Is the Wave Function Real? Evidence from the Frankenstein Photon Experiment

[Dmitry67]

Sometimes we can not even isolate 'pure' objects and have to deal with the superposition. Electron may be a lucky exception.

But take proton: (uud). What color is quark d? What we call a proton is actually a superposition of uud having all possible combinations of colors.

 

[Demystifier]

I still can't get around the idea that: A particle's WF expands in free space even after a particle is detected.

What is so strange about it? Isn't the case of quantum non-demolition measurement a clear and well-known example of this?

 

[Demystifier]

It seems like any point in open space would have a large number of these alternative paths coming through.

Oh, perhaps now I see what your problem is. No, the particle does not have a number of alternatives at any point IN SPACE (where "space" means - the 3-dimensional space), simply because the wave function does not live in (this) space. Instead, since the particle is entangled with the environment (because without such an entanglement there would be no decoherence, measurement, or effective "collapse"), the wave function lives in the MULTI-DIMENSIONAL CONFIGURATION space. That's the space in which the alternatives live.

 

[GeorgCantor]

Oh, perhaps now I see what your problem is. No, the particle does not have a number of alternatives at any point IN SPACE (where "space" means - the 3-dimensional space), simply because the wave function does not live in (this) space. Instead, since the particle is entangled with the environment (because without such an entanglement there would be no decoherence, measurement, or effective "collapse"), the wave function lives in the MULTI-DIMENSIONAL CONFIGURATION space. That's the space in which the alternatives live.

Still there must be a correspondence between wavefunctions in configuration space and 3D space. Otherwise, why do we get precise predictions with the SE?

It seems to me the problem lies more with the definition of 3D space. If we do away with it, the MWI takes care of the correspondence in a neat fashion. The 3D problem seems to me to be related more to biology than with physics. This of course is a position assuming the MWI as a starting point.

 

[zonde]

I think everyone can at least agree that a wavefunction the square of the probability density for a given system. Would you say "probability" is real? It's not something tangible, but it does carry tangible information. I think that if you can argue that a probability distribution is a real thing, then you can possibly consider the wave function real.

I would say that probability is not real because "parallel" probabilities do not interact in physical sense.

 

[Demystifier]

Still there must be a correspondence between wavefunctions in configuration space and 3D space. Otherwise, why do we get precise predictions with the SE?

Of course there is a correspondence. The wave function gives probabilities of particle positions (or, according to BI, guides continuous and deterministic changes of these positions) in the ordinary 3D space. The fact that particles live in a space which is only 3-dimensional is compensated by the fact that there is many (entangled) particles. By contrast, the wave function is only one.

 

[my_wan]

The very word 'real' is ill-defined.
There is a very good example: BM (Bohmian Interpretation). In BM,there are 2 'real' components: wavefunction (exactly the same as in MWI, with all 'parralel' worlds) and hidden particles guided by this wave.

However, in BM only waves with particles inside (non-empty waves) form what we call reality. If we see a dead cat, then there is definitely a wave of alive one. It is real, but not tagged with particles (which can not be detected!) and hence don't form the reality.

What do you call 'real'?

Agreed, real is fought with issues. In the sense I used it here it's ontic, like the particles tucked in the waves in your BM description. I have some difficulty with the BM wave as you've described. This live cat wave has empirical consequences when associated with the cat particles, then loses all empirical meaning when the cat dies even though its existence remains. Almost sounds like a justification for ghosts, if you kept some level of empirical meaning to it. Meanwhile, the cat died and gained a separate concurrently existing dead cat wave from where?

What determines a coupling between a wave and the particles, the location of the particle relative to the waveform? In my reading of BM I didn't get quiet this picture of the wavefunction, but obviously attaching the notion of 'real' to the wavefunction and having it push around particles accordingly isn't going to run into direct empirical falsification. It still seems to me that these BM waves are ad hoc imaginative conveniences, specially crafted so as not to provide any new empirical content.

