Particle-Wave duality and Hamilton-Jacobi equation

[Quantum River]

Particle-Wave duality and Hamilton-Jacobi equation

According to Particle-Wave duality, an observer can't describe a natural object just from its particle-nature or wave-nature, because a particle is always accompanied by a wave and vice versa.

This reminded me some interesting aspects of the classical Hamilton-Jacobi Equation. The Hamilton-Jacobi Equation is also the only formalism of mechanics in which the motion of a particle can be represented as a wave. In this sense, the HJE fulfilled a long-held goal of theoretical physics (dating at least to Johann Bernoulli in the 17th century) of finding an analogy between the propagation of light and the motion of a particle. [1]

Yes, to unite the particle equation and wave equation in one formalism is the original goal of Hamilton when he devised the HJE first. It is apparent from the name/theme from his two original papers [1].

I don't know whether Hamilton really did achieve his original goal even in the case of classical physics. I am interested in the Quantum Mechanics case. Is the Hamilton-Jacobi formalism the natural framework to describe the Particle-Wave duality?

In the one-order linear (or quasi-linear) partial differential equation, the wave of the equation could be buildup by the infinite orbits of particle motion. Could this hold in the two-order partial differential equation? I am curious why Hamilton thought he had achieved his goal, because the Hamiltonian of HJE is obvious not linear (there is the kinetic energy).

[1]:http://en.wikipedia.org/wiki/Hamilton-Jacobi_equation

 

[ZapperZ]

Particle-Wave duality and Hamilton-Jacobi equation

According to Particle-Wave duality, an observer can't describe a natural object just from its particle-nature or wave-nature, because a particle is always accompanied by a wave and vice versa.

Could you show me where exactly in the QM formalism that actually have this
"particle is always accompanied by a wave and vice versa"?

Zz.

 

[marlon]

The wave/particle paradox is a real paradox that has te be solved.

This "duality" is an inherent property of the BASIS of QM. QM gives us perfect predictions and descriptions of atomic scaled fenomena. Actually, the fact that you were able write your post on a PC is thanks to QM and thus, thanks to the particle wave duality. In light of that, tell me, what exactly needs to be solved ? What is the problem ? What suggests to you that this duality IS a paradox that needs to be solved ?

marlon

 

[ZapperZ]

I know. But may I also don't believe it. I have made an argument against it. Please look at that argument and make it wrong. The Duality is not possible in reality. You can't jump from a spread field to a local particle. Try to convince me with arguments. Don't think please that I am stupid.

However, you seem to think physicists are for blindly following something that you think you have falsified.

Also, we don't send our work to "big universities" for it to be well-known. We sent it for publishing in peer-reviewed journals, something you would have known if you have looked at where new things in physics are scrutinized.

There are no "duality" in QM. All particle-like and wave-like observations can be consistently described using one single formulation, not two. There are no paradox here to be solved, at least, not for this particular case.

I would also like to point out to you the PF Guidelines on overly-speculative posting. If your idea has not appeared in peer-reviewed journals, please do not post it here. If you still insist on discussing it, the Independent Research inside the General Physics section is the only place for it, per our rules.

Zz.

 

[ZapperZ]

Yes you may think that. I listen also to other phycists who are also making really practical receach.

That's funny. I'm an experimental physicist. I assume that's what you mean by "practical receach<sp>". So how come you don't listen to me?

Fare well I go away here

Sayonara!

Zz.

 

[lightarrow]

Particle-Wave duality and Hamilton-Jacobi equation

According to Particle-Wave duality, an observer can't describe a natural object just from its particle-nature or wave-nature, because a particle is always accompanied by a wave and vice versa.

Could you show me where exactly in the QM formalism that actually have this
"particle is always accompanied by a wave and vice versa"?

Considering that I don't want to discuss what "a particle is always accompanied by a wave and vice versa" means, can you show me where exactly Quantum River wrote that QM formalism have that?
Or, discussing about quantum physics = only discussing about QM formalism, for you?

 

[ZapperZ]

Considering that I don't want to discuss what "a particle is always accompanied by a wave and vice versa" means, can you show me where exactly Quantum River wrote that QM formalism have that?
Or, discussing about quantum physics = only discussing about QM formalism, for you?

Er.. if "quantum physics" isn't "QM formalism", what is it "quantum physics" then? If you don't know what I am referring to as "QM formalism", open a standard QM text. That is what I am asking for. Where, in a standard QM, is there such a thing as "a particle is always accompanied by a wave and vice versa".

You don't believe that the OP is referring to some exotic QM, do you? Because if you do, then you would have asked what version of this exotica he is referring to.

