Particle wave duality

[Aethelwulf]

Here's the way I see it. From Principles of Quantum Mechanics - 2nd Ed. by R. Shankar, page 116. The autrhor writes

 

To my thinking this is the Copenhagen interpretation. Without it we'd be without this postulate and not know what the wavefunction means. I.e. we'd have the prediction but we wouldn't know what it meant or what to do with it. We can't make a prediction without this interpretation to tell us what it is we're looking to measure. Taking away the Copenhagen interpretation takes away our understaning of the meaning of the wavefunction. In that sense I disagree with you.

 

 

I was referring to quantum mechanics, not quantum field theory.

 

 

I don't understand. What are you saying that its problems are? There is the concept that the observer making the measurements are a quantum system. Is this what you're referring to?

 

Yes, sorry. Quantum Mechanics,

 

I already pointed this out to the staff and it went ignored. juan is using the logical fallacy of a straw argument. That's against the rules since logical fallacies are not allowed. I kept it quite kike I'm supposed to and reported the use of the fallacy to the moderators like I was supposed to. Yet I was ignored. I mention it now in open forum for lack of any other recourse that I'm allowed. His arguments are contrary to mainstream quantum mechanics and thereby belon in the speculation forum. Can't you just move it there?

 

I agree, I think the posts which deserve to be moved to speculations should be moved.

[immortal]

He's not confused. They refer to exactly the same thing. I.e.

http://en.wikipedia...._interpretation

 

immortal: Please take note that juanrga has never provided nor recognized the definition for the terms that he's using. In this way he keeps his straw argument alive and kicking. I recommend ignoring him unless and until he states the definitions of wave-particle duality and Copenhagen interpretation. Also, did you notice that juanrga never provided a reason why the 'Copenhagen interpretation' is supposed to be wrong?

 

Yes he is not arguing in good spirit and addressing the arguments of the conventional thinking of Quantum Mechanics.

 

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.

 

Let us see. The above link to the CERN starts with the following quote (bold from mine):

 

 

 

"Everything" includes atoms. Indeed atoms are made of particles such as the electron. The electron is a particle of the kind fermion. The electron is mentioned in the CERN link in the section "matter particles", third paragraph.

 

What does happen in an atom? Consider an isolated atom (not an atom in a molecule nor in a solid), but a solitary atom.

 

If we ignore nuclear structure and treat the nucleus as a classical point, if we assume that this atom is in a stable pure quantum state, and if we ignore spin and relativity, then the state of the atom can be described by a wavefunction, sometimes named electronic wavefunction because it only depends on electrons coordinates. Recall that the atom continues being made of particles!

 

Assume that this same atom is in some stationary state (i.e., its physical properties do not change with time). Then its wavefunction will not depend on time.

 

If further we consider that electrons in this atom are not-interacting (which is not true because electrons are electrically charged {*} and repeal between them) then that wavefunction can be split into a product of wavefunctions for each electron. The whole wavefunction is defined in a generalized space (not in ordinary space!). Only the wavefunction for each electron-j is defined in ordinary space [math]\Psi_j=\Psi_j(x,y,z)[/math].

 

This [math]\Psi_j[/math] is what you call "standing wave", but notice that it is not a wave (i.e. it is not a physical system with energy and momentum), but a mathematical function. The correct technical name is stationary wavefunction. This [math]\Psi_j[/math] only describes the quantum state of the electron approximatedly. In fact they are a very crude approximation to real atom. Moreover, the electron continues being a particle.

 

In more advanced quantum treatments the electron continues being a particle, but its state is not more given by a wavefunction [math]\Psi_j[/math] but by a more general and complex formalism.

 

{*} An exception is the Hydrogen atom because has only one electron.

 

Its strange that not even once you have used the word 'measurement' here and have just speculated your own version of the interpretation of the quantum mechanics and this clearly belongs to the discussion of crackpot ideas in the speculation forum.

 

LIGHT

We do know that photons behave like a wave and a particle both, that's what particle wave duality tells us..

1)So which source of light behave likes a particle and which one like a wave, How do we know that??

 

In quantum mechanics we don't know the physical meaning of the properties which we are dealing with and hence it is meaningless to term it has a particle or a wave. Properties only have operational meaning based on the context of the measuring device used.

