B Particle or Wave? Duality Explained

[rahaverhma]

How anything can be a particle or wave at the same time.

 

[rootone]

Quantum scale objects (electrons say), can be one or the other depending on how you measure them.
I think it's best to just call them quantum objects.

 

[Anujkumar]

Yeah but at a particular time object or a Quantum object behave like a particle or wave but not simultaneously both

 

[rootone]

This might help.
https://en.wikipedia.org/wiki/Quantum_field_theory

 

[Arman777]

Feymann has a good view on this.They are acting just like "Quantum Mechanical Way".This a problem which turning physics to english as he claimed.I agree with Feymann

 

[weirdoguy]

How anything can be a particle or wave at the same time.

Wave-particle duality is an outdated concept, so don't bother too much with that.

 

[rahaverhma]

I just want to know that waves we talk about of particles, are they electromagnetic waves ??
,and when someone is talking about wavelike property of macroscopical objects are they talking about our oscillation up and down ie. Our wave function otherwise how can someone think of us as a wave.

 

[Nugatory]

I just want to know that waves we talk about of particles, are they electromagnetic waves ??

No, the wave we're talking about are not electromagnetic waves.

How anything can be a particle or wave at the same time.

It can't. A quantum object is neither a particle nor a wave, although it has some properties that we usually associate with waves and some properties that we usually associate with classical particles.

 

[rahaverhma]

Which waves are these?

 

[rahaverhma]

I think the quantification of an object is done when there are the interactions b/w entities .

https://www.google.co.in/url?sa=t&s...x28jtvfnGP_UlkifA&sig2=85EJvHS_97qBEmXSHnKwHg

In this video ,an electron is projected and an interference pattern is observed it is acting as wave and it might no longer be a quantum object.

 

[rahaverhma]

I mean what type of wave are they actually are?

 

[vanhees71]

As several posters have noted before, there is no wave-particle dualism in "modern quantum mechanics" (the today still valid version of QM has been developed independently in 1925/26 by Heisenberg+Jordan+Born, Dirac, and Schrödinger).

In non-relativistic quantum mechanics one associates a wave function with the "state" of a single particle like an electron, $\psi(t,\vec{x})$. It takes values in $\mathbb{C}$ (for scalar particles, spin $s=0$) or $\mathbb{C}^{2s+1}$ (for particles with spin $s \in \{1/2,1,\ldots \}$). The meaning of the wave function is that
$$P(t,\vec{x})=|\psi(t,\vec{x})|^2$$
is the probability distribution for the position $\vec{x}$ of the particle at time $t$ (Born's Rule).

All the "quantum weirdness" like "wave-particle duality" and similar ideas of "old quantum theory" vanish, as soon as you accept this probabilistic meaning of the wave function (or more generally any kind of quantum state).

 

[Stavros Kiri]

... "probability waves" ...

 

[Karolus]

As I understand, in modern quantum mechanics, the wave-particle duality was "outdated." There is no duality, there are only quantum objects, or better to say: vectors in the Hilbert space of infinite dimensions. What we perceive as a "wave" is only a "name" just to give a name to something, that "in essence" is a mathematical function, like sin and cos.
And what is sin and cos? Trigonometric functions ...

 

[Stavros Kiri]

What we perceive as a "wave" is only a "name" just to give a name to something, that "in essence" is a mathematical function, like sin and cos.
And what is sin and cos? Trigonometric functions ...

Partially true, but I think there is more to it than that, so I also partially disagree, but the full analysis would have to go on a separate thread. Roughly and briefly three points here:
1. Structure of wave as (amplitude function)×f(x-vt, y, z) [f being sin or cos etc. type function, or combination etc.], or F(x-vt, y, z) in general etc., or includes different types of modulation ...
2. Thus not limited only to sin, cos ... , unless perform Fourier alalysis (expansion).
3. Besides waves there is also wave-packets, very useful and common even in QM, and these are not sin, cos only (nothing but ... , sometimes, unless Fourier ...).

Thus it's a big issue.

 

[N88]

As several posters have noted before, there is no wave-particle dualism in "modern quantum mechanics" (the today still valid version of QM has been developed independently in 1925/26 by Heisenberg+Jordan+Born, Dirac, and Schrödinger).

