"Wave-particle duality" and double-slit experiment

[HighPhy]

Sorry to open a new thread.
There are plenty of threads on PF dealing with the issue of "wave-particle duality".
Although not unanimously, many agree that the concept of "wave-particle duality" is outdated. Electrons, photons and all of the underlying entities are neither waves nor particles, but quantum fields, and we can do certain wave-like experiments that let quantum fields behave like particles, and other particle-like experiments that let them behave like waves.

I have doubts not only about the term "duality," but also about "wave-particle duality" in the double-slit experiment. I'll try to put my doubt within a context.

From the very beginning, I was taught in school that:

Bohr conceived the atom with electron making circular orbits around the nucleus with its levels (by following Planck's quantization of energy). Later Schroedinger, thanks to Young's double-slit experiment demonstrating "wave-particle duality", abandoned the concept of an orbit to introduce that of an orbital and to see how the electron does not perform a well-defined orbit, but rather is chaotic.
The electron can be in an area described by the wave function, and the square modulus of the wave function (always greater than or equal to zero) returns the probability that the electron is at a given point, which, however, cannot be known because of Heisenberg's Undeterminacy Principle.
So the real model of an atom is not the one with a ball of mass formed by protons and neutrons and precise orbits of electrons surrounding it, but the one that predicts an electron cloud in which there is a greater probability of finding an electron.

Having finished with the context, of which I am not sure, I express my confusion.

It is said that the double-slit experiment demonstrates "wave-particle duality".
In this Insight article it is said that:

Quantum mechanics is known for its strangeness, including phenomena like wave-particle duality, which allows particles to behave like waves. The double-slit experiment is a key demonstration of this duality, showing that even single particles, like photons, exhibit wave-like behavior. When the experiment measures which slit a particle goes through, it behaves like a particle. When this measurement is not made, it exhibits interference patterns typical of waves.

The transformation from wave-like behavior to particle-like behavior is intimately related to Heisenberg’s uncertainty principle
[...] using detectors to measure each photon’s slit identity (i.e. which slit the photon passed through) prevents any wave-like behavior, just as if each photon had traveled in complete isolation as a single particle. If both slots are left open (and no photodetectors are used) then the original interference pattern is restored, as if the individual photons behave like waves [...]. This is the famous wave-particle duality.

So my question is:
Is the fact that the double-slit experiment demonstrates wave-particle duality a misconception?
Or does the double-slit experiment (1801) really prove "wave-particle duality" but must be overcome due to the fact that the latter is an outdated concept?
Or are there particular explanations that allow this experiment to be placed in the perspective of "modern quantum theory" despite the fact that it could demonstrate "wave-particle duality"?

 

[PeroK]

There are plenty of threads on PF dealing with the issue of "wave-particle duality".

There are!

Although not unanimously, many agree that the concept of "wave-particle duality" is outdated.

It is as far as experimental physics research is concerned. In the sense that no one is trying to prove that an electron is a classical particle or a classical wave. It is accepted that these two phenomena are explained by QM and experimental physics has moved on to pastures new.

Electrons, photons and all of the underlying entities are neither waves nor particles, but quantum fields, and we can do certain wave-like experiments that let quantum fields behave like particles, and other particle-like experiments that let them behave like waves.

Okay.

I have doubts not only about the term "duality," but also about "wave-particle duality" in the double-slit experiment. I'll try to put my doubt within a context.

These are words. Worrying about what words mean is largely a philosophical matter.

From the very beginning, I was taught in school that:

Bohr conceived the atom with electron making circular orbits around the nucleus with its levels (by following Planck's quantization of energy).

No.

Later Schroedinger, thanks to Young's double-slit experiment demonstrating "wave-particle duality",

Young's experiments were in 1803. They were hardly something Bohr didn't know about.

abandoned the concept of an orbit to introduce that of an orbital and to see how the electron does not perform a well-defined orbit, but rather is chaotic.

Bohr's model has the orbital as a standing wave of sorts. Schrodinger was resposnible for the wave equation. But, it was Heisenberg and others who extended Bohr's model to a wider range of orbitals. This again is the history of the development of QM.