Zz.

 

[Demystifier]

Is the Hamilton-Jacobi formalism the natural framework to describe the Particle-Wave duality?

In my opinion, yes!
In fact, the HJ formalism represents the basis for the Bohmian interpretation of QM, in which the wave-particle duality has a clear meaning. (See e.g.
http://xxx.lanl.gov/abs/quant-ph/0609163
especially Secs. II and IV.)

 

[MeJennifer]

In my opinion, yes!
In fact, the HJ formalism represents the basis for the Bohmian interpretation of QM, in which the wave-particle duality has a clear meaning. (See e.g.
http://xxx.lanl.gov/abs/quant-ph/0609163
especially Secs. II and IV.)

Thanks for that document, I read it before and I think it is very informative!

 

[Quantum River]

In my opinion, yes!
In fact, the HJ formalism represents the basis for the Bohmian interpretation of QM, in which the wave-particle duality has a clear meaning. (See e.g.
http://xxx.lanl.gov/abs/quant-ph/0609163
especially Secs. II and IV.)

In Bohmian interpretation, the action S doesn't obey the usual Hamilton-Jacobi equation. The part of Quantum Potential is the soul of Bohmian formalism. Actually, I feel somewhat sick about the Quantum Potential. I tried lots of times to remove it and just failed all the times.

 

[Anonym]

Quantum River:” the action S doesn't obey the usual Hamilton-Jacobi equation. Actually, I feel somewhat sick about the Quantum Potential.”

I feel the same.

Quantum River:” The Hamilton-Jacobi Equation is also the only formalism of mechanics in which the motion of a particle can be represented as a wave.”

Classical mechanics is the Wave Mechanics.

 

[Demystifier]

The recent paper
http://arxiv.org/abs/quant-ph?papernum=0612217
could also be relevant here.

 

[Quantum River]

Demystifier, thanks!
I think the quantum action correction function is its main result. I must say it is very good.
I have got some of its results (in the paper you provided) too. But there are still lots of fundamental problems here.
The part of Quantum potential is like a ghost. It is always there.

 

[Demystifier]

The quantum potential is, of course, necessary in order to reproduce the standard predictions of QM with particle trajectories.
However, it is possible that there is even more about quantum potential.
For example, in
http://arxiv.org/abs/gr-qc/0611037
it is suggested that quantum potential could explain dark energy. Thus, it could be more than a ghost.

 

[lightarrow]

Er.. if "quantum physics" isn't "QM formalism", what is it "quantum physics" then? If you don't know what I am referring to as "QM formalism", open a standard QM text. That is what I am asking for. Where, in a standard QM, is there such a thing as "a particle is always accompanied by a wave and vice versa".

You don't believe that the OP is referring to some exotic QM, do you? Because if you do, then you would have asked what version of this exotica he is referring to.

A lot of questions on this forum cannot be related to QM formalism only. If what you say were true, then tens of threads should be canceled. Furthermore, the title of the Forum should be changed from "quantum physics" to " QM formalism", to make sure people know that asking things which don't belong to that formalism will have the simple answer: "not defined in the present theory".
But this Forum is intended as a "discussion about physics" or something else?

 

[ZapperZ]

A lot of questions on this forum cannot be related to QM formalism only. If what you say were true, then tens of threads should be canceled. Furthermore, the title of the Forum should be changed from "quantum physics" to " QM formalism", to make sure people know that asking things which don't belong to that formalism will have the simple answer: "not defined in the present theory".
But this Forum is intended as a "discussion about physics" or something else?

I noticed that you never did address my question. All you gave is a statement with no support.

So which part of "quantum physics" isn't part of what I consider as the "quantum formalism"?

Zz.

 

[Anonym]

Quantum River:” The Hamilton-Jacobi Equation is the only formalism of mechanics in which the motion of a particle can be represented as a wave.

CarlB:”The rules of the game are never specified, but they are known to be so sophisticated that they are difficult to imagine.”

Eventually Quantum River discuss formulation of the complete set of principal physical postulates (Rules of the Game), which is the only possible absolute result in Physics.

