Quantum myth 1. wave-particle duality

[monish]

What proof is there that interactions only involve wave function collapses?...


Regards, Hans

I emphatically agree that people are trigger-happy when it comes to invoking the "collapse of the wave function" when it is not necessary. This is a result of
simple ignorance of what is possible in physics with wave-on-wave interactions.
The traditional arguments against the wave theory of light, especially those invoked
in connection with the photo-electric effect and the Compton effect, are cases in point.
Both these arguments demand the collapse of the (photon's) wave function on the
grounds that e-m wave energy is too diffuse to be able to concentrate itself onto
the tiny cross-section of an electron for the observed outcome. In fact, when the
electron is treated as a wave, there are straightforward wave-on-wave pictures that
describe both effects without the need for the collapse of the wave function.

And yet the physical reality of the wave function remains so problematical in certain instances that I find it hard to believe that Hans appears willing to defend it in this thread. Because I don't think he would make such statements lightly.

So I have to ask: how are we supposed to understand the wave function of a heavy atom with many electrons? If we have s,p, and d orbitals all overlapping, then they should interfere with each other and creating oscillating charge distributions. I understand that Heisenberg more or less ridiculed the wave function on similar grounds, and that the standard theory requires us to write the wave function in multi-dimensional phase space...it's hard to reconcile this with the idea of physical reality. So is there a way out?

 

[Hurkyl]

If we have s,p, and d orbitals all overlapping, then they should interfere with each other and creating oscillating charge distributions.

That doesn't seem right. (Please correct me if I'm wrong!) I know that the individual orbitals exist (from one point of view) because of self-interference, but I'm having trouble imagining how the separate orbitals would interfere with each other. I haven't fully thought through the antisymmetry, though.

(Let me clarify -- it's clear how that would happen if we were dealing with superimposed classical waves, but that is not the situation under consideration!)

And is the wavefunction really non-stationary? Does the Hamiltonian not have any bound eigenstates? Or did I misunderstand what you meant by "oscillating charge distribution"?

the standard theory requires us to write the wave function in multi-dimensional phase space...

For the record, so does classical theory.

it's hard to reconcile this with the idea of physical reality. So is there a way out?

What part is hard to reconcile?

 

[f95toli]

If you don't find the fact that particles behave as if they are in two places at once yet are only detected one at a time is mysterious/wonderous/amazing/whatever adjective you're comfortable with, then your threshold for that quality is quite high!

But, as I pointed out above: it is only "mysterious" if you assume that there even IS something like "particles" in the classical sense; i.e. if you insist on trying to understand QM using classical concepts.
For me QM is more "fundamental" than e.g. Newtonian mechanics and nowadays I actually feel more comfortable when doing QM calculations than classical physics. Moreover, the fact that I actually have the opportunity to see some of these "mysterious" things happening in the lab every day frankly makes them seem somewhat mundane. It is just one of these things you get used to after a few years.

 

[quantumdude]

Wow...where did you hear that? I personally have always thought this to be the case and I even said so in a recent thread in the GR forum (I even said that, as far as I can tell, even all time measurements actually reduce to position measurements...) and one of the forum monitors closed down the thread basically calling me a crackpot!

I've argued that same position with a "real life" friend of mine. He just didn't get it, and basically thought I was way off base.

 

[Ken G]

Point particles are a useful fiction. They make a theorist's life much easier -- composite particles are difficult to handle in relativistic theory, as in say photodissociation of a deuteron.

Indeed I would say that "useful fictions" are what physics is all about.

The wave yields the probability of finding a point particle. Pretty simple, and simple is good.

It can't be said better than that.

 

[Ken G]

If you don't find the fact that particles behave as if they are in two places at once yet are only detected one at a time is mysterious/wonderous/amazing/whatever adjective you're comfortable with, then your threshold for that quality is quite high!

Moreover, the fact that I actually have the opportunity to see some of these "mysterious" things happening in the lab every day frankly makes them seem somewhat mundane.

You're both right. Everything that happens in reality is mysterious/wondrous/amazing, all that happens is we become familiar with it. It's like seeing babies be born, if you only ever see it once it probably tops your list of amazing things, but if you are a doctor who does deliveries, it might become pretty mundane. So the question is not, why are quantum interferences so mysterious and classical trajectories so mundane, it is, why do we think we understand any of it?

 

[Hans de Vries]

the standard theory requires us to write the wave function in multi-dimensional phase space...it's hard to reconcile this with the idea of physical reality. So is there a way out?

Nevertheless, the success of molecular and solid state modeling theories and software
is that they do use single electronic/spin density fields.

http://en.wikipedia.org/wiki/Density_functional_theory#Description_of_the_theory

"The main objective of density functional theory is to replace the many-body
electronic wavefunction with the electronic density as the basic quantity"

If we have s,p, and d orbitals all overlapping, then they should interfere with each other and creating oscillating charge distributions.

Indeed, I don't know how this is circumvented but I can imagine that one could
postulate that full energy states (with both spin up and down) do not interfere
with other energy levels. Obviously, they need to interfere at their own energy
level as Hurkyl remarks.

This would be a postulate, just like Pauli's exclusion principle is one and there are
other postulates. If the zeeman effect would work on the spin up and down states
separately, then they would interfere and any atom would radiate in a magnetic field.
The way out is to postulate that, since the effective magnetic moment of the
combined spin up and spin down state is zero, the magnetic field does not act on
either one of the two.


Regards, Hans

 

[Hans de Vries]

If the zeeman effect would work on the spin up and down states
separately, then they would interfere and any atom would radiate in a magnetic field.
The way out is to postulate that, since the effective magnetic moment of the
combined spin up and spin down state is zero, the magnetic field does not act on
either one of the two.

