Is wave function a real physical thing?

[jerromyjon]

I believe the wave function of all EM matter exists. It is what determines physical outcomes of interactions. I have faith that the absolute representation when found and proven mathematically will obviously describe what occurs exactly. Just because the math alone isn't as descriptive as english does not mean they are incompatible, some day the equations will "sound" right.

 

[bhobba]

some day the equations will "sound" right.

The modern basis of QM is very elegant - and IMHO sounds very 'right' - just weird until you get used to it:
http://arxiv.org/pdf/quantph/0101012.pdf

That said - nature doesn't have to oblige - in this case it does - but nature is as nature is.

Thanks
Bill

 

[bohm2]

The PBR paper should be considered a pair with a paper by LJBR (BR are the same authors on both papers). The PBR paper shows sufficient conditions for the postulated hidden variables that ensures that a given state of the hidden variables uniquely specifies the wave function, so that the wave function is "ontic". However, when the conditions are weakened, LJBR were able to (partially) construct explicit examples in which a given state of the hidden variables do not uniquely specify the wave function, so that the wave function is "epistemic"...

http://arxiv.org/abs/1201.6554
Distinct Quantum States Can Be Compatible with a Single State of Reality
Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph

Note that according to one of the authors (Terry Rudolph) of both papers, while ψ-epistemic models can be constructed if no preparation independence assumption, they do not consider such models as serious proposals:

The theorem we prove – that quantum states cannot be understood as merely lack of knowledge of an underlying deeper reality described by some as yet undiscovered deeper theory – assumes preparation independence. It is an important insight that this assumption is necessary for the theorem, and the point of our second paper was to show this explicitly. That second paper is, however, simply making a mathematical/logical point – it is not a serious proposal for how the physical world operates.

http://www.preposterousuniverse.com...-post-terry-rudolph-on-nature-versus-nurture/

Terry Rudolph, argues that this preparation independence assumption of PBR is on par with the experimental free will assumption in deriving Bell's theorem. One can escape Bell's by denying it, but most physicists don't consider such models as serious proposals:

We are in a similar position with Bell’s theorem, which I consider the most important insight into the nature of physical reality of the last century, an honour for which there are some serious competitors! That theorem relies on a presumed ability to make independent choices of measurements at separated locations. Denial of such is the “super-determinism” loophole, and while intelligent people can and do consider its plausibility, and while it is an important insight into Bell’s theorem that this assumption is necessary, the jury is still out (‘t Hoofts efforts notwithstanding) as to whether a super-deterministic theory agreeing with all experiments to date can even be constructed, never mind be a plausible theory of nature.

Denial of preparation independence or invocation of super-determinism throws into question the basic methods of all science carried out to date. Most physicists would, I believe, consider the “cure” (extremely convoluted correlations between seemingly unrelated events leading to a conspiratorial interpretation of the nature of reality) worse than the “disease” (non-locality in the case of Bell’s theorem, the reality of the quantum state in the case of ours). If our theorem fails because the assumption of preparation independence fails, it is a far more amazing insight into nature than the theorem itself provides.

And yet there are a number of papers arguing that this preparation independence assumption is the most controversial assumption of the PBR Theorem. I'm not sure what to make of this? Did the authors of PBR paper underestimate the importance of the preparation independence assumption?

 

[zoki85]

Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object?

No function is a real physical object/thing

 

[Marceli]

It is to understand difference between event description and event observation. Both can be accurate having same results! For example experiments are important event observations, measurements.

 

[bhobba]

No function is a real physical object/thing

Neither is any mathematical object - however it can model it.

The EM field is considered real because for the laws of conservation of energy and momentum to hold it has momentum and energy.

The same however may or may not apply to a quantum state (the wave-function is simply the expansion in terms of position eigenstates) - it may or may not be real.

Thanks
Bill

 

[microsansfil]

No function is a real physical object/thing

I am agree here with Nugatory https://www.physicsforums.com/threads/is-wave-function-a-real-physical-thing.788665/#post-4952978.
Depend on the definition you postulate about "real".

