History of wave/particle duality

[phinds]

[Moderator's note - this thread was split out from another thread as an interesting but independent discussion]

Sir, you must give up your notion of "particle" and "waves", because at the quantum level there is a dual nature of matter, commonly referred to as wave-particle duality.

I really don't want to sidetrack this thread with something that will further confuse the OP, but I must point out to you that the concept of "wave particle duality" was dumped some 80+ years ago and is only still around due to some misguided belief that it makes things easier on beginning students. There is no wave particle duality because quantum objects are not waves and they are not particles. Those are classical concepts. Quantum objects are only that ... quantum objects. If you measure particle behavior you will see some particle-like characteristics and if you measure wave behavior you will see some wave characteristics, but that does not make quantum objects particles or waves and does not (as it was thought to do 80 years ago) mean there is a wave particle duality.

 

[phinds]

Einstein was one of many who believed in wave particle duality until somewhere around 1927 when Dirac flummoxed them all. I don't have a citation off hand but it has been discussed here many times (with specific mention of Dirac's paper). Wikipedia is just following the lead of the many basic physics texts which STILL promote wave particle duality even though it has been dead for 80 years. That plethora of misstatements has ALSO been discussed here many times.

For example, see post #3 in this thread:

https://www.physicsforums.com/threa...-according-to-de-broglie.775172/#post-4876513

 

[Ahmad Kishki]

Einstein was one of many who believe in wave particle duality until somewhere around 1927 when Dirac flummoxed them all. I don't have a citation off hand but it has been discussed here many times (with specific mention of Dirac's paper). Wikipedia is just following the lead of the many basic physics texts which STILL promote wave particle duality even though it has been dead for 80 years. That plethora of misstatements has ALSO been discussed here many times.

Well i will take your word for it, but i am very confused now :/ please try to tell me more

 

[Nugatory]

You will find a bunch of good stuff in the "Similar Threads" list at the bottom of this page

 

[bhobba]

[Well i will take your word for it, but i am very confused now :/ please try to tell me more

That's not quite it.

What happened is Bohr came up with the idea in the early days of QM as part of his views on complementarity. But better understanding showed its correct expression was quantum objects sometimes behave like particles and sometimes like waves - often (and that's most of the time) they act like neither. Because you have to understand QM to know when that sometimes is and exactly what like means (for example the waves are not real in a physical sense but propagate in an abstract mathematical space called a Hilbert space) for many such as myself its best to forget about it entirely - its of very little use and causes more issues than it solves.

What Dirac did in late 1926 can be found here:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

But basically you had the idea of De-Broglie that matter was some kind of wave and that lead to Schroedinger's equation. You also had Heisenberg's matrix mechanics that was entirely different. Dirac showed, and he was the first to satisfactory do it from a physicists viewpoint, (mathematically because he used that damnable Dirac Delta function is another matter, but physicists often don't get worried about mathematical rigour) showed they were different aspects of a deeper theory Dirac called the transformation theory, that goes by the name QM today, and De-Broglies and Schroedinger's ideas were consigned to the dustbin of history, and the correct statement of the wave-particle duality was understood.

Thanks
Bill

 

[Ahmad Kishki]

That's not quite it.

What happened is Bohr came up with the idea in the early days of QM as part of his views on complementarity. But better understanding showed its correct expression was quantum objects sometimes behave like particles and sometimes like waves - often (and that's most of the time) they act like neither. Because you have to understand QM to know when that sometimes is and exactly what like means (for example the waves are not real in a physical sense but propagate in an abstract mathematical space called a Hilbert space) for many such as myself its best to forget about it entirely - its of very little use and causes more issues than it solves.

What Dirac did in late 1926 can be found here:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

But basically you had the idea of De-Broglie that matter was some kind of wave and that lead to Schroedinger's equation. You also had Heisenberg's matrix mechanics that was entirely different. Dirac showed, and he was the first to satisfactory do it from a physicists viewpoint, (mathematically because he used that damnable Dirac Delta function is another matter, but physicists often don't get worried about mathematical rigour) showed they were different aspects of a deeper theory Dirac called the transformation theory, that goes by the name QM today, and De-Broglies and Schroedinger's ideas were consigned to the dustbin of history, and the correct statement of the wave-particle duality was understood.

Thanks
Bill

Thank you all very much, i will look up your references and i am glad i got rid of this misconception, but i wonder why was it mentioned in my physics textbook (physics for scientists and engineers, serway)

 

[bhobba]

Thank you all very much, i will look up your references and i am glad i got rid of this misconception, but i wonder why was it mentioned in my physics textbook (physics for scientists and engineers, serway)

Its one of those things you sometimes encounter in physics. The explanation at the beginner level is seen from a more advanced viewpoint to be incorrect. And even worse that explanation, when you get really advanced, is itself incorrect. Its maddening, I hate it because I am learning new things all the time and have to unlearn old things.

This particular issue is related to the semi historical approach most textbooks use to motivate the QM formalism - but they don't go back and examine what was said before in light of that formalism.

As an example check out the following on the 'real' explanation for the double slit experiment - its got nothing to do with the wave particle duality:
http://cds.cern.ch/record/1024152/files/0703126.pdf

I do encourage you to go through it.

When you have done that you will see its got nothing to do with the wave-particle duality - its got to do with the slit being a position observation so the momentum after is undetermined.

After reading it you will say - ahhhh - I see what's going on and understand Serway is glossing over important issues with half truths.

But to make matters worse even that explanation is wrong:
http://arxiv.org/pdf/1009.2408.pdf

But as a student are you really prepared to understand the correct explanation at the beginning - baby steps are needed.