Physics (and mathematics) are hard-boiled subjects that are not defined by their history, but their contemporary descriptions.

The electron can be in an area described by the wave function, and the square modulus of the wave function (always greater than or equal to zero) returns the probability that the electron is at a given point,

No. The wave function tells you were you are likely to measure the position of an electron. The electron in an atomic orbital simple has no well-defined position.

which, however, cannot be known because of Heisenberg's Undeterminacy Principle.

This is not what is normally known as the HUP.

So the real model of an atom is not the one with a ball of mass formed by protons and neutrons and precise orbits of electrons surrounding it, but the one that predicts an electron cloud in which there is a greater probability of finding an electron.

Electron cloud is a physical interpretation of the wave function. However, it is not physically very precise.

Having finished with the context, of which I am not sure, I express my confusion.

It is said that the double-slit experiment demonstrates "wave-particle duality".
In this Insight article it is said that:



So my question is:
Is the fact that the double-slit experiment demonstrates wave-particle duality a misconception?

That's just playing with words, IMO.

Or does the double-slit experiment (1801) really prove "wave-particle duality" but must be overcome due to the fact that the latter is an outdated concept?

The double-slit experiment is what it is. Clearly there is something there that could be termed "wave-particle" duality. If you accept that term, then what's to prove?

Or are there particular explanations that allow this experiment to be placed in the perspective of "modern quantum theory" despite the fact that it could demonstrate "wave-particle duality"?

This is just playing with words again.

Are you a philosophy student?

 

[Nugatory]

Is the fact that the double-slit experiment demonstrates wave-particle duality a misconception?

Yes, if by “the double slit” you mean the double-slit experiment done by Young more than two centuries ago. That experiment demonstrated the wave nature of light (and that color is related in some way to wavelength) by producing interference and diffraction patterns. It shows no quantum mechanical behavior and the observations are completely explained by classical wave optics.

No, not a misconception if you mean more recent experiments done with single photons so that the interference pattern builds up one dot at a time. This behavior cannot be explained classically. Even more striking are experiments done with massive particles like electrons - the one dot at a time behavior is expected of particles but the interference/diffraction behavior is expected of waves.
Although nice demonstrations, as far as I know none of these experiments were done until long after “wave-particle duality” had come and gone so did not contribute to the development of quantum theory.

 

[PeroK]

PS just to repeat something I've said on here many times over the years. I have two undergraduate textbooks on QM and the wave-particle duality is not a topic. In Introduction to QM by Griffiths, it is mentioned once as a historical footnote. And, in Modern QM by Sakurai, it is not mentioned at all.

This highlights the difference between QM as a branch of modern physics and QM as a subject of popular interest, where the wave-particle duality is a central theme.

 

[gentzen]

Are you a philosophy student?

Or a computer science student? Can you just tell us your academic background? It doesn't seem to be physics!

 

[HighPhy]

No.

Could you expand on this, please?
In this Insight article it is said:

If one describes atoms using only the Coulomb forces, the electron and the nucleus will attract each other and no stable atoms could exist. Obviously, this is not the case. Niels Bohr was the first (1913) to propose a better model, which consisted of electrons moving around the nucleus in circular orbits. Each orbit corresponds to a certain discrete energy level. This model is based upon the quantization of the angular momentum.

Where did I go wrong in this?

 

[PeroK]

Could you expand on this, please?
In this Insight article it is said:

Where did I go wrong in this?

Perhaps I'm wrong and Bohr's original model had electrons in classical orbits. However, within a few years Bohr was arguing that QM did not involve classical trajectories of any sort. The Bohr model in its simplest semi-classical form must have been short lived.

 

[PeroK]

@HighPhy if you are interested in the history of the development of QM, I would recommend Quantum, by Majit Kumar:

https://www.westwoodbooks.co.uk/products/quantum-manjit-kumar

 

[HighPhy]

@HighPhy if you are interested in the history of the development of QM, I would recommend Quantum, by Majit Kumar:

https://www.westwoodbooks.co.uk/products/quantum-manjit-kumar

Thanks.

This is not what is normally known as the HUP.

Electron cloud is a physical interpretation of the wave function. However, it is not physically very precise.

