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Particle wave duality


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By the technical reasons that I outlined before. As this physicist writes:

 

If you would take care to read the entire article instead of selectively quoting it, you'll see that the message is different.

 

When we observe the behavior of light, electrons, neutrons, protons, buckyballs, etc. exhibiting both wave-like and particle-like behavior, we then use the term "duality" to describe such puzzling observation. Why? Because we have to "switch gears" when we talk about wave and particles. We use one type of description/formalism when we talk about the wave-like picture, and then we change our description/formalism to talk about the particle-like picture. Thus, the duality.

 

Short answer: QM is formulated so that the duality is not an issue; classical formalism doesn't suffice.

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pmb

G = 0 or G = constant since there is no way to make that substitution

 

Actually you need this both of these to substitute into your general solution if you want to discount say H (w) or G(w).

 

There is nothing wrong with the constant function, even if the constant is zero

 

G(x-vt) = 0 for all x is perfectly OK (and twice differentiable)

 

You are correct about the tan function and the reciprocal of the tan.

 

The last one is, of course, a square wave if w is integral.

Is this a wave or not in your eyes?

 

pmb

That's correct. What you have then is a system of particles.

 

 

I'm probably not putting this very well but for example a single atom of copper is not a conductor of electricity, but an array of them is.

 

 

 

 

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Actually you need this both of these to substitute into your general solution if you want to discount say H (w) or G(w).

 

There is nothing wrong with the constant function, even if the constant is zero

I disagree. To me a function has to have a specific period to be periodioc. With the consant function there is no way to refer to a unique peiod. All real numbers are periods for the constant function. gto me that is not a periodic function. And since there is no way to dertermine whether there is motion or not then there is no wave either. Notice that for a wave there must be a way to measure the motion. If all the constant funcion does is to be unchaning in space and time then there is no way to track such motion.

 

G(x-vt) = 0 for all x is perfectly OK (and twice differentiable)

 

You are correct about the tan function and the reciprocal of the tan.

 

The last one is, of course, a square wave if w is integral.

Is this a wave or not in your eyes?

I prefer to say that its function in my eyes if and only if it fits the definition. I don't like to work under how I precieve things but only to whether they fit the definition and the dsquare wave doesn't fit the definition. I will admit that it "feels" like a wave though.

Edited by pmb
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An electron or a photon are always particles and all particles behave as particles. Danger! Particle does not mean "little-hard-sphere-following-Newtonian-laws".

 

When you a pass a quantum object in an interference experiment, how can you say that it has passed through one slit or the other and as behaved as a particle when we have not measured or observed it? Science doesn't give an objective account of reality.

 

That quote is saying you that "particle", in quantum mechanics, does not mean "little-hard-sphere-following-Newtonian-laws" but you insist on your misconception

 

Whether you call it a quantum particle or I call it a quantum object we cannot know how it has behaved without observing it and hence we cannot attribute properties to that 'entity' and describe its behaviour and hence we don't know what it is, which implies that we don't know what the world is made up of.

 

This is Intellectual dishonesty of the highest order. I'm done with you.

 

This has gone unaddressed and to emphasize more on it.

 

The physicist Max Born, an important contributor to the foundations of quantum theory, had this to say about the particle–wave dilemma:

 

The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analyzing visible motions it has developed two ways of representing them by elementary processes: moving particles and waves. There is no other way of giving a pictorial description of motions—we have to apply it even in the region of atomic processes, where classical physics breaks down.

 

Every process can be interpreted either in terms of corpuscles or in terms of waves, but on the other hand it is beyond our power to produce proof that it is actually corpuscles or waves with which we are dealing, for we cannot simultaneously determine all the other properties which are distinctive of a corpuscle or of a wave, as the case may be. We can therefore say that the wave and corpuscular descriptions are only to be regarded as complementary ways of viewing one and the same objective process, a process which only in definite limiting cases admits of complete pictorial interpretation.

