Is the measurement problem equally as vexing as entanglement?

[bland]

TL;DR Summary

To this day there is endless discussion about the foundations of quantum mechanics with regard to the measurement problem. However there does not appear to be much consternation about how two particles are entangled. Why?

Maybe I've got this wrong, because from what I've been able to glean, how a particle measurement affects another particle which can be on the other side of the Universe in principle is agreed to be 'spooky' and it seems that everyone is happy to simply say, yes this is very mysterious and strange but we've done the tests and it appears to be a fact.

Yet it seems to me that the collapse of the wave function and the foundational question about what constitutes a measurement, is an endlessly opined problem.

Why is it that entanglement does not appear to cause as much foundational consternation as measurement, when in some respects they appear to be similarly problematic.

 

[bobob]

I don't see that entanglement is problematic. It doesn't violate causality. I really think in this case, the problem isn't even quantum mechanics, but relativity. The starting and ending points of two photons produced by entanglement are separated by a proper time and proper distance of ZERO no matter what their spatial seperations are in any frame. Because they are spacelike seperated, the mesurements cannot even be time ordered, so your supposition about one particle being here and one there and having any sort of time ordering with respect to measuring them is already flawed and has nothing to do with quantum mechanics. There will always be frames in which they are measured at the same time and in wheich either one is measured before the other. Relativity tells you there can be no cause and effect relationship, not quantum theory and it has been shown repeatedly by experiments that there is no cause and effect relationship in entaglement.

I think the better question is what is quantum mechanics telling us that attempts to explain it in terms of what we perceive are misguided. People resisted relativity for a long time by clinging to the idea of an ether until it was better understood as geometry. So, some things may be "problematic" with quantum theory, but what the problem is mostly depends on the solution one wants to think solves it.

 

[Nugatory]

To this day there is endless discussion about the foundations of quantum mechanics with regard to the measurement problem. However there does not appear to be much consternation about how two particles are entangled. Why?

As far as the theoretical formalism of quantum mechanics is concerned, there's no great problem with entanglement. The quantum mechanical predictions are unambiguous and supported by a century or more of experimental evidence - the theory works just fine as an accurate description of how the universe behaves. Yes, this behavior is inconsistent with our classical intuition about how the universe ought to work, but that just goes to show that our classical intuition is a poor guide.

The measurement problem (loosely understood as, how do we get from the quantum mechanical prediction that various outcomes have various probabilities to the experimental fact that only one outcome is observed) is different. There's nothing in the mathematical formalism of the theory that says it has to be that way or that suggests that leap; one way or another an additional ad hoc and not especially natural assumption is required.

 

[bland]

... The quantum mechanical predictions are unambiguous and supported by a century or more of experimental evidence - the theory works just fine as an accurate description of how the universe behaves..

Yes I get that, however is it not so that Bell type experiments proved that with regards to entanglement that the effect is 'non local' and it's this very non locality that bothered Einstein. Isn't non locality a puzzlement, that cannot be explained, only predicted?

Also yes I see that the collapse of the wave function is a different problem, but my point was that generally it's not any sort of a problem for people who need to work with quantum mechanics because it all works out fine, it's just a problem for people who want to have an explanation. However I do not see that there's any 'explanation' for how non locality works, other that it does work.

To be more clear, I do hear that there is a measurement problem that needs explaining to everyone's satisfaction, but I never hear anyone wanting non locality to be explained, asking 'what in the hell is this mysterious connection'. Or are you saying that aspect really isn't a problem at all?

 

[f95toli]

Yes I get that, however is it not so that Bell type experiments proved that with regards to entanglement that the effect is 'non local' and it's this very non locality that bothered Einstein. Isn't non locality a puzzlement, that cannot be explained, only predicted?

Because there is no real "puzzlement". There are many things in QM (and other areas of physics) that are counter-intuitive and does not agree with our experience of the "classical" world. However, this does not mean that there is a problems or that there is anything to "explain" as such.
Also, entanglement (like so many other things) is something you sort of get used to when you work with it on a daily basis. This might be another reason for why most physicists do not worry much about it.

 

[vanhees71]

The measurement problem (loosely understood as, how do we get from the quantum mechanical prediction that various outcomes have various probabilities to the experimental fact that only one outcome is observed) is different. There's nothing in the mathematical formalism of the theory that says it has to be that way or that suggests that leap; one way or another an additional ad hoc and not especially natural assumption is required.