Let remember a “history”: A. Einstein presentation on 5-th Solvay Congress. A. Einstein opened the discussion with the statement that he personally did not contribute essentially in the development of Q.M. I know exactly what he meant: A. Einstein did not write the Equations of Motion. But in his presentation he discuss the other problem: Theory of Measurements. It’s history is very similar to the problem of mass: initially it was self-obvious that the inertial and gravitational mass are identical. GR is all about that this is not self-obvious. The measurements in the classical physics is something self-obvious, since all dynamical variables then known were what we call today self-adjoint operators with the continuous spectrum. The QM formalism (W. Heisenberg UR) demonstrated that the measurements of the same variables in QM behave differently. The theoretical physics do not exist without measurement theory. Everybody agreed with that, everybody contributed in attempt to solve a problem: A. Einstein, E. Schrödinger, W. Heisenberg, J. von Neumann, E.P.Wigner, F. London, E. Bauer,N.Bohr, M. Born, B.Podolsky, N.Rosen. It is much more than duality, but duality express it in the most clear way (without clear definition what is a particle and/or wave in CM as well as in QM). I do not want to enter in the classifications, but in my view first four principal physical postulates may be regarded as dealt with the measurements. And only the Fifth is the dynamical postulate.

What I have in mind may be considered as an additional step towards realization of a program initiated by E. Schrödinger (perhaps even by W.R. Hamilton) to treat all of the physics as wave mechanics:

The universal mathematical architecture of the physics is given in terms of ten functional - analytical frameworks, suitable to incorporate the results of the physical measurements.

Real, complex, quaternion and octonion states with real scalar product should be equivalent to the theory of classical fields. Unification of electromagnetism with gravitation should occur already in the classical field theory.

Complex, quaternion and octonion states with complex scalar product should allow realization of present unification schemes. Notice, that pure relativistic quantum electrodynamics does not exist, because there are no elementary sources of pure electromagnetic radiation. Neutrino is an elementary source of pure weak radiation.

Quaternion and octonion states with quaternion scalar product should describe wave mechanics of space-time continuum.

Octonion states with octonion scalar product should allow ultimate realization of idea of elementary particles picture of natural phenomena.

Please excuse me for something irrelevant and personal. First time I presented that at the seminar given at Technion, Haifa, 1983, Israel. On the last row in the conference room sat old man, alone. He did not ask any question during my lecture. I did not know who he was. After the lecture I remained to organize my notes. Everybody gone. He remained also. He came to me and said:” Young man, may I invite you for cup of tea?” Sure. We went to his office. Then he said:” I am Natan Rosen. You can not imagine how I sad that A. Einstein had no opportunity to listen what you told us today. He would be very pleased with it.”

Quantum River:” Actually, I feel somewhat sick about the Quantum Potential. I tried lots of times to remove it and just failed all the times.”

I wrote: “Get rid of the Quantum Potential”. I am not sure. This is only my guess. I guess that the solution of that problem will allow to justify the validity of the Principle of Least Action in CM, the physical analog of the Fifth Postulate of the Geometry and thus the Rules of the Game will be known.

But the Game will never be over, it is not possible to finish it, there is no Final Theory and never will be. The Final Theory means death of human civilization. I leave that rubbish dreams to S.Weinberg and S.Hawking.

ZapperZ:” if "quantum physics" isn't "QM formalism", what is it "quantum physics" then? If you don't know what I am referring to as "QM formalism", open a standard QM text.”

I do not understand words. I understand only the translation of the natural phenomena on the language of mathematics.

Daniel Gleekstein.

 

[lightarrow]

I noticed that you never did address my question. All you gave is a statement with no support.

So which part of "quantum physics" isn't part of what I consider as the "quantum formalism"?

A photon's position, an electron's size, time as an operator...and many other concepts that can be discussed in a "quantum physics Forum" even if they don't exist in QM formalism.

 

[lightarrow]

Quantum River:” The Hamilton-Jacobi Equation is the only formalism of mechanics in which the motion of a particle can be represented as a wave.

CarlB:”The rules of the game are never specified, but they are known to be so sophisticated that they are difficult to imagine.”

Eventually Quantum River discuss formulation of the complete set of principal physical postulates (Rules of the Game), which is the only possible absolute result in Physics.

Let remember a “history”: A. Einstein presentation on 5-th Solvay Congress. A. Einstein opened the discussion with the statement that he personally did not contribute essentially in the development of Q.M. I know exactly what he meant: A. Einstein did not write the Equations of Motion. But in his presentation he discuss the other problem: Theory of Measurements. It’s history is very similar to the problem of mass: initially it was self-obvious that the inertial and gravitational mass are identical. GR is all about that this is not self-obvious. The measurements in the classical physics is something self-obvious, since all dynamical variables then known were what we call today self-adjoint operators with the continuous spectrum. The QM formalism (W. Heisenberg UR) demonstrated that the measurements of the same variables in QM behave differently. The theoretical physics do not exist without measurement theory. Everybody agreed with that, everybody contributed in attempt to solve a problem: A. Einstein, E. Schrödinger, W. Heisenberg, J. von Neumann, E.P.Wigner, F. London, E. Bauer,N.Bohr, M. Born, B.Podolsky, N.Rosen. It is much more than duality, but duality express it in the most clear way (without clear definition what is a particle and/or wave in CM as well as in QM). I do not want to enter in the classifications, but in my view first four principal physical postulates may be regarded as dealt with the measurements. And only the Fifth is the dynamical postulate.