 

Alastair Rae clearly answers this.

 

 

Polarization is a property of an electromagnetic wave, but does it have any relevance to the particle model of light? We could test this by passing very weak light through a polarizer set up like that in Figure 8.2: we would find photons (the particles of light first mentioned in Chapter 2) emerging at random through the two output channels, corresponding to horizontal (H) and vertical (V) polarization, respectively. To confirm that the photons really can be considered as having the property of polarization, we could pass each beam separately through other polarizers also oriented to measure HV polarization. We would find that all the photons emerging from the H channel of the first polarizer would emerge from the H channel of the second one – and similarly for V. This gives us an operational definition of photon polarization: whatever this property may really be, we can say that horizontally and vertically polarized photons are those that emerge from the H and V channels, respectively, of a polarizer.

 

As you see, the properties of the quantum object are assigned depending on the context of the measuring device. It has no objective physical meaning and no reality should be attributed to it.

 

Electrons

Electrons are present around the nucleus of an atom(we all know that)

4) Are they present there as particles, standing frequency, clouds or on orbits(which is the least i would prefer) ??

 

This is also a meaningless question and Alastair answers your questions here and this is the direct consequence of the way quantum mechanics works and not based on any limitation.

 

The consequences of this way of thinking are even more radical than may appear so far. Consider a photon polarized in a 45° state and we ask the question 'Is this photon horizontally or vertically polarized?' But this is surely a meaningless question: the polarization is neither pointing upwards nor from side to side; it is pointing at an angle. It might make some sense to say that it is pointing partly up and down and partly from side to side (i.e. it is in a superposition of an H and a V state), but it is certainly not doing either one of these or the other. To ask this question is as meaningless as asking if a banana is either an apple or an orange. Thus, when we say that we 'measure' the HV polarization of a 45° photon, we are using the word in a rather different sense from the normal one. When we measure, say, the length of a piece of string, we have no problem in assuming that the string has some value of length before we put it on the ruler, but a quantum measurement is in general quite different. As we saw above, it alters the state of the system in such a way as to give reality to a quantity that was indefinable in its previous context. Now consider the implications of this way of thinking for measurements of particle position. Most of us tend to assume that a particle always has to be 'somewhere' even when it is not being observed, but this is not true in the quantum context: if a particle is in a state where its position is unknown, then to think about it even having a position is just as meaningless as ascribing H or V polarization to a particle in a 45° state. It is meaningless to say that the particle has passed through one slit or the other when an interference pattern is formed. Similarly, it is wrong to think that an electron in an atom is at any single point within it.

 

This is a direct consequence due to the alteration of the state by measurement which is the conventional interpretation of quantum mechanics.

 

Your ideas about that universe is not made of particles confronts with overwhelm standard consensus among scientists. I repeat everything in the universe is made of particles:

 

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

 

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

 

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

 

http://www.particlea...ks_leptons.html

 

http://physics.about...a/particles.htm

 

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

 

...

 

Steven Weinberg remarks are not "subjective opinions" but scientific remarks that reflect our more modern and advanced understanding of quantum theory.

 

I already stated why all your arguments are invalid. I have explained in this thread what is an elementary particle, what are its properties, how we experimentally describe them, why particles are never waves, under what limits we can associate a wavefunction to the state of a particle and when we cannot, I have emphasized that in advanced and modern textbooks duality is not even mentioned because it plays no role in QM (I have cited some of those advanced textbooks)...

 

You have not addressed any of that.

 

Those links which you gave didn't answered the questions relevant to my arguments so please stop giving me such links and yes, I have addressed it now and please answer to my arguments and don't evade it.

 

And, contrary to your claims, that quote from Physics Today states that Bohr's version of quantum mechanics was deeply flawed and states that The Copenhagen interpretation is wrong.

 

Now you confound "The Copenhagen interpretation" with "the probabilistic rules of the Copenhagen interpretation". You are confound the Copenhagen rules and the Copenhagen interpretation.

 

What will be the next?