Forget the above in the case that the magnetic field is homogeneous...

The full covariant Thomas Bargmann-Michel-Telegdi equation predicts that
the spin precession of the up and down spin due to the magnetic anomaly
is so that both stay always opposite and thus there is no interference.

Jackson (11.162):

$$\frac{dS^{\alpha}}{dt}\ =\ \frac{ge}{2mc}\left[~F^{\alpha\beta}S_\beta\ +\ \frac{1}{c^2}\ U^\alpha\left(S_\lambda F^{\lambda\mu}U_\mu\right)\ \right]\ \ -\ \frac{1}{c^2}\ U^\alpha\left(S_\lambda \frac{dU^\lambda}{d\tau}\right)$$

Unfortunately, this formula only includes the term which accounts for the spin-
precession from the acceleration of the electron due to its charge in an electro-
magnetic field. (the second term between square brackets) The electron also
accelerates due to its magnetic moment in an inhomogeneous field.

I do want to discuss this expression with the missing term in my book but I'm still
working on the right covariant form it should have, any references are welcome.


Regards, Hans

 

[DavidWhitbeck]

Wave-Particle Duality: It appeared that light had both wave like and particle like properties. This was very confusing until physicists discovered that particles actually also had wave like properties. Once you see that electrons and the like exhibit the same strange properties that light does you simply have to redefine your notion of what a particle is.

Feynman's popular book QED: The Strange Theory of Light and Matter explains how all of the wave like properties of light can be explained by a particle interpretation. And even if it's not a technical book, it's essential reading for this topic IMO.

I think that the simplest explanation is just that there was no real duality, pre-20th century physicists simply did not fully know what a particle is. The classical point particle is nonsensical anyway. We treat objects as point particles in textbooks to illuminate the principles of a theory, but even elementary particles in real life are not pointlike.

 

[Bose]

The wave function lives in configuration space not physical space. Hence, it is not physically real but instead only a calculational tool. .

I disagree. Since we can measure the wave length of electron diffraction, it must be real

 

[Ken G]

Wave-Particle Duality: It appeared that light had both wave like and particle like properties. This was very confusing until physicists discovered that particles actually also had wave like properties.

Yes, I agree this is the crucial issue. I think additional confusion came from the fact that we also have waves in media, like water and sound waves. So when light seemed wavelike, it was assumed to be like that, which also seemed to divorce it from particles. Then came the one-two punch that light had particle properties and also did not have a ponderable medium, so we didn't know what to call light. Then it turned out not only that all particles exhibit wave mechanics, but also that waves in ponderable media were just a kind of pictorial example of a deeper and more ubiquitous type of non-ponderable waves. With that, the notion of the "duality" of light should have gone out the window, but instead it was kind of "carried over" onto all imponderable waves. Had there been no sound or water waves, and had the wave mechanics of light been discovered at the same time as that of electrons, I think we would never have introduced the concept of "duality", we would have just said, as DavidWhitbeck suggests, that "oh, particles do things other than what we thought".

 

[monish]

That doesn't seem right. (Please correct me if I'm wrong!) I know that the individual orbitals exist (from one point of view) because of self-interference, but I'm having trouble imagining how the separate orbitals would interfere with each other. I haven't fully thought through the antisymmetry, though.

(Let me clarify -- it's clear how that would happen if we were dealing with superimposed classical waves, but that is not the situation under consideration!)

And is the wavefunction really non-stationary? Does the Hamiltonian not have any bound eigenstates? Or did I misunderstand what you meant by "oscillating charge distribution"?

The Schroedinger picture showed tremendous promise when it first appeared, not only in for its success in deriving the energy levels of the hydrogen atom, but for the tantalizing possiblity that it could once and for all make quantum mechanics understandable. One of the great mysteries of the Bohr atom was the "quantum leap" between energy levels; the atom could exist in the excited state, or the ground state, or it could somehow jump from one to the other while emitting a photon. But the nature of this transition state was inscrutable.

The Schroedinger picture actually gives us a perfect explanation of the transition: the superposition of the s and p states of the hydrogen atom creates a tiny oscillating dipole which gives off classical electromagnetic waves. The charge is stationary in either the s or the p state, but in the mixed state it ocillates. There is no need for a "quantum leap" to go from one state to another...Maxwell's equations take us there by radiating off precisely one quantum of energy.

The problem is this: the radiation only works when you have a single electron which is partially in both states. If you have a bigger atom, where the s state is filled and one of the p states is also filled, the filled states don't interfere with each other. Or at least, they don't seem to radiate energy, because such atoms are stable.

Why do I expect that filled states SHOULD interfere with each other? Because that's how the old familiar waves like e-m seem to behave: principle of superposition, etc. And because the hydrogen atom seems to work so well based on those principles. But the fact is it doesn't work that way as we move through the periodic table. The wave function, so it seems, is something else after all. We have to treat it as a mathematical construcion in 3n dimensions, where n is the number of electrons. This is what makes it hard to give it a physical reality.

 

[Maaneli]

Hi nrqed,

You are absolutely correct that all 'measurements' can be ultimately reduced to position measurements. This fact is a consequence of the *noncontextuality* of position measurements, and the *contextuality* of measuring other observables. This is in fact a crucial part of the measurement theory of Bohmian mechanics/de Broglie-Bohm theory. Please see the following paper:

Naive Realism about Operators, with M. Daumer, D. Dürr and N. Zanghì, Erkenntnis 45, 379-397 (1996), quant-ph/9601013
http://arxiv.org/PS_cache/quant-ph/pdf/9601/9601013v1.pdf

 

[nrqed]

Hi nrqed,

You are absolutely correct that all 'measurements' can be ultimately reduced to position measurements. This fact is a consequence of the *noncontextuality* of position measurements, and the *contextuality* of measuring other observables. This is in fact a crucial part of the measurement theory of Bohmian mechanics/de Broglie-Bohm theory. Please see the following paper:

Naive Realism about Operators, with M. Daumer, D. Dürr and N. Zanghì, Erkenntnis 45, 379-397 (1996), quant-ph/9601013
http://arxiv.org/PS_cache/quant-ph/pdf/9601/9601013v1.pdf

Thank you for the reference!