What I have in mind may be considered as an additional step towards realization of a program initiated by E. Schrödinger (perhaps even by W.R. Hamilton) to treat all of the physics as wave mechanics:

The universal mathematical architecture of the physics is given in terms of ten functional - analytical frameworks, suitable to incorporate the results of the physical measurements.

Real, complex, quaternion and octonion states with real scalar product should be equivalent to the theory of classical fields. Unification of electromagnetism with gravitation should occur already in the classical field theory.

Complex, quaternion and octonion states with complex scalar product should allow realization of present unification schemes. Notice, that pure relativistic quantum electrodynamics does not exist, because there are no elementary sources of pure electromagnetic radiation. Neutrino is an elementary source of pure weak radiation.

Quaternion and octonion states with quaternion scalar product should describe wave mechanics of space-time continuum.

Octonion states with octonion scalar product should allow ultimate realization of idea of elementary particles picture of natural phenomena.

Please excuse me for something irrelevant and personal. First time I presented that at the seminar given at Technion, Haifa, 1983, Israel. On the last row in the conference room sat old man, alone. He did not ask any question during my lecture. I did not know who he was. After the lecture I remained to organize my notes. Everybody gone. He remained also. He came to me and said:” Young man, may I invite you for cup of tea?” Sure. We went to his office. Then he said:” I am Natan Rosen. You can not imagine how I sad that A. Einstein had no opportunity to listen what you told us today. He would be very pleased with it.”

Quantum River:” Actually, I feel somewhat sick about the Quantum Potential. I tried lots of times to remove it and just failed all the times.”

I wrote: “Get rid of the Quantum Potential”. I am not sure. This is only my guess. I guess that the solution of that problem will allow to justify the validity of the Principle of Least Action in CM, the physical analog of the Fifth Postulate of the Geometry and thus the Rules of the Game will be known.

But the Game will never be over, it is not possible to finish it, there is no Final Theory and never will be. The Final Theory means death of human civilization. I leave that rubbish dreams to S.Weinberg and S.Hawking.

ZapperZ:” if "quantum physics" isn't "QM formalism", what is it "quantum physics" then? If you don't know what I am referring to as "QM formalism", open a standard QM text.”

I do not understand words. I understand only the translation of the natural phenomena on the language of mathematics.

Daniel Gleekstein.

Very, very interesting, Daniel. I sincerely wish you with my heart to accomplish your purpose.

 

[Anonym]

Lightarrow:” I sincerely wish you with my heart to accomplish your purpose.”

Lightarrow:” A photon's position, an electron's size, time as an operator...and many other concepts that can be discussed in a "quantum physics Forum" even if they don't exist in QM formalism.”

The purpose is to invite you to participate in the festival. It also will help you to understand what ZapperZ desperately try to explain to you:” A photon's position, an electron's size, time as an operator...and many other concepts” are inherent part of QM formalism as well as CM formalism (but Quantum world is not a Classical world).

 

[ZapperZ]

A photon's position, an electron's size, time as an operator...and many other concepts that can be discussed in a "quantum physics Forum" even if they don't exist in QM formalism.

Er... come again?

In quantum formalism, a "position", "time", etc.. are all observables with definite mathematical definitions. We don't call them operators for nothing. So where are these things not existing in QM formalism?

And as for the "size of a photon", how are you able to "discuss" such a thing when it is not defined? I mean, this isn't just some pedestrian discussion where we can simply use anything we like and not care about what exactly we mean. YOU may have your own definition of it, but how confusing do you think it would be if we ALL use our own definition? Who's to say my definition is less valid than yours? What shall we do? Look at the "standard" definition from QM? What is it then? Does QM have a clear definition of the size of a photon? Please show me where.

Just because you can "discuss" it doesn't mean that it has a well-formulated concept in physics.

So show me where else are there concepts in quantum physics that have no QM formulations.

Zz.

 

[Quantum River]

Anonym, Thanks for sharing with us your personal experience. It makes me feel a little nearer to Einstein now.
Could you explain your ten functional-analytical frameworks a little more? For example, could your frameworks circumvent the measurement problem?

 

[vanesch]

This reminded me some interesting aspects of the classical Hamilton-Jacobi Equation. The Hamilton-Jacobi Equation is also the only formalism of mechanics in which the motion of a particle can be represented as a wave.

