# Is the wave function real or abstract statistics?

• matrixrising
In summary: They use logic and mathematics to show that the wave function is in one-to-one correspondence with its "elements of reality."
matrixrising
Is the wave function describing reality or does it describe the observers uncertainty about the system? I say that it's real but I would like to hear any comments or evidence that suggest the wave function isn't a description that has a one to one correspondence with a underlying reality.

It's like a function that describes a car driving 50 miles an hour for 1 mile. You can predict where the car will be at a half a mile or 3 quarters of a mile. The function describes the underlying reality of the car traveling for 1 mile at 50 MPH.

With a quantum system, we can't predict where the particle will be but we can assign probabilities to where the particle might be. The wave function describes an underlying reality where the particle is in a pure quantum state and goes through both slits at the same time to a mixed state where we assign probabilities and the particle has went through one slit or the other and the observer just doesn't know which slit.

So why is the function for the car traveling 50 MPH for 1 mile real and the function for the pure or mixed state of the wave function abstract? In other words, when there's a one to one correspondence, how can it be abstract?

Here's an article from phys.org:

“Consider a meteorologist who gives a prediction about tomorrow’s weather (for example, that it will be sunny with probability 33% and cloudy with probability 67%),” they write. “We may assume that classical mechanics accurately describes the relevant processes, so that the weather depends deterministically on the initial conditions. The fact that the prediction is probabilistic then solely reflects a lack of knowledge on the part of the meteorologist on these conditions. In particular, the forecast is not an element of reality associated with the atmosphere but rather reflects the subjective knowledge of the forecaster; a second meteorologist with different knowledge may issue an alternative forecast. Moving to quantum mechanics, one may ask whether the wave function that we assign to a quantum system should be seen as a subjective object (analogous to the weather forecast) representing the knowledge an experimenter has about the system or whether the wave function is an element of reality of the system (analogous to the weather being sunny).”

Colbeck and Renner argue that, unlike a weather forecast, the wave function of a quantum system fully describes reality itself, not simply a physicist's lack of knowledge of reality. In their paper, they logically show that a quantum system's wave function is in one-to-one correspondence with its “elements of reality,” i.e., the variables describing the system's behavior.

“This [idea that the wave function represents reality] means that the wave function includes all information that is in principle available about the system, i.e., nothing is missing,” Renner told Phys.org. “Nevertheless, even if we knew the wave function of a system (and therefore reality), its future behavior cannot be predicted with certainty. This means that there is inherent randomness in nature.”

So this is really the crux of the debate. Is randomness inherent in nature or is their some hidden variable or new physics that will do away with this inherent randomness. It goes back to Einstein.

Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the "old one." I, at any rate, am convinced that He does not throw dice.

Einstein himself used variants of this quote at other times. For example, in a 1943 conversation with William Hermanns recorded in Hermanns' book Einstein and the Poet, Einstein said: "As I have said so many times, God doesn't play dice with the world." (p. 58)

So I see think there's a universal wave function in a pure state and when these pure states decohere into mixed states then local universes emerge. So it's like the wave function is the UN and everything from photons, atoms, rocks, trees and human beings are measuring devices that represent the wave function in these local environments.

A measuring device like the human brain or a photon can store bits and measure it's environment. So we can reduce classical Shanon entropy to zero. When this occurs we have a now moment for example, turning over a playing card that's face down. I think this speaks to a Quantum mind but that's a topic for another thread.

I wanted to hear the evidence that the wave function doesn't correspond to an underlying reality that's inherently random and it's just an abstract description of the observers uncertainty. How can we build quantum computers if superposition isn't an objective reality of the system's wave function?

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The paper by Colbeck and Renner you cite is http://arxiv.org/abs/1111.6597 . Two interesting papers they cite are Pusey, Barrett and Rudolph's http://arxiv.org/abs/1111.3328 and Harrigan and Spekken's http://arxiv.org/abs/0706.2661v1 .

Colbeck and Renner state that their result assumes "freedom of choice for measurement settings", while the PBR paper conclusion can be avoided if one of its assumptions is removed as Lewis, Jennings, Barrett and Rudolph show in http://arxiv.org/abs/1201.6554 .

Matt Leifer wrote an informative essay on these issues which was published in "Quantum Times" http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/ .

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matrixrising said:
Is the wave function describing reality or does it describe the observers uncertainty about the system? I say that it's real but I would like to hear any comments or evidence that suggest the wave function isn't a description that has a one to one correspondence with a underlying reality.

If you think that then you need to read Ballentine - Quantum Mechanics - A Modern Development.