For example Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices.

Why not.

This is no more neither no less absurd than to assert the reality of the wave function.

Patrick

 

[zoki85]

Neither is any mathematical object - however it can model it.

The EM field is considered real because for the laws of conservation of energy and momentum to hold it has momentum and energy.

Actually, EM field is considered real becouse we can measure/detect it.

 

[microsansfil]

Actually, EM field is considered real becouse we can measure/detect it.

A lot of "thing" are measurable http://en.wikipedia.org/wiki/Measure_(mathematics)

Patrick

 

[zoki85]

A lot of "thing" are measurable http://en.wikipedia.org/wiki/Measure_(mathematics)

Patrick

How is the wave function measured?

 

[vanhees71]

That's a very good question! Since the physics content of the wave function is probabilistic it can only be "measured" by preparing a lot of independent systems always in the same way (state preparation) and measure the same observable (measurement). Then you do the usual statistical analysis to test the hypothesis that the probabilities are described right by the squared modulus of the wave function.

No matter, what Qbists mumble about the meaning of probabilities for a single event, in the physics lab there's no other way than the frequentist interpretation of probabilities, which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

 

[bhobba]

Actually, EM field is considered real becouse we can measure/detect it.

Not quite.

The electric field is defined as the force exerted on a test charge. That doesn't mean there is anything real at that point - it just means there is some other charge around exerting a force on it. The reason its considered real is because of relativity it takes some time for that force to be felt, hence for our conservation laws of momentum and energy to hold there must be somewhere it is held - and that is the field. This is part of some famous no go theorems developed by Wigner and explained in Ohanian's book on Relativity:
https://www.amazon.com/dp/B00ADP76ZO/?tag=pfamazon01-20

A quantum state also can be measured - but, as Vanhees correctly explains - only via a large number of similarly prepared systems the same as the probabilities of a biased coin. However it is not the same as an EM field and similar no-go theorems do not exist. Personally this is part of the reason I do not consider it real - if it was real you could directly measure it rather than having to prepare a large number of systems - it is also one reason I find the minimal statistical interpretation a more direct view.

Measurement is not the requirement for being real in a physical sense.

Thanks
Bill

 

[bhobba]

which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

That's true - but I suspect you really meant the strong law of large numbers.

One of my favourite mathematicians, Terry Tao, wrote a nice article on it:
http://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/

Just as an aside he also wrote some nice stuff on distribution theory:
http://terrytao.wordpress.com/2009/04/19/245c-notes-3-distributions/
http://www.math.ucla.edu/~tao/preprints/distribution.pdf

Thanks
Bill

 

[vanhees71]

I meant the theorem that the frequencies in a probability experiment converges to the probabilities as predicted by QT in the limit of very many experiments. That's of course the strong law of large numbers. The central-limit theorem explains, why Gaussian distributions occur pretty often in probability problems.

 

[zoki85]

Not quite.

The electric field is defined as the force exerted on a test charge. That doesn't mean there is anything real at that point - it just means there is some other charge around exerting a force on it.

Meaning nothing is real, all the world is illusion. Oh, I can't sleep now :D

 

[TrickyDicky]

That's a very good question! Since the physics content of the wave function is probabilistic it can only be "measured" by preparing a lot of independent systems always in the same way (state preparation) and measure the same observable (measurement). Then you do the usual statistical analysis to test the hypothesis that the probabilities are described right by the squared modulus of the wave function.

No matter, what Qbists mumble about the meaning of probabilities for a single event, in the physics lab there's no other way than the frequentist interpretation of probabilities, which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

Exactly, so if the wave function is just a tool to calculate probabilities, i.e. is not something measurable, certainly not when used in this manner, it makes no sense to even ask about the "ontic" nature of such a tool. This would lead to similar considerations about QM states in general.
To me it is salient of QM that its explanatory power for things from tunneling or atomic spectra to chemistry, superconductors or lasers is not directly derived from the probabilistic predictions from wave functions(these applications rely basically on intrinsic quantum properties), rather such predictions are usually more like self-checks for the theory, or for calculating cross-sections in particle physics.