I have nothing against interpretive or metatheories as such, but I don't see their usefulness as singularly justified metatheories. Rather, as a group of all viable metatheories, they help define a space of viable possibilities which might in part potentially be useful in extending the empirical content of QM itself. Much like the no-go theorems help define what is not viable. For their own sake they seem pretty worthless to me.

 

[eaglelake]

It is sometimes said that wave functions are not real, and simply represent the observer's knowledge of the system. I would like to comment against this point by presenting an experimental setup which would tend to indicate that the wave function is quite real. As far as I know, this setup per se has never been executed (although I am hoping someone might recognize it as something which has been).

To follow the setup, you should be familiar with the following experiment:

Bell inequalities and quantum mechanics, J. H. Eberly (2001)

See Figure 1, the Bell analyzer loop, in which a beam is split into H and V components. Those are then recombined so that the H/V information is erased, leaving a beam with the same properties as it was originally.

So if you took a pair of entangled particles, Alice and Bob, and ran each through a Bell analyzer loop, the recombined Alice and Bob are still entangled. This is what the above paper is saying.

---------------------

Here is my twist:

Frankenstein photons:
=====================

Split Alice into Alice-H and Alice-V. Split Bob into Bob-H and Bob-V. Now recombine Alice-H with Bob-V (which is identical to Alice-V). Recombine Bob-H with Alice-V (likewise identical to Bob-V). You will now have 2 Frankenstein photons that are polarization entangled!

Now, if the above is accurate (I don't see how it could be expected to be otherwise), then you would have to admit that you are mixing the wave functions of different photons to obtain an effect that clearly does not occur with either portion of the component wave functions alone.

So I conclude that the wave function is quite real. Your thoughts?

Let us pause for a moment to remind ourselves what we do know about the "wave function", which is more often a "state vector" \left| \psi \right\rangle.
a) It is defined in a linear vector space: \left| \psi \right\rangle = \sum {\left| {\varphi _k } \right\rangle } \left\langle {{\varphi _k }}<br /> \mathrel{\left | {\vphantom {{\varphi _k } \psi }}<br /> \right. \kern-\nulldelimiterspace}<br /> {\psi } \right\rangle where the basis vectors \left| {\varphi _k } \right\rangle are the eigenvectors of the observable \hat A$ that is being measured. \hat A\left| {\varphi _k } \right\rangle = a_k \left| {\varphi _k } \right\rangle.
b) The only "interpretation" that has universal acceptance is the Born postulate: The probability of obtaining the value a_k is P_k = \left| {\left\langle {{\varphi _k }}<br /> \mathrel{\left | {\vphantom {{\varphi _k } \psi }}<br /> \right. \kern-\nulldelimiterspace}<br /> {\psi } \right\rangle } \right|^2.
c) The state vector describes an experiment designed to measure the observable \hat A. The state vector is determined by the entire experimental arrangement, including the measuring device and the measurement result. Its specific mathematical form is determined by the observable being measured.
d) The state vector satisfies the Schrodinger equation: i\hbar \partial \left| \psi \right\rangle /\partial t = \hat H\left| \psi \right\rangle.
Thus, the state vector is necessarily complex.
The formalism does not require that \left| \psi \right\rangle be "real". In fact, it is silent on the matter. Hence, our present conundrum. The real elements of classical physics are particles and waves which make up all things in the mechanical universe of Newton and Einstein. All (real) things exist in the space-time continuum. Real particles and real waves propagate in 3-space where they interact with detectors designed to measure physical properties possessed by them.
There is no evidence of any kind that state vectors are real in the classical sense. If they are real, then we should be able to design an experiment to detect them. But what are the properties possessed by state vectors that are measureable? We have no idea how to construct a state vector detector. And no one has ever observed state vectors propagating through 3-space, or collapsing, or interacting with any kind of detector known to us. Also, the Eberly paper cited in the OP, yields a contradiction. Its approach assumes a classical-like sequence of events, which does not give the correct quantum results.
So, what is the wavefunction? We only know that it is a mathematical construct used to calculate probabilities. There is no theoretical or experimental evidence that it is anything more!
Dr Chineses asks if the quantum wave function is real. I don't know, but I doubt if they are. I can only give him my own bias on such matters: I am immediately suspicious of anything that cannot be verified experimentally.
Best wishes

 

[Dmitry67]

Whats about first moments from the Big Bang when it was too hot to form any system with stable internal state - so no measurement devices, in principle, could exist?