 

M. Born, Atomic Physics, fourth edition, New York, Hafner Publishing Co., 1946, p. 92.

 

Consider the following quote from Niels Bohr:

 

"Every atomic phenomenon is closed in the sense that its observation is based on

registrations obtained by means of suitable amplification devices with

irreversible functions such as, for example, permanent marks on a photographic

plate caused by the penetration of the electrons into the emulsion."

 

 

We may conclude from this that Bohr was content to make a distinction between quantum system and classical apparatus. As we saw above, for all practical purposes, this is not difficult, and our ability to do so reliably underlies the huge success quantum physics has had. However, the Copenhagen approach goes further and denies the reality of anything other than the changes that occur in the classical apparatus: only the life or death of the cat or the 'permanent marks on a photographic plate' are real. The polarization state of the photon is an idealistic concept extrapolated from the results of our observations and no greater reality should be attributed to it. From this point of view, the function of quantum physics is to make statistical predictions about the outcome of experiments and we should not attribute any truth-value to any conclusions we may draw about the nature of the quantum system itself.

 

- Alastair Rae, pg168

 

According to the positivist philosophy of science, Science should be viewed as a set of predictive rules and it cannot claim to give an objective account of reality. So the claim everything is made up of particles and particles behaves as particles is a claim on the nature of the physical world or the nature of the quantum system and the continuous dodging of requests to give a clear definition of the particle not only proves that it is not a scientific claim and it also shows that its a problem of ontology.

 

 

I do not need to convince the scientific community of something that is well-known:

 

http://www.particlep...-particles.html

 

 

 

http://public.web.ce...rdModel-en.html

 

 

 

http://www.fnal.gov/...deof/index.html

 

 

 

http://www.pbs.org/w...elegant_09.html

 

 

 

And so on and so on.

 

The properties [#] of those particles are also well-known and listed in tables such as the table 15.2 of the same physics textbook that you cited in the past.

 

[#] Your term "attributes" must be adequate for the philosophers.

 

Assuming that CERN scientists are not using the term particle in the usual sense of the term, your terminology of the use of the standard 'quantum particle' has so far no clear definition or consensus among the scientists and philosophers working to interpret the quantum field theory. It has its own problems and its interpretations are more naive with non-seperability and with no clear definition of a particle.

 

The way particle physics is done doesn't in any way make the problems go away. It uses detectors or a classical apparatus to determine the value of a physical quantity and there are different detectors to detect different physical properties and the energy-time uncertainty principle applies to such systems and it doesn't in any way change what Bohr said that the information gained about a single physical quantity of a quantum system exhausts all objective knowledge about the quantum system.

 

When you have solved all these problems and have a clear definition of what your quantum particle is only then it would be appropriate to say that everything in the world is made up of particles. If not then you're claiming too much and its not a scientific claim.

Edited by immortal
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If you would take care to read the entire article instead of selectively quoting it, you'll see that the message is different.

 

When we observe the behavior of light, electrons, neutrons, protons, buckyballs, etc. exhibiting both wave-like and particle-like behavior, we then use the term "duality" to describe such puzzling observation. Why? Because we have to "switch gears" when we talk about wave and particles. We use one type of description/formalism when we talk about the wave-like picture, and then we change our description/formalism to talk about the particle-like picture. Thus, the duality.

 

In that paragraph he merely reproduces the misconceptions that have the people who has never studied QM. Continue reading from where you stop (the bold face is in the original):

But here's something that most people who haven't studied physics are not aware of. In quantum mechanics, there is no such switching of gears!

 

In fact, your previous question to me was:

 

Then how can you possibly insist that there is no wave-particle duality?

 

And the article that you read says at the end, in its conclusions, (bold face from mine):

 

So in QM, there is no such thing as a wave-particle duality!

 

I'm sure this might come as a surprise, because the phrase "wave-particle duality" came about mainly due to QM and in the context of quantum behavior. However, one only needs to satisfy oneself that this duality doesn't exist by simply browsing through any undergraduate QM text. This duality is even hardly mentioned since it is utterly irrelevant. You certainly do not see such a thing being an issue in physics research papers other than papers that deal with pedagogical issues of quantum mechanics.