 

[nrqed]

:
The wave function lives in configuration space not physical space. Hence, it is not physically real but instead only a calculational tool.

I disagree. Since we can measure the wave length of electron diffraction, it must be real

The wavelength of an electron is NEVER directly measured. One measures the position of several electrons and one infers the wavelength of the associated wave. I agree with Pellman that the wavefunction lives in configuration space and therefore its ontological status is not clear...

 

[Maaneli]

The wavelength of an electron is NEVER directly measured. One measures the position of several electrons and one infers the wavelength of the associated wave. I agree with Pellman that the wavefunction lives in configuration space and therefore its ontological status is not clear...

Exactly right. Surprisingly though, there are still philosophers of physics like David Albert who would insist that the wavefunction and its configuration space MUST be physically real in their own right.

The de Broglie-Bohm pilot wave theory certainly implies though that even if the wavefunction is not a physically real field, but only a mathematical representation, then it still must reflect some kind of physically real entities. The reason is that in the pilot wave theory, the wavefunction is indispensable to the empirically observed *dynamics* of the Bohmian particles that make up tables and chairs in the experimentally observed physical world. So there is still the question of what physically real fields/variables/entities are actually 'out there' in physical 3-space, to locally interact with and *cause* the Bohmian particles constituting the observed physical world, to move with a velocity dynamics that is accurately described by the pilot wave guidance equation defined in terms of the strictly mathematical wavefunction (indeed all other physical variables such as spin, helicity, charge, and mass, are properties encoded in the wavefunction, and not in the particles themselves). Otherwise, one would have to say that the Bohmian particles are the only physically real beables in the observed physical world, and that there is nothing else 'out there' in the physical world to give them their velocity dynamics; that the particles just spontaneously move with a velocity dynamics that the strictly mathematical wavefunction accurately describes via the pilot wave guidance equation. This however seems too bizarre to be true in my opinion, so I think one must ultimately look for something underlying the wavefunction, in the case that the wavefunction is not taken to be physically real.

 

[Ken G]

Why is 3-space more "real" than configuration space? Or a better question, what does physics have to do with ontology? Physics doesn't need ontology, so it seems most prudent to interpret all of physics as representational, and leave the ontology to the philosophers. What I mean by that is, philosophers can bring out the various nuances of the situation, but can never determine "which is correct", it isn't even the point of philosophy (though many seem to argue as though it were). Physics, on the other hand, does try to demonstrate what is correct, to within some practical precision target, and this is the reason to avoid ontology in physics to steer clear of what cannot be demonstrated.

 

[Demystifier]

What about QFT and so-called particle theory? Are there particles in particle theory?

This is the subject of Sec. 9.

 

[Maaneli]

Why is 3-space more "real" than configuration space? Or a better question, what does physics have to do with ontology?

3-space is regarded as more "real" for a number of reasons: electric and magnetic fields, quantum or classical, are functions on 3-space, and have amplitude and phases that can be directly and individually measured. Moreover, they are sourced fields by charge and current distributions in 3-space On the other hand, wavefunctions in configuration space have amplitude and phases that cannot be so directly measured, but only inferred by statistical ensembles of particle position measurements. Moreover, wavefunctions on configuration space are not sourced fields in any way like EM fields in 3-space. Classical Hamiltonians are also functions on even higher dimensional spaces, namely, phase space; but the phase space of a classical Hamiltonian is only a mathematical representation for the nonlocal correlations in an N-particle system, since all the corresponding classical particle trajectories are actually observed in 3-space. Another example comes from classical statistical mechanics. The Smoluchowski-diffusion equation has solutions (such as the Gibbs distribution) that, just like wavefunctions, are also functions on configuration space in phase and amplitude. Moreover, these solutions can be used to define the corresponding drift velocity for particles in the theory. However, these diffusion function solutions on configuration space do not actually represent a physically real substance diffusing in configuration space. Rather, they represent a probability measure for particles to be in a certain position or velocity configuration at a temperature T and a time t, in physical 3-space. Moreover, we know the diffusion equation and its corresponding solutions are phenomenological approximations to the Langevin equation of dynamics, which describes the microphysical degrees of freedom of particles coupled to a thermal reservoir in 3-space.

Consider also the obvious implications of a physically real configuration space, with respect to wavefunctions. If this were the case, then the dimensionality of physically real space would actually be 3N-dimensional, were N is the number of particles in the universe (~10^23). So we would actually be living in a 3*10^23 dimensional space. But then the question you must ask is how does a quantum theory (even a Bohmian quantum theory), in which the configuration space is physically real, explain how the observed physical world in 3-space arises? Consider an example from Tim Maudlin:

" It is trivial, of course, that a single mathematical point moving in a high-dimensional mathematical space can represent one or the other outcome: if there are many physical particles in a common low dimensional space moving around, then there is an evolving configuration of particles, and this can be represented (under obvious conventions) by a single point in a high-dimensional space. This abstract (non-physical) space is configuration space... But the fact that it is trivial to represent an evolving configuration of many particles by a single point (using obvious conventions) does not imply that it is comprehensible how something we thought to be an evolving configuration of many particles (such as a cat) could really be just a single particle!"

So this would be a fundamental problem for the corresponding quantum theory of measurement that would attempt to explain the emergence of our observed 3-space.