In non-relativistic quantum mechanics one associates a wave function with the "state" of a single particle like an electron, $\psi(t,\vec{x})$. It takes values in $\mathbb{C}$ (for scalar particles, spin $s=0$) or $\mathbb{C}^{2s+1}$ (for particles with spin $s \in \{1/2,1,\ldots \}$). The meaning of the wave function is that
$$P(t,\vec{x})=|\psi(t,\vec{x})|^2$$
is the probability distribution for the position $\vec{x}$ of the particle at time $t$ (Born's Rule).

All the "quantum weirdness" like "wave-particle duality" and similar ideas of "old quantum theory" vanish, as soon as you accept this probabilistic meaning of the wave function (or more generally any kind of quantum state).

Any reason for separating the scalar particles out of the $\mathbb{C}$ formula, please? Is this OK:

In non-relativistic quantum mechanics one associates a wave function with the "state" of a single particle like an electron, $\psi(t,\vec{x})$. It takes values in $\mathbb{C}^{2s+1}$ (for particles with spin $s \in \{0,1/2,1,\ldots \}$?

Thanks.

 

[sunmaggot]

I remember there were three kinds of interpretations of a measurement on a particle.

1. realist position, which implies that the particle was there before measurement. Because you didn't do measurement, you did not know it was there. This implies a loophole in quantum mechanics that there is hidden variable to determine position of the particle. This is what Einstein believed in.

2. orthodox position, the particle is not anywhere, but observation created a form of measurement (forced wavefunction of the particle to collapse into one determinate state) The method of observation deeply affects the form of measurement you get.

3. agnostic position, refuse to answer such question because it is nutty to ask for position of a particle before measurement.

Bell's inequality proved that the statistic of realist position and orthodox position are different. This eliminated agnostic position. And the result is that orthodox position is correct (This is why Einstein was wrong).

Now back to your question. If you measure position of a particle, you get position of a particle, which is a particle. Now if you measure momentum of the particle, which is related to wavelength by de broglie formula, you get wavelength, which is a wave. Because position and momentum do not commute each other, you cannot get both information accurately. When position wavefunction collapse, you get measurement of a particle, but the momentum measurement is lost. Vice versa, this shows that a free particle has position and momentum, which is particle and wave property. Measurement method will change their property, which is different from classical mechanics. In classical mechanics, properties are static, particle is particle, wave is wave.

 

[PeterDonis]

I remember there were three kinds of interpretations of a measurement on a particle

These descriptions seem oversimplified to me. They also seem to assume a collapse interpretation of QM; there are also no collapse interpretations.

 

[sunmaggot]

These descriptions seem oversimplified to me. They also seem to assume a collapse interpretation of QM; there are also no collapse interpretations.

maybe I used wrong words. Three opinions maybe better?

 

[Karolus]

I remember there were three kinds of interpretations of a measurement on a particle.

1. realist position, which implies that the particle was there before measurement. Because you didn't do measurement, you did not know it was there. This implies a loophole in quantum mechanics that there is hidden variable to determine position of the particle. This is what Einstein believed in.

2. orthodox position, the particle is not anywhere, but observation created a form of measurement (forced wavefunction of the particle to collapse into one determinate state) The method of observation deeply affects the form of measurement you get.

3. agnostic position, refuse to answer such question because it is nutty to ask for position of a particle before measurement.

Bell's inequality proved that the statistic of realist position and orthodox position are different. This eliminated agnostic position. And the result is that orthodox position is correct (This is why Einstein was wrong).

Now back to your question. If you measure position of a particle, you get position of a particle, which is a particle. Now if you measure momentum of the particle, which is related to wavelength by de broglie formula, you get wavelength, which is a wave. Because position and momentum do not commute each other, you cannot get both information accurately. When position wavefunction collapse, you get measurement of a particle, but the momentum measurement is lost. Vice versa, this shows that a free particle has position and momentum, which is particle and wave property. Measurement method will change their property, which is different from classical mechanics. In classical mechanics, properties are static, particle is particle, wave is wave.