 

Before continuing, just explains me how you can interpret the above physicist's phrase "So in QM, there is no such thing as a wave-particle duality!" as contradicting my claim that "there is no wave particle duality in QM".

Edited by juanrga
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Therefore, before continuing correcting your mistakes just say me what part of the phrase "there is no wave particle duality" you do not still understand.

All that means is that the people that you're quoting don't understand the wave-particle duality.

 

What part of

 

[math]\lambda = \frac{h}{p}[/math]

probability density = [math]|\psi(x)|^2[/math]

 

don't you understand? Those two relations epitomizes the wave-particle duality. Which of those two expression are you claiming is wrong and why?

Edited by pmb
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Experimental physics led to this understanding, that a particle is not just a wave but a particle as well. The reason is rooted from the double slit experiment.

 

No. Experimental physics does not claim that a particle is a wave. You do not understand anything of what is being discussed here.

 

I think I understand why juan is so confused. He seems to think that the wave-particle duality states that a sinlge particle is a wave, which is clearly not true.

 

you confound my with Aethelwul. You and Aethelwul are saying that the wave-particle duality states that a single particle is a wave. Both of you are plain wrong.

 

According to the positivist philosophy of science

We are not discussing philosophy of science, but physics. Post your thoughts about philosophy in the corresponding forum.

 

Assuming that CERN scientists are not using the term particle in the usual sense of the term

 

The links given are not all from CERN. Of course, none of them is using your personal definition of particle, but they are using the standard definition.

 

When you have solved all these problems and have a clear definition of what your quantum particle is only then it would be appropriate to say that everything in the world is made up of particles. If not then you're claiming too much and its not a scientific claim.

 

You continue rejecting overwhelm scientists consensus about the physical nature of the world. Post your personal views in the speculations forum and stop from abusing this thread. Any scientist knows that the world is made of particles: electrons, photons, quarks...

Edited by juanrga
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No. Experimental physics does not claim that a particle is a wave.

Nobody in this thread has suggested that a particle is a wave. That's why I quoted Feynman. He said just the opposite, i.e. from post #16

"Quantum mechanics" is the description of the behavior of matter and light in all details and, in particular, of the happenings on an atomic scale. Things on an atomic scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.

Newton thought that ligt was made up of particles, but then it was discovered that it behaves like a wave. Later, however (in the beginning of the twentieth century), t was found thalight did indeed sometimes behave like a particle, and then it was found that in many respects it behaved like a wave. So it really behaves like neither. Now we have given up. We say: "It i like neither."

See what I mean? We know that they don't behave like waves.

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All that means is that the people that you're quoting don't understand the wave-particle duality.

 

I am not quoting you.

 

What part of

 

[math]\lambda = \frac{h}{p}[/math]

probability density = [math]|\psi(x)|^2[/math]

 

don't you understand? Those two relations epitomizes the wave-particle duality. Which of those two expression are you claiming is wrong and why?

 

You are blatantly confounding me with another poster, because I never did such claim.

 

Nobody in this thread has suggested that a particle is a wave.

 

Both you and Aethelwul write that a single particle is a wave. Both of you are plain wrong.

Edited by juanrga
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We are not discussing philosophy of science, but physics. Post your thoughts about philosophy in the corresponding forum.

 

Philosophy is the boss!! Physics is a branch of science and science is a branch of philosophy and it has the authority to question what claims can scientists make and how much they can claim to know what. So far you have not addressed any of my arguments so shall I assume that scientists are doing bad philosophy.

 

The links given are not all from CERN. Of course, none of them is using your personal definition of particle, but they are using the standard definition.

 

Then please can you give the standard definition for the quantum particle?

 

You continue rejecting overwhelm scientists consensus about the physical nature of the world. Post your personal views in the speculations forum and stop from abusing this thread. Any scientist knows that the world is made of particles: electrons, photons, quarks...

 

Oh really? Then everyone should be made aware of the controversial problems surrounding it. Go and read it.