 

http://plato.stanfor.../qm-copenhagen/

 

 

Copenhagen Rules -

 

1. The interpretation of a physical theory has to rely on an experimental practice.

 

2. The experimental practice presupposes a certain pre-scientific practice of description, which establishes the norm for experimental measurement apparatus, and consequently what counts as scientific experience.

 

3. Our pre-scientific practice of understanding our environment is an adaptation to the sense experience of separation, orientation, identification and reidentification over time of physical objects.

 

4. This pre-scientific experience is grasped in terms of common categories like thing's position and change of position, duration and change of duration, and the relation of cause and effect, terms and principles that are now parts of our common language.

 

5. These common categories yield the preconditions for objective knowledge, and any description of nature has to use these concepts to be objective.

 

6. The concepts of classical physics are merely exact specifications of the above categories.

 

7. The classical concepts—and not classical physics itself—are therefore necessary in any description of physical experience in order to understand what we are doing and to be able to communicate our results to others, in particular in the description of quantum phenomena as they present themselves in experiments;

 

8. Planck's empirical discovery of the quantization of action requires a revision of the foundation for the use of classical concepts, because they are not all applicable at the same time. Their use is well defined only if they apply to experimental interactions in which the quantization of action can be regarded as negligible.

 

9. In experimental cases where the quantization of action plays a significant role, the application of a classical concept does not refer to independent properties of the object; rather the ascription of either kinematic or dynamic properties to the object as it exists independently of a specific experimental interaction is ill-defined.

 

10. The quantization of action demands a limitation of the use of classical concepts so that these concepts apply only to a phenomenon, which Bohr understood as the macroscopic manifestation of a measurement on the object, i.e. the uncontrollable interaction between the object and the apparatus.

 

11. The quantum mechanical description of the object differs from the classical description of the measuring apparatus, and this requires that the object and the measuring device should be separated in the description, but the line of separation is not the one between macroscopic instruments and microscopic objects. It has been argued in detail (Howard 1994) that Bohr pointed out that parts of the measuring device may sometimes be treated as parts of the object in the quantum mechanical description.

 

12. The quantum mechanical formalism does not provide physicists with a 'pictorial' representation: the ψ-function does not, as Schrödinger had hoped, represent a new kind of reality. Instead, as Born suggested, the square of the absolute value of the ψ-function expresses a probability amplitude for the outcome of a measurement. Due to the fact that the wave equation involves an imaginary quantity this equation can have only a symbolic character, but the formalism may be used to predict the outcome of a measurement that establishes the conditions under which concepts like position, momentum, time and energy apply to the phenomena.

 

13. The ascription of these classical concepts to the phenomena of measurements rely on the experimental context of the phenomena, so that the entire setup provides us with the defining conditions for the application of kinematic and dynamic concepts in the domain of quantum physics.

 

14.Such phenomena are complementary in the sense that their manifestations depend on mutually exclusive measurements, but that the information gained through these various experiments exhausts all possible objective knowledge of the object.

 

The Copenhagen rules is not claiming anything and it is accepting that we don't know but you're the one who is insisting by making positive claims that we can give an objective description of reality based on particle physics without in any way addressing how it solves the measurement problems and its questions. So the onus is on you to show it and provide us evidence challenging the accepted consensus.

 

This is a question of how science should be done and its clear that you're claiming too much and you need to back up your claims with evidence and address the criticisms.

Edited July 7, 2012 by immortal

[qft123]

The Copenhagen Interpretation is one the main important postulate of quantum mechanics, and i would not ignore it..

And to my question that if an electron behave like a particle or wavelength(at a specific period of time), can't be answered, because we don't know what is happening physically inside a particle, unlike classical physics.

But yes, we can always draw possibilities about it, that is what quantum physics is about..

[juanrga]

I didn't describe a theory I described a real world practical situation. I can actually observe, measure and display the wavelike behaviour.

 

The behaviour is incontrovertibly there and real. It is not 'derived from any theory'.

The nodes and antinodes of the wave are not parts of a quantum waveform, but they exist.

 

The question is like asking 'why do I not see a standing voltage waveform between my house and the power station?'

 

One is a wave theory that offers this for the real periodic variation in voltage that I observe and measure.