I agree, then the "wave particle duality", or whatever you want to call it, is not outdated

 

[Stavros Kiri]

maybe I used wrong words. Three opinions maybe better?

But, as PeterDonis implies, there are more ...
[Three are the most basic and common ones]

 

[sunmaggot]

But, as PeterDonis implies, there are more ...
[Three are the most basic and common ones]

these three are from griffith's book, so maybe there are more.

 

[calinvass]

We call photons quantum objects, that can behave like a wave or like a particle. How can an object behave like a wave? An object is supposed to have its own identity. Can it keep its identity when it behaves like a wave?

 

[PeterDonis]

. How can an object behave like a wave? An object is supposed to have its own identity.

You are using an inadequate definition of "object". Or perhaps "object" is simply an inadequate term to use to describe quantum entities like a photon. "Identity" in the sense you are using that concept simply doesn't apply to such entities.

 

[vanhees71]

Any reason for separating the scalar particles out of the $\mathbb{C}$ formula, please? Is this OK:

In non-relativistic quantum mechanics one associates a wave function with the "state" of a single particle like an electron, $\psi(t,\vec{x})$. It takes values in $\mathbb{C}^{2s+1}$ (for particles with spin $s \in \{0,1/2,1,\ldots \}$?

Thanks.

That's of course true.

 

[vanhees71]

We call photons quantum objects, that can behave like a wave or like a particle. How can an object behave like a wave? An object is supposed to have its own identity. Can it keep its identity when it behaves like a wave?

Again: Wave-particle dualism is an outdated concept for nearly 100 years now, and if there is anything that is no particle, then it's a photon. It is not even possible to define a position observable for it!

 

[Stavros Kiri]

Again: Wave-particle dualism is an outdated concept for nearly 100 years now, and if there is anything that is no particle, then it's a photon. It is not even possible to define a position observable for it!

Then that goes into "particles &_fields (or field particles)", which is a different but relevant kind of dualism question ...

Also

... photon. It is not even possible to define a position observable for it!

that's because in the 2nd quantization the wave function becomes a field operator and gets quantized (into states, e.g. photon states) ...

 

[Stavros Kiri]

We call photons quantum objects, that can behave like a wave or like a particle. How can an object behave like a wave? An object is supposed to have its own identity. Can it keep its identity when it behaves like a wave?

Photons are field particles, and fields can be waves (e.g. Electomagnetic field and EM waves). Furthermore, [in QED] photons (or photon states) are the results of the 2nd Quantization (of the EM Lagrangian). [See also previous post, but please maintain separate.]

Added note: other field particles (or gauge bosons) in the Standard Model are the 8 gluons (mediators or quanta of the Strong interaction), the two W particles (W⁺, W^-) and the one Z particle (Z⁰), i.e. the three Electroweek mediators of the Weindberg-Salam theory, [and, of course, the photon, ... makes a total of 12 field particles]. Then of course there is the Higgs boson(s), that give rise to mass.
Beyond the standard model, the graviton, hasn't been discovered yet.
[Field particles (or gauge bosons) are usually massless, unless they acquire mass with the Higgs mechanism (e.g. Spontaneous Symmetry Breaking) ...]

 

[Debaa]

Wave-particle duality is an outdated concept, so don't bother too much with that.

Its not a concept it's a proven theory and it's not outdated we still use it.

 

[vanhees71]

I've not seen a single empirical evidence for wave-particle duality. So how can you say, it's a "proven theory"? Since 1925, fortunately we do not need to use such shaky and self-contradictory concepts anymore!

 

[Stavros Kiri]

But using photons (or other field particles) as an example to resolve the wave-particle issue is not a good idea, because these are (or can be considered as) virtual particles (see https://en.m.wikipedia.org/wiki/Virtual_particle)

It would be better if one considered as an example the Schrodinger equation and 1st quantization, to resolve the issue ...

 

[Ddddx]

I don't know why people keep saying wave-particle duality is outdated. The energy and momentum of a particle are associated with the frequency and wavelength of a wave. You have to introduce wave concepts like frequency into the description of particles.

The equation E = hf and the corresponding one for momentum are the foundation of quantum theory, as fundamental as t² - x² = s² is to relativity. They will never become outdated.