I believe defining wavefunction in a semi-classical context (observables, Born rule, experiments and measurements) comes from Bohr era. It is very important historically, but it is time to leave it behind.

 

[my_wan]

I read RUTA's paper "http://philsci-archive.pitt.edu/archive/00003247/" ". Very interesting, and gives me a greater perspective of RUTA's perspective here.

This got me to thinking about this question of wavefunction realism both in historical context and a range of other physical parameters. Even Newton had his detractors, most notably wrt gravity, based on the lack of a mechanistic explanation. This was a prime motivation behind the classical ether, even though the empirical absurdities should have effectively killed it even before relativity. With relativity based in kinematics the limit speed C became the de facto proxy for maintaining causality. Yet many remained dissatisfied with the unspecified causal mechanism in pure kinematics. With QM it became even more difficult to maintain this brand of natural philosophy.

The point here is that our questions of realism, wrt to the wavefunction in this case, at some level still points to our predisposition toward real causal actors to underpin dynamics. I think we should continue asking these questions, so long as a priori demands of truth are avoided, like some of the aetherist that are not too uncommon here.

If we consider realism in terms of other phenomena, such as curvature of spacetime, virtual particles, etc., then Frankenstein particles are not so unique. Of course the ontology attached to realness can vary greatly in these cases, and even in various opinions about these cases. Can DrChinese's argument make the case that the wavefuntion has same level of realism as a vacuum? Physically valid or not, these kinds of questions can help define constraints and sort possibly valid solutions that are generally difficult to analyze.

 

[DevilsAvocado]

So I conclude that the wave function is quite real. Your thoughts?

If I were a philosopher, I would start like this: Please define real & reality.
(but I’m just a rambling layman, so I jump right-on the interesting stuff)

Great 'Frankenstein-gadget' you got there DrC! I’m curious and do have questions:


1) I’ve quickly read the Eberly paper, and understood < 50% , but I must ask about your "polarizing beam splitter". In the paper Eberly describe the "Analyzer loop", as "Calcite analyzer" + "Reversed analyzer", and you have only 'one part' – the polarizing beam splitter? Wouldn’t that count as 'measurement' on Alice & Bob, 'destroying' the wavefunction/entanglement? If we compare with the http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser" the interference pattern is lost if we don’t apply another beam splitter to join the (virtual) paths of the photon:

Wikipedia - Delayed choice quantum eraser
In the two diagrams to the right a single photon is emitted at the yellow star, passes through a 50% beam splitter (green block) that reflects 1/2 of the photons, and travels along two possible paths, depicted by the red or blue lines.

In the top diagram, one can see that the trajectories of photons are clearly known — in the sense that if a photon emerges at the top of the apparatus it appears that it had to have come by the path that leads to that point (blue line), and if it emerges at the side of the apparatus it appears that it had to have come by way of the other path (red line).

Next, as shown in the bottom diagram: a second beam splitter is introduced at the top right. It can direct either beam towards either path; thus note that whatever emerges from each exit port may have come by way of either path.

It is in this sense that the path information has been "erased."

2) If the 'Frankenstein-gadget' can handle the above: Would that mean that Chris & Dale are entangled both with themselves and each other? (Cool!)

I stop here and get back on the "Real stuff" later...