The other is a theory of particles that, as far as I know, should lead to a different solution that of no periodic waveform, rather a constant voltage or constantly decreasing voltage with the only variations due to random motion of those particles.

 

I will try to explain this again.

 

Lecher lines are macroscopic conductors and are described by electromagnetic wave theory. Electromagnetic wave theory can be derived as approximation to a quantum theory of particles (photons and electrons). The derivation of classical electrodynamics from the underlying quantum theory is made in textbooks.

 

Those waves that you can observe are the result of collective phenomena involving a large amount of elementary particles.

[hypervalent_iodine]

Yeah, but I'm sure that you know by now that juan doesn't give straight answers to direct questions. More often that not he simply won't respond to it at all.

 

 

Perhaps you missed it but in an earlier post I pointed this out to him, i.e. that he's using a straw argument in which the heart of his straw is a different, yet undefined, understanding of the terms we're talking about.

 

I explained this to juan in the post # 92

http://www.sciencefo...post__p__688843

 

which basically states de broglies hypothesis and the QM postulate whereby the squared magnitude is the probability density. Then I explained to him that de Broglie hypithesis epitomizes the wave-particle duality and explained that an ensemble of identical experiments with sinlge particles. He ignord it of course. He simply won't address counter arguments to his premises.

 

 

I already pointed this out to the staff and it went ignored. juan is using the logical fallacy of a straw argument. That's against the rules since logical fallacies are not allowed. I kept it quite kike I'm supposed to and reported the use of the fallacy to the moderators like I was supposed to. Yet I was ignored. I mention it now in open forum for lack of any other recourse that I'm allowed. His arguments are contrary to mainstream quantum mechanics and thereby belon in the speculation forum. Can't you just move it there?

 

!

Moderator Note

pmb,

 

You were not ignored. Your reports were received and are being discussed. We don't immediately act on all reports for a number of reasons:

 

1. We're not all here all the time so things aren't often acted upon until one or two mods happen to see a report and comment on it. This is especially true for reports that require a staff member familiar with the theoretical content.

 

2. More pertinently, we are not here to serve your every whim. We encourage members to report what they think may be a violation of the rules, but it is entirely not your position to say whether it actually is or how a report should be actioned.

 

This post of yours is off topic and is derailing this thread and I am going to ask you to cease this line of conversation here. Additionally, the back-seat moderating is not appropriate and it is to stop.

 

If you have any further questions regarding this mod note, please PM a member of staff or use the report feature.

[pmb]

!

Moderator Note

pmb,

 

You were not ignored. Your reports were received and are being discussed. etc

Sorry. My mistake.

 

Pete,

 

I said periodicity is fundamental to wave behaviour and have pointed out some uses of the word periodic that do not conform to your 'definition'.

Brillouin zones are periodic in space. The periodic table is periodic in atomic number.

I think we're thinking about two different things.

 

The Copenhagen Interpretation is one the main important postulate of quantum mechanics, and i would not ignore it..

And to my question that if an electron behave like a particle or wavelength(at a specific period of time), can't be answered, because we don't know what is happening physically inside a particle, unlike classical physics.

But yes, we can always draw possibilities about it, that is what quantum physics is about..

I think that the essense of the Copenhagen Interpretation is to connect theory with experiment.

Edited July 7, 2012 by pmb

[juanrga]

You didn't answer it before. You wrote something, but you didn't actually answer the question. I asked a question to which the answer would be a yes or a no.

 

You did not asked one thing but two. And I offered a detailed answer before, but the short version is "yes" and "yes".

 

Unlike what I asked, that's a loaded question. A simple yes or no does not suffice,

 

I did not restrict you with a simple yes/no.

 

"Quantum particle" is also your words. Part of your standard terminology.

 

Yes, it is rather standard. You can google "quantum particle".

 

The bottom line is that you are arguing a different point than everybody else. That we have labeled everything as a particle does not address the question, and you acknowledge this when you add the disclaimer that particle doesn't mean classical/Newtonian particle or little sphere. Because they don't behave that way, do they? They do other things, like interfere and diffract, which are wave-like phenomena.

 

IOW, the question being asked is not what label we have attached to electrons, etc., which is the question you've been answering.