 

[Karolus]

The fact that the vision particle wave, as has been definitively surpassed in 1925, (why?), In 1927 de Broglie introduced the concept of "wave and particle", as illustrated by John Bell in his "speakable and unspeakable in quantum mechanics" , where in chapter 20 "six possible worlds in quantum mechanics", discusses the problem of the various interpretations of quantum mechanics, including the wave-particle. The book is about 1960, and here, what need had John Bell to dedicate a book if, since 1925 these problems were already solved?

 

[PeroK]

I don't know why people keep saying wave-particle duality is outdated.

One of the reasons might be that they are experts in the field and know what they are talking about!

For example, if you look at one of the most popular undergraduate textbooks on QM by Griffiths, the wave-particle duality gets one mention on page 420 as a "historical footnote".

 

[Ddddx]

I don't know what Griffiths wants to attack in that footnote, but he doesn't seem to be questioning the validity of the fundamental equations like E = hf.

 

[PeroK]

I don't know what Griffiths wants to attack in that footnote, but he doesn't seem to be questioning the validity of the fundamental equations like E = hf.

He's not attacking anything. He's simply teaching QM without the wave-particle duality.

In Sakurai's book it doesn't even get a mention.

The equation E = hf and the corresponding one for momentum are the foundation of quantum theory,

They are not the foundation of quantum mechanics.

 

[Ddddx]

They certainly are the foundation of quantum mechanics. You will probably recognize them more easily if I write them in the form

H |psi> = ih ∂_t |psi>

P = -ih ∂_x

Or other equivalent ways.

 

[vanhees71]

Here, you mix up several things in a very confused way. Neither of these formulas have anything to do with "wave-particle dualism", whatever this should mean. It's really good advise not to learn these old-fashioned concept when starting to learn quantum theory.

Conerning your two formulas: The first one describes the time evolution of an abstract state ket (by the way, one should indeed learn as soon as possible the abstract formalism a la Dirac, because then such confusion as demonstrated in this thread is avoided early on) in the Schrödinger picture.

The 2nd equation gives the momentum operator in the position representation. The correct formula is
$$\hat{\vec{p}}=-\mathrm{i} \hbar \vec{\nabla}.$$

In the position formulation your 1st formula reads
$$\mathrm{i} \hbar \partial_t \psi(t,\vec{x})=\hat{H} \psi(t,\vec{x}).$$
Now for free particles you have
$$\hat{H}=\frac{\hat{\vec{p}}^2}{2m}=-\hbar^2 \Delta,$$
and then you can find plain-wave solution for this free-particle Schrödinger equation by making the Ansatz
$$\psi(t,\vec{x})=A \exp(-\mathrm{i} \omega t+\mathrm{i} \vec{k} \cdot \vec{x}).$$
Inserting this into the equation leads to
$$\hbar \omega=\frac{\hbar^2}{2m} \vec{k}^2.$$
Now what's also clear is that this solution are (generalized) eigenfunctions of the Hamiltonian (energy operator) and the momentum operator, i.e., you can indeed (for this special case!) identify
$$E=\hbar \omega, \quad \vec{p}=\hbar \vec{k}$$
as energy and momentum of a non-relativistic particle, but it has still nothing to do with any kind of "wave-particle duality". Rather the wave function has the probabilistic meaning that $|\psi(t,\vec{x})|^2$ is the probability distribution for the position of the particle, but this holds of course only for square-integrable wave functions, not for the energy-momentum eigenmodes of free particles, but that's another subtlety.

 

[Aufbauwerk 2045]

I learned in QM that we only have a right to talk about what we can observe. The rest is metaphysics. Mathematically we use the Hilbert Space. Observables are operators in HS.

As for words like "particle and "wave" it's fine to use them as long as we realize their limitations. We invented these words to describe everyday experience. To say that this "thing" must be either a "particle" or a "wave" but not both is just an attempt to describe complicated nature with our primitive words and primitive logic.

 

[bhobba]

Some of the answers hae been very good. There is no wave-particle duality.

However some hisorical perspective may shed some light on why it still hangs around and what the early pioneers thought.