 

http://scholar.google.co.in/scholar?q=not+quite+particles+not+quite+fields+humana+mente&btnG=&hl=en&as_sdt=0%2C5

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Philosophy is the boss!! Physics is a branch of science and science is a branch of philosophy and it has the authority to question what claims can scientists make and how much they can claim to know what. So far you have not addressed any of my arguments so shall I assume that scientists are doing bad philosophy.

 

No, science is not a branch of philosophy.

 

Then please can you give the standard definition for the quantum particle?

 

The definition is well-known, studied in textbooks and was also given here by me.

 

Oh really? Then everyone should be made aware of the controversial problems surrounding it. Go and read it.

 

http://scholar.googl...en&as_sdt=0%2C5

 

Once again, move your philosophical ruminations and your links to the philosophical journal "Humanamente" to the correct subforum

 

http://www.sciencefo...101-philosophy/

Edited by juanrga
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This is a collection of nonsense.

 

 

 

The definition is well-known, studied in textbooks and was also given here by me.

 

 

 

Once again move your philosophical ruminations and your links to the philosophical journal "Humanamente" to the correct subforum

 

http://www.sciencefo...101-philosophy/

 

Address my arguments or accept that we don't know the physical nature of the world first then I'll think about it.

 

No, science is his not a branch of philosophy.

 

Ah, you've edited your post, what does that statement mean?

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You are blatantly confounding me with another poster, because I never did such claim.

No, he isn't. He is saying that those expressions are representative of the wave-particle duality, and if you are claiming that there is no wave-particle duality, then you are, ipso facto, claiming that one or both of them is wrong. He is asking which it is.

Edited by Delta1212
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Ah, you've edited your post, what does that statement mean?

 

I have edited and eliminated a superfluous "his".

 

No, he isn't. He is saying that those expressions are representative of the wave-particle duality, and if you are claiming that there is no wave-particle duality, then you are, ipso facto, claiming that one or both of them is wrong. He is asking which it is.

 

He directly asked me to explain "why" I think that those expressions are wrong. Since I have never made such one claim about those expressions, I do not need to answer him.

 

Now you are claiming that (i) those expressions are representative of the waveparticle duality, and that if there is not wave-particle duality then those (ii) expressions are, "ipso facto", wrong, but both are your claims, not mine.

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I have edited and eliminated a superfluous "his".

 

 

 

He directly asked me to explain "why" I think that those expressions are wrong. Since I have never made such one claim about those expressions, I do not need to answer him.

 

Now you are claiming that (i) those expressions are representative of the waveparticle duality, and that if there is not wave-particle duality then those (ii) expressions are, "ipso facto", wrong, but both are your claims, not mine.

No, that is very clearly what his post said. I made no claims except that you failed to understand what he was asking and apparently continue to do so.

 

Edit: But now that you mention it, do you understand that (i)if an expression represents wave-particle duality and (ii)you claim that wave-particle duality does not exist then you are making one of two definite claims: either the expression is wrong in some way or it does not actually represent a wave-particle duality.

 

So you are definitely claiming one of those two things by asserting the non-existence of the wave-particle duality and while you are certainly not obligated to respond to anyone's arguements about anything, no one is obligated to take your arguments seriously if you refuse to address counter points.

 

I'm not a quantum physicist, and I've seen enough "pop science" that I learned in my youth turn out to be inaccurate or flat out wrong to be receptive to the idea. When you first said that the wave-particle duality was wrong, my response was "Oh, really? That's interesting."

 

In the time between that point and the point at which I started posting, I became rather comfortably convinced that you are wrong based on the fact that you're not backing up your point nearly as effectively as everyone else.

 

If you want to convince anyone that you know what you are talking about, you have to address the points that people raise, and while I have seen you state that you have several times, the post that you dismissed as being an argument against a claim you didn't make was very clearly an argument against your entire premise. Either you are ignoring it, or you are truly failing to understand the applicability and in either case, that is undermining your credibility.

 

If you do not wish to convince anyone, then carry on.

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No, that is very clearly what his post said. I made no claims except that you failed to understand what he was asking and apparently continue to do so.