Physics is an empirical science. There's a mathematical formalism, which doesn't tell you anything about the physical meaning of the symbols and the manipulations with them used in this formalism. The interpretation of these symbolism is given by observations, and all observations made with great precision up today tell you that any measurement has a definite outcome within the accuracy of the measurement device and that all that can be predicted, given an experimental setup (a preparation procedure of the measured object and a measurement procedure to measure an observable on the so prepared object) are the probabilities for the outcomes of the corresponding measurement. This is just what 120 years of quantum physics has boiled down to, and the conclusion simply is that nature is not deterministic, i.e., there is irreducible randomness. Whether or not this is "a compete description", we can never say with certainty. Up to now there's no "better" theory than QT.

 

[Demystifier]

Why is it that entanglement does not appear to cause as much foundational consternation as measurement, when in some respects they appear to be similarly problematic.

One should distinguish entanglement from correlations described by entanglement. Entanglement does not depend on the probabilistic interpretation of the wave function, while the correlations do. (Entanglement is just a mathematical property that the state of the full system is not a product of states of the subsystems.) Hence in quantum foundations entanglement is not problematic, while correlations are.

 

[DrChinese]

To be more clear, I do hear that there is a measurement problem that needs explaining to everyone's satisfaction, but I never hear anyone wanting non locality to be explained, asking 'what in the hell is this mysterious connection'. Or are you saying that aspect really isn't a problem at all?

As a useful description of quantum behavior, there is no specific problem with Quantum Mechanics as regards entanglement.

Some of what you are asking really comes down to interpretations, which is a subforum of Quantum Physics here. You will find that the answers you seek vary according to certain assumptions each scientist makes. For many top scientists, the question of "quantum nonlocality" (as opposed to "nonlocality" per your terminology) is in fact an open question of importance. The issue for them being "how" it manages to operate in apparent violation of relativistic spacetime limitations. Others - especially amongst the "shut up and calculate" contingency - see no problem at all. The issue for them being that there are detail descriptions of how to calculate expected correlations that match experiment within suitable limits.

So there is no single correct answer.

 

[atyy]

The measurement problem arises because of the Born rule. Measurement is a physical process, yet it cannot be completely included in the quantum description. Is there a lawful physical description of the whole system, including all measurement apparatus?

Hidden variables are an approach to solving the measurement problem. Entanglement and non-commuting observables mean that the hidden variables cannot be local.

 

[vanhees71]

There can be a description including the measurement apparatus, but as with any macroscopic system you have to use quantum statistical methods to describe the macroscopic relevant observables. Also one should add that entanglement is not somehow a problem of quantum mechanics but a feature since it describes very accurately what's observed, whenever entanglement can be prepared and maintained long enough to be observable. Experimentalists are more and more successful with that, which explains why today there's a rapid devolopment in quantum information theory, including practical applications as quantum cryptography and quantum computers.

Also Born's rule is not a problem but one of the basic postulates of quantum theory that makes its application to real-world observations possible. The "problem" of some people simply is that they still cannot accept that Nature behaves inherently random in a specific sense described by quantum theory, but Nature doesn't care about which worldview suits our prejudices ;-).

Whether or not there's a (then indeed necessarily non-local) hidden-variable theory that is as successful as QM is, imho, an open question. For non-relativistic QT there's at least a working example, Bohmian mechanics. For the relativistic case, I don't see a convincing version thereof yet.

 

[atyy]

There can be a description including the measurement apparatus, but as with any macroscopic system you have to use quantum statistical methods to describe the macroscopic relevant observables. Also one should add that entanglement is not somehow a problem of quantum mechanics but a feature since it describes very accurately what's observed, whenever entanglement can be prepared and maintained long enough to be observable. Experimentalists are more and more successful with that, which explains why today there's a rapid devolopment in quantum information theory, including practical applications as quantum cryptography and quantum computers.

Also Born's rule is not a problem but one of the basic postulates of quantum theory that makes its application to real-world observations possible. The "problem" of some people simply is that they still cannot accept that Nature behaves inherently random in a specific sense described by quantum theory, but Nature doesn't care about which worldview suits our prejudices ;-).

Whether or not there's a (then indeed necessarily non-local) hidden-variable theory that is as successful as QM is, imho, an open question. For non-relativistic QT there's at least a working example, Bohmian mechanics. For the relativistic case, I don't see a convincing version thereof yet.

