I ran into a, "Brief Introduction to Consistent (Decoherent) Histories" which read (in part):

"The consistent histories approach combines wave functions and probabilities in a fully consistent way which does not rely upon the use of measurements"....."Histories can be used to describe how a particle interacts with a measuring apparatus, and how the outcome of a measurement (e.g., the position of a pointer) is related to some property of the particle before the measurement took place. However, they can also be employed for a single particle, or any number of particles, in the absence of any measurement. For example, by using consistent histories it is possible to assign a probability for the time at which an unstable particle, such as a radioactive atom, will decay, even if it is out in interstellar space far from any measuring device."

The above makes such an interpretation sound like a silver bullet against the ambiguities that appear pandemic to these kinds of discussions. From what little I've gathered on the topic (just in the course of other inquiries), I thought rigorously defining such histories (and identifying when decoherence takes over, etc.) was not[/] a trivial task. Can anyone tell me what the quoted author has left out, or the thinking behind such a rosy picture?

Thanks
Jeff

[source:http://quantum.phys.cmu.edu/CHS/histories.html] [Broken]

bhobba · Aug 18, 2012

There is no catch - like any interpretation on its own terms it resolves the issues. The basic problem is do you like its terms? To me (and I have to say CH is one of my favorite interpretations) its defining your way out of problems.

Thanks
Bill

Quantumental · Aug 18, 2012

There is a catch: it's indeterministic. Making it severily ugly

lugita15 · Aug 18, 2012

You're right, from that description you might think like consistent histories has little in the way of downsides. Here's an aesthetically undesirable (at least for me) feature of consistent histories, taken from the website you linked to:

What are frameworks, and what is the single-framework rule?
A framework or consistent family is a set of mutually-exclusive possibilities to which one can assign probabilities according to the rules of quantum theory. It is the analog of a sample space in ordinary probability theory. For example, the two possibilities +1/2 and -1/2 for the z component S_z of spin angular momentum of a spin-half particle are mutually exclusive and form a quantum framework. On the other hand, +1/2 for the z component and +1/2 for the x component S_x are incompatible in that it is meaningles to combine S_z=+1/2 and S_x=+1/2 in a single quantum description. The reason is that there is nothing in the quantum Hilbert space which can correspond to this combination, and assuming that S_z=+1/2 AND S_x=+1/2 makes sense leads to logical difficulties [4]. Values for S_z and S_x are not mutually exclusive in the sense that if one is true the other is necessarily false. Instead, they are non-comparable: trying to construct logical relationships between them does not make sense. Since they are not mutually exclusive, S_z and S_x cannot appear in the same framework. While S_z and S_x can be described by means of separate frameworks, these two frameworks are incompatible . One cannot combine a quantum description based upon some framework with a description based upon an incompatible framework, because the result would be meaningless (i.e., quantum theory can assign it no meaning). This is known as the single-framework rule.

Frameworks are used for families of histories as well as for quantum states at a single time. In this case, not only must the different possibilities be mutually exclusive, but they must satisfy consistency conditions in order that quantum probabilities can be assigned in a consistent way. Frameworks of histories that cannot be combined in a way that satisfies the consistency conditions are by definition incompatible, and once again the single-framework rule states that descriptions using incompatible frameworks cannot be combined.

Given two or more frameworks, which one provides the correct description of a quantum system?
There is no fundamental principle of quantum mechanics, no law of nature, that singles out one framework as the only possibility for a "correct" description. Consider a classical spinning body and a description, X, which assigns some value to the x component of its angular momentum L_x. Let Z be a second description that assigns a value to the z component of angular momentum L_z. Can one say that X rather than Z is the correct description? Clearly this would be silly. Instead one thinks of X and Z as part of a total description of the angular momentum that includes both of them. The case of a quantum spin-half particle is similar: it makes no sense to say that a description assigning a value to S_x is the correct description rather that a description that assigns a value to S_z. However, unlike the classical case, there is no total description that includes both S_x and S_z, for these two frameworks are incompatible and cannot be combined, due to the mathematical properties of the quantum Hilbert space.

In practice, physicists choose among the various possible quantum descriptions depending upon the question they want to answer. In the case of Schrödinger's cat there is a framework which is useful for answering (at least in a probabilistic sense) the question of whether the cat is dead or alive, and this framework is incompatible with the one corresponding to unitary time evolution according to Schrödinger's equation, which leads to a superposition state. Either description is a valid one from the perspective of fundamental quantum theory. On the other hand, they are not at all the same in terms of the sorts of questions that they allow one to address. If one employs the framework based on unitary time evolution, the question of whether the cat is dead or alive is not meaningful, since it is like asking for the value of S_z when S_x=+1/2 for a spin-half particle. Indeed, it does not even make sense to talk about a cat, since those properties that we normally associate with a cat (small furry animal with four legs and a tail, etc.) are incompatible with the description based on the superposition state.