 

He was asking me about something that I never said. His exact words:

 

Which of those two expression are you claiming is wrong and why?

 

One time more. I have not made such claims. I have never said that those expressions are wrong!

 

Edit: But now that you mention it, do you understand that (i)if an expression represents wave-particle duality and (ii)you claim that wave-particle duality does not exist then you are making one of two definite claims: either the expression is wrong in some way or it does not actually represent a wave-particle duality.

 

And the correct answer is that the expression does not represent wave-particle duality.

Edited by juanrga
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And my question as someone without expertise in this field is: Why not?

 

Because such expressions do not imply that there is a wave therein, neither that the electron (a particle) behaves like a wave. Consider the length

 

[math]\lambda = \frac{h}{|p|} = \frac{2\pi}{|k|}[/math]

 

with the vector [math]k[/math] being the momentum of the particle in 'units' of hbar: [math]p = \hbar k[/math]. The vector [math]k[/math] allows for a simplification of many QM formulae involving [math](i/\hbar)[/math] factors. For instance, instead writting [math]\exp(ipx/\hbar)[/math] you write [math]\exp(ikx)[/math]. There is no mystery here. Using [math]k[/math] instead of [math]p[/math] does not introduce a duality. Although by historical reasons [#] [math]k[/math] is often named the wavevector, in modern literature it is named the vector [math]k[/math] (the term "wave" is dropped, which is a good idea). Taking of the inverse of [math]|k|[/math] does not introduce a duality neither does multiplying by [math]2\pi[/math]

 

For a free particle, under the approximations outlined in previous posts from mine, the quantum state is given by a function [math]\psi(x) \propto \exp(ikx)[/math]. This is not a wave (a physical system), but a function. The use of [math]\psi(x)[/math] does not introduce a duality in the formalism (the electron is always a particle and behaves as a particle), although by historical reasons [$] it is still named the wavefunction.

 

We can explain the same quantum behavior using formulations of QM that do not rely on [math]\psi(x)[/math]. I use one of that formulations in my research work. In fact, in more advanced and general formalisms of QM the wavefunction [math]\psi(x)[/math] is superseded by the state vector [math]|\Psi\rangle[/math] (note that the term "wave" is dropped, which is again a good idea). Evidently, associating this state vector [math]|\Psi\rangle[/math] to a particle does not introduce a vector-particle duality.

 

Trying to believe that [math]\psi(x)[/math] or [math]\lambda[/math] are representative of a fundamental wave-particle duality is a gross misunderstanding of QM because the state of a quantum particle is not given by [math]\psi(x)[/math] in the general case. Moreover, [math]\lambda[/math] is only defined when momentum is well-defined for a particle, which is far from the general case. In the general case, [math]\lambda[/math] is not even defined for a particle.

 

Moreover, you can find similar expressions on classical mechanics. Advanced textbooks in classical dynamics show how the state of a classical particle can be also formally expanded in terms of planewaves [math]exp(ikx)[/math], with k being the classical wavevector associated to the classical particle. Of course attributing a classical wavevector k to a classical particle does not mean that there is a wave-particle duality in classical mechanics. This formulation of classical mechanics in terms of wavevectors is very useful in the study of collisions of classical particles, but particles continue being particles and behave as particles.

 

It is worth to mention that the own wikipedia page on duality cited before contains a comment from L. Ballentine, Quantum Mechanics, A Modern Development, p. 4, explaining why wave-particle duality is a misnomer (although I prefer the term myth; bold face from mine):

 

When first discovered, particle diffraction was a source of great puzzlement. Are "particles" really "waves?" In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989). Evidently, quantum particles are indeed particles, but whose behaviour is very different from classical physics would have us to expect.

 

 

[#] Wavelength was first introduced by DeBroglie, but he believed on the existence of a real wave, which is nowhere. His subsequent work/interpretation was shown to be wrong (De Broglie-Bohm theory) although the original name/term "wavelength" remained, causing confusion up to today.