It may be real, but doesn't have to be. IMHO its more like probabilities which most would not say is real in any usual sense.

Here is the skinny. Imagine we have a system and some observational apparatus that has n possible outcomes associated with values yi. This immediately suggests a vector and to bring this out I will write it as Ʃ yi |bi>. Now we have a problem - the |bi> are freely chosen - they are simply man made things that follow from a theorem on vector spaces - fundamental physics can not depend on that. To get around it QM replaces the |bi> by |bi><bi| to give the operator Ʃ yi |bi><bi| - which is basis independent. This is the first axiom of the treatment in Ballentine foundational axiom of QM, and heuristically why its reasonable.

Next we have this wonderful theorem called Gleasons theorem which, basically, follows from the above axiom:
http://kof.physto.se/theses/helena-master.pdf

This is the second axioms in Ballentine's treatment.

This means a state is simply a mathematical requirement to allow us to calculate expected values in QM. It may or may not be real - there is no way to tell. But its very similar to the role probabilities play in probability theory, and like I said, most would not say they are real.

Further in that vein, nowadays its often thought of as just a novel version of probability theory - there basically being just two reasonable models applicable to physical systems. Check out:
http://arxiv.org/abs/quant-ph/0101012
http://arxiv.org/abs/0911.0695

That would probably be the most recent view - QM is basically a probability model - there are many of those and the study of such is a modern development - but for modelling physical systems some very reasonable assumptions leads to basically two - bog standard probability theory you learned about at school and QM - but what distinguishes QM is it allows entanglement, which would seem the rock bottom, basic, essential weirdness of QM.

Thanks
Bill

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Thanks for the response bhobba,

I think ensemble interpretations are another form of shut up and calculate. This is because they make an argument that we should exclude individual measurement's that have a one to one correspondence with the wave function and just look at these things in the context of an ensemble of probabilities and ignore the one to one correspondence between the wave function and individual particles. The two things don't have to be mutually exclusive.

This is from Wikepedia:

However, hopes for turning quantum mechanics back into a classical theory were dashed. Gribbin continues:

"There are many difficulties with the idea, but the killer blow was struck when individual quantum entities such as photons were observed behaving in experiments in line with the quantum wave function description. The Ensemble interpretation is now only of historical interest."[9]

This is the ball game.

When you have one to one correspondence between a single photon and the description of it's wave function, then the wave function is describing reality. That doesn't exclude that this single measurement can't be looked at in the context of an ensemble.

Let's look at a slot machine in a Casino. By itself, one spin of the slot machine can't tell the Casino owner how an ensemble of spins will be in his favor statistically speaking but that one spin being "real" is important to the ensemble of spins.

I think the crux of the matter goes back to my original post. People don't like what QM says or shows in experiments, so these things can't be "real." God doesn't play dice so to speak.

Look at an uranium atom in it's ground state. When the single atom is subjected to external forces it moves in a way that is predicted by it's wave function. There's a one to one correspondence between a single atom and it's wave function.

Why does an ensemble interpretation exclude the "reality" of a single photon with one to one correspondence with it's wave function in order to say we can only look at it as an ensemble of particles. In other words, shut up and calculate.

This is from Wikipedia:

The ensemble interpretation, unlike many other interpretations of quantum mechanics, does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it is simply a statement as to the manner of wave function interpretation.

Again, even though we wave a one to one correspondence between the wave function and the system, we're supposed to look a way and only see the statistical interpretation of an ensemble and ignore the one to one correspondence between a single photon and it's wave function.

Here's a paper from nature titled Direct measurement of the quantum wavefunction.

The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition1, 2. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule3. At present, the wavefunction is determined through tomographic methods4, 5, 6, 7, 8, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement9, 10, 11, 12, 13, 14, 15, 16, 17, 18, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems—for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations19. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html

How can there be a direct measurement of something that's not real? Isolation of a single particle and it's wave function being real doesn't exclude a statistical interpretation of the data over an ensemble of particles. In fact, you have to include the single photon as being real in order to look at the wave function of an ensemble of photons which are in accordance with the predictions of Quantum Theory.

So if I create a stream of photons with identical wave functions there shouldn't be a one to one correspondence with the wave function if the ensemble theory is correct. Why should the wave function of a single photon be in a one to one correspondence with the description of the wave function according to QM if the wave function of a single photon isn't real?

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matrixrising said:
How can there be a direct measurement of something that's not real? Isolation of a single particle and it's wave function being real doesn't exclude a statistical interpretation of the data over an ensemble of particles. In fact, you have to include the single photon as being real in order to look at the wave function of an ensemble of photons which are in accordance with the predictions of Quantum Theory.

