# QM Interpretations and the Measurement Problem

• kote
In summary, the Duhem-Quine thesis is an assertion that all testable scientific theories must have an interpretation, and that any part of the theory besides the pure math belongs to the interpretation. The measurement problem is the unresolved problem of how (or if) wavefunction collapse occurs, and any interpretation leading to the measurement problem is either incomplete and in need of further exposition or is not self-consistent and is therefore wrong.
kote
In order to stop hijacking https://www.physicsforums.com/showthread.php?t=361216", I'll restart a discussion here about the role of background assumptions and the conceptual aspects of scientific theories, in particular how the "measurement problem" fits in with quantum mechanics and its interpretations. Rather than respond to posts out of context, let me start over with some background.

Wikipedia gives the following introduction to http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics" :
An interpretation of quantum mechanics is a statement which attempts to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has received thorough experimental testing, many of these experiments are open to different interpretations. ...

Although today this question is of special interest to philosophers of physics, many physicists continue to show a strong interest in the subject. Physicists usually consider an interpretation of quantum mechanics as an interpretation of the mathematical formalism of quantum mechanics, specifying the physical meaning of the mathematical entities of the theory.

Using Wikipedia's definition of an interpretation, we can consider it to be the conceptual framework that ties together the math of a theory and the relevant observations taken. It tells you what the physical meanings of your mathematical variables are. According to the Duhem-Quine thesis, it is a requirement of all testable scientific theories that they have an interpretation - a conceptual framework of auxiliary assumptions (Philosophy_of_science#Test_of_an_isolated_theory_impossible).

This is relevant to quantum mechanics in that a) we need an interpretation, and b) any part of the theory besides the pure math belongs to the interpretation. The experiments, of course, also are not part of the interpretation, but they can only be viewed through an interpretation.

As the lens through which one assigns basic ontological meaning to experiments, one's interpretation of QM is also his http://en.wikipedia.org/wiki/Paradigm#Scientific_paradigm").

If we can agree on the above, then I will make some claims for discussion. First, I claim that all work done in nonrelativistic quantum mechanics since Heisenberg and Schrodinger has been to either to verify or reformulate their math, or to shed light on interpretations. This would mean that Bohm, for example, came up with an interpretation, and not a new theory, using the language of philosophy of science defined above (this is also supported by Bohm calling his own work an interpretation). Am I getting the terminology wrong here? This is more of a question of semantics than a meaningful claim, but it's needed for further discussion.

Let's also take a look at http://en.wikipedia.org/wiki/Measurement_problem" :
The measurement problem in quantum mechanics is the unresolved problem of how (or if) wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the process under examination. Whatever that "something" may be does not appear to be explained by the basic theory.

Looking back at the definition of an interpretation, its role is to give physical meaning to the mathematical variables. It must determine which physical things match with which variables. According to the above version of the measurement problem, there exists, in wavefunction-collapse interpretations, a phenomenon (the "something") which we are unable to assign a physical significance to. This leads to my other thesis that any interpretation leading to the measurement problem is either incomplete and in need of further exposition or is not self-consistent and is therefore wrong.

Further evidence of this is that the measurement problem is not a function of QM itself, but of certain interpretations. The explanation of the problem above limits its scope to collapse interpretations. There are certainly also interpretations that claim to avoid any measurement problem. In http://plato.stanford.edu/entries/qm-bohm/" the following:
Hence, those physicists who accuse this interpretation of operating with a mysterious collapse of the wave function during measurements haven't got it right. Bohr accepted the Born statistical interpretation because he believed that the ψ-function has only a symbolic meaning and does not represent anything real. It makes sense to talk about a collapse of the wave function only if, as Bohr put it, the ψ-function can be given a pictorial representation, something he strongly denied.
Am I wrong that the measurement problem is a non-issue for QM as a whole? Is there some compelling reason I've missed to go with an interpretation that leads to the measurement problem? Does the measurement problem actually apply to more than just explicit collapse interpretations? Did the measurement problem just arise out of a misunderstanding of Bohr?

Please support your reply with literature or argument from literature as I have made an attempt to do. Let me know what I've gotten wrong or what needs more support or clarification.

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The bits of current interpretational machinery that I feel are the ingredients of some better interpretation would be decoherence (in some guise) and Cramer's transactional approach. The current interpretations aren't yet "crazy enough" and crazier approaches are the way. (MWI I just consider silly, and Bohm disproven by Bell's inequality).