A good book to read is the folllowing:
https://www.amazon.com/dp/1491531045/?tag=pfamazon01-20

In 1924, in his PhD thesis, Louis de Broglie suggested that just as light exhibits wave and particle properties, all microscopic material particles such as electrons, protons, atoms, molecules etc, have also dual character. His examiners didn't know what to make of it but a copy made its way to Einstein (the above book gives the exact detail). He too did not believe it but recognized immediately it was an important breakthrough and highly recommended it. He knew it was wrong but believed, correctly, it was an important step, but not the final solution to the quantum puzzle. Einsteins intuition, as always was of the highest caliber - in fact his ability to penetrate to the heart of a problem was unmatched - not perfect - but better than anyone else's, even the greatest of scientists like Von-Neumann and Feynman who also were known for that ability.

Then this guy Schrodinger entered in the picture. At a lecture someone suggested if matter has wave properties then it should obey a wave equation. Using false reasoning he obtained the correct answer that now goes by the name of Schrodinger's equation:
https://arxiv.org/abs/1204.0653

We can derive it much simpler these days by writing down the most general relativistically invariant field equation in a single complex field, and believe it or not you get the Klein Gordon equation. Take the classical limit and you get Schrodinger's equation - you can find the detail here:
https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20

More can be said about this approach but this is not the thread for it - suffice to say waves have nothing to do with it - it's that complex field and what in the damnation it means that's the issue.

Anyway from that point on things moved quickly:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

It was then apparent, just as Einsteins intuition told him, wave-particle duality was wrong - or at the most of limited applicability.

But due to the semi historical approach taken in most beginner texts and popularization's they never point this out. It quite bad really and people are left with this insidious incorrect misconception. A misconception BTW even Einstein knew from the start was wrong.

Just as a personal aside I much prefer a non traditional presentation that avoids the whole thing such as in the book on symmetry above and the following:
http://www.scottaaronson.com/democritus/lec9.html

That avoids the confusion right from the start.

Thanks
Bill

 

[Stavros Kiri]

... as energy and momentum of a non-relativistic particle, but it has still nothing to do with any kind of "wave-particle duality".

Why not? It's a particle, we know that (or a quantum object, or quantum particle). And

... duality". Rather the wave function has the probabilistic meaning that |ψ(t,⃗x)|2|ψ(t,x→)|2|\psi(t,\vec{x})|^2 is the probability distribution for the position of the particle, but this holds of course only for square-integrable wave functions, not for the energy-momentum eigenmodes of free particles, but that's another subtlety.

Thus probability waves ...

Thus both, thus duality, q.e.d. (=quite easily demonstrated)

 

[bhobba]

The book is about 1960, and here, what need had John Bell to dedicate a book if, since 1925 these problems were already solved?

Because physicists often speak in loose language, and virtually all other physicists had been exposed to the semi-historical approach of beginner texts where they do not go to the trouble to explicitly correct it. You are supposed to sort of figure it out for yourself - and most do, but still speak loosely using it.

What do you think is more likely - the many professors who post here that teach this stuff to students are wrong, or you are misinterpreting papers like Bell? The latter is much much more reasonable, and in this case provably true - are waves complex valued and travel in a complex Hilbert space? That's the wave-like solutions you get to Schrodinger's equation, and most are not wave-like eg the solutions for the Hydrogen atom:
http://darksilverflame.deviantart.com/art/The-Shapes-Of-Hydrogen-Poster-327297786

They don't look very much like waves to me. As a matter of fact only the free particle solution looks wave-like. There is a deep reason for that explained in the following lectures:


Experts reading it know the intent of what he saying, they know its wrong, although not usually pointed out even Einstein knew it was wrong.

I am unaware of any QM textbook at the advanced level, and I have read quite a few, that talks about it. My, and many others who post here, reference is Ballentine. Not a single mention of it. It is very widely respected as one of the best, maybe even the best, textbook written on QM.

Thanks
Bill

 

[bhobba]

Why not? It's a particle, we know that (or a quantum object, or quantum particle).

You already contradicted yourself. Its a particle or quantum object or quantum particle.

Particles have definite position and momentum, quantum objects do not. Sometimes we can measure the position of a quantum object (you can't for photons - it has no position observable) and we say it is displaying particle like characteristics. But mostly it behaves nothing like a particle.