So if I create a stream of photons with identical wave functions there shouldn't be a one to one correspondence with the wave function if the ensemble theory is correct. Why should the wave function of a single photon be in a one to one correspondence with the description of the wave function according to QM if the wave function of a single photon isn't real?
But is it a direct measurement? Those experiments rely on the notion of weak measurement. A criticism raised against a weak measurement is that it says little about the properties of an individual system. Demystifier discusses this issue here:
A strong measurement reveals a property of an individual system, but a weak measurement only reveals a property of a large STATISTICAL ENSEMBLE of equally prepared systems. A weak measurement says nothing about properties of an individual system. All weirdness of weak values results from attempts to interpret properties of an ensemble (2.6 children) as properties of an individual system (a family).
Weak measurements in quantum mechanics and 2.6 children in an American family
https://www.physicsforums.com/blog.php?b=1226

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Bohm2,

Thanks for the response. I think it's apples & oranges when it comes to the comparison you cited.

It's basically saying the wave function doesn't correspond to classical reality so it isn't real. There isn't a one to one correspondence between 2.6 children and the formula that says there's 2.6 children in an American family. So of course you can say that nf=Nc/Nf is just statistical because it doesn't correspond to a physical reality.

This isn't the case with the wave function. There's a one to one correspondents to the system's wave function. You can't say because the wave function doesn't correspond to a classical underlying reality that it isn't real. What you can say is that there's a one to one correspondents with the quantum system's wave function therefore the quantum system's wave function represent an underlying reality.

What you're basically saying in an ensemble approach is that a quantum reality isn't real because it doesn't correspond to the classical world we experience.

Experiment after experiment has thrown a monkey wrench into this view because there's a one to one correspondents with the wave function and the way the system behaves.

Like I said, it's shut up and calculate just wrapped in a slightly different package. We will just ignore the wave function as representing any underlying reality because it doesn't have a one to one correspondence with the classical world. Why should the wave function have a one to one correspondence with the classical world when it's describing the wave function of a quantum system?

matrixrising said:
How can there be a direct measurement of something that's not real?

To get what they mean by a direct measurement, you need to know how measurements of the state of a light field are usually done. The information you have in the wavefunction is equivalent to that contained in the density matrix or the Wigner function of the state. The latter is a quasiprobability distribution in two quadratures of the light field which cannot be measured simultaneously due to uncertainty. However, one can measure the projection of the whole function along a slice at some angle through the function. The typical strategy then relies on taking a set of those slices at different angles. Afterwards, one has to reconstruct the Wigner function or density matrix that is most likely to give all the measured slices. So you start out by guessing some function and then run an iterative procedure that converges towards the state that has the maximum likelihood of reproducing the results. The procedure is quite similar to what happens when tomography is done in a hospital - this is why that procedure is called quantum state tomography. It is obviously a very indirect technique as you use maximum likelihood reconstruction. Lundeen's technique is more direct because it gets along without that reconstruction thing. It is still a measurement on an ensemble of identically prepared single photons. See the introduction of the paper for details:
"In contrast, we introduce a method to measure Ψ of an ensemble directly. By ‘direct’ we mean that the method is free from complicated sets of measurements and computations"

Direct does not mean that you can do the measurement on a single photon realization.
matrixrising said:
So if I create a stream of photons with identical wave functions there shouldn't be a one to one correspondence with the wave function if the ensemble theory is correct. Why should the wave function of a single photon be in a one to one correspondence with the description of the wave function according to QM if the wave function of a single photon isn't real?

Let me mention that your wiki quote is somewhat taken out of context. This part is explicitly about "Early proponents of statistical approaches regarded quantum mechanics as an approximation to a classical theory." which is not what the actual ensemble approach is about.

When people talk about the wave function of a single photon they mean a single photon state. They never talk about just one realization. The wave function of a single realization is not really defined or of interest in standard qm. You can interpret the wavefunction in a realistic way, but there is nothing urging one to do so. There is also nothing urging us to do it in a different way.

matrixrising said:
I think ensemble interpretations are another form of shut up and calculate. This is because they make an argument that we should exclude individual measurement's that have a one to one correspondence with the wave function

Individual measurements that have a one to one correspondence with the wave function?

I have zero idea what you mean by that.

Your query was why can the wavefunction (ie state) be considered not real.

I gave arguments from the modern viewpoint where its simply a device to calculate expected values, like probabilities is in probability theory. In that view, just like probabilities, its not real in any usual sense, simply a theoretical device to aid in calculations.