Let us not forget that the H-J equation defines a scalar "field" over configuration space, which can only be put in bijective relationship with 3-dim space for the single-particle system. As such, the H-J equation is not a genuine field equation in "real space".

 

[Anonym]

For example, could your frameworks circumvent the measurement problem?

I hope you mean solution, not circumvention. Yes, quant-ph/0606121.
Notice that tr(ei)=0 for i=1,2,3 also and for i=1,…,7 as well.
The measurement problem is a problem within classical physics, since the measurement instruments are macroscopic. Additional explanation is presented in post #115 , The wave packet description session, discussion with Reilly. If you need clarification about Hurwitz algebras and Hurwitz theorem, I will give you.

 

[lightarrow]

Er... come again?

In quantum formalism, a "position", "time", etc.. are all observables with definite mathematical definitions. We don't call them operators for nothing. So where are these things not existing in QM formalism?

And as for the "size of a photon", how are you able to "discuss" such a thing when it is not defined? I mean, this isn't just some pedestrian discussion where we can simply use anything we like and not care about what exactly we mean. YOU may have your own definition of it, but how confusing do you think it would be if we ALL use our own definition? Who's to say my definition is less valid than yours? What shall we do? Look at the "standard" definition from QM? What is it then? Does QM have a clear definition of the size of a photon? Please show me where.

Just because you can "discuss" it doesn't mean that it has a well-formulated concept in physics.

So show me where else are there concepts in quantum physics that have no QM formulations.

Zz.

I wrote "an electron's size". Is it defined in QM formalism? If not, why on this Forum, people more clever than me sometimes discuss about it, about if an electron is pointlike or not?

 

[ZapperZ]

I wrote "an electron's size". Is it defined in QM formalism? If not, why on this Forum, people more clever than me sometimes discuss about it, about if an electron is pointlike or not?

I'm not sure how this has degenerated into the issue of a discussion in this forum.

Remember, your initial claim made it appear to be that there is a difference between "quantum physics" and "quantum formalism", the latter being the phrase I had used (and is often used in other instances and books). I continue to ask for examples to support your claim. Somehow, you have managed to change this into an issue of what is being discussed on here.

If someone talks about the 'size of [insert favorite item here]', then one must always look at how that [insert favorite item here] is defined. If someone thinks there is a size of an 'electron', then I'd like to hear how such a thing is measured, especially when in a standard formalism, we simplify our theory by adopting a point particle. We still see no deviation between that simplification and what we observe YET. Thus, anyone claiming that an electron has a "size" will have to redefine all the properties of an electron and how such a quantity should be measured.

However, how is this related to my original question to you? Or is this simply nothing more than a red herring?

Zz.

 

[Anonym]

Let us not forget that the H-J equation defines a scalar "field" over configuration space, which can only be put in bijective relationship with 3-dim space for the single-particle system. As such, the H-J equation is not a genuine field equation in "real space".

I did not understand your argument. In my discussion with Quantum River I have in mind Ch.10, eqs. 10-3,10-4 and demonstration 10-13 that F2=S,S action (?) in H.Goldstein CM (second edition). 10-3 look like real valued SE. See also discussion in the paragraph 10-8.

 

[marlon]

I wrote "an electron's size". Is it defined in QM formalism? If not, why on this Forum, people more clever than me sometimes discuss about it, about if an electron is pointlike or not?

Because we try to explain to people (like you) why it does NOT exist or why such questions violate the QM formalism. We also try to explain why classical concepts like point particle need to be properly defined etc etc

marlon

 

[Anonym]

Marlon:” Because we try to explain to people (like you) why it does NOT exist or why such questions violate the QM formalism.”

I do not know who your “we” are, that try to explain to us (Lightarrow, ZapperZ and me at least and I guess Quantum River also) why and how the questions may violate the QM formalism.

ZapperZ:” Could you show me where exactly in the QM formalism that actually have this "particle is always accompanied by a wave and vice versa"?”

The answer is obvious : QED, but not the same particles or waves. Bosons by fermions and fermions by bosons. And perhaps the boson accompanied by bosons in the adequate formulation of relativistic QM will allow to define size of boson and similarly for the fermions.

ZapperZ:” If someone talks about the 'size of [insert favorite item here]', then one must always look at how that [insert favorite item here] is defined. If someone thinks there is a size of an 'electron', then I'd like to hear how such a thing is measured, especially when in a standard formalism, we simplify our theory by adopting a point particle. We still see no deviation between that simplification and what we observe YET. Thus, anyone claiming that an electron has a "size" will have to redefine all the properties of an electron and how such a quantity should be measured.”