 

[$] Again during the development of QM, DeBroglie, Schrödinger, and others believed on the existence of a real wave. The original name "wavefunction" remained with us, although any textbook in QM remarks that [math]\psi(x)[/math] is a non-observable function, not a real wave.

Edited by juanrga
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Because such expressions do not imply that there is a wave therein, neither that the electron (a particle) behaves like a wave. Consider the length

 

[math]\lambda = \frac{h}{|p|} = \frac{2\pi}{|k|}[/math]

 

with the vector [math]k[/math] being the momentum of the particle in 'units' of hbar: [math]p = \hbar k[/math]. The vector [math]k[/math] allows for a simplification of many QM formulae involving [math](i/\hbar)[/math] factors. For instance, instead writting [math]\exp(ipx/\hbar)[/math] you write [math]\exp(ikx)[/math]. There is no mystery here. Using [math]k[/math] instead of [math]p[/math] does not introduce a duality. Although by historical reasons [#] [math]k[/math] is often named the wavevector, in modern literature it is named the vector [math]k[/math] (the term "wave" is dropped, which is a good idea).

 

For a free particle, under the approximations outlined in previous posts from mine, the quantum state is given by a function [math]\psi(x) \propto \exp(ikx)[/math]. This is not a wave (a physical system), but a function. The use of [math]\psi(x)[/math] does not introduce a duality in the formalism (the electron is always a particle and behaves as a particle), although by historical reasons [$] it is still named the wavefunction.

 

We can explain the same quantum behavior using formulations of QM that do not rely on [math]\psi(x)[/math]. I use one of that formulations in my research work. In fact, in more advanced and general formalisms of QM the wavefunction [math]\psi(x)[/math] is superseded by the state vector [math]|\Psi\rangle[/math] (note that the term "wave" is dropped, which is again a good idea). Evidently, associating this state vector [math]|\Psi\rangle[/math] to a particle does not introduce a vector-particle duality.

 

Trying to believe that [math]\psi(x)[/math] is representative of a fundamental wave-particle duality is a gross misunderstanding of QM because, as textbooks explain, the state of a quantum particle is not given by [math]\psi(x)[/math] in the general case.

 

Moreover, you can find similar expressions on classical mechanics. Advanced textbooks in classical dynamics show how the state of a classical particle can be also formally expanded in terms of planewaves [math]exp(ikx)[/math], with k being the classical wavevector associated to the classical particle. Of course attributing a classical wavevector k to a classical particle does not mean that there is a wave-particle duality in classical mechanics. This formulation of classical mechanics in terms of wavevectors is very useful in the study of collisions of classical particles, but particles continue being particles and behave as particles.

 

It is worth to mention that the own wikipedia page on duality cited before contains a comment from L. Ballentine, Quantum Mechanics, A Modern Development, p. 4, explaining why wave-particle duality is a misnomer (although I prefer the term myth; bold face from mine):

 

 

 

 

[#] Wavelength was first introduced by DeBroglie, but he believed on the existence of a real wave, which is nowhere. His subsequent work/interpretation was shown to be wrong (De Broglie-Bohm theory) although the original name/term "wavelength" remained, causing confusion up to today.

 

[$] Again during the development of QM, DeBroglie, Schrödinger, and others believed on the existence of a real wave. The original name "wavefunction" remained with us, although any textbook in QM remarks that [math]\psi(x)[/math] is a non-observable function, not a real wave.

 

What about these equations of applying matter waves to matter?

 

∆x ∆k ≈ 1, ∆t ∆ω ≈ 1 and vg = v

 

where the group velocity of the wave packet is equal to the speed of the particle which implies that a quantum object can be described as a particle or as a wave and these equations lead us to the Heisenberg's uncertainty relation which says that in theory it is impossible to determine the wave and particle properties simultaneously which is not due to some consequence of technological limitations. Are these equations wrong? What do they imply?

 

 

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What about these equations of applying matter waves to matter?

 

∆x ∆k ≈ 1, ∆t ∆ω ≈ 1 and vg = v

 

where the group velocity of the wave packet is equal to the speed of the particle which implies that a quantum object can be described as a particle or as a wave and these equations lead us to the Heisenberg's uncertainty relation which says that in theory it is impossible to determine the wave and particle properties simultaneously which is not due to some consequence of technological limitations. Are these equations wrong? What do they imply?