Could you expand on these two statements?

 

[PeroK]

Could you expand on these two statements?

You can look up the HUP to see what it really says.

Electron cloud, IMO, is one of these ideas that stems from a general reluctance or inability not to think classically. If the electron does not have a well-defined position, then it could still admit a classical model by being a cloud (or distribution) of electric charge. Whereas, it is not a cloud of electric charge. In the QM model of the atom bound energy states are fundamental, not the position of the particles. Thinking of a proton and an electron (in the case of Hydrogen) as an energy eigenstate is a fundamentally non classical concept. Popular science authors may avoid this because, without the mathematical background, it is perhaps meaningless. So, they may prefer "electron cloud" as more amenable to lay people, who may despair at anything vaguely mathematical.

 

[PeterDonis]

Electron cloud, IMO, is one of these ideas that stems from a general reluctance or inability not to think classically. If the electron does not have a well-defined position, then it could still admit a classical model by being a cloud (or distribution) of electric charge.

That was Schrodinger's initial proposed model: an electron in an atom was a smeared-out cloud of electric charge instead of a point particle. Unfortunately this model did not work, and was discarded in favor of Born's probability interpretation of the wave function.

 

[HighPhy]

That was Schrodinger's initial proposed model: an electron in an atom was a smeared-out cloud of electric charge instead of a point particle. Unfortunately this model did not work, and was discarded in favor of Born's probability interpretation of the wave function.

AFAIK, the Bohr model of the atom is false, and nowadays we replace the idea of the semi-classical "orbit" of Bohr with the fully quantum mechanical notion of "orbitals or electron cloud", which give a probability distribution for the position of the electron around the nucleus, but do emphatically not imply that the electron is moving in any classical sense.
So the key difference between Bohr model and Schroedinger model is that in most modern interpretations of the Schrodinger model the electron of a one-electron atom, rather than traveling in fixed orbits about the nucleus, has a probability distribution permitting the electron to be at almost all locations in space, some being much more likely than others (or according the Schrodinger's original thinking, the electron is actually smeared out over space, rather than being at a point).
What am I missing?

You can look up the HUP to see what it really says.

Thanks, I'll look up. But, just out of curiosity: did the Schroedinger equation not incorporate HUP?

The double-slit experiment is what it is. Clearly there is something there that could be termed "wave-particle" duality. If you accept that term, then what's to prove?

Thank you for pointing out that my use of words is typical of a philosophy student; I take it as valuable advice.
But unfortunately I didn't understand what you mean here.
"Wave-particle duality" is an obsolete concept, as you also confirmed. The double-slit experiment (at least those performed after Young's experiment?) would reveal a "wave-particle duality".
What I meant to say is: do these two aspects imply that such experiments should be abandoned and considered only from a classical perspective?

 

[PeterDonis]

AFAIK, the Bohr model of the atom is false

Yes, it was known in the 1920s that this model makes incorrect predictions.

nowadays we replace the idea of the semi-classical "orbit" of Bohr with the fully quantum mechanical notion of "orbitals or electron cloud"

"Orbitals", yes--those are the stationary states of electrons in atoms.

"Electron cloud", no, for the reasons already given.

which give a probability distribution for the position of the electron around the nucleus

Yes, that is what an "orbital" is (at least in the position representation, which is the one usually used).

but do emphatically not imply that the electron is moving in any classical sense.

Yes.

 

[PeterDonis]

the key difference between Bohr model and Schroedinger model is that in most modern interpretations of the Schrodinger model the electron of a one-electron atom, rather than traveling in fixed orbits about the nucleus, has a probability distribution permitting the electron to be at almost all locations in space, some being much more likely than others

Yes.

(or according the Schrodinger's original thinking, the electron is actually smeared out over space, rather than being at a point).

No. As I have already said, this original proposed model of Schrodinger's was found not to work.

 

[PeterDonis]

did the Schroedinger equation not incorporate HUP?

The Schrodinger equation is an equation for unitary evolution of the wave function. It is completely deterministic. If all you ever use is the Schrodinger equation, you will never see any uncertainty or any probabilities.

 

[PeterDonis]

"Wave-particle duality" is an obsolete concept, as you also confirmed.