What ZapperZ said is what I know. I do not know anything else. The only thing that the theory must do is to explain it.

I did not participate in that part of our discussion. Simply, I have no idea, but I am working on that now.

Let me explain what I mean. The first time when the size of QM system (atom) was calculated (explained) to best of my knowledge and memory was Ph.D thesis of A.Einstein (if somebody feel nervous that I almost always refer to A.Einstein, notice that I am not responsible for that, he is responsible). He took a macroscopic box and used Avogadro number to obtain the delta x>0. For point-like object one would obtain delta x=0 and instead Avogadro-infinity. The statmechguys said that he calculated not a size of the atom but the size of the space occupied by that atom. However, A.Einstein got the right answer (1 or 3.23 angstrom does not a matter). Now came W. Heisenberg and tell us that in QM delta x*delta p>0. Then came J. von Neumann and tell us that in the macroscopic physics delta x should be=0 . Now I say may be that is not necessary, only delta x*delta p=0. Now Reilly say that delta x must be >0. And now ZapperZ say that in relativistic QM (high energy physics) delta x must be =0.

Lightarrow, if that story do not sound for you fascinating, you are not a physicist. That what I meant when invite you to participate in the festival.
I would like to attract your attention to the beautiful explanations given by StatMechGuy in the Energy Vs Information session when I asked him the identical questions using the statistical mechanics formalism.

Edit: I did mistake above (corrected). Everything consistent with delta x=0. Perhaps,it may be used as definition what point-like object (particle) means in wave mechanics. Obvious. Bounded fermion is extended object. Free moving fermion/boson is point-like. ZapperZ what do you say? If so, the gluons are not point-like!Thanks to everybody.

 

[marlon]

Marlon:” Because we try to explain to people (like you) why it does NOT exist or why such questions violate the QM formalism.”

I do not know who your “we” are, that try to explain to us (Lightarrow, ZapperZ and me at least and I guess Quantum River also)

Don't use the Marlon versus everybody else in this thread analogy because it is wrong. At least, Zz should be at MY side because i am saying the very same things.

why and how the questions may violate the QM formalism.

An electron's "position" violates the HUP. A photon's size contradicts with the DEFINITION of a photon. A size is a spatial coordinates thing whuile a photon is a point particle in an energy base. At least, take the effort of defining what you mean to say ...

ZapperZ:” Could you show me where exactly in the QM formalism that actually have this "particle is always accompanied by a wave and vice versa"?”

The answer is obvious : QED,

QED ? Really ? What wave is associated with, let's say an electron ? What is the equation in QED ? This is certainly new to me.


marlon

 

[Anonym]

Don't use the Marlon versus everybody else in this thread analogy because it is wrong.

I know that. But you use the provocative stile instead relevant discussion.
I pay you in your own coin.

At least, take the effort of defining what you mean to say ...

And you did not read what I already said:”I am working on that now.”

 

[dextercioby]

An electron's "position" violates the HUP.

I don't think so.

Daniel.

 

[vanesch]

I did not understand your argument. In my discussion with Quantum River I have in mind Ch.10, eqs. 10-3,10-4 and demonstration 10-13 that F2=S,S action (?) in H.Goldstein CM (second edition). 10-3 look like real valued SE. See also discussion in the paragraph 10-8.

I don't have the book handy, but have some souvenirs of that chapter. The point I was simply making, is that the H-J equation is a partial differential equation of a function S(q1,q2,...qn,t). If the system consists of more than 1 point particle, then this S does NOT correspond to any field over real space, which should be a function F(x,y,z,t). It is only in the case of a single point particle that the configuration space is 3-dim, and can be parametrized by x,y, and z. As such, S is not a "wave" or a "field" in real space (the x,y,z space), but only over configuration space (the q1,q2,...qn space).

 

[Anonym]

I don't have the book handy, but have some souvenirs of that chapter. The point I was simply making, is that the H-J equation is a partial differential equation of a function S(q1,q2,...qn,t). If the system consists of more than 1 point particle, then this S does NOT correspond to any field over real space, which should be a function F(x,y,z,t). It is only in the case of a single point particle that the configuration space is 3-dim, and can be parametrized by x,y, and z. As such, S is not a "wave" or a "field" in real space (the x,y,z space), but only over configuration space (the q1,q2,...qn space).

What I have in mind is entire reformulation of the classical physics in terms of functional analysis. Then it will be a functional.

 

[marlon]

I know that. But you use the provocative stile instead relevant discussion.
I pay you in your own coin.