Indeed general considerations single out probability theory and QM as the only two possibilities in modelling physical systems - but QM is special - it allows entanglement, which modern research shows is quite likely the real rock bottom essence and weirdness of QM.

Check out:
http://theoreticalminimum.com/courses/quantum-entanglement/2006/fall
'The old Copenhagen interpretation of quantum mechanics associated with Niels Bohr is giving way to a more profound interpretation based on the idea of quantum entanglement. Entanglement not only replaces the obsolete notion of the collapse of the wave function but it is also the basis for Bell's famous theorem, the new paradigm of quantum computing, and finally the widely discussed "many-worlds" interpretation of quantum mechanics originated by Everett.'

Thanks
Bill

Cthuga,

It's still a direct measurement of a photon's wave function. This is the point. The system behaves in a way that's described by the wave function. So even in a stream of identically prepared photons, the system and the wave function still behaves in a way that's predicted by quantum theory.

It's like my Casino example. One spin of the slot machine has to be real in order to give you a statistical picture of an ensemble of spins.

How can the system be in a probable state that's not an underlying reality? The wave function has to be an underlying reality that describes the probable states of the system.

I can say that I will be in the Bahamas next week. There's a slim chance that this will occur because I have no plans to go to the Bahamas next week but it's only a probable state because of the underlying reality of the Bahamas or getting in an airplane.

I couldn't say I'm going to planet Lexar next week which is 20,000 light years away. This isn't a probable state because there isn't any underlying reality of the planet Lexar or of me traveling to a planet 20,000 light years away.

The wave function has to be real because it's an underlying reality of all probable states of the system. Like I said earlier, there's a one to one correspondence between the wave function and the system.

So you can see the wave function as a pool table. The pool table describes all the states the pool ball can be in. So you couldn't say, 8 ball in the pocket 3 inches away from the corner pocket. This is because this isn't a probable state described by the underlying reality of the pool table.

So the wave function has to be real because there's a one to one correspondence between the wave function and the quantum system. The wave function represents an underlying reality of all probable states of the system. How can the system be in a probable state that isn't first a "real" possibility?

I can't take a trip to Middle Earth to visit the Hobbits because there's no underlying reality to make this a probable state. I can say that I'm flying out to Vegas to visit my cousins because there's an underlying reality of my cousins living in Vegas so it is a probable state.

The wave function describes the probable states the system can be in just like the pool table describes the probable states the pool balls can be in.

matrixrising said:
How can there be a direct measurement of something that's not real?

If the state is like probabilities your question is how can there be a direct measurement of probabilities?

Just like probabilities there is no way a single observation can determine a systems state - its encoded in the Born rule.

If we observe a state with an apparatus that gives 0 if its not in that state and 1 if it is then the quantum formalism tells us that since states can be a superposition of those two outcomes it may be in a state that sometimes gives 0 and sometimes 1. To determine it is in that state you need to carry out the observation a sufficiently large number of times for the null result to be below your level of confidence - you can never be sure - all you can do is simply make the chances of being wrong arbitrarily small ie is zero for all practical purposes.

Just to be 100% clear - there is no way - zero - zilch - nada (it's not a subtle point I am trying to make) a state can be determined except in a statistical sense - just like there is no way to determine probabilities except to an arbitrarily small confidence level. The quantum formalism is unequivocal on this point - you can't determine a systems state exactly.

Thanks
Bill

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matrixrising said:
It's still a direct measurement of a photon's wave function..

I may be missing something.

Please describe to me the direct measurement of a SINGLE photons wave function.

Because if you can, you have contradicted the quantum formalism.

I am not talking about the bulk wavelength etc of a beam of photons - that can be measured - I am talking about the state of a single photon.

Thanks
Bill

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Cthugha said:
Direct does not mean that you can do the measurement on a single photon realization.

Indeed you cant.

If you could then you contradict QM's basic postulates - particularly the Born rule.

I have tried to explain this as carefully and unambiguously as I can in a previous post from the basic postulates of QM.

Thanks
Bill

matrixrising said:
It's still a direct measurement of a photon's wave function. This is the point. The system behaves in a way that's described by the wave function. So even in a stream of identically prepared photons, the system and the wave function still behaves in a way that's predicted by quantum theory.

Ok, nobody denies that.

matrixrising said:
It's like my Casino example. One spin of the slot machine has to be real in order to give you a statistical picture of an ensemble of spins.

I do not get your comparison.

matrixrising said:
How can the system be in a probable state that's not an underlying reality? The wave function has to be an underlying reality that describes the probable states of the system.