Personally I believe the typical approach taken in books like Serway causes problems with actual thinking students rather than what many do - simply follow a cookbook. IMHO the following is a much better place to start that leads to the essence of QM:
http://www.scottaaronson.com/democritus/lec9.html

Its full development can be found here:
http://arxiv.org/pdf/quantph/0101012.pdf

You will notice nothing is mentioned about Schroedinger's equation etc. That's because, believe it or not, it follows from symmetry. Curios? Hopefully you are. Get a hold of the following book and read the first three chapters:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Fully understanding it, like some of the links I gave, is probably beyond your current mathematical level - but you should get the gist.

You have shown yourself a thinking student - what I have told you is the real deal - nothing suger coated or held back. Hopefully things will be a lot clearer.

Thanks
Bill

 

[atyy]

Thank you all very much, i will look up your references and i am glad i got rid of this misconception, but i wonder why was it mentioned in my physics textbook (physics for scientists and engineers, serway)

Another way to see it is that wave-particle duality a vague concept from a time when quantum mechanics was not fully formalized. Now that it is fully formalized, we don't have a single concept that everyone agrees is called "wave-particle duality". So it is better to learn the formal structure of quantum mechanics, which is the full theory.

However, can one say that "wave-particle duality" survives in the full theory in some forms? It isn't standard language, but here are a few ways one might think about it in the full theory.

1. In non-relativistic QM, the position basis can be considered particle-like because it is well localized in space, while the momentum basis is wave-like because it is wavy and not well-localized in space. A particle with a definite position is a superposition of different momentum waves. This is one way in which wave particle duality survives in the full theory. In a sense, the canonical commutation relation underlies this, and so the canonical commutation relation can be considered the generalization of wave-particle duality. Because the canonical commutation relation is related to Fourier transform pairs, one can see that wave-particle duality or position-momentum uncertainty is analogous to time-frequency uncertainty in classical signal processing.

2. In non-relativistic QM, the Hilbert space is defined by the number of particles. However, the equation for the evolution of the state in the Schroedinger picture is a wave equation. This is another way in which wave-particle duality survives in the full theory.

3. In non-rigourous quantum field theory, the Hilbert space is a Fock space of particles. In the Heisenberg picture, the equation of motion for the field operator is a wave euqation. This is yet another way in which wave-particle duality survives in the full theory.

My own take: once one has identified quantum system/classical apparatus, commutation relations, Hilbert space, it is a mistake to consider quantum mechanics as unintuitive. From that point on, if we consider the wave function to be the full physical state of the system, we make no mistake for all practical purposes (FAPP). The main reason quantum mechanics is unintuitive is that although the apparatus is described by a wave function, we cannot also describe the apparatus by a wave function, unless we have another set of classical apparatus outside, which is real for us. A system with only wave function and no classical apparatus does not produce definite measurement outcomes, contrary to experience. The necessity of a classical apparatus which is real makes us realize that the wave function is not necessarily real, and it is just a tool to make correct predictions of probabilities of measurement outcomes. This agnosticism of the reality of the wave function is why the wave function is the full physical state of the system, but only FAPP.

 

[Ahmad Kishki]

Another way to see it is that wave-particle duality a vague concept from a time when quantum mechanics was not fully formalized. Now that it is fully formalized, we don't have a single concept that everyone agrees is called "wave-particle duality". So it is better to learn the formal structure of quantum mechanics, which is the full theory.

However, can one say that "wave-particle duality" survives in the full theory in some forms? It isn't standard language, but here are a few ways one might think about it in the full theory.

1. In non-relativistic QM, the position basis can be considered particle-like because it is well localized in space, while the momentum basis is wave-like because it is wavy and not well-localized in space. A particle with a definite position is a superposition of different momentum waves. This is one way in which wave particle duality survives in the full theory. In a sense, the canonical commutation relation underlies this, and so the canonical commutation relation can be considered the generalization of wave-particle duality. Because the canonical commutation relation is related to Fourier transform pairs, one can see that wave-particle duality or position-momentum uncertainty is analogous to time-frequency uncertainty in classical signal processing.

Well that was what Serway defined as the wave particle duality. Just a wave packet - a quantum particle. If position is measured you get a wave packet that's practically a pulse i.e. the wave packet is localised and has particle characteristic of locality, while the contrary for waves i.e. measuring momentum means that the wavelength of the responsible wave is known. This is what Serway says, which i think is not in disagreement with what you said. Right?

 

[atyy]

Well that was what Serway defined as the wave particle duality. Just a wave packet - a quantum particle. If position is measured you get a wave packet that's practically a pulse i.e. the wave packet is localised and has particle characteristic of locality, while the contrary for waves i.e. measuring momentum means that the wavelength of the responsible wave is known. This is what Serway says, which i think is not in disagreement with what you said. Right?

Right. Actually, what Serway says is not the most general possibility, but it's not misleading and good to start.

 

[bhobba]

Well that was what Serway defined as the wave particle duality. Just a wave packet - a quantum particle.

Waves of what? Think about it.

Without giving a long post with the correct answer simply read the first 3 chapters of Ballentine.

Thanks
Bill

 

[Ahmad Kishki]

Waves of what? Think about it.

Without giving a long post with the correct answer simply read the first 3 chapters of Ballentine.

Thanks
Bill

Well I always thought "whats waving" but I thought that nobody knows... I will definitely read Ballentine now :)

 

[bhobba]

Well I always thought "whats waving" but I thought that nobody knows... I will definitely read Ballentine now :)

It depends on your view of what a state is.

I won't steal Ballentines thunder as he explains the ensemble interpretation.

Thanks
Bill