Is the wave function real or abstract statistics?

[Cthugha]

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.

 

[bhobba]

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.

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

 

[bhobba]

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

 

[bhobba]

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

 

[bohm2]

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

 

[matrixrising]

cthugha,

This is exactly what I have been saying. This is why I talked about a stream of photons and I talked about the Casino where each individual spin is real in an ensemble of spins that create a statistical picture.

How can you say the individual spins that create the statistical picture are not real? Don't they have to be?

How can you produce single photons possessing the same spatial wave functions if the wave functions of a single photon are not real?

 

[matrixrising]

bhobba,

Simple question.

How can you have probabilities without the underlying reality being "real?"

 

[bhobba]

How can you produce single photons possessing the same spatial wave functions if the wave functions of a single photon are not real?

How can you produce coins that have the same probabilities when thrown if probabilities aren't real?

Obviously objects having the same property has nothing to do if that property is real.

You just don't seem to get a definite property an object has may not be real.

Thanks
Bill

 

[matrixrising]

Thanks bohm2,

You said:

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.

In this case the sheets(photons) are equal and this is exactly what I've been saying. 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.

So according to this criteria, Lundeen is a huge success.

 

[bhobba]

How can you have probabilities without the underlying reality being "real?"

The same way coin faces are real and you can assign probabilities to them - the probability is a definite property and its not real - at least most wouldn't think it is.

We can assign a state to a quantum system. What a quantum system is, is a difficult issue - and even if its real - but that has nothing to do with this issue. Well actually it does - if a system isn't real the state is unlikely to be - but I am not even going there

If you want to chat about that one start a new thread - but the mods may shut it down because its probably well into philosophy territory rather than physics.

Thanks
Bill

 

[bhobba]

So according to this criteria, Lundeen is a huge success.

But not in the way you think it is.

It does not prove the state is real.

Thanks
Bill

 

[matrixrising]

bhobba, you said:

How can you produce coins that have the same probabilities when thrown if probabilities aren't real?

These probabilities can't exist if the underlying reality of the coins isn't real. It's just like there couldn't be probabilities of a quantum system if the wave function doesn't describe the underlying "reality" of the quantum system.

Again, probabilities must always be coupled with an underlying reality.

For instance, I couldn't give you the probability of finding Hobbits on planet Lexar because there's no underlying reality. But I can give you the probability of finding the electron in 2 different states because both states must be real.

I couldn't give you the probability that I'm a 19 year old basketball star because I'm 35 years old. There's no underlying reality so there's no probability of the event occurring.

Do you have an example of probability that's not associated with an underlying reality?

 

[Cthugha]

This is exactly what I have been saying. This is why I talked about a stream of photons and I talked about the Casino where each individual spin is real in an ensemble of spins that create a statistical picture.

How can you say the individual spins that create the statistical picture are not real? Don't they have to be?

You are mixing things up. This is absolutely unrelated to what people talk about when discussing whether the wave function is real or not.

Let me give you one (admittedly exaggerated and hilarious) example:

Morpho is kind of a superhero with the amazing ability to teleport somewhere spontaneously if some part of him is already there. This ability is triggered by rain falling on him and he cannot control it. He would like to go to the Bahamas for vacation every year for 10 years in a row, but getting there is not cheap, so he only goes there 30% of the time. Now, there are two possibilities:

1) Morpho actually goes to the Bahamas in 3 out of the 10 years and stays at home during the other 7 years.

2) Every year, Morpho cuts off one of his arms and legs (no problem, he is a superhero - he has healing powers) and sends it to the Bahamas. Once his arm and leg arrived there, he waits for the rain. Unfortunately, there is not that much rain on the Bahamas and in 7 out of 10 years it rains at his home first and he teleports home as a whole. In the other 3 years he teleports to the Bahamas.

Morpho's holiday wave function is now given by 3/10 Morpho at the Bahamas + 7/10 Morpho at home (please ignore normalization issues). Now the two possibilities above give examples of a non-realistic vs. a realistic interpretation of the wave function? The question to ask in order to find out whether the wave function is considered realistic, is whether the wave function LITERALLY decribes Morpho's state while each single plane is flying to the Bahamas.

In possibility one, this is not the case. Morpho is always really either fully at home or fully in the plane to the Bahamas. The wave function is not realistic because it does not describe the real state of Morpho in each run as Morpho is not 7/10 at home, but either fully at home or fully in the plane. The two states are real. The wave function is not.

