Is the wave function physical ?

[DoobleD]

Is the wave function physical ? I've searched for this on the web, and most people seem to agree that it does not represent a physical thing. It'd be just a probability distribution. There is still debate and uncertainty about that question though.

What annoys me then is what about the observed diffraction effect in a double slit experiment ? If we shoot an electron trough slits, the odds of finding it on a screen on the other side correspond to a diffraction pattern right ? As if the electron was somehow interfering with itself. And the diffraction pattern correspond to the wave function I think ? (Please correct me if this is wrong, I'm just starting QM and I am not confortable with its very basic concepts.)

So if there is an observable diffraction pattern that "matches" a wave function, isn't the wave function something physical, as if the electron was "spread" in space ? And how to explain diffraction if the wave function is not a "real physical thing" ?

 

[vanhees71]

The behavior of the electron is described by quantum theory (in its minimal interpretation; everything in addition to the minimal interpretation is not physics but metaphysics or even esoterics). Physics is not about explaining why things are as they are but to describe things as they are as accurately as one can in a quantitative way, and quantum theory is the most comprehensive theory we have to do so. That's as far as it gets to answer your question about the known facts, i.e., the physics about it. If you are not satisfied with this answer, you can't get anything "better" from physics.

 

[jfizzix]

In order to get to the bottom of your question, you'll have to clearly understand what you mean by "physical".

If physical means:
measurable
objectively real (i.e., in certain circumstances, everyone can agree on what it is without further measurement)

.. then it is valid, if not universally accepted to think of the wavefunction as "physical".

 

[Truecrimson]

So if there is an observable diffraction pattern that "matches" a wave function, isn't the wave function something physical, as if the electron was "spread" in space ? And how to explain diffraction if the wave function is not a "real physical thing" ?

A wave function of N objects lives in $\mathbb{R}^{3N}$. Are interference and diffraction of waves in 3N spatial dimensions physical?

 

[jimgraber]

Is it R^3N or C^3N? And does this make a difference as far as realness or physicality?

 

[Nugatory]

Is it R^3N or C^3N? And does this make a difference as far as realness or physicality?

$\mathbb{R}^{3N}$ is the domain of the function - you'll see this if you write it in the position basis. However, that makes no difference to truecrimson's point, which is quite compelling enough already.

 

[DoobleD]

Thanks for those answers !

Physics is not about explaining why things are as they are but to describe things as they are as accurately as one can in a quantitative way

But often in physics when we observe a phenomenon we search for a (physical) cause, for a "why this observable phenomenon happens". In the case of interference, if I observe a diffraction pattern in water, I'll say "oh right, it's because there are water waves combining". And the wave equation I'll have will be a correct description of the physical water waves.

In the case of QM, we have a wave function correctly describing an observed interference, but this function doesn't describe a physical wave that would be the source of that interference ? This must bother all physicists of the world !

EDIT : the sentence "In the case of QM, we have a wave function correctly describing an observed interference, but this function doesn't describe a physical wave that would be the source of that interference ? " might not make sense : the wave pattern of an interference is not described by the same wave equation that the one describing the "sources" waves creating the interference (well, I think ?).
I should have written : "In the case of QM, we have a wave function correctly describing an observed interference, but there is no associated physical wave that would be the source of that interference ? "

A wave function of N objects lives in R3NR3N \mathbb{R}^{3N} . Are interference and diffraction of waves in 3N spatial dimensions physical?

Well, to me, yes. :D But obviously I must be wrong. My thinking is : you can observe (or measure) it <=> it is physical. In our case : we can observe diffraction <=> there is a physical wave responsible for it.

In the other hand if really the wave function has nothing physical, then why do I observe diffraction ? Where it comes from ? What generates it ? What is the cause ?

 

[jimgraber]

Oh Yes. I was thinking of the range, not the domain. Is that C^3N? Or Only R^3N? Or sometihng bigger and more complicated?
TIA
Jim Graber

 

[Nugatory]

In the other hand if really the wave function has nothing physical, then why do I observe diffraction ? Where it comes from ? What generates it ? What is the cause ?

Because the universe works in such a way that certain mathematical manipulations of some abstract mathematical objects provide good predictions of what the universe will do.