 

I added the disclaimer (which was also added by another poster), because some people confounds "particle" with "classical particle".

 

The OP asked me "But is electron present as a standing wave or as a particle in the atom?" My response was that the electron in an atom is a particle. Another poster wrote that the electron in an atom is a particle. Both answers are correct. I also give a link to IUPAC, where they define the electron as a particle. Of course, the chemists definition also applies to quantum chemistry.

 

I also explained to the OP how a collection of particles can show wave-like behaviour. I remarked this about 100 posts ago. The usual interference pattern observed in double-slit experiment with electrons is generated by thousands of particles (electrons). Electromagnetic waves are a collection of particles named photons...

 

Some people here misinterprets any bit of modern physics and has posted wrong claims: one poster said that nobody really believes that the electron is a particle (wrong), other said that the wavefunction is real and physical (wrong), other said that an electron is sometimes a wave (wrong)...

Edited July 7, 2012 by juanrga

[elfmotat]

Postulate III<br style="font-size: 13px; line-height: 16px; background-color: rgb(243, 249, 246); "><br style="font-size: 13px; line-height: 16px; background-color: rgb(243, 249, 246); ">If the particle is in a state , a measurement of the variable (corresponding to) will yield one of the eigenvalues with probability . The state of the system will change from to as a result of the measurement.

 

Quick thing: use \langle and \rangle when using bra-ket notation. Makes things nicer:

 

[math]P(\omega )=|\langle\omega |\psi \rangle|^2[/math]

[pmb]

I also explained to the OP how a collection of particles can show wave-like behaviour. I remarked this about 100 posts ago. The usual interference pattern observed in double-slit experiment with electrons is generated by thousands of particles (electrons). Electromagnetic waves are a collection of particles named photons...

And since then you've been refraining from acknowledging that an ensemble of identical single particle experiments shows intereference. You have also been refaining from acknowledging that for a single particle with a specifc momentum has a wavelength associated with it. You're also ignoring the fact that collections of particles display wave-characteritics because individual particles have a wavlength to them. Without that associated wavelength the particles can't have wave characteristics.

 

We all know what you say juan. The problem is in what you refuse to say when you are shown evidence contrary to your assertions. That's the problem here. Everyone keeps telling you that an making the obervation that you refuse to respond to the evidence pesented to you whereby you simply revert to another subject.

[juanrga]

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.

 

Its strange that not even once you have used the word 'measurement' here and have just speculated your own version of the interpretation of the quantum mechanics and this clearly belongs to the discussion of crackpot ideas in the speculation forum.

 

In that discussion the word was unneeded. Also that part is a standard discussion of ordinary quantum mechanics, contrary to your beliefs.

 

Those links which you gave didn't answered the questions relevant to my arguments so please stop giving me such links and yes, I have addressed it now and please answer to my arguments and don't evade it.

 

You are who evade the questions. Those six links explain to you, in layman terms, how everything around us is made of particles. You continue rejecting this well-known fact and posting stuff as "Science doesn't give an objective account of reality."

 

http://plato.stanfor.../qm-copenhagen/

Copenhagen Rules -

 

1. The interpretation of a physical theory has to rely on an experimental practice.

 

2. The experimental practice presupposes a certain pre-scientific practice of description, which establishes the norm for experimental measurement apparatus, and consequently what counts as scientific experience.

 

3. Our pre-scientific practice of understanding our environment is an adaptation to the sense experience of separation, orientation, identification and reidentification over time of physical objects.

 

4. This pre-scientific experience is grasped in terms of common categories like thing's position and change of position, duration and change of duration, and the relation of cause and effect, terms and principles that are now parts of our common language.

 

5. These common categories yield the preconditions for objective knowledge, and any description of nature has to use these concepts to be objective.

 

6. The concepts of classical physics are merely exact specifications of the above categories.

 

7. The classical concepts—and not classical physics itself—are therefore necessary in any description of physical experience in order to understand what we are doing and to be able to communicate our results to others, in particular in the description of quantum phenomena as they present themselves in experiments;

 

8. Planck's empirical discovery of the quantization of action requires a revision of the foundation for the use of classical concepts, because they are not all applicable at the same time. Their use is well defined only if they apply to experimental interactions in which the quantization of action can be regarded as negligible.