Those are some reasons.

Physics doesn't need ontology, so it seems most prudent to interpret all of physics as representational, and leave the ontology to the philosophers. What I mean by that is, philosophers can bring out the various nuances of the situation, but can never determine "which is correct", it isn't even the point of philosophy (though many seem to argue as though it were). Physics, on the other hand, does try to demonstrate what is correct, to within some practical precision target, and this is the reason to avoid ontology in physics to steer clear of what cannot be demonstrated.

Completely disagree. Physics does need (and does already have!) ontology if it is going to claim to explain anything in nature. Think of the obvious examples of physical ontologies from classical mechanics and electrodynamics. You should also learn that quantum theory without a physical ontology (such as orthodox quantum theory) suffers from the well-known measurement problems. It was only when quantum theories with ontology were developed that the measurement problems were solved. So this is an example where thinking about ontology in physics has been extremely useful and necessary. Also, you should recognize that there is no sharp distinction between physics and philosophy precisely because consistent physical theories already make ontological and metaphysical claims about the physical world. You should also recognize that the need for physical theories to make ontological claims about the physical world does not at all conflict with the fact that physics is representational, as you said. There is a difference between the ontology of a theory and the actual ontology of the real world, the latter of which can ultimately only be approximately represented by the former. Finally, I question your understanding of the word "correct", in the context that you used it.

Cheers,
Maaneli

 

[FunkyDwarf]

As far as I am (an undergraduate in his last year) concerned there is no need for wave particle duality. You can just as easily verify the same experiments by considering everything as point particles and allocating all the wavelike properties to the wavefunction which preceeds it an encodes all its information. Sure you COULD say that this separation is just nit picking and really if the wavefunction has wavelike behaviour so does the particle, but well that's just a matter of philosophy. Again physics is only concerned with things you can measure. If you create a system which is fundamentally unmeasureable, or at least a quantity in it is, then we don't care. When we're not looking at electrons through slits they could turn into a turtle to batman and back, we don't care. The only reality we have is what we can measure, and for that reason, all these things like electrons and photons are particles, not waves.

 

[Hurkyl]

Why is 3-space more "real" than configuration space? Or a better question, what does physics have to do with ontology?

One of the key parts of science is formulating hypotheses, and testing them with experiments performed in 'reality'. This requires a way to interpret the hypothesis in terms of reality -- that is an ontology.

e.g. if I don't ascribe any meaning to the word "sun" (or the other things), how could I empirically test the hypothesis "the sun will rise tomorrow"?

 

[f95toli]

Completely disagree. Physics does need (and does already have!) ontology if it is going to claim to explain anything in nature.

But the question is if we really should expect physics (and science in general) to explain anything. Ultimately, we can only judge whether or not a theory is valid by comparing its predictions with the outcome of experiments; there is no way of knowing if e.g. the assumptions made in formulating the theory or eve if its "philosophical" implications are fundamentally "correct" ; as long as the numbers coming out of the theory agrees with the number coming from our scientific instruments we will just have to accept that it is the best we got.
In principle we could have a situation where someone comes up with a theory where interactions are carried by invisible pink unicorns (IPU); if that theory turned out to be more successful in predicting numbers than or existing theories we would have to accept it. The fact that the idea of IPUs is ridiculous is irrelevant.

 

[monish]

Nevertheless, the success of molecular and solid state modeling theories and software
is that they do use single electronic/spin density fields.

http://en.wikipedia.org/wiki/Density_functional_theory#Description_of_the_theory

"The main objective of density functional theory is to replace the many-body
electronic wavefunction with the electronic density as the basic quantity"


Regards, Hans

At the risk of not having understood your point, I have to raise the following objections:

1. Is density function theory not actually an approximation method which still relies on the underlying 3n-dimensional Schroedinger wave function for its validity?

2. If this is in fact a viable, self-consistent theory, have we not at best replaced the single 3n-dimensional Schroedinger function with n 3-dimensional functions, in other words an individual wave function for each electron? Yes, each function appears to have some physical reality on its own, but its hard to picture a universe which has to keep track of so many functions all overlapping at the same point in space.

 

[Maaneli]

But the question is if we really should expect physics (and science in general) to explain anything. Ultimately, we can only judge whether or not a theory is valid by comparing its predictions with the outcome of experiments; there is no way of knowing if e.g. the assumptions made in formulating the theory or eve if its "philosophical" implications are fundamentally "correct" ; as long as the numbers coming out of the theory agrees with the number coming from our scientific instruments we will just have to accept that it is the best we got.
In principle we could have a situation where someone comes up with a theory where interactions are carried by invisible pink unicorns (IPU); if that theory turned out to be more successful in predicting numbers than or existing theories we would have to accept it. The fact that the idea of IPUs is ridiculous is irrelevant.

Tsk, tsk, this is what happens when you don't have concrete experience with foundational reformulations of physics, and how precisely they differ from the orthodox theories that you know. You actually can determine, independent of experiments, if the ontology of one physical theory is really more fundamental than another. The way is simply by seeing if one theory T1 can make the same predictions as the other theory T2, while also showing that T1 makes fewer ad-hoc postulates than T2, and can even physically derive the postulates of T2, as well as the physical ontology of T2, within some approximation limit. The concrete exemplar of this is Bohmian quantum mechanics (BQM) vs orthodox quantum mechanics (OQM), which are empirically equivalent theories. BQM and OQM share in common the assumption of the wavefunction and Schroedinger equation. But OQM has several measurement postulates (I assume you are familiar with them), as well as the Born rule postulate (I assume you know this one as well). BQM on the other hand, has no need nor any room for any of the measurement postulates, because it in fact derives all of their consequences. For example, the appearance of wavefunction collapse (which is the ontology of OQM) is derived in a crystal clear way from BQM. Moreover, BQM derives the Born rule and even suggests the possibility of deviations from the statistical predictions of OQM. For these reasons, in comparing BQM with OQM, it is clear that the latter is just a phenomenological formalism and approximation to the former. The equations of BQM have become extremely useful to condensed matter theorists and theoretical physical chemists, primarily because it computationally simplifies many problems.