Hmm, you might be confusing terminology here. If the wave function just describes the probable states of the system, it is assumed to be not a real entity. In this sense it is rather a statistical entity that tells us in which state we might find the system and what the probabilities may be. If you consider the wave function as a realistic entity, you express that the wave function is more than that and applies directly to every single realization of an ensemble. In this case the wave function does not represent the probable states of the system, but a system that actually indeed is in all of these probable states with some weights given by the wave function.

matrixrising said:
The wave function has to be real because it's an underlying reality of all probable states of the system. Like I said earlier, there's a one to one correspondence between the wave function and the system.

This has nothing to do with what is meant by the wave function being considered real or not. Nobody doubts that the probable states are there. Assuming that the wave function is real means, that they are all realized - not only probable - within each realization of a single experimental run.

matrixrising said:
The wave function describes the probable states the system can be in just like the pool table describes the probable states the pool balls can be in.

Well, to stick with your pool table setting, the pool ball actually and literally IS in all the pockets (and everywhere on the table) simultaneously when you consider the wave function as real. It actually is in all of these pockets and "collapses" to one of the pockets as soon as you take a look. A non-realistic wave function approach instead just considers the wave function as describing all the probable states the ball could be in.

matrixrising said:
So the wave function has to be real because there's a one to one correspondence between the wave function and the quantum system.

There is a 1-1 correspondence between probabilities and the sides of a coin in the sense you can conceptually attach them to a side and consider them a vector - but that doesn't make probabilities any more than a calculation device.

The same with a quantum state.

Thanks
Bill

bhobba,

Thanks for the response.

I was talking about the weak measurements carried out in the experiment I listed above. My point was, the system still behaves in a way Quantum Theory predicts. If an ensemble interpretation is correct, why don't we find huge deviations at these levels?

Here's an interesting paper:

Is a system's wave function in one-to-one correspondence with its elements of reality?

]Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function---the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e. an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality. A recent result [Pusey et al. arXiv:1111.3328] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system's wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively.

http://arxiv.org/abs/1111.6597

So how can you say the wave function of a photon isn't real when the wave function has been measured? In the experiment I listed above they did weak measurements on a stream of photons and both real and imaginary components of the wave function appear directly in the measuring apparatus. It says:

We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method.

Here's more from Lundeen Lab:

Central to quantum theory, the wavefunction is a complex distribution associated with a Artistic depiction of the wavefunction and apparatusquantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of it through its use to calculate measurement outcome probabilities through the Born Rule. Tomographic methods can reconstruct the wavefunction from measured probabilities. In contrast, we demonstrated a method to directly measure the wavefunction so that its real and imaginary components appear straight on our measurement apparatus. At the heart of the method is a joint measurement of position and momentum that is made possible by weak measurement (see below for what that is). As an example of the method we experimentally directly measured the transverse spatial wavefunction of a single photon. This new measurement gives the wavefunction a plain and general meaning in terms of a specific set of operations in the lab.

Briefly, the idea is as follows: The average result of a weak measurement of A on state psi and which is then strongly measured to be in state phi is called the weak value. It is given by A_w on the right. Weakly measuring the projector |x><x| followed by a strong measurement with result p=0 results in a weak value proportional to the wavefunction.

http://www.photonicquantum.info/Research.html

This goes to my point of one to one correspondence.

There's a one to one correspondence when a pitcher pitches in the strike zone. When he pitches outside of the strike zone then he's no longer in correlation with getting a strike.

In every experiment, the wave function has been in a one to one correlation with the quantum system. Is there any evidence that the wave function and the system is uncorrelated? If the wave function isn't real, why do we see this one to one correspondence? Where's the deviation if it's all abstract statistics?

matrixrising said:
I was talking about the weak measurements carried out in the experiment I listed above. My point was, the system still behaves in a way Quantum Theory predicts. If an ensemble interpretation is correct, why don't we find huge deviations at these levels?

The ensemble interpretation fully conforms to the quantum formalism. If a system still behaves in the way Quantum Theory predicts then that can't be used as evidence against it.

Thinking otherwise is simply, utterly, and outright SILLY.

Can I ask you exactly where you have learned QM from? For example can you state the Born rule? Not the basic version, but the proper one developed by Von-Neumann.

Thanks
Bill

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matrixrising said:
In every experiment, the wave function has been in a one to one correlation with the quantum system.

Your logic is erroneous - and obviously and trivially so.

In every experiment the probabilities assigned to the sides of a coin is in 1-1 correlation with the outcomes. That does not make probabilities real.