So is there a collapse issue or not? Decoherence I believe puts collapse out where it belongs, in the world, occurring over all scales.

Then we need to get crazier with the "when" of when these collapses occur.

The collapse moment is a problem because it seen as an event that follows the development of a wavefunction. It "just happens" at some future instant of time with nothing in the preceeding wavefunction to act as the causal agent. So this is why it seems some human must come along in the future to make a decision to make a measurement, etc.

But transactional interpretations would say that - in effect - the collapse is about the creation of a classical spacetime pathway. So collapse does not happen "in" time. It is what creates a thread of classical time - one of the many such "event strands" which together would weave a dense fabric of spatiotemporal relations.

Taking an example like a photon crossing millions of lightyears from distant/ancient star to reach your eyeball tonight. Twin slit quantum eraser and other experiments would show that the nonlocal aspects of collapse are real. And in the transactional interpretation (or in my interpretation of that interpretation) what has happened is that nothing travelled, nothing moved, from the star to the eye. Instead, two locations in spacetime have just equilibrated their heat as a sum over histories over the spacetime path that was found to exist between them.

So the key idea here is that of equilibration. All spacetime locales want to be cooler in obedience to the second law. Exchanges then happen to achieve this and the result is the classical appearance of an emission and absorption which crosses spacetime at light speed. But what really happened is the other way round. The potential for this event to happen (an event with high probability given the heat of the star, the coolness of your eye, and the lack of anything much else inbetween) is what created a definite fragment of spacetime.

This is the local scale view. Two locales, two atoms, click and there is a spacetime path now added to the developing fabric of the universe. But then this same activity is going on over all scales, and most such interactions will in fact be very shortrange. So in the time it took the star to hook up to your eye, there will be a dense history of other things that have happened inbetween, and which this particular photon exchange will have to pass through. For example, some experimenter might have set up a twin slit experiment inbetween. This will become part of the history of the universe that you and the star will have to sum histories over.

So collapse is part of the machinery of the universe. It happens over all scales. But mostly it happens over very short scales and so there is a dense and stable core of history that other slower to collapse exchanges have to pass through on the way to their own collapse and thus contribution to the further writing of the universe's history.

And the collapse is not something that happens at the end of the trail. The collapse is the forming of the trail. It is part of the nonlocal aspect of reality rather than a part of the local. It is outside time rather than being itself an event in time.

You may of course consider this nonsense. But I think it is a little story that at least brings attention to one of the assumptions about collapse - that it is event-like and happens as some local action that changes things irreversibly at some point in time.

But why can't collapse be wrapped up in the non-local aspects of QM?

Again in summary, between any two points in spacetime, there will be some probability of an exchange event. And for a star, it will have already factored in all the future things that do happen between it and your eyeball. Yet there is still some probability of that being the event that does happen (rather than other potential fates like interacting with that dust particle in the upper atmosphere first). Then if the event does happen, you register the ancient photon, that becomes another definite fact that all other developing facts must now pass through in determining their own probabilties.

Bohm's apporach is only somewhat "realistic" as it incorporates nonlocality.

"Bohmian mechanics is manifestly nonlocal: The velocity, as expressed in the guiding equation, of anyone of the particles of a many-particle system will typically depend upon the positions of the other, possibly distant, particles whenever the wave function of the system is entangled, i.e., not a product of single-particle wave functions. This is true, for example, for the EPR-Bohm wave function, describing a pair of spin-1/2 particles in the singlet state, analyzed by Bell and many others. Thus does Bohmian mechanics make explicit the most dramatic feature of quantum theory: quantum nonlocality."

http://plato.stanford.edu/entries/qm-bohm/

I have rasied this question here and in the QM forum but didn't get an answer - What do proponents of BM mean by "realism" that is coupled with nonlocality? This obviously isn't the local realism in which we go to restaurants, or drive our cars, etc. How is realism defined in BM? As far as i am able to understand their position, they are saying "everything is real but in a completely new way that needs yet to be worked out".

Bohm believed in the oneness of reality, that at some sub-level, its all one unbroken wholeness(his 'implicate order').

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Wavejumper,

I think Bohmian mechanics serves as a deterministic foundational intepretation. Hence it is really a philosophical statement because it asks us to not accept qm at face value with all its uncertainty, but instead creates a background framework where a particle has a defined position or momentum before measurement/observation.

