Quantum myth 1. wave-particle duality

[pellman]

Demystifier has a paper available entitled "Quantum mechanics: myths and facts". http://xxx.lanl.gov/abs/quant-ph/0609163 This is a fine overview of a lot of stuff which I would like to understand better. Please join me in discussing.

There are 9 myth categories. By myth the author means widely repeated statements which, true or false, are not something we can validly assert given our current understanding.

myth category 1. Wave particle duality (see section 2 of the paper)

The gist of section 2.1 is that based on the usual interpretation of QM, there is only the wave. What we call particle is merely the special case of a localized wave packet--of finite width and only ideally a delta function in the limit of \Delta x \rightarrow 0.

I have two tentative objections.

(1) The single particle wave function \psi (x,t) can be misleading. It suggests something like an EM wave or a fluid wave. That is, a field, a value at each point in physical space at a given time. But this is wrong of course. For two particles we don't have \psi_1(x,t) and \psi_2(x,t) (although that may be approximately true if they don't interact) but rather \psi (x_1, x_2; t). The wave function lives in configuration space not physical space. Hence, it is not physically real but instead only a calculational tool.

That is, unless we are willing to grant configuration space a sort of platonic reality that is more real than the physical world that we experience with our senses. A logical possibility of course. The world of normal space time of our experience may merely be the result of how our brains+senses fit in as part of the universal wave function. In that case one could say that the wave function is the reality and it is the world of our experience which is the "calculational tool" provided to us by evolution for survival.

But this is a position of which I think we should be very suspicious. The most glaring problem with it in my opinion is the "measurement problem" and the fact that we don't observe superposition of macro objects, a fact for which the wave function alone has no answer. And for other reasons which will come up as we discuss the "myths".

(2) Particle position plays such a central role in actual measurements. I have heard it said that all measurements ultimately reduce to positions measurements. (But is this one more myth?)

This suggests to me that the usual formulation of QM is only an approximation and that a better theory would be a particle theory. And indeed, in Sec 2.2 Demystifier discusses such a possibility in the Bohmian interpretation.


But what do we even mean by "particle"? I have to admit that at this level I have better mental grasp of the wave function than what a "particle" is or might be.

 

[Demystifier]

(2) Particle position plays such a central role in actual measurements. I have heard it said that all measurements ultimately reduce to positions measurements. (But is this one more myth?)

Could be. But I don't know any counterexample. Does anybody?

 

[Moridin]

There is no duality, and things such as light is neither a "particle" or a "wave". Quantum mechanics provide a singular and consistent description.

 

[Haelfix]

Could be. But I don't know any counterexample. Does anybody?

calorimeter?

 

[nrqed]

... I have heard it said that all measurements ultimately reduce to positions measurements. (But is this one more myth?)

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!

interesting thread by the way. I have always wanted to discuss that very interesting paper by Demystifier

 

[reilly]

There are 9 myth categories. By myth the author means widely repeated statements which, true or false, are not something we can validly assert given our current understanding.

myth category 1. Wave particle duality (see section 2 of the paper)

The gist of section 2.1 is that based on the usual interpretation of QM, there is only the wave. What we call particle is merely the special case of a localized wave packet--of finite width and only ideally a delta function in the limit of \Delta x \rightarrow 0.

I have two tentative objections.

(1) The single particle wave function \psi (x,t) can be misleading. It suggests something like an EM wave or a fluid wave. That is, a field, a value at each point in physical space at a given time. But this is wrong of course. For two particles we don't have \psi_1(x,t) and \psi_2(x,t) (although that may be approximately true if they don't interact) but rather \psi (x_1, x_2; t). The wave function lives in configuration space not physical space. Hence, it is not physically real but instead only a calculational tool.

Re \psi (x_1, x_2; t)..A similar form for E and B will hold in classical E&M for example, for two charged particles interacting and radiating with the E&M field. And there's always a mapping from configuration space -- as you define it -- to physical space. Think, for example, also about Hamilton-Jacobi Theory and how it is formulated.
Regards,
Reilly Atkinson

 

[pellman]

Wow...where did you hear that?

I don't know. I am sure I have heard and read it a number of times. That is, ... er ..I was sure ...

calorimeter?