Yes.

The double-slit experiment (at least those performed after Young's experiment?) would reveal a "wave-particle duality".

No. Discarding "wave particle duality" as an obsolete concept means discarding it--i.e., you stop trying to interpret anything using it. That means you need to rethink your understanding of the double slit experiment without using the concept of "wave-particle duality" at all.

What I meant to say is: do these two aspects imply that such experiments should be abandoned and considered only from a classical perspective?

Not at all. @Nugatory has already explained why modern double slit experiments cannot be explained classically.

 

[HighPhy]

The Schrodinger equation is an equation for unitary evolution of the wave function. It is completely deterministic. If all you ever use is the Schrodinger equation, you will never see any uncertainty or any probabilities.

Let me say that: I am completely shocked at the amount of inaccurate or incorrect information I have learned so far before this discussion.
So, why is the concept of HUP usually (at school) included in a discussion of Schroedinger's model?

No. Discarding "wave particle duality" as an obsolete concept means discarding it--i.e., you stop trying to interpret anything using it. That means you need to rethink your understanding of the double slit experiment without using the concept of "wave-particle duality" at all.

I understand what you say about the need to discard "wave-particle duality."
I hardly understand the analogy with the double-slit experiment: if some of these experiments demonstrate or imply "wave-particle duality", how do I rethink them without including the concept wave-particle duality?
Mine is a real question, not a rhetorical question.

 

[PeroK]

I hardly understand the analogy with the double-slit experiment: if some of these experiments demonstrate or imply "wave-particle duality", how do I rethink them without including the concept wave-particle duality?

You learn QM!

 

[PeterDonis]

I am completely shocked at the amount of inaccurate or incorrect information I have learned so far before this discussion.

I believe the unwisdom of trying to learn science from the wrong sources was already pointed out in another of your threads.

why is the concept of HUP usually (at school) included in a discussion of Schroedinger's model?

What discussions do you mean? What do you mean by "Schrodinger's model"? Some specific references would be helpful.

I understand what you say about the need to discard "wave-particle duality."

Ok, good.

I hardly understand the analogy with the double-slit experiment: if some of these experiments demonstrate or imply "wave-particle duality"

THEY DON'T. Sorry to shout, but that's what we've been trying to tell you for quite a few posts now. Apparently you missed the point.

how do I rethink them without including the concept wave-particle duality?

By learning the actual math and what it predicts and why, and what it does not say. In other words, as @PeroK says, by learning QM.

 

[HighPhy]

What discussions do you mean? What do you mean by "Schrodinger's model"? Some specific references would be helpful.

I was taught in school that:

The electron can be in an area described by the wave function, which tells us where we are likely to measure the position of an electron which, however, cannot be known because of Heisenberg's Undeterminacy Principle.
If, as @PeroK says, this is not the formulation of HUP, why is this concept included in this kind of discussion?

THEY DON'T. Sorry to shout, but that's what we've been trying to tell you for quite a few posts now. Apparently you missed the point.

OK, maybe I got the point. The double-slit experiments demonstrated wave-particle duality in the classical/old quantum theory perspective, but with the advent of the modern quantum theory, these found a quantum-mechanical explanation with the introduction of the concept of quantum fields. Is this now correct, more or less?

 

[PeroK]

I was taught in school that:

The electron can be in an area described by the wave function, which tells us where we are likely to measure the position of an electron which, however, cannot be known because of Heisenberg's Undeterminacy Principle.
If, as @PeroK says, this is not the formulation of HUP, why is this concept included in this kind of discussion?

The UP (Uncertainty Principle) generally is ofen used as a "lazy heuristic" (that's my terminology, by the way) for explaining QM results without looking at the details. Whereas, a textbook like Griffiths will be precise about what it means. In fact, Griffiths has really good section where he explains what the energy-time uncertainty relation really means. And that is something that is badly abused in many sources.

 

[PeterDonis]

I was taught in school

That's not a reference. Can you give any specific textbooks or other sources that you were taught from?

The electron can be in an area described by the wave function, which tells us where we are likely to measure the position of an electron which, however, cannot be known because of Heisenberg's Undeterminacy Principle.