Thanks
Bill

matrixrising said:
Is a system's wave function in one-to-one correspondence with its elements of reality?
http://arxiv.org/abs/1111.6597

Yea - know that one - its been debunked:
http://arxiv.org/pdf/1302.1635v1.pdf

matrixrising said:
So how can you say the wave function of a photon isn't real when the wave function has been measured?

The point is, as myself and Cthugha have tried, obviously unsuccessfully, to explain is it hasn't been measured.

If you could measure it in a single observation, and not in a statistical sense, you have violated the basic postulates of QM.

That's why I have asked where you have learned QM from, because this is utterly foundational and basic to QM. It follows from the Born rule.

What you are talking about are WEAK measurements, which does exactly what I said could be done - does it in a statistical sense - not in a single measurement. In the same way you can measure probabilities in a statistical sense - but that doesn't make them real either.

Thanks
Bill

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cthugha,

Thanks for the response. You said:

Well, to stick with your pool table setting, the pool ball actually and literally IS in all the pockets (and everywhere on the table) simultaneously when you consider the wave function as real. It actually is in all of these pockets and "collapses" to one of the pockets as soon as you take a look. A non-realistic wave function approach instead just considers the wave function as describing all the probable states the ball could be in.

This is true in part.

The pool balls can't be in a state that isn't described by the pool table. In the book Hyperspace, Dr. Kaku was talking about Hawking Wave Function of the universe. Here's what he said:

The starting point of quantum theory ... is a wave function that describes all the possible various possible states of a particle. For example, imagine a large, irregular thundercloud that fills up the sky. The darker the thundercloud, the greater the concentration of water vapor and dust at that point. Thus by simply looking at a thundercloud, we can rapidly estimate the probability of finding large concentrations of water and dust in certain parts of the sky.

The thundercloud may be compared to a single electron's wave function. Like a thundercloud, it fills up all space. Likewise, the greater its value at a point, the greater the probability of finding the electron there. Similarly, wave functions can be associated with large objects, like people. As I sit in my chair in Princeton, I know that I have a SchrÖdinger probabllity wave function. If I could somehow see my own wave function, it would resemble a cloud very much in the shape of my body. However, some of the cloud would spread out all over space, out to Mars and even beyond the solar system, although it would be vanishingly small there. This means that there is a very large likelihood that I am, in fact, sitting here in my chair and not on the planet Mars. Although part of my wave function has spread even beyond the Milky Way galaxy, there is only an infinitesimal chance that I am sitting in another galaxy.

The point here is, system can only be in a state that's an underlying reality described by the wave function. The wave function couldn't be spread out to planet Lexar 20,0000 light years away because it's not an underlying reality. How can the quantum system be in a probable state that isn't an underlying reality that's described by the wave function?

How can the quantum system be in a probable state that isn't first a "real" possibility?

bohm2 said:
But is it a direct measurement? Those experiments rely on the notion of weak measurement. A criticism raised against a weak measurement is that it says little about the properties of an individual system. Demystifier discusses this issue here:

Weak measurements in quantum mechanics and 2.6 children in an American family
https://www.physicsforums.com/blog.php?b=1226

It isn't a direct measurement, and it only can be measured in a statistical weak sense - a point the OP doesn't seem to get.

Probabilities can be measured that way to - but that doesn't make them real either.

Thanks
Bill

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matrixrising said:
In the book Hyperspace, Dr. Kaku was talking about Hawking Wave Function of the universe.

Mate - forget these popularizations - they will probably confuse more than enlighten.

Learn the REAL stuff:
http://theoreticalminimum.com/biography

You obviously have quite a few misconceptions and are confused about fundamental things.

There is one, and only one way, to rectify that - study it properly.

Thanks
Bill

matrixrising said:
I was talking about the weak measurements carried out in the experiment I listed above. My point was, the system still behaves in a way Quantum Theory predicts. If an ensemble interpretation is correct, why don't we find huge deviations at these levels?

Ehm...why should we? Ensemble interpretations do not predict any deviations.
matrixrising said:
Here's an interesting paper:

Is a system's wave function in one-to-one correspondence with its elements of reality?