Also, you should think about intertheoretic relations. QED formulated strictly in terms of the second quantized ZPE, is empirically equivalent (on the lengthscale of QED phenomena) to QED formulated strictly in terms of second quantized radiation reaction. These two completely different physical pictures however, just depend on how field operators are ordered. Now when one tries to mix QED in either formulation with the general theory of relativity (GTR), one finds that QED with only second quantized ZPE is physically inconsistent with GTR because of the infinite vacuum energy density contributed to the right hand side of the Einstein field equation. On the other hand, QED with only quantized radiation reaction effects does not predict this infinite vacuum energy density, and is thus physically consistent with the Einstein field equation of GTR; but you would never have recognized this intertheoretic consequence if you were insensitive to the differences in physical ontology between these two approaches to QED, in spite of their empirical equivalence on the lengthscales of QED phenomena. Ed Jaynes made this particular point a long time ago, but it seems to have been forgotten by many people.

So you see, thinking about physical ontology, in spite of empirical equivalence, does have value beyond beyond your foresight.

 

[Ken G]

Those are some reasons.

All interesting aspects of 3-space vs. configuration space. However, I did not see any that showed 3-space is "real" and configuration space is not. I think what is lacking here is your definition of "real". Can you provide it?

Completely disagree. Physics does need (and does already have!) ontology if it is going to claim to explain anything in nature.

On the contrary, physics needs no ontology to "explain" anything. An "explanation" is nothing but a unifying language to help us picture things that we are familiar with. If we have no familiarities, that nothing is an explanation. If you don't agree, try explaining something to a 2 year old. The absence of familiarity is a huge problem. Conversely, explaining things to people with a great many familiarities is much easier. How does that simple fact invoke ontology?

Think of the obvious examples of physical ontologies from classical mechanics and electrodynamics.

Perfect examples of what I mean. Each of them, in its day, was thought to represent an ontology, and every one of those ontologies collapsed. Now we have new ones-- I guess we should imagine we got it right this time?

You should also learn that quantum theory without a physical ontology (such as orthodox quantum theory) suffers from the well-known measurement problems.

Measurement problems stem from ontologies. Without the ontologies, there is no measurement problem. For example, I have no "problem" with measurement at all.

It was only when quantum theories with ontology were developed that the measurement problems were solved.

No, it was only when we kept track of what we were actually doing (coupling quantum systems to open classical ones) that they were solved.

So this is an example where thinking about ontology in physics has been extremely useful and necessary.

I'm sorry, how does thinking about ontology "solve" the measurement problem? I see it as being solved by leaving out ontology, by thinking of the wave function as being about information rather than requiring it to be something that must obey arbitrary "reality criteria".

Also, you should recognize that there is no sharp distinction between physics and philosophy precisely because consistent physical theories already make ontological and metaphysical claims about the physical world.

There is no sharp distinction between right and wrong either, the issue is whether or not there is value in drawing the distinction. When no value is seen in a distinction between physics and philosophy, we backtrack two thousand years and Galileo rolls over in his grave.

You should also recognize that the need for physical theories to make ontological claims about the physical world does not at all conflict with the fact that physics is representational, as you said. There is a difference between the ontology of a theory and the actual ontology of the real world, the latter of which can ultimately only be approximately represented by the former.

What is the "ontology of a theory", I would like to know. Why is it a necessary part of that theory, for example? To me, that's like saying that a theory about how fish swim has to be able to swim too.

 

[Ken G]

One of the key parts of science is formulating hypotheses, and testing them with experiments performed in 'reality'.

With that I will agree wholeheartedly.

This requires a way to interpret the hypothesis in terms of reality -- that is an ontology.

Huh? Why do I need such a concept to establish whether or not a test has succeeded? We can agree that reality exists, but we have that prior to doing any science. Science adds nothing more to that equation, it has nothing to do with ontology, because the whole point of science is to replace what exists with conceptualizations of what exists. Conceptualizations exist in that they are indeed existent conceptualizations. There is no need for anything beyond that in science. I can prove it: anyone can do science without it.

e.g. if I don't ascribe any meaning to the word "sun" (or the other things), how could I empirically test the hypothesis "the sun will rise tomorrow"?

No one said anything about meaning, we were talking about existence. Of course we need meaning, meaning is how we invoke our familiarities in order to communicate. All that must exist are those familiarities, there is no need at all for "the Sun" to exist. What is "the Sun," anyway? It is a label we have invented to conjure a set of familiarities. Those familiarities exist, and are needed to communicate science, but there is no need for science to make any statements about the existence of the Sun in order to invoke those familiarities.

Now, of course I realize we all use the shortcut of assuming there is something out there called "the Sun", but nevertheless it is important to note that that shortcut is entirely superfluous to science. Whenever you say "the Sun", any scientist is free to replace that with "whatever real phenonomena exists that manifests itself to us as a set of familiarities we conjure when we use the term the Sun". No one wants to say that every time, but the science is not one iota different. In point of fact, "the Sun" really doesn't have to mean anything more than a direction to point a telescope or a satellite, or a guide in making idealized models of reality. No existence needed, not one shred. If we're all hooked up to the Matrix but can't tell by experiment, how is science any different? Science simply doesn't care, ontology in science is just a convenience of language.