Bohmians (post Bells' theorem) dropped the hidden variables re locality because otherwise they would have had to drop the determisntic side of their interpretation. So they sacrficed locality for realism.

Or that's how it seems to me.

Coldcall said:
Wavejumper,

I think Bohmian mechanics serves as a deterministic foundational intepretation. Hence it is really a philosophical statement because it asks us to not accept qm at face value with all its uncertainty, but instead creates a background framework where a particle has a defined position or momentum before measurement/observation.

Bohmians (post Bells' theorem) dropped the hidden variables re locality because otherwise they would have had to drop the determisntic side of their interpretation. So they sacrficed locality for realism.

Or that's how it seems to me.

That's exactly what i stated in my previous post. However my confusion remains about the term "nonlocal realism"(which, by the way, was refuted to a large extend by Zeilinger and co. in 2007. See http://arxiv.org/abs/0704.2529, http://www.nature.com/nature/journal/v446/n7138/abs/nature05677.html).

What exactly is nonlocal "Realism"? What kind of "realism" is this, if our classical notion of locality(a fundamental postulate of GR) is violated(the speed of light)? It seems Bohmians ascribing "realism" to their theory are trying to make Einstein look like an idiot for fighting QM for its apparent nonlocality(that by any sensible human standard also violates realism).

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WaveJumper said:
That's exactly what i stated in my previous post. However my confusion remains about the term "nonlocal realism"(which, by the way, was refuted to a large extend by Zeilinger and co. in 2007. See http://arxiv.org/abs/0704.2529, http://www.nature.com/nature/journal/v446/n7138/abs/nature05677.html).

What exactly is nonlocal "Realism"? What kind of "realism" is this, if our classical notion of locality(a fundamental postulate of GR) is violated(the speed of light)? It seems Bohmians ascribing "realism" to their theory are trying to make Einstein look like an idiot for fighting QM for its apparent nonlocality(that by any sensible human standard also violates realism).

Yes i think Zeilinger is doing great work.

I have no idea how they explain or make sense of the idea of a non-local realism. Problem is they keep moving the gola posts which sort of makes me sceptical from the word go.

In contrast Bohr's Copenhagen is today as relevant as it was when he formulated it without any need for tweaking or back-pedddling.

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Coldcall said:
Bohmians (post Bells' theorem) dropped the hidden variables re locality because otherwise they would have had to drop the determisntic side of their interpretation. So they sacrficed locality for realism.

Bohm was always nonlocal from 1952. I think the realism in the Bohmian interpretation (I'm careful not to call it Bohm's interpretation) refers to the EPR criterion for reality and the objective persistence of properties. I absolutely agree that denying locality seems to get us further from naive realism than denying "realism." I just meant to bring up Bohm in regard to the measurement problem, since I can't see how there is any measurement problem for Bohmians. I'd join another thread on Bohm and "realism" in QM though .

## 1. What is the Measurement Problem in Quantum Mechanics?

The Measurement Problem refers to the paradoxical nature of the collapse of the wave function in quantum systems when they are observed or measured. This phenomenon is not fully understood and has been a topic of debate among physicists for decades.

## 2. What are the different interpretations of Quantum Mechanics?

There are several interpretations of Quantum Mechanics, including the Copenhagen interpretation, the Many-Worlds interpretation, the Pilot-Wave Theory, and the Transactional interpretation. Each of these offers a different explanation for the measurement problem and the nature of reality in the quantum world.

## 3. How does the Copenhagen interpretation explain the Measurement Problem?

The Copenhagen interpretation, proposed by Niels Bohr, states that the wave function of a quantum system collapses upon measurement, and the observer plays a crucial role in this collapse. It suggests that the observer's interaction with the system causes the collapse, and the outcome of the measurement is probabilistic.

## 4. What is the Many-Worlds interpretation of Quantum Mechanics?

The Many-Worlds interpretation, proposed by Hugh Everett III, suggests that every possible outcome of a measurement exists in a separate parallel universe. It explains the measurement problem by stating that the observer's measurement causes the universe to split into multiple parallel universes, each with a different outcome.

## 5. Is there a consensus on which interpretation of Quantum Mechanics is correct?

No, there is no consensus on which interpretation of Quantum Mechanics is correct. Each interpretation has its own strengths and weaknesses, and it ultimately depends on the individual's philosophical beliefs and interpretation of experimental results. Some scientists believe that a combination of these interpretations may be necessary to fully understand the quantum world.

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