Of course that just invites the question of why the universe has to work that way. There's no satisfying answer to that question.

 

[Truecrimson]

Well, to me, yes. :D But obviously I must be wrong. My thinking is : you can observe (or measure) it <=> it is physical. In our case : we can observe diffraction <=> there is a physical wave responsible for it.

In the other hand if really the wave function has nothing physical, then why do I observe diffraction ? Where it comes from ? What generates it ? What is the cause ?

My point was not that it is definitely unphysical or that you were wrong, but that it is not so obvious and depends heavily on what you mean by "physical."

And you cannot directly observe the wave function i.e. its value at a point in space and time cannot be measured in one shot (even if we are allowed to fix a basis and a global phase). It is more like a probability distribution of, say, people height in the sense that it quantifies our uncertainty or a distribution of values of a physical property but it is not the physical property itself. This is to me a more compelling reason not to be so quick to conclude that the wave function is a physical thing that we can "touch" or "feel" (even by modern instruments).

 

[Tollendal]

Dear DoubleD,

The significance of the Wave Function was not understood until Max Born interpreted it as defining the probability of finding a particle in a determinate position of space. He received the Nobel Prize for it in 1932. So, if you call a probability something "physical", the choice is yours.

In 1924, Louis DeBroglie made an important discovery. Considering Einstein's relation

lambda = h/p ( h is Plank's constant and p is momentum)

he demonstraded that the relation faculted the determination of the wave length of any material object. For this equation he earned the Nobel prize in 1929. The hypothesis was confirmed in 1927 by Clinton Davisson and Lester Germer.

Yet the habit of treating with corpuscles hinders until today that people understand that DeBroglie really had demonstrated particles inexistence. There is no duality, as generally affirmed, but only waves. A wave, as the photon, that manifests itself in a limited space, will seem to the observer a particle, but it is really a wave.

In June 2011 the Canadian scientist Aephraim Steinberg measured by indirect means one photon both position and momentum, verifying that it behaves as an wave even when it traverses just one single slit (http://phys.org/news/2011-06-quantum-physics-photons-two-slit-interferometer.html).

 

[Truecrimson]

In June 2011 the Canadian scientist Aephraim Steinberg measured by indirect means one photon both position and momentum, verifying that it behaves as an wave even when it traverses just one single slit (http://phys.org/news/2011-06-quantum-physics-photons-two-slit-interferometer.html).

The "verification" here is nothing rigorous. The same goes for "directly measuring the wave function" by Lundeen et al. http://arxiv.org/abs/1112.3575 (also using weak measurements with postselection). You still have to measure many many identically prepared systems and take the average of the results. Evoking the analogy by Demystifier, the fact that average American household has 2.6 children doesn't mean that any household actually has 2.6 children.

 

[atyy]

Is the wave function physical ? I've searched for this on the web, and most people seem to agree that it does not represent a physical thing. It'd be just a probability distribution.

The wave function may be physical. However, because quantum mechanics requires an observer to determine when something "real" like an observation occurs, the whole question of what quantum mechanics has to say about reality (is the moon there when you are not looking at it) is unsolved. This is the famous "measurement problem".

For non-relativistic quantum mechanics, take a look at Bohmian Mechanics which seems to solve the measurement problem. In Bohmian Mechanics, there is a wave function which is real (and one which isn't so real). You can also look at the Many-Worlds interpretation, which is an attempt to solve the measurement problem, and in which the wave function is real.

 

[bhobba]

In June 2011 the Canadian scientist Aephraim Steinberg measured by indirect means one photon both position and momentum, verifying that it behaves as an wave even when it traverses just one single slit (http://phys.org/news/2011-06-quantum-physics-photons-two-slit-interferometer.html).

That's incorrect. Its a misunderstanding of weak measurements as has been discussed here many times.

Photons are neither particles or waves - they are quantum stuff. A better view, but still far from the truth, is to consider them as 'knots' in a quantum field. Especially in QFT analogies can be very misleading, but have value in developing intuition as long as its realized that's what's going on. Many threads can be found here where people take the analogies too far and will not be dissuaded from such views.