Let's see if I understand. A calorimeter is a thing in which an energetic particle is directed and its energy ultimately transferred to a dense material. From the change in temperature of the material we infer the energy of the original particle. Right?

Now that I think about it, the claim about all measurements reducing to position measurements is probably in the sense that the measurement is made by checking the position of something, not necessarily a quantum particle. In the calorimeter case, the change in length or volume of the material associated with its change in temperature? (I don't know how the temp change is measured.) Something like that.

But this position measurement would be a quantum variable. There would be an uncertainty in the observation. In this case it would likely have to do with energy/time uncertainty. When do we note the temperature change? When can we safely say all the energy has dissipated throughout the material?

Clearly, I haven't thought it through carefully. But that is the gist of it, I suppose.

The time/energy uncertainty relation is handled in a later section of the paper, btw.

 

[RandallB]

There is no duality, and things such as light is neither a "particle" or a "wave". Quantum mechanics provide a singular and consistent description.

I can understand “consistent description” limited to detail no finer than allowed by HUP.
But what might you mean by “singular description” ?

Seems to me there are a multitude of descriptions, all consistent within the limits of QM.
BM, MWI, oQM, Strings, etc.

This seems to fall more in the category of something we currently cannot validly assert, or a myth as defined in the OP.

 

[Moridin]

RandallB, I made a poor choice of words.

I meant that there wasn't really a particle/wave duality. Perhaps I should have used single (in contrast with dualist) instead.

 

[strangerep]

[...] This suggests to me that the usual formulation of QM is only an approximation
and that a better theory would be a particle theory. And indeed, in Sec 2.2 Demystifier discusses such a possibility in the Bohmian interpretation.

But what do we even mean by "particle"? I have to admit that at this level I have better
mental grasp of the wave function than what a "particle" is or might be.

In QFT, the standard meaning of "particle" is "unitary irreducible representation (unirrep)
of the Poincare group", which I think is a good meaning - as far as it goes.
Multi-particle/composite states are then constructed as tensor products of these
basic unirreps. But this runs into trouble when interactions are introduced, and controversy
when we try to define localization operators. There's more problems when we try to do
QFT beyond the confines of special relativity and the Poincare group.

 

[peter0302]

I really don't think wave/particle duality should be called a myth. Maybe "misnomer" is more appropriate. The apparent paradox between wave-like and particle-like behavior remains the most fundamental mystery of QM and is hardly a non-issue.

 

[Hurkyl]

I really don't think wave/particle duality should be called a myth. Maybe "misnomer" is more appropriate. The apparent paradox between wave-like and particle-like behavior remains the most fundamental mystery of QM and is hardly a non-issue.

It doesn't look very mysterious to me.

 

[Hans de Vries]

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

What is wrong with the wave function as a physical reality?

Is the EM field not a physical reality? What about the success of all the modeling
theories which use the electron field in a similar way as the EM field, as a continuous
charge and spin distribution?

Just ask Google:

1,660,000 hits for: "Density Functional Theory"
_,_75,000 hits for: "Copenhagen Interpretation"
_,_45,000 hits for: "Bohmian"

The hits are there because it's a proven reality, an industrial success.

(2) Particle position plays such a central role in actual measurements. I have heard it said that all measurements ultimately reduce to positions measurements. (But is this one more myth?)

Nobody has ever detected a point-like particle...

A flash on a detector screen is easily 10^15 times larger as the minimum size
for which some aspects of Quantum Field Theory have proven to be still valid.


Regards, Hans

 

[peter0302]

It doesn't look very mysterious to me.

Guess you're just smarter than me.

 

[Demystifier]

What is wrong with the wave function as a physical reality?

If the wave function collapses due to a change of information available about the system (which the classical electromagnetic field does not do), then it seems that the wave function does not represent reality, but only our information about reality. Unless, of course, you are an extreme positivist who identifies information about reality with reality itself.

 

[Demystifier]

It doesn't look very mysterious to me.

Does the wave function collapse look mysterious to you?

 

[Demystifier]

Guess you're just smarter than me.

Or maybe you are just smarter than him. Feynman said something like "If you are not confused with quantum mechanics, than you do not understand it."