It is worth emphasizing that as long as one is considering a particular physical question, such as the probability that the cat will be dead or alive, the multiplicity of possible frameworks causes no problem, for they will all give the same answer (for a given experimental situation, initial conditions, etc.) to the same question.

lugita15 · Aug 18, 2012

Quantumental said: ↑

There is a catch: it's indeterministic. Making it severily ugly

But that's true of most interpretations, other than things like Bohmian mechanics.

bhobba · Aug 19, 2012

lugita15 said: ↑

But that's true of most interpretations, other than things like Bohmian mechanics.

That's true. However my concern is the idea indeterminism is somehow objectively ugly - it aren't - any more than determinism is or isn't. That's simply a reaction some have when exposed to the theory and has nothing to do with its validity. I personally find a probabilistic theory very beautiful since it is more general than determinism which only allows probabilities of 0 and 1.

All interpretations have appealing features to some and sucks to others - that's why a consensus has never nor it is doubtful will ever be reached.

I have read a number of papers and books on Consistent Histories and they are all well written and argued. For an introduction to the mine field of interpretation you can do a lot worse.

Thanks
Bill

Quantumental · Aug 19, 2012

Bhobba, I disagree.
Indeterminism is immensly ugly philosophically.

Why would any sort of indeterminism follow a statistical law (Born rule) ? That needs explanation (cause) and then we are back at determinism. But no, people like that want to believe that the universe magically CHOOSE free willingly to follow a statistical law.
It makes absolutely no sense whatsoever.

In the history of science, determinism has ALWAYS triumphed and I would be genuinely shocked if it does not happen in QM too.
For me indeterminism is as likely as solipsism.

bhobba · Aug 19, 2012

Quantumental said: ↑

Bhobba, I disagree.
Indeterminism is immensly ugly philosophically.

And every philosopher would agree with that? If so it would be a first.

Quantumental said: ↑

Why would any sort of indeterminism follow a statistical law (Born rule) ? That needs explanation (cause) and then we are back at determinism. But no, people like that want to believe that the universe magically CHOOSE free willingly to follow a statistical law. It makes absolutely no sense whatsoever.

Well lets see shall we. Suppose we have some kind of observational apparatus with n possible outcomes. We have two possibilities - knowing everything about the system allows us to predict with certainty the outcome of the observation or it does not. If it does not then its quite reasonable the proportion of any outcome approaches a stable limit after a large number of trials in which case we have probabilities. If not then all hope is lost of actually making any kind of prediction. So what you are saying is why should nature allow us to at least make probabilistic predictions. Gee mate I don't know - but I am glad it does considering the alternative.

Also there are some very deep mathematical arguments suggesting QM is pretty much the only real way this can happen:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

As to why the Born rule - check out Gleason's theorem:
http://en.wikipedia.org/wiki/Gleason's_theorem
'Gleason's theorem therefore seems to hint that quantum theory represents a deep and fundamental departure from the classical way of looking at the world, and that this departure is logical, not interpretational, in nature.'

Although as Von Neumann noted in his proof of no hidden variables it also follows from the additivity of expectation values. Basicall this is very simple - if the average outcome of observable A is <A> and observable B is <B> then the average outcome of observable A + B is <A> + <B>. With that assumption Born's rule follows. But as Bell and others showed that assumption is not necessarily true for hidden variable theories. But still such additivity is a very very reasonable assumption - so reasonable it took a long time for it to be questioned.

Basically its the most reasonable probabilistic theory that allows continuous transformations between pure states.

Quantumental said: ↑

In the history of science, determinism has ALWAYS triumphed and I would be genuinely shocked if it does not happen in QM too. For me indeterminism is as likely as solipsism.

And why would nature care how likely you think something is?

Seriously though opinions are like bums and based on all sorts of things such as aesthetic sensibility, but while its important to hold opinions it does not make them correct. That applies very much to me and I would suggest to views like you expressed as well.

Thanks
Bill

eloheim · Aug 21, 2012

Thanks to everyone for the replies (I did not check back since the original posting). I'm getting that CH theories don't made definite predictions about the future, and that although they can say what sets of measurement/events fit together (in a history), they won't say WHICH one will be the "real" one?

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Consistent Histories (What's the catch?)

eloheim

bhobba

Staff: Mentor

Quantumental

lugita15

lugita15

bhobba

Staff: Mentor

Quantumental

bhobba

Staff: Mentor

eloheim