coincidence :: does it exist?

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Quantum theory predicts quite a lot; Bell's Theorem is a good example. Are you familiar with it?

The notion that local hidden variables are not sufficient to fully explain waveform collapse was a prediction that no one was expecting, and which completely shook many people's notions of reality, including Einstein's himself. Note that the truth of Bell's Theorem is not dependent on any specific interpretation of quantum mechanics.

If you accept quantum mechanics, you must accept coincidences of the "we don't have enough information" variety. There is no alternative. Coincidences of the "there is no reason for it at all" variety are still up in the air, but the only way to get rid of the first is to deny QM altogether.

Jeremy

That's no problem to me. If we look at the history of human science the chances a theory will last for for ever is about 0. So ...

That sounds like the most accurate we can get to me.

I am to a point. Bell's theorem doesn't predict anything in itself. It merely states that predictions of quantum mechanics cannot be explained if one assumes locality.

There are other implied assumptions about the properties of stuff at the quantum level which go along with this.

Quantum mechanics itself doesn't predict events, it merely 'predicts' the rate at which certain events occur given enough samples.

Any theories which attempt to explain quantum phenomenon usually are in the form of experimentally falsifying logical suppositions, like Bell's theorem.



Experiments like, for example, the Stern-Gerlach experiment, do not in themselves imply any form of coincidence. Like ANY experiment or observation, we cannot interpret any event or pattern of events without prior theory stemming from an existing framework of knowledge. Now, the existing framework of knowledge may interpret the experimental results as coincidence, but in reality any number of assumptions could be challenged, including locality. That doesn't mean the only two scenarios are locality or coincidence.

Depends.

A theory deduced from a priori knowledge doesn't lend itself to experimental falsification.

A theory which says, for example, what goes up must come down, is different than one which says the preference of one good for another is determined by the marginal utility.

One is disproved by escape velocity, the other can only be disproven by finding a logical flaw or questioning the existence of a premise. If the logic is sound, it is true a priori and cannot be disproven a posteriori. In fact, everything in economics would be unintelligible without such theories as the numbers can be twisted into any kind of loose association of gibberish (which actually happens all the time, now that I mention it).

Of course in this case QM doesn't pretend to know what mechanisms are producing the measurable results, although some quantum theories make some falsifiable claims such as the inability to predict individual events.

It does if "coincidence" is defined as "an event which cannot be predicted or explained using available information," which is equivalent to how the first "yes" option in the poll is defining it. If local realism doesn't hold, then yes, that version of coincidence is a given for at least some events, either because of nonlocality or nonrealism.

Jeremy

An event disproving a specific theory only disproves that theory. It doesn't imply anything greater, like, for example, what part of the theory is at fault.

Events can't even be observed without a theory as to what to look for.

You have to expand on what you mean by events and information. You seem to be using information synonymously with theory, which it isn't, and events differently with information. None of these things exist independently.

It's tempting to take that position, but really, the days of a well-tested scientific model being completely abandoned more or less went out with the renaissance.

At this point, our experimental results for quantum mechanics or other major theories are thorough enough that, even if they are eventually shown to be incorrect, whatever theory replaces them will have to include them as a special case, just as special relativity includes Newtonian mechanics as a special case when large velocities are not involved.

If quantum mechanics is eventually disproved, whatever replaces it will a) be even stranger, and b) be "quantum-like" in most real-world situations.

Jeremy

It's difficult to disprove something which doesn't even provide explanations.

Ohms law breaks down too.

QM doesn't make many predictions which weren't a premise for QM to begin with. In other words the observations came first, then the snazzy mathematics which 'fit' the 'probabilities'.

At some sub-quanta level QM may also break down.

What I mean by "event" in this case is any quantum measurement, i.e. any action which causes a collapse of the waveform. What I mean by "information" is exactly that: information which will allow us to predict the outcome of the measurement.

For example, consider some of the major interpretations of quantum mechanics, and how a coincidence (i.e. an event which cannot be explained or predicted using available information) would manifest itself:

Copenhagen Interpretation: Coincidence exists because quantum measurements are assumed to be fundamentally nondeterministic.

Bohm Interpretation: Coincidence exists because measurements are sometimes dependent on nonlocal variables.

Everett "Many-Worlds" Interpretation: Coincidence exists because you don't know which "universe" you're in, so you can't know which possible outcome for the measurement you will experience.

Transaction Interpretation: As with Bohm, dependent on nonlocal variables.

Note that the reality of this type of coincidence doesn't depend on the interpretation. I included that list merely to show how each interpretation deals with the abolition of local realism, which is true culprit.

I should add that yes, my position is predicated on an acceptance of quantum mechanics. I feel that the experimental evidence is sufficient at this point that it's rational to do so.

Jeremy

Last edited by toddjh on 13 Dec 2005, 10:50 pm, edited 1 time in total.

No it's not. You just perform an experiment and show that the results disagree with the predicted values.