That is self-contradictory - quantum theory does not describe how Nature behaves - it describes what we are able to predict about Nature (excluding the observer).

 

[vanhees71]

This you can say about any physical theory, i.e., also classical physics. Of course, all physics does is to describes how we observe Nature's behavior using all kinds of measurement devices to extend our "natural senses" and enable a quantitative description.

The point is that all the quantum theoretical predictions, including the "irreducible randomness" for the outcome of measurements given a state preparation, are well confirmed by all observations. This also includes Born's rule. In this purely natural-science sense there are no problems with quantum theory as a physical description how nature behaves according to our human ability to observe her. What's thought by obviously still many people to be problems with the foundations of quantum theory is purely philosophical.

 

[Tendex]

This you can say about any physical theory, i.e., also classical physics. Of course, all physics does is to describes how we observe Nature's behavior using all kinds of measurement devices to extend our "natural senses" and enable a quantitative description.

I think that if measurement itself cannot be included in any physical theory description so far this should be acknowledged and properly explained why(in order to find some way around it) in the mathematical/scientific sense, rather than trying to ignore it/deny it.

 

[vanhees71]

Of course is measurement included in the physical description. How else than using the laws of nature found by nature could you ever construct any measurement device? This of course also includes a description of how the measured objects interacts with the measurement device and how this interaction implies that the device measures what you intent to measure. E.g., the detection of photons with a CCD detector is based on the photoelectric effect, and this is well described by QT and this implies that you indeed detect a photon with such a device. Nothing is ignored here. The only point I want to make is that there are no fundamental problems with measurements from a scientific point of view. The very success of the application of quantum theory to both enabling the experimenter to construct adequate measurement devices and the prediction of the measured data shows that absence of problems.

For some people there are epistemological problems with the probabilistic worldview QT implies, but that's an issue of philosophy (or maybe psychology or even religion?) but not of the natural (and engineering!) sciences per se.

 

[Tendex]

Of course is measurement included in the physical description. How else than using the laws of nature found by nature could you ever construct any measurement device? This of course also includes a description of how the measured objects interacts with the measurement device and how this interaction implies that the device measures what you intent to measure. E.g., the detection of photons with a CCD detector is based on the photoelectric effect, and this is well described by QT and this implies that you indeed detect a photon with such a device. Nothing is ignored here. The only point I want to make is that there are no fundamental problems with measurements from a scientific point of view. The very success of the application of quantum theory to both enabling the experimenter to construct adequate measurement devices and the prediction of the measured data shows that absence of problems.

The results of measurements are of course included in the physical description, we are talking about measurement included in the physical system description beyond just the Born rule as an axiom. The main reason to be concerned about this is that the math that describes the theory must use mathematical spaces and fields in those spaces, and the consistency of those objects rests upon being able to describe in the same system the concept of measurement and measurement apparatus together with what is measured and its outcomes. We know for instance that Fock space is not enough to describe all this for the actual physics of Nature(interacting fields and measurements). So does this really seem to you a philosophical/psychological question or a mathematical physics one? Is now the Clay Institute concerned with psychological problems?

 

[vanhees71]

I never understood the obsession to somehow derive Born's rule. It's to the best of our knowledge simply one of the postulates of QT, and it's compatible with all observations.

Concerning the problems relativistic QFT still has, you are of course right. That are open mathematical questions, but it has nothing to do with any measurement problem. That's just the question, how to deal correctly with distributions without a satisfactory solution yet.

From the physics side what's also unsolved is a consistent quantum description of the gravitational interaction. These are indeed the real mathematical and theoretical-physical problems to be solved, but not some philosophical quibbles about the probabilistic behavior of Nature or a measurement problem.

 

[Tendex]

Concerning the problems relativistic QFT still has, you are of course right. That are open mathematical questions, but it has nothing to do with any measurement problem. That's just the question, how to deal correctly with distributions without a satisfactory solution yet.

Measurements are interactions and if there is a mathematical problem with relativistic interacting quantum fields then there is a mathematical measurement problem. That's the measurement problem of outcomes in a relativistic setting which is the one where it must be addressed since in the nonrelativistic single particle case the Born rule axiom is perfectly fine, both physically with absolute time and mathematically with a perfectly rigorous theory in the nonrelativistic domain including the Born rule as axiom.