Understanding Wave-Particle Duality with Water Analogy

[Technon]

I'm thinking about the wave–particle duality and I like to understand it through analogy. So I'm thinking about how it relates to for example water. Water can be seen as both having wave characteristics, but also as particles (water molecules). Do you think this is a good analogy to the wave–particle duality of quantum physics? Give arguments why and/or why not you think so.

(Note: The picture is not mine, I just searched "wave particle duality water" and it came up, and I thought it relates somewhat to my question).

 

[phinds]

"wave particle duality" is a severely deprecated concept and has been for 100 years. It persists in pop-science but not in actual science. I suggest a forum search since the topic has been beaten to death here on PF. For example: https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

 

[PeterDonis]

Water can be seen as both having wave characteristics, but also as particles (water molecules). Do you think this is a good analogy to the wave–particle duality of quantum physics?

No. Classically, the wave view of water is only an approximation, useful when you only care about what's happening on distance scales large compared to the size of the particles (molecules). The particle view is not an approximation; it's exact (but uncomputable in practical terms, which is why nobody tries to predict the behavior of a jug water by computing the behavior of all its molecules). The wave view is built from the particle view by assuming a large number of molecules and making simplifying assumptions to reduce the complexity to something manageable.

In quantum mechanics, the "wave" and "particle" aspects are both approximations (there are cases where neither one really works well), and neither one is built on the other.

 

[Technon]

"wave particle duality" is a severely deprecated concept and has been for 100 years. It persists in pop-science but not in actual science. I suggest a forum search since the topic has been beaten to death here on PF. For example: https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

Hello phinds. The post you linked discusses why photons should not be considered particles in the classical sense. That is another topic than what I write about.

Here's a question that can help determine whether the analogy is good or not:

1. Are the wave characteristics also true also for a single particle?

 

[phinds]

1. Are the wave characteristics also true also for a single particle?

I don't even see that as a meaningful question. Quantum objects such as photons are NOT "waves" nor are they "particles". They are quantum objects. Period. If you measure for wave properties, that's what you'll see and if you measure for particle properties, that's what you'll see, but that does not make them waves or particles.

 

[PeroK]

Hello phinds. The post you linked discusses why photons should not be considered particles in the classical sense. That is another topic than what I write about.

Here's a question that can help determine whether the analogy is good or not:

1. Are the wave characteristics also true also for a single particle?

I have two standard undergraduate textbooks on QM. The first, by Griffiths, mentions the wave-particle duality once, as historical footnote in the Afterword. The other, by Sakurai, doesn't mention it at all.

So, in fact, there is no wave-particle duality in the theory QM.

Where there is a wave-particle duality is in the interpretation of experimental results. Some people may look at an experiment and say that looks like "wave" behaviour. Other people may look at another experiment and say that looks like "particle" behaviour. But, the electron or the photon are oblivious to how people may interpret their behaviour.

 

[Technon]

I have two standard undergraduate textbooks on QM. The first, by Griffiths, mentions the wave-particle duality once, as historical footnote in the Afterword. The other, by Sakurai, doesn't mention it at all.

So, in fact, there is no wave-particle duality in the theory QM.

Where there is a wave-particle duality is in the interpretation of experimental results. Some people may look at an experiment and say that looks like "wave" behaviour. Other people may look at another experiment and say that looks like "particle" behaviour. But, the electron or the photon are oblivious to how people may interpret their behaviour.

This book is used by my university for master's courses in engineering: https://www.amazon.com/dp/142920124X/?tag=pfamazon01-20
As you can see in the table of contents, chapter 34 has the title "Wave-Particle Duality and Quantum Physics".

 

[PeroK]

This book is used by my university for master's courses in engineering: https://www.amazon.com/dp/142920124X/?tag=pfamazon01-20
As you can see in the table of contents, chapter 34 has the title "Wave-Particle Duality and Quantum Physics".

First, QM is a very small part of that book. The chapters clearly are giving a historical background. In the context of "Light from Newton to Maxwell", the wave-particle duality is of historical significance.

You could interpret that chapter title as:

Wave-particle duality (the classical world before QM) and Quantum Mechanics (which resolved the wave-particle duality).

That said, I admit that many authors still like to talk about wave-particle duality; but, at no point is there any division in QM into wave-like and particle like. In that sense, there is no analogy needed for a distinction that does not manifest itself within the theory.

Anyway, the consensus here at PF is that wave-particle duality is an issue that was resolved 80 years ago by modern QM and is now historical baggage that still gets people excited and some people are very disappointed to hear that it's not been an issue for 80 years or so!

 

[PeterDonis]

1. Are the wave characteristics also true also for a single particle?

What wave characteristics? Instead of talking in abstractions, give us a concrete example of an experiment where "wave characteristics" are observed.

 

[ZapperZ]

This book is used by my university for master's courses in engineering: https://www.amazon.com/dp/142920124X/?tag=pfamazon01-20
As you can see in the table of contents, chapter 34 has the title "Wave-Particle Duality and Quantum Physics".

First of all, this is very odd.

That text that you cited is typically used in intro General Physics courses for 1st year undergraduate students (physics and engineering majors). I'm very surprised that it is being used for a "master's course" at your university.

Secondly, you need to read it very carefully. The "wave-particle" duality refers to the outcome of numerous experiments in which quantum objects show wave-like results, while others show particle-like results. We use the name "wave" and "particle" to refer to a baseline reference that we are familiar with within our classical world.

Unfortunately, the quantum world is not like that. There are no physical wave or physical particle being describe within quantum mechanics. The "wave" that describes, say, electrons, is not a physical wave such as those you see in water. This "wave" is a mathematical description that "lives" in what we call a configuration space. We do not have direct access to it. We only detect the outcome of it upon measurement. So when the measurement resembles what we know a classical wave produces, we consider this a wave-like result. If it resembles what we know as the classical particle, we consider this a particle-like result.