Such is part of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163.pdf

Thanks
Bill

 

[DoobleD]

Thank you for the new answers. I see that the question I asked has no really satisfying answer.

take a look at Bohmian Mechanics which seems to solve the measurement problem

I've checked a bit on Wikipedia and here, and this is very interesting. I wonder how much this view is accepted / rejected among physicists, and what are its pitfalls. It's quite appealing as it seems to solves QM paradoxes and conceptual weirdness. I suppose there are reasons why it is not more accepted than the "Copenhague interpretation" of QM though. If someone passing by has some knowledge about that, it'd be great to know more about it.

Such is part of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163.pdf

Man, this is an AWESOME paper ! I have read only partially so far, but it's VERY useful.

 

[vanhees71]

Thanks for those answers !
But often in physics when we observe a phenomenon we search for a (physical) cause, for a "why this observable phenomenon happens". In the case of interference, if I observe a diffraction pattern in water, I'll say "oh right, it's because there are water waves combining". And the wave equation I'll have will be a correct description of the physical water waves.

In the case of QM, we have a wave function correctly describing an observed interference, but this function doesn't describe a physical wave that would be the source of that interference ? This must bother all physicists of the world !

EDIT : the sentence "In the case of QM, we have a wave function correctly describing an observed interference, but this function doesn't describe a physical wave that would be the source of that interference ? " might not make sense : the wave pattern of an interference is not described by the same wave equation that the one describing the "sources" waves creating the interference (well, I think ?).
I should have written : "In the case of QM, we have a wave function correctly describing an observed interference, but there is no associated physical wave that would be the source of that interference ? "

In the minimal interpretation, i.e., the one you need to apply the quantum theoretical formalism to observables and the only piece of interpretation which is relevant as far as physics is concerned, the "wave function" has the meaning and only the meaning of a probability amplitude. Let's concentrate on the single-particle case for simplicity first. You have a function $\psi(t,\vec{x})$ which fulfills and equation of motion, the Schrödinger equation, and $P(t,\vec{x})=|\psi(t,\vec{x})|^2$ is the probability distribution for finding the particle at position $\vec{x}$ when measured at time $t$ (Born's Rule).

What does this mean in practice. First, to solve the Schrödinger equation you need the initial state, represented by $\psi(t=0,\vec{x})=\psi_0(\vec{x})$. This you get by preparing the particle in a specific way. For a double-slit experiment you prepare the particle with a quite well defined momentum, i.e., a wave packet that's well-peaked in momentum space, while in position space it's pretty broad (the position-space wave function is the Fourier transform of the momentum-space wave function). Now you put a double-slit in the way of this particle and in some distance from this double slit you put a screen which registers the position where it is hit by the particles. A single particle makes a single dot on the screen, not a broad distribution according to $P(t,\vec{x})$. This underlines that Born's Rule is a (and as far as I know so far the only) definition of the physical meaning of the wave function consistent with observations.

Now to verify the interference pattern, predicted by the Schrödinger equation for the double-slit experiment, you have to prepare many single particles in the same way as described above. Then you can measure the distribution of the particles running through the double slit and compare it with the predictions of the formalism. Quantum theory turned out to be right. That's it from the point of view of physics.

Now you can bring up various questions about this, particularly the question what a microscopic particle (perhaps even an elementary particle like an electron) "really" is. Quantum theory tells you, it's neither a little lump of matter behaving like a classical "particle" in the sense of Newtonian (or relativstic) classical mechanics, i.e., as a determined trajectory in phase space. The interference pattern predicted by the Schrödinger equation and verified in experiment tells you that indeed the particle, if prepared in the way described above, is really not localized in the classical sense, and since the wave function has an overlap with both slits in the double slit such that you cannot predict accurately that it must come through the one or the other slit (and you also make no other attempt to mark through which slit the particle goes), you get this interference effect. On the other hand, as stressed above, a single particle always appears as a single point i.e., it interacts with the screen in a small region but not as a washed-out continuum of intensity (of whatever) as in a classical field theory like classical electrodynamics (for the em. field what's measured as intensity is the energy density of the electromagnetic field). Thus it doesn't make sense to say that the electron is something described by a classical Schrödinger wave whose square is a kind of intensity (in this case its square would be something like the particle-number density in a fluid, but that's a contradiction in itself, because the single-particle wave function is supposed to describe a single particle not (very) many as the particl-number density in fluid dynamics does).