And you did not read what I already said:”I am working on that now.”

This is all very nice but how about talking QM, ok ? Let's go back to the electron's position stuff.

marlon

 

[Anonym]

how about talking QM, ok ? Let's go back to the electron's position stuff.

Sorry, Marlon. It is just personal feature. I am not able to talk when I have no idea what I am talking about. You invite me to discuss the relativistic QM, not it's non-relativistic limit. If and when I will have an answer, I will talk.However, I am optimist. " Raffinert ist der Herr Gott, aber boshaft ist Er nicht"

 

[marlon]

Sorry, Marlon. It is just personal feature. I am not able to talk when I have no idea what I am talking about. You invite me to discuss the relativistic QM, not it's non-relativistic limit. If and when I will have an answer, I will talk.However, I am optimist. " Raffinert ist der Herr Gott, aber boshaft ist Er nicht"

It's not going to be THAT easy. I asked you a specific question in post 38 concerning your claim "that a particle is always accompanied by a wave in QED". Why won't you answer that question.

Also, i explained to you why we cannot be talking about stuff like "a photon's size" because it violates the ONLY existing QM formalism.

marlon

 

[vanesch]

What I have in mind is entire reformulation of the classical physics in terms of functional analysis. Then it will be a functional.

In post #23, I was just making the objection that quantum river seemed to imply that in classical physics, particles are guided by a wave (I took it: a field in real space, of the F(x,y,z,t) kind) which was given by the function S in the H-J equation. This is only possible in the case of a single particle, because only there, S corresponds potentially to a function of the kind S(x,y,z,t) which can be a genuine field in space.
The S in the H-J equation *can* be seen as a "field", but over configuration space, in which the entire world is just one point, and then this field guides the "world point" in configuration space.

 

[Anonym]

The S in the H-J equation *can* be seen as a "field", but over configuration space, in which the entire world is just one point, and then this field guides the "world point" in configuration space.

That sounds similar to what we are doing when we introduce Fock space and second quantization. What do you think?

 

[vanesch]

That sounds similar to what we are doing when we introduce Fock space and second quantization. What do you think?

Of course, that's a basic postulate of quantum theory: superposition ! A quantum state being a superposition of all non-quantum states (points in configuration space), this automatically defines a "field" (wavefunction) over the previous configuration space, where the "field values" are nothing else but the complex weights in the superposition. The configuration space in the non-quantum version becomes the index space of a basis for quantum state space (= hilbert space). That's exactly what happens in the Fock space description: to each individual non-quantum E-M configuration corresponds a basis vector in Fock space - although these are not the usual basis vectors in Fock space, which is usually spanned with the eigenvectors of the (E,P) observables, and not the EM configuration states.

 

[Anonym]

Of course, that's a basic postulate of quantum theory: superposition ! A quantum state being a superposition of all non-quantum states (points in configuration space), this automatically defines a "field" (wavefunction) over the previous configuration space, where the "field values" are nothing else but the complex weights in the superposition. The configuration space in the non-quantum version becomes the index space of a basis for quantum state space (= hilbert space). That's exactly what happens in the Fock space description: to each individual non-quantum E-M configuration corresponds a basis vector in Fock space - although these are not the usual basis vectors in Fock space, which is usually spanned with the eigenvectors of the (E,P) observables, and not the EM configuration states.

First of all: thank you. But what you mean "these are not the usual basis vectors in Fock space, which is usually spanned with the eigenvectors of the (E,P) observables, and not the EM configuration states"?

 

[Anonym]

It's not going to be THAT easy. I asked you a specific question in post 38 concerning your claim "that a particle is always accompanied by a wave in QED". Why won't you answer that question.

Marlon, come on! Renormalization.

 

[Anonym]

If someone talks about the 'size of [insert favorite item here]', then one must always look at how that [insert favorite item here] is defined. If someone thinks there is a size of [insert favorite item here], then I'd like to hear how such a thing is measured, especially when in a standard formalism, we simplify our theory by adopting a point particle. We still see no deviation between that simplification and what we observe YET.

I did mistake above (#29, corrected). Everything consistent with delta x=0. Perhaps,it may be used as definition what point-like object (particle) means in wave mechanics. Bounded fermion is extended object. Free moving fermion/boson is point-like. If so, the gluons are not point-like. Excuse me that I am lazy. What we see in deep-inelastic? Only quarks, right? Why we do not see gluons? May be they are “blurred” over entire volume of the hadron?

 

[marlon]

Marlon, come on! Renormalization.