 

[reilly]

I emphatically agree that people are trigger-happy when it comes to invoking the "collapse of the wave function" when it is not necessary. This is a result of
simple ignorance of what is possible in physics with wave-on-wave interactions.
The traditional arguments against the wave theory of light, especially those invoked
in connection with the photo-electric effect and the Compton effect, are cases in point.
Both these arguments demand the collapse of the (photon's) wave function on the
grounds that e-m wave energy is too diffuse to be able to concentrate itself onto
the tiny cross-section of an electron for the observed outcome. In fact, when the
electron is treated as a wave, there are straightforward wave-on-wave pictures that
describe both effects without the need for the collapse of the wave function.

And yet the physical reality of the wave function remains so problematical in certain instances that I find it hard to believe that Hans appears willing to defend it in this thread. Because I don't think he would make such statements lightly.

So I have to ask: how are we supposed to understand the wave function of a heavy atom with many electrons? If we have s,p, and d orbitals all overlapping, then they should interfere with each other and creating oscillating charge distributions. I understand that Heisenberg more or less ridiculed the wave function on similar grounds, and that the standard theory requires us to write the wave function in multi-dimensional phase space...it's hard to reconcile this with the idea of physical reality. So is there a way out?

First allow me to say that Condon and Shortley's The Theory of Atomic Spectra pretty much touch upon your various ideas. This book was first puiblished in 1935, with more than 200 pages on multi-electron atoms. Because C&S discussed experimental data and theory, their book was a bible well into the early 60s. Also Pauling's General Chemistry discusses multi-electroan atoms as well. And even a quick read of one or the other should convince you that wave functions for, say, Uranium or deuterium are perfectly undestandable, CF the Thomas- Fermi , or Hartree-Fock approachs.

A hydrogen atom in a superpostIon of any states is possible; but it is not then , in general, an eigenstate of the Hydrogen atom. However, in reality, such a system will decay, by radiation, to the lowest hydrogen state possible.

However the electronic wave function of, say, a Lead atom, atomic weight is 207, and A=82, is very different. That is the wave function describes 82 electrons; and a description in terms of central field orbitals. A good first approximation is simply a state in which the lowest orbitals are filled -- like filling up to the Fermi-level. The closest one comes to superposition is the due to anti-symmetry imposed by the Pauli Principle. But, the state will be an eigenstate of the unperturbed Hamiltonian.

If you look up Fermi-Thomas and Hartree-Fock you'll find remarkable work that does quite well in understanding and computing ionization energies and other multi-electron atom properties. Suggests, within the Feynman constraint, these old guys did a fantastic job in atomic physics, so they must have understood and handled the multi-electron wave functions with great dispatch.As a look into the literature will show, that's exactly what they did.

Regards,
Reilly Atkinson

Question : how would you describe a gas?

 

[Ken G]

You actually can determine, independent of experiments, if the ontology of one physical theory is really more fundamental than another.

My bold shows that the razor you are applying does not establish any need for ontology in science, you have simply assumed we need it. What difference does it make to science if it uses a "more fundamental ontology", when ontology itself is not scientifically establishable? The most fundamental ontology we ever had came from the ancient Greeks, and had something to do with the Earth being the center of the universe. Now, you are saying that we should stick to the most fundamental ontology that agrees with observation, and change it as necessary. I say, why not just admit that we are not doing ontology, and not be so bothered when things we thought "existed", according to whatever is the fleetingly valid current most fundamental ontology, turn out to not exist, and just admit that isn't the purpose of the exercise in the first place? We are trying to make contact with reality, we have no need at all to specify any knowledge of what exists or doesn't exist, we just try to understand how it acts. No big deal if it acts in ways we didn't expect, no "ontological crises" needed.

Let me ask you this: which from this list exist, and which do not:
the Sun
particles
light waves
wave functions
trajectories
spacetime
If you can address this list, I'd be very curious, and if you cannot, what does your ontology really give you?

The concrete exemplar of this is Bohmian quantum mechanics (BQM) vs orthodox quantum mechanics (OQM), which are empirically equivalent theories.

And that is also the perfect example of what I'm talking about. You simply assume that certain attributes of BQM make it superior to OQM. The scientific evidence is obviously to the contrary: it isn't used much at all. That clearly shows why "ontological fundamentalism" is not important to science, which frankly doesn't surprise me.

Moreover, BQM derives the Born rule and even suggests the possibility of deviations from the statistical predictions of OQM.

By heaping on undemonstrable postulates of its own! But if there really are different predictions, then it is really science-- now go out and falsify it.

For these reasons, in comparing BQM with OQM, it is clear that the latter is just a phenomenological formalism and approximation to the former.

That you feel you can assert, without experimental evidence, which one is an "approximation" to the other, exposes crystal clearly that you really do think philosophy can be substituted for science, which is precisely what the Greeks thought two thousand years ago, and is what I am cautioning against.

The equations of BQM have become extremely useful to condensed matter theorists and theoretical physical chemists, primarily because it computationally simplifies many problems.

That is interesting, I agree, but can you argue this is anything but a niche application? There are all kinds of bizarre interpretations that become convenient in specific applications. For example, geocentrism is commonly practiced by navigators on Earth, without any ontological requirement that the Earth really be at the center of the universe.

Now when one tries to mix QED in either formulation with the general theory of relativity (GTR), one finds that QED with only second quantized ZPE is physically inconsistent with GTR because of the infinite vacuum energy density contributed to the right hand side of the Einstein field equation. On the other hand, QED with only quantized radiation reaction effects does not predict this infinite vacuum energy density, and is thus physically consistent with the Einstein field equation of GTR; but you would never have recognized this intertheoretic consequence if you were insensitive to the differences in physical ontology between these two approaches to QED, in spite of their empirical equivalence on the lengthscales of QED phenomena.