 

I believed that the quote from Quantum Mechanics, A Modern Development, explaining why the early idea of a duality of particle and wave properties was an historical accident would suffice, but I was being too naive and once again you retort to 'ancient' misguided ideas such as DeBroglie "matter waves".

 

In my previous post, which you quote verbatim, I also tried to explain how we also use wave packets and wave vectors in classical mechanics. Indeed the state of a classical particle in classical mechanics can be represented using wave packets. But those wave packets are mathematical functions that represent the state of the classical particle, are not physical waves. Equations such as ∆t ∆ω ≈ 1 , with ∆ω being the range of frequencies of the packet, can be also found in textbooks dealing with classical mechanics.

 

That v in the classical wave packet is, indeed, equal to the velocity of the classical particle, but this is not anything mysterious. It merely reflects the obvious fact of that the state of the particle is parametrized by properties of the particle. How could not depend on the particle velocity [math](p/m)[/math] if the Hamiltonian of the particle depends on it [math]H=m/2 (p/m)^2[/math] and the equation of motion depends on the Hamiltonian?

 

The introduction of a wave packet for the representation of some states of a classical particle does not introduce a wave-particle duality in classical mechanics.

 

Believing that the wave packet is a physical wave is a mistake, believing that the wave packet represents a wave moving in ordinary space is a mistake. Believing that the equality between the group velocity of the wave packet and the velocity of the classical particle implies that a classical object can be described as a particle or as a wave is a complete misunderstanding of classical mechanics.

 

Now substitute "classical" by "quantum" in the above discussion about wave packets and you are gone. I only want to emphasize that there are lots of myths/misconceptions regarding quantum mechanics, duality is only one of them.

Edited by juanrga
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It is strange that we have been debating/ discussing wave v particle v w_p_duality for 170 posts in this thread and we do not yet have an agreed definition of either.

 

The proper way to discuss is to agree such things at the outset so that the argument of each side has something to measure against.

Edited by studiot
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The proper way to discuss is to agree such things at the outset so that the argument of each side has something to measure against.

 

I often think this and see threads fall apart or at least get very prickly because the basic definitions haven't been agreed before commencing.

Edited by StringJunky
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Personally I have considered the original definition of duality, which postulated that quantum particles are both particles and waves (two or three posters used this), and the posterior definition, which postulates that quantum particles exhibit both wave and particle properties (at least one poster used this).

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Even in the Tonomura (1989) paper which is given in the wiki quote it clearly says that our results unambiguosly demonstrate the wave-particle duality.

 

http://www.ifi.unica...08%202010s1.pdf

 

These results unambiguosly demonstrate the wave-particle duality of electrons. On the one hand, a single electron passes through the slits as a wave and forms a probability interference pattern; electron-electron interaction plays no role in this process since the subsequent electron is not even produced from the Cathode till long after the preceding electron is detected. At the detector, on the other hand, an electron is observed as a localized particle. We must conclude that a certain position on the screen is selected, onto which the electron wavefunction collapses. The position cannot be predicted, but occurs in the probabilistic way dictated by the probability amplitude.

 

 

This was what I was searching for how does the more advanced formulation of Quantum Mechanics which is the QFT(Quantum field theory) treats the case of double slit interference experiment. I think it is a must read for everyone.

 

Teaching Quantum Physics Without Paradoxes

 

Although the quantized field approach resolves the wave-particle paradox, it does not remove wave-particle duality. EM radiation and matter have both wave and particle characteristics. For example, they come through both slits, but they hit the screen like particles.

 

Even in the more advanced formulation of QFT wave-particle duality do exists.

 

 

In discussing the wave-particle duality in connection with the two-slit interference experiment, Richard Feynman said, "We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery."