But only after you study QM in detail (beyond using that textbook), will you see that this is a whole new world that does not resembles what you are familiar with. We have no language to describe that, so we tend to use the old language that we are familiar with. Do not be attached to those words and labels that are used commonly, and think that this transpose smoothly to quantum properties. They do not!

Zz.

 

[bhobba]

What may help you is a paper written by a science adviser here and a professor of physics who likely has actually taught this stuff:
https://arxiv.org/abs/quant-ph/0609163

There are many myths in QM promulgated by popularization's and introductory texts..

You may be thinking of the double slit experiment as showing wave particle duality. That's just an introductory level analysis - here is a better one:
https://arxiv.org/abs/quant-ph/0609163

But even the above is not correct - just better than the basic explanation:
https://arxiv.org/pdf/1009.2408.pdf

Unfortunately physics is like that - you build up to the final understanding - you start with half truths then gradually get the right answer as you progress. One of the great teachers, Feynman, hated it, but could never figure out how to get around it.

For QM the following is IMHO a better place to start about what it all means:
https://www.scottaaronson.com/democritus/lec9.html

Your engineering textbook is primarily about, as you would naturally expect, engineering - not physics and understandably is not that worried about niceties like is the wave-particle duality actually true. It's like an engineering text I read that was explaining Borel summation which it did simply, but to a trained mathematician was not correct. It said for the sum of a series an, ∑an = ∑(an/n!)n!. We then use a general well known property of the gamma function Γ(n+1) = n! = ∫t^n*e^-t to get ∑an = ∑(an/n!)∫t^n*e^-t = ∑∫(an/n!)*t^n*e^-t. So far everything is fine but then it does a big no-no - reversing the sum and integral to get ∫∑(an/n!)*t^n*e^-t. You can't do that generally - only in some cases - yet engineers do such things with gay abandon. I don't blame them - its engineering after all - not math and it works a lot of the time (not in this case though - but that is a whole new thread). You really can't find out about the niceties of physics in engineering books, nor the niceties of math - nor would I expect it to be any different. Here however we will give you those niceties - for better or worse.

Thanks
Bill

 

[Technon]

What wave characteristics? Instead of talking in abstractions, give us a concrete example of an experiment where "wave characteristics" are observed.

There are many. For example: electron interference and diffraction, de Broglie-wavelength, wave function, probability function, particle distribution, particle in a box, standing waves.

 

[PeterDonis]

There are many.

I asked for experiments, not abstractions. The only experiments you listed are electron interference and diffraction.

For those experiments, what would it mean for "wave characteristics" to be "true for a single particle"? Remember we're talking about experiments, not abstractions, so you need to explain what experimental result would make this true.

 

[Technon]

I asked for experiments, not abstractions. The only experiments you listed are electron interference and diffraction.

You asked for just one example, and you confirmed I listed two examples.

 

[PeterDonis]

You asked for just one example, and you confirmed I listed two examples.

Ok. Can you answer the question I asked in post #13?

 

[Technon]

For those experiments, what would it mean for "wave characteristics" to be "true for a single particle"? Remember we're talking about experiments, not abstractions, so you need to explain what experimental result would make this true.

Actually in that question I was referring to a water molecule, and was considering whether a single water molecule could show wave characteristics or just particle characteristics?

Diffraction.

 

[PeroK]

Actually in that question I was referring to a water molecule, and was considering whether a single water molecule could show wave characteristics or just particle characteristics?

There's a veritaseum video about the "oildrop" experiment that is an analogy for the pilot wave theory that you might find interesting in this respect.

 

[Nugatory]

Actually in that question I was referring to a water molecule, and was considering whether a single water molecule could show wave characteristics or just particle characteristics?

A water molecule is a complicated thing; it's made up of three atoms and many more subatomic particles, so has many internal degrees of freedom to consider. But if we ignore all this and try to talk about it as we would a simpler quantum object...

It depends on what you're doing with it. If you try to identify its position, you will find that it is located somewhere - and having a definite position is the essential attribute of a classical particle, so naturally you'll call that particle behavior.

Getting it to show wave behavior is trickier because in practice we can't determine anything about what it's doing without localizing it. For example, in the quantum mechanical double-slit experiment each individual quantum object is localized when it makes its single dot at a single point on the screen. There's no way of seeing the wavelike interference in a single dot. Instead we have to let the interference pattern build up one dot at a time as multiple particles pass through the slits.

However, as other have pointed out in this thread, "wave-particle duality" is no part of the modern understanding of quantum mechanics. It's just not a helpful way of thinking about the behavior of quantum objects. An analogy, with tongue only slightly in cheek:
Pillows are fuzzy.
Tables have four legs.
But when you encounter a sheep, which is fuzzy and has four legs... you will not find the concept of "table-pillow duality" to be helpful in understanding this new phenomenon.

 

[PeterDonis]

whether a single water molecule could show wave characteristics or just particle characteristics?

Diffraction.

And again, I'm asking you what would show "wave characteristics" and what would show "particle characteristics" for a single water molecule in a diffraction experiment. As @Nugatory points out, a water molecule is a complicated system--it would be better to start with something simpler like a single electron. But either way the question is the same, and you haven't answered it.

 

[bhobba]

There are many. For example: electron interference and diffraction,

Did you read the link I gave that explained diffraction and interference without wave-particle duality? If so - your reaction is? If not - there are a number of mentors posting here and we do expect at least an attempt to try an understand the answer.

Thanks
Bill