 

[bhobba]

i.e. is not something measurable,

It is measurable - only from a large ensemble of similarly prepared systems, but it is measurable.

Thanks
Bill

 

[TrickyDicky]

It is measurable - only from a large ensemble of similarly prepared systems, but it is measurable.

Thanks
Bill

I suspect you are probably referring here to the mathematical concept of probability measure while I'm referring to measurements in physics.

 

[bhobba]

I suspect you are probably referring here to the mathematical concept of probability measure while I'm referring to measurements in physics.

No - its from the properties of a state.

That said it is indeed different to things like an electric field etc.

Thanks
Bill

 

[stevendaryl]

No matter, what Qbists mumble about the meaning of probabilities for a single event, in the physics lab there's no other way than the frequentist interpretation of probabilities, which BTW is based on the central-limit theorem which is a mathematical fact within the usual axiomatic foundation of probability theory (e.g., the Kolmogorov axioms).

I don't know why you would say that in the lab, there is no other way than the frequentist interpretation. Bayesian probability works perfectly fine in the lab. The differences between bayesian and frequentist really only comes into play at the margins, when you're trying to figure out whether your statistics are good enough to make a conclusion. The frequentists use some cutoff for significance, which is ultimately arbitrary. The bayesian approach is smoother--the more information you have, the stronger a conclusion you can make, but you can use whatever data you have.

Since frequentist probability only applies in the limit of infinitely many trials, there isn't a hard and fast distinction between a single event and 1000 events. Neither one implies anything about the probability, strictly speaking.

 

[JPBenowitz]

I don't understand how one reconciles a "real" wave function with its instantaneous collapse. To me this is an obvious violation of causality.

 

[atyy]

I don't understand how one reconciles a "real" wave function with its instantaneous collapse. To me this is an obvious violation of causality.

A simple example is to simply taken the quantum formalism as it is and add that the wave function in a particular frame (the aether) is real. The wave function in other frames will not be real, but predictions made using the quantum formalism in any frame will be the same as predictions made in the aether frame, so one cannot tell which frame is the aether frame. This can be seen in http://arxiv.org/abs/1007.3977.

This is not consistent with classical relativistic causality, but it doesn't matter since relativity does not require classical relativistic causality, only that the probabilities of events are frame-invariant and that classical information should not be transmitted faster than light. The main problem with this way of making the wave function real is not relativity, but that it leaves the measurement problem open.

 

[vanhees71]

I don't know why you would say that in the lab, there is no other way than the frequentist interpretation. Bayesian probability works perfectly fine in the lab. The differences between bayesian and frequentist really only comes into play at the margins, when you're trying to figure out whether your statistics are good enough to make a conclusion. The frequentists use some cutoff for significance, which is ultimately arbitrary. The bayesian approach is smoother--the more information you have, the stronger a conclusion you can make, but you can use whatever data you have.

Since frequentist probability only applies in the limit of infinitely many trials, there isn't a hard and fast distinction between a single event and 1000 events. Neither one implies anything about the probability, strictly speaking.

My point is that no matter how you metaphysically interpret the meaning of probabilities, in the lab you have to "get statistics" by preparing ensembles of the system under consideration. The Qbists always mumble something about that there is some meaning of probabilities for a single event, but in my opinion that doesn't help at all to make sense of the probabilistic content of the quantum mechanical state.

What I don't like most about this Qbism is the idea that the quantum state is subjective. That's not, how it is understood by the practitioners using QT as a description of nature: A state is defined by preparation procedures. A preparation can be more or less accurate, and usually you don't prepare pure states but mixed ones, but nevertheless there's nothing subjective in the meaning of states.

It's also often claimed that the outcome of measurements is observer dependent or that QT brings back in the observer into the game. That's, however a pretty trivial statement: Of course the experimentalists decides which observable(s) with which accuracy he likes (or can with the means/money at hand) to measure it (them), and of course, the outcome of the measurement depends on what I decide to measure. I get a different result when measuring a momentum than I get when I detect the location of a particle.