 

[Demystifier]

Nobody has ever detected a point-like particle...

A flash on a detector screen is easily 10^15 times larger as the minimum size
for which some aspects of Quantum Field Theory have proven to be still valid.

That is true. But it is also true that nobody ever detected a particle as a wave. For example, in famous double slit experiments that demonstrate the wave nature of particles, in every measurement of a single particle you actually observe this small flash.

 

[Demystifier]

Just ask Google:

1,660,000 hits for: "Density Functional Theory"
_,_75,000 hits for: "Copenhagen Interpretation"
_,_45,000 hits for: "Bohmian"

The hits are there because it's a proven reality, an industrial success.

422,000,000 hits for: "God"
14,200,000 hits for: "Santa Claus"
I guess it is because these are even better proven realities.

 

[Fra]

What is wrong with the wave function as a physical reality?

If the wave function collapses due to a change of information available about the system (which the classical electromagnetic field does not do), then it seems that the wave function does not represent reality, but only our information about reality. Unless, of course, you are an extreme positivist who identifies information about reality with reality itself.

IMHO, the real practical as well as fundamental problem, is that anything we learn about anything, needs to be acquired. There seems to be an information process through which knowledge is acquired, and I think that the nature of this process is a non-trivial way acutally has profound impacts on reality itself. Becaseu this isn't the isolated problem of a human scientist, I think all elements of the universe, including particle systems are bound to face the analog problem. A particle can hardly predict it's environment completely. And this should have consequences when you look statistically on group dynamics and complex systems.

So no matter what you think nature really is, I focus on exactl how do you conclude that, and how confident are you in the conclusion itself?

I can not even imagine the meaning of trying to picture that nature "really is" in a way that bypasses the learning/acquisition process? Such classical realism IMO seems to release itself from observability ideals, that IMO releases itself from my idea of the scientific method.

I consider the information a given observer have about it's environment is as real as anything possibly gets. It's an "image of reality" but this image is all he has, wether he wants is or not. But of course this images is in constant motion. The dynamics of this image is what I think interactions is about. Clearly the actions of this observer will depend on this image as well, which is thus also dynamical.

But I agree that QM as it currently stands doesn't reflect this to the full extent. One problem IMO is that QM is still too deterministic. The concept of deterministic probabilities makes no sense to me in this sense. I think the deterministic evolution is emergent in special cases. It's the limiting case where our incomplete guesses, happens to be in agreement with the expectations of the environment, then our guesses will appear to be like deterministic predictions. But thinking they are fundamentally deterministic, and taking that to be a principle of the foundations, that can be used for reasoing and extending the theory is IMO a mistake.

I think one confusion conclusive criticts that realists have on this, is that it would limit our ability to learn and make progress. And that accepting QM weirdness is like throwing in the towel. IMO that is a totally twisted conclusion, because IMO the fact that I don't know, does NOT mean I can't learn in the future. My personal poitn is that it is not possible at the present to determine the dice of tomorrow with certainty! So what is rated with probability zero today, might happen tomorrow. That is part of the indeterminism of the probabilities. But this is not realized in current QM formalism, which is why I still think that we need a fundamental revision of QM.

But I still maintain strong observability ideals and information perspectives. There is no contradiction here. I think the key is the physical basis of probability, this needs more attention in physics. The physical basis of the axioms of probability in relation to something observalbe it IMO very vague in current models.

/Fredrik

 

[pellman]

Re \psi (x_1, x_2; t)..A similar form for E and B will hold in classical E&M for example, for two charged particles interacting and radiating with the E&M field.

It is true that the E&M field depends on the position of particles. So for two sources we could write the value of the field at the point x as F^{\mu\nu}(x,t;x_1,x_2). But the point is that this is the value of the field at the point x. There is nothing analogous to this for the quantum wave function. There is no "value of the wavefunction at the point x". In principle, there is a single wavefunction for the whole universe, \Psi(x_1,...,x_N; t) where N is the number of particles in the universe. (I'm talking non-relativistic QM here of course.) And it's value is not dependent on actual positions of those particles. Rather, it has a value for every possible arrangement of the "particles".

Pretty tough to swallow as the reality, IMHO.