Sorry, that was post 30...Anyhow, no i don't get it...renormalization ? Besides, i asked for an equation of that wave that accompanies a particle in QED. Why won't you give me that equation ? Answering with renormalization is a bit hollow and basically useless.

marlon

 

[marlon]

If so, the gluons are not point-like. Excuse me that I am lazy. What we see in deep-inelastic? Only quarks, right? Why we do not see gluons? May be they are “blurred” over entire volume of the hadron?

But a gluon is defined based upon the colour quantumnumber. Why are you then talking about the gluon's "position" in a hadron ? Don't you see the flaw in that ? Same goes for what you say about photon size BTW.

marlon

 

[lightarrow]

I'm not sure how this has degenerated into the issue of a discussion in this forum.

Remember, your initial claim made it appear to be that there is a difference between "quantum physics" and "quantum formalism", the latter being the phrase I had used (and is often used in other instances and books). I continue to ask for examples to support your claim. Somehow, you have managed to change this into an issue of what is being discussed on here.

It is in what you write after:
"If someone talks about the 'size of [insert favorite item here]', then one must always look at how that [insert favorite item here] is defined. If someone thinks there is a size of an 'electron', then I'd like to hear how such a thing is measured, especially when in a standard formalism, we simplify our theory by adopting a point particle. We still see no deviation between that simplification and what we observe YET. Thus, anyone claiming that an electron has a "size" will have to redefine all the properties of an electron and how such a quantity should be measured."

If in theory is adopted a point particle for the electron, then the value of it's size is defined: it is zero. But, at the same time, the electron's size is not defined in QM formalism, so how can we know its value?. It's this that I don't understand.
As you always point, and I thank you for this, we must always give precise definitions of concepts, especially in quantum physics. Are we well aware (I'm not) of what are the consequences of assuming the electron as point like?
I know this has worked well, up to now, however I don't believe the electron is point like; at the same time, I still don't know if and how would be possible to create a definition for an electron's size.

 

[ZapperZ]

If in theory is adopted a point particle for the electron, then the value of it's size is defined: it is zero. But, at the same time, the electron's size is not defined in QM formalism, so how can we know its value?. It's this that I don't understand.

But you seem to have missed the point of that reply from me that you quoted. It is a matter of CONVENIENCE that we select these things to be "point particle" and that so far, this convenience WORK. However, nowhere in the formulation is the property of the width of it is DEFINED!

Secondly, we are now playing with semantics. You are adopting the "x=0 is not the same as x is undefined" concept. While I agree that technically this is correct, it doesn't fit into this scenario. Why? Because if you want to be absolutely technical about it, setting something to have a width of zero means that that something isn't there! We're not talking infinitesimal here, we're talking about ZERO. So that object isn't there! Yet, how could it have a mass, charge, and can collide with other particles and make itself known? So herein lies the contradiction.

So by calling an electron to be "point particle", we IGNORE the issue of its width till we know more to be able to address it. Till then, the concept of an electron being "point" particle works in the majority of the situation we deal with. But by doing that, does that mean the width of an electron is well-defined? Nope! Just because I can set the geometry of a cow on Alpha Centauri to be a sphere doesn't mean that it is. That is why you don't see anywhere in the Particle Data book the radius of an electron being set to zero.

But where in here is the example of "quantum physics" different than "quantum formalism"?

Zz.

 

[marlon]

If in theory is adopted a point particle for the electron, then the value of it's size is defined: it is zero. But, at the same time, the electron's size is not defined in QM formalism, so how can we know its value?. It's this that I don't understand.

First of all, a point does not have a size equal to zero. "Nothing" has a size which equals zero. You should have written "the size of a point particle has zero dimensions"

Now, a photon is a point particle in the energy base. Just like in a spatial coordinate base (like the Euclidean frame of reference) where the points denote coordinate values, the points of the energy base denote energy values. A photon is nothing more than such an energy value and thus a point in the energy base. It is with respect to this base that a photon is a point particle with zero dimensional size (which is NOT the same as saying that the size is zero). Again, a photon is NOT a point particle in a spatial base so it is NOT defined as an object with finite spatial boundaries.

marlon

 

[lightarrow]

..the DEFINITION of a photon. A size is a spatial coordinates thing whuile a photon is a point particle in an energy base.

Can you explain me better the exact definition of photon? I have never found it; the only one I have found is "quantum of energy in the electromagnetic field".

 

[marlon]

Can you explain me better the exact definition of photon? I have never found it; the only one I have found is "quantum of energy in the electromagnetic field".

Not a quantum of energy in the electromagnetic field but a quantum of energy ASSOCIATED to the electromagnetic field. The "association" is ofcourse the quantisation of the EM waves. That is all

marlon