They are really excitation's of a quantum field - and that's what is meant by quantum particle. These excitation's do not obey wave-particle duality. In fact they do not obey any mental picture I am aware of at all, although physicists speak loosely of other falsehoods associated with quantum fields like virtual particles to have an intuitive picture, only in the math can it be described correctly. That's actually quite important - the development of intuition is vital - but its just that - an aid to intuition.

Thanks
Bill

 

[Stavros Kiri]

You already contradicted yourself. Its a particle or quantum object or quantum particle.

It's not a contradiction. There are classical (point-like) particles and quantum particles (or quantum objects). 'Particle' is a constituent of "matter" (that's why we say "Particle Physics" ...). [Then, matter versus waves, fields, energy etc., all can virtually be unified ... , but not quite ... ; there is unity and oppotition.]

Particles have definite position and momentum, quantum objects do not.

These are classical particles ...

 

[Stavros Kiri]

That's the wave-like solutions you get to Schrodinger's equation, and most are not wave-like eg the solutions for the Hydrogen atom:
http://darksilverflame.deviantart.com/art/The-Shapes-Of-Hydrogen-Poster-327297786

They don't look very much like waves to me. As a matter of fact only the free particle solution looks wave-like.

What is your definition of 'wave'? See #15 above: https://www.physicsforums.com/threads/particle-or-wave.907971/#post-5719052

 

[bhobba]

It's not a contradiction. There are classical (point-like) particles and quantum particles (or quantum objects). 'Particle' is a constituent of "matter" (that's why we say "Particle Physics" ...). [Then, matter versus waves, fields, energy etc., all can virtually be unified ... , but not quite ... ; there is unity and oppotition.]

There is nothing more silly that arguing semantics.

Now, explain to me how an excitation in a quantum field obeys the wave particle duality?

In it precisely define what you mean by a particle, a wave, and duality. I am willing to accept pretty much any reasonable definition - but melding them together - well let's see what you come up with and if it fits the intuitive idea of those concepts. That's what the issue boils down to - you can define your terms to say whatever you like - but is it what physicists usually mean?

Thanks
Bill

 

[bhobba]

What is your definition of 'wave'? See #15 above: https://www.physicsforums.com/threads/particle-or-wave.907971/#post-5719052

The undulation of some medium like water waves. Even in classical fields like the EM field. Schrodinger originally thought that it's what his equation described. When it was proven it didn't he lamented he ever became involved in this whole mess that Dirac and others had turned into something entirely different.

But I am willing to accept any reasonable definition you come up with for wave - fire away. Here is one - its waves in a quantum field - we can examine that - but if you do define it that way and understand QFT you will immediately see difficulties - but fire away.

Thanks
Bill

 

[Stavros Kiri]

Now, explain to me how an excitation in a quantum field obeys the wave particle duality?

It is a particle if considered as a part of matter, but it is actually a virtual particle. However see previous posts above (especially #31 https://www.physicsforums.com/threads/particle-or-wave.907971/page-2#post-5719577 ).

It is a wave because it has a wave function, and obeys a wave equation (thus it is a possible solution to it). Physical interpretation: probability wave.

I think that says it all!

Note: It can also just be a wave-packet, not always wave.

 

[bhobba]

but it is actually a virtual particle.

Really? You know that virtual particles are simply the pictorial representation of terms in a Dyson series used purely as an aid to calculation? Are you willing to call lines that appear when physicists do theoretical calculations particles? If that's your definition its far too weird for me and I think the vast majority of physicists.

Be aware that anything written about QFT outside a QFT textbook is likely wrong - virtual particles as actual particles is just one example. If you go down the QFT path I suggest first learning some of its basics from a proper textbook eg:
https://www.amazon.com/dp/0984513957/?tag=pfamazon01-20

Thanks
Bill

 

[Nugatory]

Closed pending moderation.

[updated]
We're going to leave this thread closed.

The original question was "How anything can be a particle or wave at the same time?" and that has been answered with as much accuracy is possible in a B-level thread: That's not what the modern formulation of quantum mechanics says.