QM is famously not about explanations. It's about the math.



Entirely possible, but like I said, whatever theory replaces it will have to make very similar predictions on some scales in order to match our established experimental results. Hence, it will be "quantum-like," just as QM itself is "classical-like" on macroscopic scales.

Jeremy

This shows exactly everything wrong with QM. People who deal with QM, teach QM, learn QM in college etc. know nothing about epistemology.

You can't use the same term as meaning both what readings you catalog and how they are interpreted. And no, interpreted is not the same as information.

If the reading is labeled "coincidence," then there is no dispute if coincidence exists. You have already established it. The question is do you know what the hell you're looking at, not what "information" (as you curiously use the term) explains "coincidence."

By the way, information doesn't explain ANYTHING! Information isn't an explanation, it is historical data. There is no such thing as explanation-data, there are theories in a framework of knowledge. And before you ask, knowledge is not the same as information.

Information is like an event which occurred at a particular time. Explanation as to how information is related is never due to insufficient information. Insufficient information is a condition in which different theories cannot be ruled out.

You can't rule out coincidence with information unless "coincidence" is not an event, but a theory. So once again, please clarify what you mean.

You're getting too hung up on terminology. I find philosophical rigor too dry and tedious to describe, and I had more than enough of it in school, so instead I'm speaking English, which is perfectly appropriate on an internet forum. Are you really unclear about what I mean? I find that hard to believe, since you seem pretty intelligent.

Which part of what I'm saying do you have a problem with? My definition of coincidence as a quantum measurement whose value cannot be predicted, even in principle? My definition of local realism? My assertion that Bell's Theorem renders local realism incompatible with quantum mechanics? My acceptance of quantum mechanics in the first place?

Which step of my reasoning is the one that loses you?



I think maybe you're misunderstanding me. When I say that the result of a quantum measurement can't be predicted using available information, I mean exactly what you suggest: the observer cannot be in possession of historical data which allows him to predict the outcome of the measurement.



Honestly, I don't think I can be much clearer. An "event" is a quantum measurement. "Information" is historical data of some type; for the purposes of this example, assume that it consists of the numerical results of previous quantum measurements written on a piece of paper. A "coincidence" is an event whose outcome cannot be predicted using the available information.

As a real-world example, consider the measurement of the polarization of an entangled photon, when the other member of the entangled pair is a billion light years away. In order to predict the outcome of that measurement, we would need access to the status of the polarization of the other photon. Since we can't obtain that piece of data (even in principle, thanks to the speed of light limitation), we don't have the information needed to predict the outcome of our measurement. The measurement would thus be fundamentally unpredictable, and would therefore meet the criteria for being a "coincidence."

I hope that's clear, because I don't know how much more plainly I could describe it.

Jeremy

Again, QM doesn't predict events. It explains (on a purely mathematical basis) how tendencies occur based on some assumptions on the (again, mathematical) behavior of certain observable phenomena like 'spin'.



There is no theory which predicts what that measurement will be. QM doesn't predict events.

If that is your definition of "coincidence" then the fact you can't know if there is anything in my fist is a coincidence as well. The condition is fundamentally unpredictable, as you put it.

What QM predicts, if one also assumes locality and that the electrons have a condition of spin, is that the rate of both measurements being the same spin is greater than or equal to 5/9ths. The rate is actually 50%.

It's true that QM doesn't predict events -- BUT! -- if local realism were preserved, it would be conceivable that some future extension of QM might be able to. Einstein's famous "God does not play dice" comment reflects his hope that QM would eventually be amended in such a fashion.

But Bell's Theorem throws that idea out the window entirely. It makes explicit that no possible extension of QM could ever offer complete predictive power, and, conversely, any model which could predict the outcomes of all events would be fundamentally incompatible with QM. This is not a trivial thing.

Coincidences are not simply optical illusions created by the limits of QM's predictive power. The existence of coincidences is actually demanded by QM via Bell's Theorem.

Jeremy

Nobody ever suggested this measurement ought to be able to be predicted in the first place. We don't even know what is being measured, all we have is a set of measurements which can NOT be explained with QM AND locality.

There could easily be an underlying theory as to why measurements of spin in the same direction always agree and in a different direction agree less than would be implied given the assumption that spin is a property of an electron (whatever the heck an electron is). All QM does is provide a way to predict the rate of agreement. All Bell's theorem does is show that you cannot assume BOTH QM AND locality in the context of QM. This is mind-bending for some physicists because locality is a pillar of physics, but it has nothing to do with the ability to predict specific events.

As for your jibe about the existences of coincidences being demanded by QM, again, QM was derived to deal with this phenomena! It's like saying Newton's law of gravitation demands the existence of gravity.

Neither QM nor Bell's theorem suggest it is impossible to predict the instrument's spin measurement. All that is said is you cannot predict one given the other.

QM is a mathematical expression of observed measurements. You can't extend this framework to disprove its assumptions any more than Ohm's law.