In possibility two, the wave function is realistic. In every single year 3/10 of Morpho (his arm and his leg) are making the trip to the Bahamas. The wave function literally describes what is going on and is thus real. This is NOT about the underlying states at all.

How can you produce single photons possessing the same spatial wave functions if the wave functions of a single photon are not real?

Like in case 1 above. Single photon wave functions are always defined for an ensemble of identically prepared photons. If photons have the same wave function, this means the measurements are governed by the same probability distribution.

 

[bohm2]

A really cool site of how those researchers of the study in the 'direct' measurement of wavefunction did the measurements can be found below. The slides and video section is particularly useful:

Direct Measurement of the Wavefunction
http://www.photonicquantum.info/Research.html

 

[bhobba]

These probabilities can't exist if the underlying reality of the coins isn't real.

But that's not the issue you are arguing about.

You are claiming the STATE must be real.

I am claiming, like probabilities describing the sides of a coin, and a coin is a very real thing, the STATE, not the system, but the STATE, doesn't have to be real.

The issue of if a quantum system is actually real like a coin is not the issue here. For the sake of argument I am assuming it is in some sense real. However if it isn't, and many don't think it is, then it's very hard to think of the state as real - but I am not arguing like that.

Added Later
I am well aware of the issues of the PBR theorem and the view the underlying quantum system is in some sense real - but that is not the point I am making here.

Now I have mentioned it the OP may latch onto it, but if he does then I would ask him to please actually understand it:
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

Thanks
Bill

 

[Demystifier]

In this case the sheets(photons) are equal and this is exactly what I've been saying.

I think you have a problem to distinguish two different meanings of the word "photon". One meaning is a click in a detector (or perhaps a point-particle in the Bohmian interpretation) which of course is real. Another meaning is the wave function, which may or may not be real.

According to some interpretations, these two concepts of the photon are one and the same. For example, this is so in a von Neumann variant of Copenhagen interpretation, according to which the real wave function really collapses when a measurement is performed. It seems that you take such an interpretation for granted and do not consider a possibility for an alternative.

But according to other interpretations, such as Ballentine's or Bohm's ones, the word "photon" means only the former and not the latter. In such interpretations, wave function is not real.

So, when one prepares photons "in the same state", that means they have the same wave function. But it does not necessarily mean that the photons themselves are identical, because there are interpretations in which this may not be so.

Or to comment the quote above, the sheet is an analogue of the photon in the first sense, but not necessarily an analogue of the photon in the second sense.

 

[audioloop]

Simple question.

How can you have probabilities without the underlying reality being "real?"

or probabilities in absence of anything..

 

[bohm2]

I think you have a problem to distinguish two different meanings of the word "photon". One meaning is a click in a detector (or perhaps a point-particle in the Bohmian interpretation) which of course is real. Another meaning is the wave function, which may or may not be real.

Correct me if I'm wrong, but even within the Bohmian/deBB camp there is quite a big difference with respect to the ontology of the wave function. As I understand it, the Goldstein/Durr/Zanghi/Maudlin group treat the wave function differently (less real or non-committal, kind of like Bohmian Copenhagenists) than say Valentini and company (who perceive the wave function as more real). I took it that this is the reason why Valentini was so ecstatic about PBR and the Couder et al. oil drop experiments while not much about it was mentioned from the other camp? For instance see:

The nature of the wave function in de Broglie's pilot-wave theory
http://streamer.perimeterinstitute.ca/Flash/3f521d41-f0a9-4e47-a8c7-e1fd3a4c63c8/viewer.html

 

[Jilang]

Do you have an example of probability that's not associated with an underlying reality?

Er yes. The probability of a spinning coin being found to be heads or tails before you bring your hand down on it.

 

[matrixrising]

bhobba,

Yes, I'm claiming that the state must be real or there's no probability of the state occurring if it isn't coupled with an underlying reality.

The way I see it, QM isn't about whether the state is real. I think it has to be. Where probability comes into play is which state will be measured.

It's like a race with for runners. I could give you probabilities on who will come in 1st, 2nd, 3rd and 4th. What I can't do is give you probabilities of who will come in 10th because that's not an underlying reality and there's no probability of the event occurring.

So the probable states of the wave function have to be real states because if their not real states there's no probability of them becoming measured states. Like I said, there's no probability that you will measure the state where I'm a 19 year old basketball star because I'm 35 years old. Probability has to be coupled with an underlying reality.