So Born's interpretation as a probability distribution for the position of the particle is one that is in accordance with all observations and, in my opinion, also so far the only convincing one among all the various "interpretations", i.e., metaphysical additions one uses on top of the physical minimal interpretation to satisfy some philosophers of science in their seek of "an ontology" of the microscopic world, which behaves according to the laws of quantum physics rather than classical physics. From the point of view of a physicists who cares about physics only, that's a pretty hopeless endeavor, because the different variations of interpretations (there are countless more or less esoteric flavors of interpretations like Copenhagen interpretations, Bohmian mechanics, many-world interperations,...) cannot be tested by objective experiments since they all predict the same outcome as the minimal interpretation, and that's why I consider the minimal interperation the only one needed by physicists.

 

[DoobleD]

@vanhees71 thank you for the clarifications. This seems a very reasonable approach. A pragmatic one. And I think I'll stick to it while I learn QM. It's good to know that some people work on other interpretations though, as with Bohmian mechanics. This kind of work and questions might not be necessary strictly speaking, as the minimalist QM matches observations no matter how we interpret it or add stuff to it. But who knows, people might find a way to test some interpretations someday, bringing more conceptual answers, and maybe new science. Or not. :D It's also true that QM has been around for a while and no such test and answer emerged so far.

Anyway this discussion helped to clarify things for me.

 

[bluecap]

In the minimal interpretation, i.e., the one you need to apply the quantum theoretical formalism to observables and the only piece of interpretation which is relevant as far as physics is concerned, the "wave function" has the meaning and only the meaning of a probability amplitude. Let's concentrate on the single-particle case for simplicity first. You have a function $\psi(t,\vec{x})$ which fulfills and equation of motion, the Schrödinger equation, and $P(t,\vec{x})=|\psi(t,\vec{x})|^2$ is the probability distribution for finding the particle at position $\vec{x}$ when measured at time $t$ (Born's Rule).

What does this mean in practice. First, to solve the Schrödinger equation you need the initial state, represented by $\psi(t=0,\vec{x})=\psi_0(\vec{x})$. This you get by preparing the particle in a specific way. For a double-slit experiment you prepare the particle with a quite well defined momentum, i.e., a wave packet that's well-peaked in momentum space, while in position space it's pretty broad (the position-space wave function is the Fourier transform of the momentum-space wave function). Now you put a double-slit in the way of this particle and in some distance from this double slit you put a screen which registers the position where it is hit by the particles. A single particle makes a single dot on the screen, not a broad distribution according to $P(t,\vec{x})$. This underlines that Born's Rule is a (and as far as I know so far the only) definition of the physical meaning of the wave function consistent with observations.

Now to verify the interference pattern, predicted by the Schrödinger equation for the double-slit experiment, you have to prepare many single particles in the same way as described above. Then you can measure the distribution of the particles running through the double slit and compare it with the predictions of the formalism. Quantum theory turned out to be right. That's it from the point of view of physics.

Now you can bring up various questions about this, particularly the question what a microscopic particle (perhaps even an elementary particle like an electron) "really" is. Quantum theory tells you, it's neither a little lump of matter behaving like a classical "particle" in the sense of Newtonian (or relativstic) classical mechanics, i.e., as a determined trajectory in phase space. The interference pattern predicted by the Schrödinger equation and verified in experiment tells you that indeed the particle, if prepared in the way described above, is really not localized in the classical sense, and since the wave function has an overlap with both slits in the double slit such that you cannot predict accurately that it must come through the one or the other slit (and you also make no other attempt to mark through which slit the particle goes), you get this interference effect. On the other hand, as stressed above, a single particle always appears as a single point i.e., it interacts with the screen in a small region but not as a washed-out continuum of intensity (of whatever) as in a classical field theory like classical electrodynamics (for the em. field what's measured as intensity is the energy density of the electromagnetic field). Thus it doesn't make sense to say that the electron is something described by a classical Schrödinger wave whose square is a kind of intensity (in this case its square would be something like the particle-number density in a fluid, but that's a contradiction in itself, because the single-particle wave function is supposed to describe a single particle not (very) many as the particl-number density in fluid dynamics does).