But you have not established that the key difference is ontological! In fact, the difference is the difference-- it is not ontology that makes one succeed where the other fails, but you did cite an operator ordering. There is no need to associate an ontology to an operator ordering, it's pure convenience of language! Does quantum mechanics work on atoms where classical mechanics fails because it has a different ontology, or just because it uses different models and different equations?

So you see, thinking about physical ontology, in spite of empirical equivalence, does have value beyond beyond your foresight.

I would simply say that understanding all the equivalent ways we have to think about reality has value, because you never know which one will be the best way to attack some new situation. That's exactly why you do not need ontology in science-- ontology carries with it a sense of uniqueness that one should seek to avoid.

 

[f95toli]

Tsk, tsk, this is what happens when you don't have concrete experience with foundational reformulations of physics, and how precisely they differ from the orthodox theories that you know.

So? You replace one theory with another, then what?
My point was that we can of course assume that our theories have something to do with a "reality" (which also assumes that there is a such a thing, but let's leave that aside for the moment), but that can never be more than an assumption.
What I was getting at is that testing theories always ultimately boils down to getting number that we can then compare with other numbers that we get from experiments.
We just have to very careful when we assume that the ideas/formulas that generate those numbers have anything to do with "reality". In some cases formulas are best understood as formulas. Most of the problems people have with QM comes from the interpretation; and perphaps it would sometimes be better NOT trying to interpret the mathematical models at all, but to simply accept them for what they are: A way to model the world and predict the outcome of experiments.

I use QM to plan my experiments and analyze data. In my work one of the most important tools is the Block sphere, simply because it allows me to visualize what is going on in the devices I work with. Hence, the Block sphere is a good tool, but does that neccesarily mean that it has anything to do with "reality"? Probably not. But I would argue that this is many ways besides the point, in many ways the Bloch sphere tells me just as much about the nature as microscopic theories that describe what is going on in the actual condensate or even subatomic level in the systems I work with.

 

[Ken G]

We just have to very careful when we assume that the ideas/formulas that generate those numbers have anything to do with "reality". In some cases formulas are best understood as formulas.

I agree. To me, ontology in science is a form of "verbal convenience", akin to personification of particles. How many of us have ever said "the electron experiences the electric field" or words to that effect-- personification for color and clarity of communication, nothing more. No one really thinks an electron "experiences" things, so why should we feel it has to "exist" for us to use it in our theories?

Hence, the Block sphere is a good tool, but does that neccesarily mean that it has anything to do with "reality"? Probably not.

Thank you for the concrete example, they speak volumes. Indeed, you can let the Block sphere have something to do with reality, but stop short of saying that it therefore has to be real. Perhaps I don't understand how they are using the term ontology, but it sounds like the latter usage is the intention, not the former.

 

[peter0302]

Let me ask you this: which from this list exist, and which do not:
the Sun
particles
light waves
wave functions
trajectories
spacetime
If you can address this list, I'd be very curious, and if you cannot, what does your ontology really give you?

You must agree that there are things that are more "real" than others. The number pi is a fundamental mathematical quantity but yet has no physicality to it. It merely allows us to measure and predict other observations. So there must be a fundamental difference between an abstract concept like pi that LEADS to observaitons, and the thing that actually is being observed.

The sun clearly exists because it can be observed directly through its light, heat, gravity, and magnetic field. The wave function cannot be directly observed - its properties can only be inferred based on where we see particles show up on a detector - thus it may or may not exist - it may be like pi. Same with trajectories, and spacetime. They are concepts that help us make sense of our observations but they themselves are not observed. They are like pi.

So with all that said, the universe of what is "physical" has to be limited to something that can interact with something else that is "physical." And since the wave function doens't interact with anything, but merely defines where something might show up, I have a hard time thinking that it's physical. If quantum bosons were somehow detected and BM proven, then that would be a different story.

 

[Ken G]

You must agree that there are things that are more "real" than others.

I certainly act that way, but I also recognize that this is largely a subjective distinction, that cannot be made objective via the means of science. It's a gray area, to be sure, like many in the actual application by imperfect humans of a scientific methodology that is defined in highly idealized ways. But I see more harm than benefit in thinking that science requires ontology, because I think it takes it a step toward dogma and a step away from discovery.

So there must be a fundamental difference between an abstract concept like pi that LEADS to observaitons, and the thing that actually is being observed.

I do think there is a difference between concepts and reality, I just think the former is the goal of science by observing the latter. Note that never allows us to mistake the former for the latter.

The sun clearly exists because it can be observed directly through its light, heat, gravity, and magnetic field.

Does this require that light, heat, gravity, and magnetic fields exist? We need a definition of what exists. If we take the standard approach that what exists is what we can measure, then I point out we never measure "the Sun", so that definition does not establish the existence of the Sun as anything but a unifying concept, which is exactly the only existence that I claim it has, consistent with scientific thought.

The wave function cannot be directly observed - its properties can only be inferred based on where we see particles show up on a detector - thus it may or may not exist - it may be like pi. Same with trajectories, and spacetime. They are concepts that help us make sense of our observations but they themselves are not observed.

They are unifying concepts-- like the Sun. When is our concept of something the thing itself, and isn't "thing" also a concept? Is not the existence of a concept different from what exists in reality? Does science need to make these distinctions, or can it simply accept that it lives in "concept space"?

So with all that said, the universe of what is "physical" has to be limited to something that can interact with something else that is "physical."

We don't know that everything that exists is "physical", it is just an assumption of science, required for obvious reasons. That's another reason for science to avoid ontology.

And since the wave function doens't interact with anything, but merely defines where something might show up, I have a hard time thinking that it's physical.

I certainly feel the wave function lives in "concept space", right next to electrons, spacetime, and the Sun.