I think the problem is when you try to apply the quantum wave function to our classical universe. You get things like Schrödinger's cat. I think decoherence answers some of these questions as the real quantum states decohere into mixed states. When this occurs the classical universe emerges but the real quantum properties don't just vanish, we just can't measure them in the classical world we experience.

This is why the emerging field of Quantum Biology is so exciting. If classical systems can use quantum properties for things like migration of birds, photosynthesis or with DNA, then why not with consciousness? Is consciousness connected to decoherence via quantum gravity a la Roger Penrose? These are exciting times.

I think in experiment after experiment has shown these quantum properties can be experimentally measured because the pure quantum states are real states that become mixed states via decoherence. Probability comes into play because the observer doesn't know which state will be measured.

IMHO, there's a universal wave function that can't be measured. This is why there's inherent randomness in nature. The pure "real" states of this universal wave function become mixed states and classical universes emerge.

At the end of the day, I think the wave function has to describe underlying states that are objective realities that exhibit quantum properties that we can measure.

 

[matrixrising]

Jilang,

The underlying reality is the states of the spinning coin (heads or tails). You couldn't have probabilities of where the coin would land if heads or tails weren't objective, real states. The states of the quantum system have to be objectively real if there's a probability that the states can be measured. How can you measure a state that doesn't exist?

The ensemble interpretation and most Copenhagen interpretations say you can't know the state of the system prior to measurement so just shut up and calculate. I believe they say this is because if you accept that the states are real states, then you have to accept the weirdness as being real also. So the objection of the states being real isn't scientific but semantic. It's based on the rejection that quantum weirdness is objectively real. So far, most experiments have suggested otherwise and there's no hidden theory that will turn Heisenberg into Newton so to speak.

 

[atyy]

Here is a paper that claims to show that the wave function can be interpreted as representing a state of knowledge - ie. the underlying true state may correspond to more than one wave function.

http://arxiv.org/abs/1303.2834
Psi-Epistemic Theories: The Role of Symmetry
Scott Aaronson, Adam Bouland, Lynn Chua, George Lowther

 

[Jilang]

Jilang,

The underlying reality is the states of the spinning coin (heads or tails). You couldn't have probabilities of where the coin would land if heads or tails weren't objective, real states. The states of the quantum system have to be objectively real if there's a probability that the states can be measured. How can you measure a state that doesn't exist?

The ensemble interpretation and most Copenhagen interpretations say you can't know the state of the system prior to measurement so just shut up and calculate. I believe they say this is because if you accept that the states are real states, then you have to accept the weirdness as being real also. So the objection of the states being real isn't scientific but semantic. It's based on the rejection that quantum weirdness is objectively real. So far, most experiments have suggested otherwise and there's no hidden theory that will turn Heisenberg into Newton so to speak.

Sure you can. Heads or tails are real states but until you bring your hand down you cannot say which one it in. Until that point it is best described by a superposition of the two states. There are theories that can reconcile the weirdness with what we understand so far about the universe. See previous posts. If you can believe in zero point energy, then the motion of particles can cause disturbances in this that can describe interference effects etc in quite a classical way. If you don't believe in it, then you are going to struggle as I did for quite a long time.

 

[matrixrising]

Demystifier,

You make some good points and this is why I think Lundeen was a huge success. It showed a one to one correspondence between the spatial wave function of a single photon and an ensemble of photons with identical spatial wave functions. So the state of a single photon was reconstructed even as the ensemble grew. Here's more about weak measurements from Wiki:

The weak value of the observable becomes large when the post-selected state, |\phi_2\rangle, approaches being orthogonal to the pre-selected state, |\phi_1\rangle.[1][4][5] In this way, by properly choosing the two states, the weak value of the operator can be made arbitrarily large, and otherwise small effects can be amplified.[6][7]

Related to this, the research group of Aephraim Steinberg at the University of Toronto confirmed Hardy's paradox experimentally using joint weak measurement’ of the locations of entangled pairs of photons.[8][9] Independently, a team of physicists from Japan reported in December, 2008, and published in March, 2009, that they were able to use joint weak measurement to observe a photonic version of Hardy's paradox. In this version, two photons were used instead of a positron and an electron and relied not upon non-annihilation but on polarization degrees of freedom values measured.[10]

Building on weak measurements, Howard M. Wiseman proposed a weak value measurement of the velocity of a quantum particle at a precise position, which he termed its "naïvely observable velocity". In 2010, a first experimental observation of trajectories of a photon in a double-slit interferometer was reported, which displayed the qualitative features predicted in 2001 by Partha Ghose[11] for photons in the de Broglie-Bohm interpretation.[12][13]

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.[14]

I think that last part is the ball game and like John Gribbin said, the last nail in the coffin of ensemble interpretations. He said:

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]

I think it's even worse with the recent Lundeen result. The identical spatial wave functions of individual photons were reconstructed over an ensemble of photons. This is a one to one correspondence of the spatial wave function of an individual photon and an ensemble of photons.