So Born's interpretation as a probability distribution for the position of the particle is one that is in accordance with all observations and, in my opinion, also so far the only convincing one among all the various "interpretations", i.e., metaphysical additions one uses on top of the physical minimal interpretation to satisfy some philosophers of science in their seek of "an ontology" of the microscopic world, which behaves according to the laws of quantum physics rather than classical physics. From the point of view of a physicists who cares about physics only, that's a pretty hopeless endeavor, because the different variations of interpretations (there are countless more or less esoteric flavors of interpretations like Copenhagen interpretations, Bohmian mechanics, many-world interperations,...) cannot be tested by objective experiments since they all predict the same outcome as the minimal interpretation, and that's why I consider the minimal interperation the only one needed by physicists.

In the von Neumann cut which can be moved anywhere, at that time it was proposed the cut can be located in the consciousness of the observer. All the interpretations predict the same outcome as the minimal interpretations, except one.. where consciousness is involved (or some aspects of it.. not necessarily the consciousness causes collapse thing). Don't we have any official experiments at least to refute this (or aspects of it)? We have so many reports of positive.. but the mainstream physicists violently opposed any or even possibility of replicating it. Is it not science and physics to replicate results? So violent is the opposition to it that any mention of it (even one that make sense) is instantly banned in all physics sites including this one (without even explanations give). Can the Mentor please make an exception to this message by at least giving a physicist a chance to explain?! Progress won't happen by too violent and absolute prohibition and censorship of things that may challenge even a bit the minimalist interpretation.

 

[bhobba]

All the interpretations predict the same outcome as the minimal interpretations, except one.. where consciousness is involved

Even that interpretation predicts the same thing.

Its just a weird interpretation leading to all sorts of issues especially in the age of computers where you can have computers recording the outcomes of experiments and later looked at by humans. But weirdness is not a scientific criteria and its a valid interpretation. But its like solipsism - most reject it as being too weird - but can't be disproved..

Also it needs to be said Von Neumans arguments no longer apply due to our better knowledge of decoherence - there is a place that different, and the natural place to put the Von Neumann cut - just after decoherence.

Thanks
Bill

 

[atyy]

It is important to note the Bohmian Mechanics does predict deviations from quantum mechanics. However the deviations are very small. If such deviations were observed, Bohmian Mechanics would be accepted instead of quantum mechanics.

 

[bhobba]

It is important to note the Bohmian Mechanics does predict deviations from quantum mechanics

It has been done:
http://arxiv.org/abs/quant-ph/0206196

But that it deviates at all from standard QM is controversial. It has been much criticized. However I will let those into BM comment more.

Thanks
Bill

 

[atyy]

It has been done:
http://arxiv.org/abs/quant-ph/0206196

But that it deviates at all from standard QM is controversial. It has been much criticized. However I will let those into BM comment more.

Thanks
Bill

No, that's not a correct paper. That paper misunderstands Bohmian Mechanics.

For a discussion of deviations from QM, one should look at http://arxiv.org/abs/quant-ph/0506115.

 

[DoobleD]

If such deviations were observed, Bohmian Mechanics would be accepted instead of quantum mechanics.

That would be amazing.

 

[atyy]

That would be amazing.

Don't you think MWI or retrocausation would be so much more elegant

 

[bluecap]

Cant we refer to the minimalists (or shut up & calculate guys) as the last Newtonians? They believe the quantum mechanics part is only in the equations and the world is still Newtonian or bolts and nuts..

 

[Nugatory]

Cant we refer to the minimalists (or shut up & calculate guys) as the last Newtonians? They believe the quantum mechanics part is only in the equations and the world is still Newtonian or bolts and nuts..

Whatever they believe, that is not it - what makes the minimal interpretation minimal is that it rejects anything beyond the equations.

The last Newtonians would have been those who suggested that QM is incomplete and that the underlying complete theory would involve local hidden variables governed by non-quantum physics. That hope, of course, disappeared long ago with the discovery of violations of Bell's inequality.

 

[Nugatory]

We generally close interpretation threads when they get to the point where no one is saying anything new, and this one has reached that point. It's closed.