 

9. In experimental cases where the quantization of action plays a significant role, the application of a classical concept does not refer to independent properties of the object; rather the ascription of either kinematic or dynamic properties to the object as it exists independently of a specific experimental interaction is ill-defined.

 

10. The quantization of action demands a limitation of the use of classical concepts so that these concepts apply only to a phenomenon, which Bohr understood as the macroscopic manifestation of a measurement on the object, i.e. the uncontrollable interaction between the object and the apparatus.

 

11. The quantum mechanical description of the object differs from the classical description of the measuring apparatus, and this requires that the object and the measuring device should be separated in the description, but the line of separation is not the one between macroscopic instruments and microscopic objects. It has been argued in detail (Howard 1994) that Bohr pointed out that parts of the measuring device may sometimes be treated as parts of the object in the quantum mechanical description.

 

12. The quantum mechanical formalism does not provide physicists with a 'pictorial' representation: the ψ-function does not, as Schrödinger had hoped, represent a new kind of reality. Instead, as Born suggested, the square of the absolute value of the ψ-function expresses a probability amplitude for the outcome of a measurement. Due to the fact that the wave equation involves an imaginary quantity this equation can have only a symbolic character, but the formalism may be used to predict the outcome of a measurement that establishes the conditions under which concepts like position, momentum, time and energy apply to the phenomena.

 

13. The ascription of these classical concepts to the phenomena of measurements rely on the experimental context of the phenomena, so that the entire setup provides us with the defining conditions for the application of kinematic and dynamic concepts in the domain of quantum physics.

 

14.Such phenomena are complementary in the sense that their manifestations depend on mutually exclusive measurements, but that the information gained through these various experiments exhausts all possible objective knowledge of the object.

 

In the first place, the term "Copenhagen rules" does not appear in any part of the link that you are giving, but you added the term before the list, which you copied from the link and has a different meaning.

 

When Weinberg writes about the Copenhagen rules in Physics Today, he is referring to "the probabilistic rules of the Copenhagen interpretation", Weinberg is not referring to a set of ambiguous philosophical points by Bohr.

 

Also as Weinberg writes in Physics Today: "Bohr's version of quantum mechanics was deeply flawed". But this is another point that you refuse to accept.

 

The Copenhagen Interpretation is one the main important postulate of quantum mechanics, and i would not ignore it.

 

The Copenhagen Interpretation of quantum mechanics is not a postulate but one of several interpretations of quantum mechanics.

 

http://en.wikipedia....antum_mechanics

 

The Copenhagen Interpretation has been superseded by more modern interpretations which work in situations beyond the scope of the old Copenhagen Interpretation. Recall also Weinberg writing in Physics Today:

 

The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe.

Edited July 7, 2012 by juanrga

[pmb]

Pete,

 

I said periodicity is fundamental to wave behaviour and have pointed out some uses of the word periodic that do not conform to your 'definition'.

Brillouin zones are periodic in space. The periodic table is periodic in atomic number.

studiot,

 

I think that our disagreement rests in an equivolcation whereby the term periodic is used to refer to two different things at the same time. The periodic in periodic table refers to the shell structure of atoms and how the shells are filled with electrons going from one atom to the next in the table. There is kind of a physical similarity with atoms having certain numbers of electrons in shells. Then there is the use of periodic to refer to a function having exact repetivtive values. That sense of the term is defined in Mathematical Methods in the Physical Sciences by Mary L. Boas, (2006), page 343

By definition, the function f(x) is periodic if f(x + p) = f(x) for every x; the number p is the period.

That is what it means to be periodic.

 

There are indeed other structures which are periodic but are not waves.

That is correct. E.g. f(x) = sin x is periodic but not a wave.

 

However I still maintain all waves are periodic.

A function f(x, t) is called a wave if it has either of the forms G(x - vt) or H(v + vt). Such a function need not be periodic. Consider the Gaussian function

 

[math]\psi(x, t) = e^{x - vt}^2[/math]

 

This is a wave, by definition, but it isn't periodic, by definition.

 

Back to waves, have you ever heard of the 'periodic equation' for a wave?