The main point that distinguishes QT from classical physics is not so much that I cannot measure observables without disturbing the system, but it's the prediction of the QT formalism that a certain preparation procedure (e.g., make particles with a well-defined momentum) excludes necessarily the sharp definition of other incompatible observables (e.g., the position of the particle), but that's also an objective decision of the experimentalist, what he prepares. To figure out whether the predictions about incompatibility of observables is correct (and even correctly quantitfied in terms of the probabilities inherent in the determination of the pure or mixed quantum state due to the chosen preparation procedure) can be checked only by preparing a lot of such experiments and getting the statistics to check this hypothesis as with any other probabilistic statement. A single event doesn't tell you anything about the correctness or incorrectness of the probabilistic predictions!

 

[vanhees71]

A simple example is to simply taken the quantum formalism as it is and add that the wave function in a particular frame (the aether) is real. The wave function in other frames will not be real, but predictions made using the quantum formalism in any frame will be the same as predictions made in the aether frame, so one cannot tell which frame is the aether frame. This can be seen in http://arxiv.org/abs/1007.3977.

This is not consistent with classical relativistic causality, but it doesn't matter since relativity does not require classical relativistic causality, only that the probabilities of events are frame-invariant and that classical information should not be transmitted faster than light. The main problem with this way of making the wave function real is not relativity, but that it leaves the measurement problem open.

This is a contradiction in itself: If you assume a relativistic QFT to describe nature, by construction all measurable (physical) predictions are Poincare covariant, i.e., there's no way to distinguish one inertial frame from another by doing experiments within quantum theory. As Gaasbeek writes already in the abstract: The delayed-choice experiments can be described by standard quantum optics. Quantum optics is just an effective theory describing the behavior of the quantized electromagnetic field in interaction with macroscopic optical apparati in accordance with QED, the paradigmatic example of a relativistic QFT, and as such is Poincare covariant in the prediction about the observable outcomes, and quantum optics indeed is among the most precisely understood fields of relativistic quantum theory: All predictions are confirmed by high-accuracy experiments. So quantum theory cannot reintroduce an "aether" or however you like to call a "preferred reference frame" into physics! By construction QED and thus also quantum optics fulfills relativistic causality constraints too!

 

[atyy]

What I don't like most about this Qbism is the idea that the quantum state is subjective. That's not, how it is understood by the practitioners using QT as a description of nature: A state is defined by preparation procedures. A preparation can be more or less accurate, and usually you don't prepare pure states but mixed ones, but nevertheless there's nothing subjective in the meaning of states.

I don't think QBism makes sense, but many aspects of it seem very standard and nice to me. For example, how can we understand wave function collapse? An analogy in classical probability is that it is like throwing a die, where before the throw the outcome is uncertain, but after the throw the probability collapses to a definite result. Classically, this is very coherently described by the subjective Bayesian interpretation of probability, from which the frequentist algorithms can be derived. It is fine to argue that the state preparation in QM is objective. However, the quantum formalism links measurement and preparation via collapse. If collapse is subjective by the die analogy, then because collapse is a preparation procedure, the preparation procedure is also at least partly subjective.

 

[atyy]

This is a contradiction in itself: If you assume a relativistic QFT to describe nature, by construction all measurable (physical) predictions are Poincare covariant, i.e., there's no way to distinguish one inertial frame from another by doing experiments within quantum theory. As Gaasbeek writes already in the abstract: The delayed-choice experiments can be described by standard quantum optics. Quantum optics is just an effective theory describing the behavior of the quantized electromagnetic field in interaction with macroscopic optical apparati in accordance with QED, the paradigmatic example of a relativistic QFT, and as such is Poincare covariant in the prediction about the observable outcomes, and quantum optics indeed is among the most precisely understood fields of relativistic quantum theory: All predictions are confirmed by high-accuracy experiments. So quantum theory cannot reintroduce an "aether" or however you like to call a "preferred reference frame" into physics! By construction QED and thus also quantum optics fulfills relativistic causality constraints too!