P.S. You didn’t collaborate with this guy, did you?
[PLAIN]http://middlezonemusings.com/wp-content/uploads/2008/03/abby-normal.jpg

 

[DrChinese]

Great 'Frankenstein-gadget' you got there DrC! I’m curious and do have questions:


1) I’ve quickly read the Eberly paper, and understood < 50% , but I must ask about your "polarizing beam splitter". In the paper Eberly describe the "Analyzer loop", as "Calcite analyzer" + "Reversed analyzer", and you have only 'one part' – the polarizing beam splitter? Wouldn’t that count as 'measurement' on Alice & Bob, 'destroying' the wavefunction/entanglement? If we compare with the http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser" the interference pattern is lost if we don’t apply another beam splitter to join the (virtual) paths of the photon:

[/PLAIN]

Why, yes, you are absolutely correct! I did indeed intend to represent the reverse components which would be needed to properly execute this. I guess I had realized that there might be several ways to accomplish this in practice, and failed to designate anything for handling this function. To be consistent with the reference, I should have placed the additional items in the diagram. I will see if I can upload something a bit tidier.

Thanks for pointing this out!

 

[DrChinese]

Here is some background, by the way, on which Eberly based his paper.

From French & Taylor, An Introduction to Quantum Mechanics, 1979:

 

[DrChinese]

Ok, here is an updated diagram, I hope this is a little better:

Creating Entangled "Frankenstein" Photons: Is this Possible?

 

[DevilsAvocado]

Ok, here is an updated diagram, I hope this is a little better:

Creating Entangled "Frankenstein" Photons: Is this Possible?

This looks much better! You know I’m basically 'guessing' here, but there is still one thing that might be a little 'troublesome'... and that’s polarizing in "polarizing beam splitter"...

I have no idea if this is correct – but my understanding of entangled photons is that the spin "of the pair" is actually null or nothing – it’s first when we do a measurement that a V/H spin is 'established'... Where did I read or hear this... I must check it out...?

But if the Eberly paper is correct, and if he runs the "polarizing beam splitter" with preserved entanglement, then your 'Frankenstein particles' must also work!

And if so – I think this is really amazing! If this works, it must lead to new possibilities in BTE!

Would be real interesting to hear what RUTA has to say about the technical validity of your 'Frankenstein-gadget'?


Edit1: I think I got it – you 'erase' the V/H spin in the "Reverse PBS" and THAT’S IT!


Edit2: But then the question arise – is there anything left of Alice & Bob's 'identity' after PBS...??

 

[DrChinese]

Would be real interesting to hear what RUTA has to say about the technical validity of your 'Frankenstein-gadget'?


Edit1: I think I got it – you 'erase' the V/H spin in the "Reverse PBS" and THAT’S IT!

Yup, the round trip would restore the original state and then the measurement results would be erased. Pretty fascinating, isn't it? In real life, I think you have to do things to preserve phase in the process or else there is destructive interference. (Not entirely certain though.)

 

[DevilsAvocado]

Pretty fascinating, isn't it?

I almost fell of my chair realizing this... I have had a thought in the back of my head in starting a new thread that would deal with the 'synchronization' of Alice & Bob (hoping to get around the interpretation business)... and here we have 'two ends' of an entanglement TOGETHER!?

What on Earth will happen if you run Chris thru another polarizing beam splitter?? This must settle the properties for 'two ends' of an entanglement INSTANTANEOUSLY??

... amazing ...

 

[madhatter106]

For some reason it makes me think of the holographic process when reading about the interferometer. Even our visual sight is based on two separate light paths.

I also was wondering how one splits what isn't? I'm not trying to play semantics. I understand the formalism, it's the wording that seems to cause confusion. Since the photon is 'energy' isn't polarization an induced magnetic state? If the photon is treated in that regard as a magnetic state then the polarization is just changing the electrical signature of the photons? and the entanglement is the shared magnetic state? although it would have to be a monopole right? odd bugger this energy signature.

 

[DevilsAvocado]

If the wavefunction is not real, then how do we explain this?

[PLAIN]http://www.sciencefriday.com/images/shows/2004/073004/AfsharExperimentSmall.jpg