No, I haven't. Sorry. What does it mean?

[Delta1212]

juan, would you agree that quantum particles have some of the properties attributed to "little hard spheres following Newtonian laws", some of the properties attributed to waves, and some properties attributed to neither?

[juanrga]

juan, would you agree that quantum particles have some of the properties attributed to "little hard spheres following Newtonian laws", some of the properties attributed to waves, and some properties attributed to neither?

 

In order:

 

1) Yes. I already emphasized how "classical particle" is a limiting case of a "quantum particle", which can be derived by taking the classical limit of the quantum theory.

 

2) Yes, if you mean that a collection of quantum particles can have (collectively) wave properties. I already emphasized how an electromagnetic wave is a collection of photons and how the interference pattern in a double slit-experiment with electrons is generated by thousands of electrons as the experiment shows:

 

 

However, if you mean that an individual quantum particle has wave properties or is a wave (some posters here said that an electron is sometimes a wave). No.

 

3) Yes.

Edited July 7, 2012 by juanrga

[immortal]

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.

 

 

 

 

You are who evade the questions. Those six links explain to you, in layman terms, how everything around us is made of particles. You continue rejecting this well-known fact and posting stuff as "Science doesn't give an objective account of reality.

 

 

Solve the measurement problem and convince all of the scientists in the scientific community and then come back to me and assert that the world is made up of particles(in your own terminology) clearly defining what it is and what its attributes are.

Edited July 7, 2012 by immortal

[pmb]

However, if you mean that an individual quantum particle has wave properties or is a wave (some posters here said that an electron is sometimes a wave). No.

 

3) Yes.

You sure are beating that straw to death. We keep telling you that for a collection of particles to disoplay wave properties each individual particle must have an associated wave-characteristic. That's why a free electron with momentum p has wavelenth L = h/p. That is the wave-particle duality, and that's what we're talking about and what you keep ignoring.

 

We know you're ignoring it because you can't procve that its wrong. Since you refuse to argue cogently immortal and I am now done with you.

Edited July 7, 2012 by pmb

[juanrga]

Solve the measurement problem and convince all of the scientists in the scientific community and then come back to me and assert that the world is made up of particles(in your own terminology) clearly defining what it is and what its attributes are.

 

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

 

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

 

Everything in the universe, from stars and planets, to you and the chair that you're sitting on, is made from the same basic building blocks - particles of matter.

 

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

 

The theories and discoveries of thousands of physicists over the past century have resulted in a remarkable insight into the fundamental structure of matter: everything in the Universe is found to be made from twelve basic building blocks called fundamental particles, governed by four fundamental forces.

 

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

 

Physicists have identified 12 building blocks that are the fundamental constituents of matter. Our everyday world is made of just three of these building blocks: the up quark, the down quark and the electron. This set of particles is all that's needed to make protons and neutrons and to form atoms and molecules. The electron neutrino, observed in the decay of other particles, completes the first set of four building blocks.

 

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

 

The world is made up of elementary particles called quarks, which include the up, down, charm, strange, top, and bottom quarks; and leptons, which include the electron, the muon, the tau, and their corresponding neutrinos.

 

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.

Edited July 7, 2012 by juanrga

[studiot]

Pete,

 

A function f(x, t) is called a wave if it has either of the forms G(x - vt) or H(v + vt). Such a function need not be periodic.

 

Thank you for discussing properly.

 

What restrictions would you place on G or H ?

[pmb]

Pete,

 

Thank you for discussing properly.

Always a pleasure!

 

What restrictions would you place on G or H ?

There are none that I know of except for physical meaning restrictions. For example: If G was a wave which was expanding out from the origin then it'd have the general form G(r - vt). The function H(r + vt) represents a wave converging on the origin and must be ruled out for physical reasons.

 

The expression G(r - vt) might also be of the form f(r - vt)/r which would be a potential wave decreasing in magnitude as it expanded out from the origin.

 

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. As we have all agreed, a single particle has an associated wavelength and an associated wavefunction. If the wave-particle duality really meant that a single particle is a wave then it'd be called the wave-particle identity which it's not, and for good reason.