This is somewhat like a follow-up of Nature Phys. 8, 476 (2012) which was in turn followed by Phys. Rev. Lett. 109, 150404 (2012). Both papers have almost the same author list. (2 out of 3/4 authors are the same). If you have a look at the ArXiv preprints of these manuscripts, the first versions were called "The quantum state cannot be interpreted statistically" and "The quantum state can be interpreted statistically", which I consider a magnificent job of boosting the importance of one's own work (and citations) by showing how to avoid the no-go-theorem one just proposed. If you know the field, all these papers are about maximally psi-epistemic interpretations only which still leaves us with pretty much all the relevant epistemic theories. However, I do not know your level of physics education. If you are not at a PhD-level in some quantum information related field, I am afraid most of what I wrote in this thread might be pretty incomprehensible to you.

edit: I just saw you cited Michio Kaku, so I suppose you are not formally educated in quantum information theory. Sorry if my last comments were very technical. Let me put it simple: Interpreting a wave function in a realistic manner has a well defined and fixed definition in qm, but it is not related to what you call realism of the wave function at all.

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matrixrising said:
How can the quantum system be in a probable state that isn't first a "real" possibility?

You are confused.

A system is in a definite state, like there is a definite probability state vector describing the sides of a coin. Determining what that is can only be done in a statistical sense and to a certain confidence level. The fact it is a definite well defined thing does not make it real, nor does it allow its exact value to be determined except in a statistical sense.

I think we can safely assume you have not studied QM except from popularizations.

Until you correct that you will not be able to discuss it in a meaningful way and will be caught in a myriad of misconceptions.

Thanks
Bill

Yes, it has been measured.

From Lundeen:

As an example of the method we experimentally directly measured the transverse spatial wavefunction of a single photon.

I didn't say a single photon was measured, I said there's been direct measurement of a single photon's wave function.

When you look at the stream of photons, each photon in this ensemble follows the predictions of QM. The experimenter prepared single photons with identical wave functions. Here's more on the experiment from Lundeen Lab:

How the experiment works:Apparatus for measuring the wavefunction

1. Produce a collection of photons possessing identical spatial wavefunctions by passing photons through an optical fiber.
2. Weakly measure the transverse position by inducing a small polarization rotation at a particular position, x.
3. Strongly measure the transverse momentum by using a Fourier Transform lens and selecting only those photons with momentum p=0.
4. Measure the average polarization rotation of these selected photons. This is proportional to the real part of the wavefunction at x.
5. Measure the average rotation of the polarization in the circular basis. (i.e. difference in the number of photons that have left-hand circular polarization and right-hand circular polarization). This is proportional to the imaginary part of the wavefunction at x.
6. Repeat for all x to scan through the wavefunction.

Again, the WAVE FUNCTION of a single photon has been directly measured.

matrixrising said:
Yes, it has been measured. I didn't say a single photon was measured, I said there's been direct measurement of a single photon's wave function.

Its the WEAK measurement thing that was pointed out to you early on.

It can be measured but only in a statistical sense.

Before you can disentangle technical papers you need to understand those technicalities - which you obviously don't.

You need to learn some basic QM.

Thanks
Bill

bhobba, you said:

A system is in a definite state

This is exactly my point. In a definite state described by the system's wave function. Again, how can the underlying reality of the wave function not be real? It has to be. How can the system be in a state that's not firs a "real"possibility? Could you answer that simple question?

matrixrising said:
Again, the WAVE FUNCTION of a single photon has been directly measured.

Again - it HASN'T - except in a statistical sense.

And if it was in any other sense it would contradict basic fundamental axioms of QM - specifically the Born rule.

Thanks
Bill

matrixrising said:
bhobba, you said:

A system is in a definite state

This is exactly my point. In a definite state described by the system's wave function. Again, how can the underlying reality of the wave function not be real? It has to be. How can the system be in a state that's not firs a "real"possibility? Could you answer that simple question?

I have, and repeatedly, but you simply do not get it.

Just because something is definite, just like probabilities are definite, does not mean it's real.

This is basic and utterly trivial.

Thanks
Bill

bhobba, you said:

Its the WEAK measurement thing that was pointed out to you early on.

The thing about 2.6 kids? That makes zero sense unless you're saying that the wave function has to conform to classical reality in order to be real. Why would the wave function that describes a quantum system conform to classical physics?

Weak measurements are fine because we're talking about a quantum system.

When you mention 2.6 kids, you're just giving an example of how a formula describing the classical world doesn't correspond to physical reality.

This has nothing to do with weak measurements and the DIRECT measurement of a single photons wave function.

bhobba, you said:

Just because something is definite, just like probabilities are definite, does not mean it's teal.

What?

How can it be definite if the underlying reality isn't real?

matrixrising said:
Again, the WAVE FUNCTION of a single photon has been directly measured.

No, it is the wave function of a single photon state. If you measured the wave function of a single photon, you would not need an ensemble and you would not need to measure AVERAGE polarization rotations - and you probably would get a Nobel prize.