 

[Maaneli]

All interesting aspects of 3-space vs. configuration space. However, I did not see any that showed 3-space is "real" and configuration space is not.

Then you didn't understand the examples. My point was to present clear and specific examples of cases where configurations space is only a mathematical representation for many body systems in 3-space, and to point out that consequently, it is quite possible and plausible, given our experiences with these well-known examples, that the configuration space of QM is probably no different.

On the contrary, physics needs no ontology to "explain" anything. An "explanation" is nothing but a unifying language to help us picture things that we are familiar with. If we have no familiarities, that nothing is an explanation. If you don't agree, try explaining something to a 2 year old. The absence of familiarity is a huge problem. Conversely, explaining things to people with a great many familiarities is much easier. How does that simple fact invoke ontology?

Any unifying language that helps you "picture" things you are familiar with, and that has ANY capacity to make predictions about how the physical world works, already has an ontology. Indeed every scientific explanation includes SOME kind of ontology. It may not though be the ontology of the real world though (recall to distinguish between ontology of a theory/explanation, and the ontology of the real world).

Perfect examples of what I mean. Each of them, in its day, was thought to represent an ontology, and every one of those ontologies collapsed. Now we have new ones-- I guess we should imagine we got it right this time?

I get the sense that you don't know what ontology means. Ontology is just what entities exists in the physical world. A physical theory always has an ontology, whether it accurately describes the world or not. Those classical ontologies did not "collapse", whatever the hell that means. They are just best regarded as approximations to the actual ontology of the world. No theory will ever have a perfectly accurate ontology, but that doesn't mean a theory doesn't have an ontology or ontology isn't useful.

Measurement problems stem from ontologies. Without the ontologies, there is no measurement problem. For example, I have no "problem" with measurement at all.

NO! the measurement problems stems from having NO ontology! The fact that you don't understand that and that you say you have no "problem" with measurement clearly tells me that you are far off from understanding what the measurement problem is, and it makes me question why I should continue having this discussion with you if you're that far behind.

No, it was only when we kept track of what we were actually doing (coupling quantum systems to open classical ones) that they were solved. I'm sorry, how does thinking about ontology "solve" the measurement problem? I see it as being solved by leaving out ontology, by thinking of the wave function as being about information rather than requiring it to be something that must obey arbitrary "reality criteria".

If you understood the measurement problem, you would understand why decoherence theory doesn't solves the problem. Not even Zurek or Zeh would claim that yet! Ontology solves the measurement problem because it tells you what your theory is fundamentally about, and how that fundamental entities of your theory behaves so as to gives rise to the appearance of of the classical world you experience. Without an ontology for quantum mechanics, you have to postulate wavefunction collapse at an arbitrary, human-specified place and time. This becomes especially problematic when you try to understand the quantum-classical limit.

There is no sharp distinction between right and wrong either, the issue is whether or not there is value in drawing the distinction. When no value is seen in a distinction between physics and philosophy, we backtrack two thousand years and Galileo rolls over in his grave.
What is the "ontology of a theory", I would like to know. Why is it a necessary part of that theory, for example? To me, that's like saying that a theory about how fish swim has to be able to swim too.

There is value in the distinction, as I have shown. A simple example of the ontology of a theory is classical mechanics: the world is made up of point particles that follow trajectories in 3-space, due to mechanical forces locally acting upon them. Or electromagnetism: the world is made up of charged point particles and electric and magnetic fields in 3-space, the latter of which induce Lorentz forces on the former and gives them their empirically observed trajectories in 3-space. It's really not a complicated idea.

 

[Maaneli]

So? You replace one theory with another, then what?
My point was that we can of course assume that our theories have something to do with a "reality" (which also assumes that there is a such a thing, but let's leave that aside for the moment), but that can never be more than an assumption.
What I was getting at is that testing theories always ultimately boils down to getting number that we can then compare with other numbers that we get from experiments.
We just have to very careful when we assume that the ideas/formulas that generate those numbers have anything to do with "reality". In some cases formulas are best understood as formulas. Most of the problems people have with QM comes from the interpretation; and perphaps it would sometimes be better NOT trying to interpret the mathematical models at all, but to simply accept them for what they are: A way to model the world and predict the outcome of experiments.

I use QM to plan my experiments and analyze data. In my work one of the most important tools is the Block sphere, simply because it allows me to visualize what is going on in the devices I work with. Hence, the Block sphere is a good tool, but does that neccesarily mean that it has anything to do with "reality"? Probably not. But I would argue that this is many ways besides the point, in many ways the Bloch sphere tells me just as much about the nature as microscopic theories that describe what is going on in the actual condensate or even subatomic level in the systems I work with.

You really should respond directly to my examples, if you expect me to reply to yours. As far as I can tell, you didn't bother to read them, which is why you entirely missed the argument.

 

[f95toli]

You really should respond directly to my examples, if you expect me to reply to yours. As far as I can tell, you didn't bother to read them, which is why you entirely missed the argument.

No, I did read what you wrote. And I did not mean to criticize what you wrote about the value of ontology. What I was addressing was the second part of this sentence:
"Physics does need (and does already have!) ontology if it is going to claim to explain anything in nature.".
This is a very good point, and I suspect many people would agree with you.
But the point of my post is that one can argue that the goal of physics is NOT necessarily to explain anything; but to just make models of the world and predict the outcome of experiments. Someone described this a while ago as the "shut up and calculate approach".
I agree that we should strive to come up with better theories, reduce the number of ad hoc assumptions, unify theories etc; but ultimately this can still never be more than an intellectually stimulating game which may or may not have something to do with "reality". It happens is a game I enjoy playing (which is one reason why I am a physicist), but one I do not neccesarly ascribe any deeper significande to anymore.