That's not what the HUP says. The HUP places no limits whatever on how accurately we can measure a single observable, such as position.

If, as @PeroK says, this is not the formulation of HUP, why is this concept included in this kind of discussion?

You can't expect us to explain to you why some discussion you were "taught in school", from references you haven't given us, includes the HUP. Or, more generally, why so much of what you were "taught in school" appears to be wrong, or at least misleading, when you have told us nothing about what school, what you were studying, what sources you were taught from, etc.

 

[Vanadium 50]

There are plenty of threads on PF dealing with the issue of "wave-particle duality".

But instead of reading them, you decided to start your own. You can see how this might rub people the wrong way. "Write everything over again just for me, because I am extra special" is not a good look.

Apart from that, you have several problems.

(1) As pointed out several times, trying to learn QM from the wrong sources is destined for failure.

(2) Your strategy seems to revolve around getting the right words together in the right order - this is what triggered the question about philosophy and your background. Sorry - that's not how physics words. Physics is a quantitative science, and the words are just a pale reflection of that.

(3) You complained about a model being false. Guess what? They all are. Every single model we make has simplifications, approximations and regions of validity. That's just how science works, and we're not going to change it to suit you.

Some models, are of course, better than others. But if you want absolute "truth", you have to look elsewhere.

I can understand you not wanting to change. But these are standing in the way of your understanding. If you want to understand, you need to do these things.

 

[HighPhy]

But instead of reading them, you decided to start your own. You can see how this might rub people the wrong way. "Write everything over again just for me, because I am extra special" is not a good look.

Apart from that, you have several problems.

(1) As pointed out several times, trying to learn QM from the wrong sources is destined for failure.

(2) Your strategy seems to revolve around getting the right words together in the right order - this is what triggered the question about philosophy and your background. Sorry - that's not how physics words. Physics is a quantitative science, and the words are just a pale reflection of that.

(3) You complained about a model being false. Guess what? They all are. Every single model we make has simplifications, approximations and regions of validity. That's just how science works, and we're not going to change it to suit you.

Some models, are of course, better than others. But if you want absolute "truth", you have to look elsewhere.

I can understand you not wanting to change. But these are standing in the way of your understanding. If you want to understand, you need to do these things.

OK. I made a mistake. I apologize.

 

[Vanadium 50]

Yes, but are you doing to do things differently?

 

[HighPhy]

Yes, but are you doing to do things differently?

I'll try from now on. Thank you.

 

[SammyS]

That was Schrodinger's initial proposed model: an electron in an atom was a smeared-out cloud of electric charge instead of a point particle. Unfortunately this model did not work, and was discarded in favor of Born's probability interpretation of the wave function.

AFAIK, the Bohr model of the atom is false, and nowadays we replace the idea of the semi-classical "orbit" of Bohr with the fully quantum mechanical notion of "orbitals or electron cloud", which give a probability distribution for the position of the electron around the nucleus, but do emphatically not imply that the electron is moving in any classical sense.
So the key difference between Bohr model and Schroedinger model is that in most modern interpretations of the Schrodinger model the electron of a one-electron atom, rather than traveling in fixed orbits about the nucleus, has a probability distribution permitting the electron to be at almost all locations in space, some being much more likely than others (or according the Schrodinger's original thinking, the electron is actually smeared out over space, rather than being at a point).
What am I missing?

Read what @PeterDonis wrote more carefully. In that quote of his which you replied to above, he refers to Max Born, not Niels Bohr .

 

[HighPhy]

After getting to the bottom of my mistakes, I have adequately documented myself, but I’d like to understand whether I have really learned correctly.

This is not what is normally known as the HUP.

That's not what the HUP says. The HUP places no limits whatever on how accurately we can measure a single observable, such as position.

So, HUP places no limits on the precision with which we can measure the position or momentum of a particle. More simply, we cannot confine the electron in a very small space and control its momentum in a very small range. It is possible to know both velocity and position simultaneously with some precision, but only up to a certain point. We cannot know both with arbitrary precision.

So, it is not correct to say that the Heisenberg Uncertainty Principle states that we can't know both the velocity/energy and position of an electron, right?