And there's always a mapping from configuration space -- as you define it -- to physical space. Think, for example, also about Hamilton-Jacobi Theory and how it is formulated

But this is just what I mean. Don't we agree that the Hamilton-Jacobi function is merely a calculational tool? It's value is only in its ability to lead us the equations of motion of the individual particles.

 

[peter0302]

Or maybe you are just smarter than him. Feynman said something like "If you are not confused with quantum mechanics, than you do not understand it."

LOL. I didn't want to sound too arrogant, but yes that came to mind.

 

[peter0302]

If the wave function collapses due to a change of information available about the system (which the classical electromagnetic field does not do), then it seems that the wave function does not represent reality, but only our information about reality. Unless, of course, you are an extreme positivist who identifies information about reality with reality itself.

That's exactly right. As soon as you try to impart physical meaning into the wave function is when you start to get paradoxes. That's why I lean toward MWI, because its explanation of wave function collapse (i.e., the universe splitting to reflect the new information that is obtained) is the simplest and most intuitive _physical_ interpretation IMO.

On the other hand, it's possible that we simply don't understand enough about statistical and information theory to link the wave function to reality, and that if we ever develop better logical/informational models the paradoxes will disappear.

 

[Hans de Vries]

If the wave function collapses due to a change of information available about the system (which the classical electromagnetic field does not do), then it seems that the wave function does not represent reality,

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

A photon which refracts through a lens and travels at 65% of the speed
of light has to interact with ~10^20 dielectric molecules which all need to
move "up and down" with each period of the photon to make this possible.

What proof is there that these interactions don't take place because there
is only one flash on the detection screen?

The same is true for the wave function of the electron field. How can the motion
of the nuclei due the electron field be modeled by Quantum Molecular Modeling
if the wave function is only a mathematical construct and the "real physics"
involves just little billiard balls?


Regards, Hans

 

[Fra]

On the other hand, it's possible that we simply don't understand enough about statistical and information theory to link the wave function to reality, and that if we ever develop better logical/informational models the paradoxes will disappear.

That sounds like my horse :)

/Fredrik

 

[RandallB]

I really don't think wave/particle duality should be called a myth. Maybe "misnomer" … … wave-like and particle-like behavior remains the most fundamental mystery of QM and is hardly a non-issue.

It doesn't look very mysterious to me.

That doesn’t seem logical and rational to me.

You don’t explain why this paradox is no mystery to you, so I can only assume it is because you accept QM CI as not just accurate but correct and complete.
That should mean you accept reality must not be both “local and realistic”, allowing for weird action at a distance. I.E. you accept that reality itself is in fact mysterious. Which also should mean you accept “wave-like vs. particle-like” as a part of a mysterious fact of nature.

Thus I can only conclude you think “wave-like vs. particle-like” is mysterious, but question the degree of mystery as not being large enough to call it “very” mysterious.

Otherwise you would be a total mystic that rejects rationalism to the point of not accepting the scientific method and I don’t read you as one of those.

 

[Hurkyl]

RandallB -- I cannot follow any of the reasoning in your post. It certainly does not appear to be 'rational and logical' grounds for me to discard my self-assessment of being "not mystified".

And, quite honestly, I do not really understand why someone would be mystified at the fact a quantum state can, approximate the behavior of a classical particle in some circumstances, and approximate the behavior of a classical wave in some circumstances. I could speculate, but it would merely be speculation.

allowing for weird action at a distance. I.E. you accept that reality itself is in fact mysterious.

For the record, I also do not find "weird action at a distance" mysterious.

 

[f95toli]

I agree with Hurkyl. It seems most people that that a problem with wave-particle duality, Bell's etc make the implicit assumption that nature should "make sense". However, as far as I can tell there is no reason to believe this to be the case.
The litmus test for a scientific theory is if it makes predictions that agrees with experiments, if it does we say that it is "correct" in the scientific sense.
Hence, it might turn out that our most accurate theories will one day tell us that e.g. nature is both non-local and non-realistic which would certainly be "weird", but if those theories agree with experimental data then we will have to accept them. And, as with most "weird ideas", once we get used to them they won't appear so "mysterios" anymore. Jjust think about SR, time dilation was definately something "mysterios" idea back in 1905, but now we are used to the idea.