No, there is no contradiction, it just seems very superfluous to modern sensibilities where we are used to having done away with the aether, since we cannot figure which frame is the aether frame. But Lorentz Aether Theory and its "invisible aether" makes the same predictions as the standard "no aether" formulation of special relativity, and in fact one can derive the standard "no aether" formulation of special relativity from Lorentz Aether Theory, so there cannot be a contradiction, unless special relativity itself is inconsistent.

 

[stevendaryl]

What I don't like most about this Qbism is the idea that the quantum state is subjective.

Well, it seems to me that certain aspects of it are subjective. For example, in an EPR-type experiment, Alice measures the spin of one of a pair of particles. Afterwards, she would describe the state of the two-particle system using a "collapsed" wavefunction. Bob has not yet measured the spin of his particle (and hasn't heard of Alice's result) and so would continue to use the initial entangled wave function to describe the pair. If they are (correctly) using different wavefunctions to describe the same situation, then that seems subjective to me. Or "relative to the subject".

When density matrices are used, instead of wave functions, it seems even more subjective, since a density matrix can be interpreted as mixing two different kinds of probability--classical ignorance of the true state, and quantum nondeterminism. The first type of probability seems subjective.

 

[stevendaryl]

My point is that no matter how you metaphysically interpret the meaning of probabilities, in the lab you have to "get statistics" by preparing ensembles of the system under consideration. The Qbists always mumble something about that there is some meaning of probabilities for a single event, but in my opinion that doesn't help at all to make sense of the probabilistic content of the quantum mechanical state.

I don't think Qbism adds much (if anything) to the understanding of quantum mechanics, but I was simply discussing bayesianism (not necessarily quantum). Bayesian probability isn't contrary to getting statistics--there is such a thing as "bayesian statistics", after all. As I said, the difference is only in how you interpret the resulting statistics.

 

[stevendaryl]

No, there is no contradiction, it just seems very superfluous to modern sensibilities where we are used to having done away with the aether, since we cannot figure which frame is the aether frame. But Lorentz Aether Theory and its "invisible aether" makes the same predictions as the standard "no aether" formulation of special relativity, and in fact one can derive the standard "no aether" formulation of special relativity from Lorentz Aether Theory, so there cannot be a contradiction, unless special relativity itself is inconsistent.

I know several physicists who are perfectly competent (as opposed to crackpots) who favor Lorentz Aether Theory over Einstein's relativity, specifically because they think it would allow collapse of the wave function to be a real event (which it can't be, in a completely Lorentz-invariant way).

 

[vanhees71]

I don't think Qbism adds much (if anything) to the understanding of quantum mechanics, but I was simply discussing bayesianism (not necessarily quantum). Bayesian probability isn't contrary to getting statistics--there is such a thing as "bayesian statistics", after all. As I said, the difference is only in how you interpret the resulting statistics.

Ok, then what's in your view the difference between Bayesian and frequentist interpretations of probabilities, particularly the statement probabilities make sense for a single event?

E.g., when they say in the weather forecast, there's a 99% probability to have snow tomorrow, and tomorrow it doesn't snow. Does that tell you anything about the validity of the probability given by the forecast? I don't think so. It's just a probability based on experience (i.e., the collection of many weather data over a long period) and weather models based on very fancy hydrodynamics on big computers. The probabilistic statement can only be checked by evaluating a lot of data based on weather observations.

Of course, there's Bayes's theorem on conditional probabilities, which has nothing to do with interpretations or statistics but is a theorem that can be proven within the standard axiom system by Kolmogorov:
$$P(A|B) P(B) = P(B|A) P(A),$$
which is of course not the matter of any debate.

I'm really unable to understand why there is such a hype about Qbism, which I consider a rather poor reinvention of old statements about subjectivism in quantum theory, which in my view is unfounded in the quantum theoretical formalism and in the way quantum theory is used by theorists and experimentalists in the physics labs around the world ;-).