Moreover, it is not correct to say that the square modulus of the wave function represents the probability of finding an electron in a given region or in a particular volume of space within the atom, right?

The electron could be at almost all locations in space: the square modulus of the wave function only allows some locations being much more likely than others, but not given and precise locations.

 

[PeroK]

After getting to the bottom of my mistakes, I have adequately documented myself, but I’d like to understand whether I have really learned correctly.



So, HUP places no limits on the precision with which we can measure the position or momentum of a particle. More simply, we cannot confine the electron in a very small space and control its momentum in a very small range. It is possible to know both velocity and position simultaneously with some precision, but only up to a certain point. We cannot know both with arbitrary precision.

So, it is not correct to say that the Heisenberg Uncertainty Principle states that we can't know both the velocity/energy and position of an electron, right?

The operative word is "know". The HUP is essentially a statistical law. It's put a lower limit on the product of the variance of position measurements times the variance of momentum measurements. Again, it's only the mathematics that is precise and unambiguous.

Moreover, it is not correct to say that the square modulus of the wave function represents the probability of finding an electron in a given region or in a particular volume of space within the atom, right?

That is correct. What's not correct is to see the squre modulus as a probability distribution for where the electron is. This is a subtle but ultimately important distinction.

The electron could be at almost all locations in space: the square modulus of the wave function only allows some locations being much more likely than others, but not given and precise locations.

Again, more precisely, it tells how how likely it is to measure an electron in a given position. We can't say that the electron was definitely there just before we measured it. That's where QM is non-classical.

 

[HighPhy]

That is correct. What's not correct is to see the squre modulus as a probability distribution for where the electron is. This is a subtle but ultimately important distinction.

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

 

[gentzen]

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

If you assume that particles have definite positions, then you get the de Broglie-Bohm interpretation. To avoid this, you just talk about measurement results, instead of making statements about supposedly real positions of particles.

 

[PeterDonis]

HUP places no limits on the precision with which we can measure the position or momentum of a particle.

For single measurements of either position or momentum, no.

More simply, we cannot confine the electron in a very small space and control its momentum in a very small range.

This is not a "more simply" version of your previous statement. It is a different statement, which relates to trying to control both position and momentum at the same time. The HUP places a limit on the product of the uncertainties of the two.

It is possible to know both velocity and position simultaneously with some precision, but only up to a certain point. We cannot know both with arbitrary precision.

Not at the same time, no.

Another way of putting it is that the HUP is giving a limitation on the possible states of the quantum system: for any given state, the product of the position and momentum uncertainties must satisfy the HUP inequality.

 

[PeroK]

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

Ultimately this is what all the fuss was about, especially regarding quantum entanglement, which culminated in the EPR paper and Bell's Theorem. If the electron has a definite position, then that is a so-called local hidden-variables theory. Bell proved that QM can do better in terms of the correlation of spin/polarization measurements on entangled particles than is possible using local hidden variables. And, when the tests where carried out, they corroborated QM. This means that an electron cannot have a fully-determined spin in all directions. Hence, dynamic quantities such as position, momentum, angular momentum and spin, simply do not have well-defined values until they are measured.

This implies that QM is not locally realistic (that phrase has a precise meaning). In other words, you shouldn't think of the electron having a definite position before measurement. It's only after a measurement of position that talking about the position of an electron makes any sense.

Again, this is non-classical thinking. QM is not classical mechanics with a bit of probability and uncertainty thrown in. It's a completely different theory of nature, where abstract states are the fundamental building blocks, rather than well-defined dynamic quantities.

 

[PeterDonis]

If the electron has a definite position, then that is a so-called local hidden-variables theory.

Not necessarily; as @gentzen pointed out earlier, particle positions are definite in the Bohmian interpretation--but that is a nonlocal hidden variable model. You are correct that local hidden variable models are ruled out.

 

[sillyputty]

I'm so sorry, but I couldn't understand this distinction (which, as you say, is subtle). Could you please explain it better?

He means this: The probability distribution is for where the particle will be when measurement happens, and is NOT for where the particle is before measurement happens. He is trying to make you understand that the particle does not have position before measuring it.