A similar weak measurement has been performed on single photon trajectories in a two-slit interferometer (Science 332, 1170 (2011)). The authors point out that "It is of course impossible to rigorously discuss the trajectory of an individual particle, but in a well-defined operational sense we gain information about the average momentum of the particle at each position within the interferometer, leading to a set of “average trajectories.”"

The same holds true for Lundeen's experiment. You do not discuss the wave function of an individual particle, but you get the averaged trajectories described by the wave function.

matrixrising said:
The thing about 2.6 kids? That makes zero sense unless you're saying that the wave function has to conform to classical reality in order to be real. Why would the wave function that describes a quantum system conform to classical physics?

The issue here isn't if the wavefunction can be real - its if it MUST be real. I freely admit it can be real. But there is nothing in the formalism saying it MUST be real - in fact I don't think it is because my view is its like the probabilities of probability theory. But that is an OPINION - its like bums - everyone has one - it doesn't make it correct.

matrixrising said:
Weak measurements are fine because we're talking about a quantum system. When you mention 2.6 kids, you're just giving an example of how a formula describing the classical world doesn't correspond to physical reality. This has nothing to do with weak measurements and the DIRECT measurement of a single photons wave function.

Whoa. First I didn't mention anything about 2.6 kids - its probably in a link someone else gave.

And exactly what is your claim? Weak measurements are OK? No one is denying that - they can be used to determine a state - the claim is they require many measurements and only give answers in a statistical sense.

If you would look up the Wikipedia article you would see this very basic fact:
http://en.wikipedia.org/wiki/Weak_measurement
'In 2011, weak measurements of many photons prepared in the same pure state, followed by strong measurements of a complementary variable, were used to reconstruct the state in which the photons were prepared.'

What they did is measure the state of a large number of photons in the same state. This is exactly the claim - you need a large number of observations to do it - just like you need a large number of observations to determine a probability. The fact you can do that for probabilities and states makes neither real.

Thanks
Bill

Cthugha said:
The same holds true for Lundeen's experiment. You do not discuss the wave function of an individual particle, but you get the averaged trajectories described by the wave function.

Exactly.

No one is denying you can't measure a state - but you must do it a large number of times, or on a collection of objects in the same state.

That you can do that does NOT imply the state is real any more than you can measure probabilities in a similar way implies probabilities are real.

Thanks
Bill

matrixrising said:
How can it be definite if the underlying reality isn't real?

The same way probabilities are definite and not real.

I have said it I can't recall how many times.

Take a coin. We can flip it and describe probabilistically which side will come up. This is represented by two numbers associated with each side. They both have a definite value. To determine those values we need to flip it many times, and even then we can never find those values exactly, but by doing it enough times we can get as close as we like to a vanishingly small level of confidence.

The view of many is that a quantum state is exactly the same thing. It a definite property associated with a quantum system - but exactly like probabilities is not real - its simply something that aids us in calculating expected values.

The measurements you have cited determining a quantum state are the exact analogue of that - it was a measurement done on many photons in the same state. Its like if we had many coins exactly the same and flipped them simultaneously then counted the heads we can tell in a 'single' measurement the probabilities. Nothing mysterious - and it doesn't make probabilities real.

Thanks
Bill

matrixrising said:
Weak measurements are fine because we're talking about a quantum system.

Here's a very simple description from Demystifier's post of what a weak measurement involves and why it isn't a direct measurement:
To understand what weak measurement is, the following analogy from everyday life is useful. Assume that you want to measure the weight of a sheet of paper. But the problem is that your measurement apparatus (weighing scale) is not precise enough to measure the weight of such a light object such as a sheet of paper. In this sense, the measurement of a single sheet of paper is - weak.

Now you do a trick. Instead of weighing one sheet of paper, you weigh a thousand of them, which is heavy enough to see the result of weighing. Then you divide this result by 1000, and get a number which you call - weak value. Clearly, this "weak value" is nothing but the average weight of your set of thousand sheets of papers.

But still, you want to know the weight of a SINGLE sheet of paper. So does that average value helps? Well, it depends:

1) If all sheets of papers have the same weight, then the average weight is equal to weight of the single sheet, in which case you have also measured the true weight of the sheet.

2) If the sheets have only approximately equal weights, then you can say that you have at least approximately measured the weight of a single sheet.

3) But if the weights of different sheets are not even approximately equal, then you have not done anything - you still don't have a clue what is the weight of a single sheet.
https://www.physicsforums.com/blog.php?b=3077

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