 

 

No one is arguing that Particles are waves. What I'm arguing for is the Bohr's Complementarity principle which says that it is impossible to simultaneously know which way information and to observe the fringe pattern completely. No experiments done so far have violated the Bohr's Complementarity principle. This is the heart of quantum mechanics and anyone who denies this has clearly misunderstood quantum mechanics and wave-particle duality do exists.

Edited by immortal
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Even in the Tonomura (1989) paper which is given in the wiki quote it clearly says that our results unambiguosly demonstrate the wave-particle duality.

 

http://www.ifi.unica...08%202010s1.pdf

 

In an early post I introduced the quote (bold from mine):

 

Sources, speaking on the "duality", either obsolete or are popular, educational, or philosophical literature. Serious contemporary theoretical sources don't mention about duality, they use more effective approaches, almost all based on PI. There is a good analogy with the notion of so-called "relativistic mass", which served its in the interpretation of relativistic effects in terms of Newtonian physics, but in the modern 4-dimensional formulation only creates a confusion Raoul NK (talk) 08:55, 20 September 2010 (UTC)

 

You continue citing Am. J. Phys. papers, which are educational papers for basic level stuff, they are not serious contemporary theoretical sources. The Tomonura et al. paper reports a beautiful experiment that proves that electrons are quantum particles (as everyone knows). From Ballentine's Quantum Mechanics a Modern development page 4:

 

When first discovered, particle diffraction was a source of great puzzlement. Are "particles" really "waves"? In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989). Evidently, quantum particles are indeed particles, but particles whose behavior is very different from what classical physics would have led us

to expect.

 

A rigorous quantum mechanical and statistical analysis of Tomonura diffraction experiment does not support the duality interpretation.

 

Where is the mistake? It was emphasized before, but I will repeat once more. Tomonura et al. use the term "particle" to mean little localized point or Newtonian particle. They need to appeal to an imagined duality (with waves) to explain the experiment, because an electron is not a Newtonian particle. If you look to the figures they represent the electron as a little black sphere with a little wave superposed!!! Moreover, the article makes very misleading claims as the one that you quote: "a single electron passes through the slits as a wave". There are three misconceptions of QM in this small quote!!!

 

Quantum mechanics does not say that the electron was a little localized point (a Newtonian particle); when the quantum character of the electron is taken into account, there is no need to appeal to a hypothetical duality. As emphasized before, and by several people, there is no duality in quantum mechanics.

 

This was what I was searching for how does the more advanced formulation of Quantum Mechanics which is the QFT(Quantum field theory) treats the case of double slit interference experiment. I think it is a must read for everyone.

 

Teaching Quantum Physics Without Paradoxes

 

Even in the more advanced formulation of QFT wave-particle duality do exists.

 

In the first place, QFT is not the more advanced formulation of Quantum Mechanics. In the second place, you again cite an educational paper: The Physics Teacher does not belong to serious contemporary theoretical sources. In the third place, nowhere in that paper the author develops or applies any QFT, but he only takes the idea of field quanta in a pictorial way. In the fourth place, this paper is one of the most misleading papers about quantum physics that I read in a long time. This paper even contradicts itself!!!

 

No one is arguing that Particles are waves.

 

Maybe you do not, but others in this thread argued just that.

 

What I'm arguing for is the Bohr's Complementarity principle which says that it is impossible to simultaneously know which way information and to observe the fringe pattern completely. No experiments done so far have violated the Bohr's Complementarity principle. This is the heart of quantum mechanics and anyone who denies this has clearly misunderstood quantum mechanics and wave-particle duality do exists.

 

Bohr's complementary principle, where he postulated the existence of complementary aspects of reality which would be revealed to us when "the account of all evidence must be expressed in classical terms" is plain wrong, as Steven Weinberg emphasized in Physics Today November 2005, page 31 [*]:

 

Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought.

 

And Weinberg explains why Bohr was wrong. I do not need to repeat again but it is rooted in Bohr's artificial split of universe into quantum and classical 'spheres of existence'.

 

[*] Notice that it is "Physics Today", not "Physics 100 Years Ago". Our understanding of quantum physics has advanced a lot of since Bohr.

Edited by juanrga
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