Whether or not our theories have anything to do with a "reality" in a philosophical sense(which tend to be what these threads end up discussing) might be an interesting issue to debate, but it is ultimately irrelevant from a scientific point of view.

Personally, I don't worry about it anymore but maybe that is because I am an experimentalist; as long as I am able to use the various aspects of QM to plan, analyze and understand the outcome my experiments I am happy

 

[pellman]

The title of this section in Demystifier's paper is In QM there is a wave-particle duality. That, I think we can all agree, is certainly a myth. In the theory there is only the wave-function or state-vector |\psi\rangle. The theory has nothing to say about particles, only about "observables" and the probability of observing one to have a certain value--though leaving "observing" undefined.

If there is a particle-wave duality in our understanding of the data, it is outside of QM theory proper.

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

 

[RandallB]

Feynman said something like "If you are not confused with quantum mechanics, than you do not understand it."

I agree with Demystifier & Feynman. But science has many opinions & views that can be held with certainty and passion.

 

[Ken G]

I think most of the confusion around "wave-particle duality" stems from the fact that none of the words in that phrase are precisely enough defined such that we really know what that phrase even means-- depending on how you interpret it, it could be false, it could be a myth (i.e., unknown), or it could be demonstrably true. The way it's false is if you interpret it as meaning that quanta follow trajectories like particles, such that they have to "pass through one slit or the other, we just don't know which". The way it is an unknown myth is if you imagine that the quantum has a kind of split personality, where it will actually be a particle if you do a particle measurement, and it will actually be a wave if you do a wave measurement. That's just taking the interpretations of quantum mechanics way too seriously, resulting in mythical attributes. But the way it is just completely true is if you note that a wave function has wavelike behavior (as noted above), but you also note that we are doing quantum mechanics here, that is, there is an important logic that is being used that forces us to treat one quantum process at a time. So does "particle" just mean "quantum", or does it mean "follows a classical trajectory"? I don't think the posts above are consistently in agreement on that issue.

Personally, I think the best solution is to replace the term "particle" with the term "quantum", like the way "particle physicists" use the term, such that we have quanta whose behavior is described by wave mechanics, which in the short-wavelength limit may be associated with particlelike behaviors such as trajectories. Said like that, I see no source of confusion, and the duality is like the "duality" of a particle with a finite rest mass that can act relativistically or nonrelativistically in opposing energy limits. Does that count as a "relativistic/non-relativistic duality"?

Using the word "quantum" avoids the issue of "wave-quantum duality", and allows you to simply say you have quanta governed by waves that have a "very wavelike" and a "very particlelike" limit. Is that a "duality"? Sure, if that's all that is meant, but it's not a split personality and it's not much different from relativistic vs. nonrelativistic behaviors. But you still use the concept of "particle", in the form of a "quantum", let us not forget that quantum mechanics is not purely a wave theory.

 

[Hurkyl]

Feynman said something like "If you are not confused with quantum mechanics, than you do not understand it."

I agree with Demystifier & Feynman. But science has many opinions & views that can be held with certainty and passion.

Quantum mechanics is (IMHO) a large and complicated subject -- I am not asserting the entire field is not confusing. I certainly cannot speak for the parts I don't know, or for the parts I don't even know that I don't know!

But we're not discussing deep 'mysteries' here -- were talking about some of the simplest facets of QM.

 

[peter0302]

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!

 

[reilly]

But this is just what I mean. Don't we agree that the Hamilton-Jacobi function is merely a calculational tool? It's value is only in its ability to lead us the equations of motion of the individual particles.

Yes and no. As it comes from the notions of contact transformations, the H-J leads to considerable insight into (classical) dynamics. Also, the very elegant structure of the H-J approach, gives, in my opinion, a view into theoretical physics that's often the first "real" view of advanced physics -- particularly dynamics as a mapping, say from then to now. That's my opinion, as a one-time student, and as a teacher.
Regards,
Reilly Atkinson

 

[reilly]

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.

So I do think that wave-particle duality is a misnomer. The wave yields the probability of finding a point particle. Pretty simple, and simple is good.
Regards,
Reilly Atkinson

 

[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):

<br /> \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)<br />

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...