 

However, as we all well know, with each particle there is an associated wave [math]\psi[/math], called the probability amplitude or simply amplitude, whose modulus squared [math]|\psi(x)|^ 2[/math] gives the probability density of finding the particle at x.

 

It's for these reasons that physicists ascribes a single particle with a wavefunction.

Edited July 7, 2012 by pmb

[studiot]

So would you call any of these a wave?

 

G = 0

 

G = constant

 

G = tan(x)

 

G = 1/tan(x)

 

G = {1 : x odd, :x : even}

 

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. As we have all agreed, a single particle has an associated wavelength and an associated wavefunction. If the wave-particle duality really meant that a single particle is a wave then it'd be called the wave-particle identity which it's not, and for good reason.

 

However, as we all well know, with each particle there is an associated wave , called the probability amplitude or simply amplitude, whose modulus squared gives the probability density of finding the particle at x.

 

It's for these reasons that physicists ascribes a single particle with a wavefunction.

 

I fully agree with this but there is more.

 

All this quantum mechanics stuff that has been mentioned so far has been single isolated particle stuff.

 

How many single isolated particles do you know?

 

As soon as we get to real materials we are into molecular QM and the original particles loose their identity.

Edited July 7, 2012 by studiot

[pmb]

So would you call any of these a wave?

 

G = 0

 

G = constant

 

G = tan(x)

 

G = 1/tan(x)

 

G = {1 : x odd, :x : even}

No. None of them are functions of "x - vt"

 

I fully agree with this but there is more.

 

All this quantum mechanics stuff that has been mentioned so far has been single isolated particle stuff.

That's because its the topic of conversation.

[swansont]

You did not asked one thing but two. And I offered a detailed answer before, but the short version is "yes" and "yes".

 

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

[studiot]

No. None of them are functions of "x - vt"

 

pmb

Sorry that was my fault for not using x as the dummy variable.

 

Replace x by w, with w=(x-vt)

 

The question about restrictions is not a trick question.

The partial wave equation and tour general solution only works for one case - that of an infinite wave in an infinite medium.

All other cases introduce boundary condition restrictions to limit the choice of arbitrary functions.

Our objective is to end up with only one choice.

 

Further the choice of arbitrary funtion is not unlimited, they are at least bounded continuous functions, at least twice differentiable.

 

That's because its the topic of conversation.

 

I added my remark because, just as many forget the boundary conditions limit the choice of solution function as above, many treat the quantum mechanics of real matter as though it was just an assemblage of particles. This, of course, is not the case. As soon as you go to molecules you loose the identity of each particle and create a new structure. When you get as far as metals and semiconductors even more happens and you get effects that are impossible for single isolated particles.

 

 

 

So tan (w) is disallowed because, although periodic, it regularly goes off to infinity.

Edited July 8, 2012 by studiot

[pmb]

pmb

Sorry that was my fault for not using x as the dummy variable.

 

Replace x by w, with w=(x-vt)

In that case, noe of them are waves. G = 0 or G = constant since there is no way to make that substitution. The other functions aren't continuous so they don't satisy the wave-equations continuity condition.

 

Further the choice of arbitrary funtion is not unlimited, they are at least bounded continuous functions, at least twice differentiable.

Ah! Smart man! Way t go there laddy!

 

I added my remark because, just as many forget the boundary conditions limit the choice of solution function as above, many treat the quantum mechanics of real matter as though it was just an assemblage of particles.

And you think that's wong? Why?

 

This, of course, is not the case. As soon as you go to molecules you loose the identity of each particle and create a new structure. When you get as far as metals and semiconductors even more happens and you get effects that are impossible for single isolated particles.

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

 

So tan (w) is disallowed because, although periodic, it regularly goes off to infinity.

That's correct. Thanks for pointing that out to me. I just learned somethning new! Thanks!

[juanrga]

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

 

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

 

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.

Edited July 8, 2012 by juanrga

[Aethelwulf]

Look Juan, the wave nature of particles is certainly NOT speculation or a myth. It's a matter of hard scientific facts. 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.

 

Indeed, a particle moved as a wave through the two slits, however it exhibited a particle nature as well when it reached the screen as a ''dot''.

Edited July 8, 2012 by Aethelwulf