 

[matrixrising]

Jilang, you said:

Heads or tails are real states but until you bring your hand down you cannot say which one it in.

You're just describing the uncertainty of the observer as to which state will be measured. The states have to be objectively real in order for them to be probable states. The only reason you have a probability of measuring heads or tails is because the states heads and tails are an underlying reality.

How can the observer measure a probable state that's not an underlying reality? The states of the quantum system have to objectively exist in order for them to be probable states than can be measured by the observer.

 

[Jilang]

Jilang, you said:

Heads or tails are real states but until you bring your hand down you cannot say which one it in.

You're just describing the uncertainty of the observer as to which state will be measured. The states have to be objectively real in order for them to be probable states. The only reason you have a probability of measuring heads or tails is because the states heads and tails are an underlying reality.

How can the observer measure a probable state that's not an underlying reality? The states of the quantum system have to objectively exist in order for them to be probable states than can be measured by the observer.

Yes, you are correct the state heads and the state tails are an underlying reality, but the state half heads and half tails isn't. Quantum states are generally of the second kind until they are measured.

 

[matrixrising]

Jilang,

Why isn't that state half heads or half tails an underlying reality for the quantum system? This is the fallacy of Schrödinger's cat. People say it can't be an underlying reality for a quantum system as described by the wave function because it doesn't make classical sense. Why should it? Experiment after experiment has shown a quantum system just doesn't make classical sense unless you say the classical world emerged from these states of the quantum system. This way, there's no need to conform the underlying reality of the quantum system with your classical experience.

 

[atyy]

@matrixrising: yes it is possible that the wave function is the full and true state of single systems. However, take a look at the paper I linked to in post #52, where one could construct theories that reproduce quantum mechanics in which not only is an underlying true state can correspond to more than one wave function - ie. the wave function is at least in part a state of ignorance of the true underlying state.

 

[matrixrising]

atyy,

Thanks, I missed that and I will look at the paper.

 

[bohm2]

You're just describing the uncertainty of the observer as to which state will be measured. The states have to be objectively real in order for them to be probable states. The only reason you have a probability of measuring heads or tails is because the states heads and tails are an underlying reality. How can the observer measure a probable state that's not an underlying reality? The states of the quantum system have to objectively exist in order for them to be probable states than can be measured by the observer.

Maybe I'm misunderstanding but isn't this just the whole question about non-locality versus realism issue? Norsen in a previous post in this forum provided a local and non-realist (in some sense) model:

Here's a model that non-realistic but perfectly Bell local: each particle has no definite, pre-existing, pre-scripted value for how the measurements will come out. Think of each particle as carrying a coin, which, upon encountering an SG device, it flips -- heads it goes "up", tails it goes "down". That is certainly not "realistic" (in the sense that people are using that term here) since there is no fact of the matter, prior to the measurement, about how a given particle will respond to the measurement; the outcome is "created on the fly", so to speak. And it's also perfectly local in the sense that what particle 1 ends up doing is in no way influenced by anything going on near particle 2, or vice versa. Of course, the model doesn't make the QM/empirical predictions. But it's non-realist and local. And hence a counter-example to any claim that being Bell local requires/implies being "realist".

This is actually the type of model that some like Khrenikov advocate (from my understanding) but he also says that underneath, there's a subquantum reality and his does make different predictions. Actually he argues that this was also Einstein's view. Consider:

...The main distinguishing feature of the present Vaxjo interpretation is the combination of realism on the subquantum level with nonobjectivity of quantum observables (i.e., impossibility to assign their values before measurements). Hence, realism is destroyed by detectors transforming continuous subquantum reality into discrete events, clicks of detectors. The Vaxjo interpretation-2012 is fundamentally contextual in the sense that the value of an observable depends on measurement context. This is contextuality in Bohr’s sense. It is more general than Bell’s contextuality based on joint measurements of compatible observables.

https://www.physicsforums.com/showthread.php?t=721995

But I'm not mathematically competent enough to understand if his argument against Bell's assumptions for Bell inequality are valid. I was hoping someone would shed some light? Then, again I might be messing this up.