What De Broglie has said about wave-particle duality have been highlighted with underline and Yellow colors in attached paper (Nobel lecture by De Broglie himself).

Dear Sofia D. Wechsler ,

You forget your pet theory QFT ? How Sad !!! ....

In QFT, there are creation and annihilation operators. Both of these VIRTUAL operator do everything...Literally everything in VIRTUAL WORLD... In real world, there is no argument which can support your claims. There is a very similar process, called Quantum tunneling, but in quantum tunneling, particle tunnel from one space into another. But once particle tunnel, it locate completely in one side (probability is absolutely equal to 1. Many device like Resonance tunneling diode, SQUID, Spacer of read-head in hard drive working on this principle )

Sofia D. Wechsler ,

I think that dealing with relativity of simultaneity with a non-relativistic quantum mechanics show problems that are inherent to theory, which is not Lorentz invariant. If you make a Lorentz transformation on the Schrodinger equation for the confined particle, you may find a different equation, wich don't even describe the same kind of problem. So, the frame where particle disapear may be observing a completely different system (here, I make an analogy with eletromagnetic waves equation: if you make a Galileo transformation , you will find a diffent equation that don't even describe a electromagnetic wave. Same thing occurs when we Lorentz-transform Schrodinger's equation). Also, the violation of conservation of the number operator is surely a problem that shows the incompatibility between "classical" quantum mechanics and relativity. But this in not a problem in a relativistic quantum theory like QFT.

About the experiment: I am not used to work in a lab, so I am not aware of experimental complications. But, would be possible to put a ionized material in the inacessible area? For instance, think about a experiment where you put a fermionic gas in a box, and there is a potential barrier in the middle of the box, where the probability to find a particle is null. Now, in the middle of the potential barrier, you put a ionized material. If the particle just dissapear at one side and reappears at the other, you will observe nothing, but if the particle "pass through" the potential, it will be captured by the ionized material. Again, i'm not an eperimentalist, so I can be talking a lot of nonsense.

The example you cite appears to be a standing wave function such as an atomic p-orbital wave function created by two electrons with opposite spin with a node in between. The node by definition is a region of wave cancellation where neither of the two electrons can exist. This can be demonstrated utilizing an elastic band or rubber tubing set to vibrate at given frequency that possesses two constructive interference standing waves (anti-nodes) and one destructive interference node in between. The probability of capturing one of the electrons in the destructive interference node is essentially zero. In order to do so, the standing wave function would have to be destroyed (collapsed) by the experimenter which would which would result in a voided trial.

I admire your innovative thinking. Pease keep working at it and you will find unexpected results.

Sincere Regards,

Daniel Van Gent, M.S., M.H.P.

Gokaran,

If yu talk with me in a mocking style, our good relations would change. I have n o "pet theory". You didn't read the question properly. I didn 't speak of a system with variable n umb er of particles but about ONE particle. In my system the number of particle is conserved.

@ Marcos,

Thanks for the prompt reading of my question.

Now, I didn't speak of the Schrodinger equation.

About your proposed experiment, please see, I can't afford working with a gas, I need an experiment with one particle at a time, otherwise I won't be able to check whether the particle disappeared "here" and re-appeared there.

Besides, the things are very difficult. As you know, if I detect the particle "here", the "collapse" would ensure that in any next experiment the particle be found also "here". This is why I invited people to make proposals - maybe someone would come with some smart idea.

@ Daniel Van Gent,

Many thanks for your good words!

Now, my problem is sharper than you described. It's not a wave-function with a node, but a wave-function of type ( |a> + |b>), i.e. the particle may be either in the region a or in the region b, and these two regions are distant from one another, and in between the wave-function is null.

Best regards,

Sofia

Dear Sofia,

In fact, the key to solving quantum puzzles is by understanding the reality of the motion and how it occurs, and yes I think that the motion is a sequence of appearances and disappearances events in space and time.

but how can we apply our physics formulation like relativity (that is based on continue formulation) to the discontinuous motion?

I think we need some Technics here, the first idea come in place is to apply the relativity as mean values, so in mean values, the velocity should be is < c , but the instantly velocity can be > c.

I put some idea to resolve this issue in my paper:

Preprint The theory of disappearance and appearance

I hope from God to give you some time to read it :)

With best regards.

Lovely Mazen,

I would gladly read your article. But I don't believe in such a thing that a particle disappears from one region of the space, and re-appears in an other region, eventually, very distant. You see, if such a thing would happen, then we could find frames of coordinates according to which the particle disappears from the space for an interval of time. Also, we could find frames of coordinates by which a particle multiplied itself, i.e. it apears for a while in both regions.

We can do many theories - as people say in my country "the paper bears anything" - i.e. we can write whatever we want. You have to CONVINCE me to believe in such an idea, not to show me a theory based on it.

With kind regards,

Sofia

Well, would not tunneling have some characteristic you are looking for?

You still have to get into the problematics of tunneling time, a popular topic, with little current agreement. Some facets of tunneling are alredy known.

With the uncertainty principle maybe you can borrow the energy needed

to get over the hump, in a short enough time.(but this is not really current thought)

Rather they propose a decreasing wave function in the barrier region, within schrodinger.

@ Juan,

Unfortunately, no! Tunneling is peanuts for a case when the distance between the regions is meters or much more. Moreover, tunneling is for passing through a barrier along which the wave function is not null, where in my case in the space between the two regions the wave-function is null.

I just want to stress that the problem I pose is of huge importance in the question whether the so-called wave-particle duality is real, or, the concept of "particle" is wrong. I mean, whether there are no "particles" and no duality, only waves. If you can afford a few minutes, please read section 5 of my article, and the section 6 (conclusions)

Deleted research item The research item mentioned here has been deleted

You'll see what I talk about.

With kind regards!

My Dear Sofia,

First thank you for your kindness.

We have some details here:

I assume that the particle first appears in point A and is still in this point during some time, then disappear for a while time then appear in point B etc..., so we have here 3 events:

1- the appearing in point A.

2- disappearing from point A.

3- appearing in point B.

we can safely apply the special relativity between event 1 and event 3 because the mean velocity between these events is < c, in this case, we didn't have any violation of the number of particles etc..., but maybe we have a violation if we applied the relativity between the two events 2 and 3 (because, in this case, the instant velocity maybe > c),

but in the real world, I think we always encounter only the events of type 1 and 3 !, because I claimed that the wave collapse is exactly the appearance event (like 1 and 3) and if we try to do another measure very quickly (after the collapse event) we prevent the motion itself (that mean we delay the event 3) as we know in "Quantum Zeno effect", so it is very difficult to view the intermediate event 2 ! and I don't have any idea about how we can catch this event in real experience.

With best regards.

Dear Mazen,

I am not covinced that particles disapear from the space for some time. Besides, a wave-function which is an eigen-function of the number operator, does not permit disappearace as you say.

Best regards!

Well, after this discussion, I would say that a phenomena with your requirements simply does not ocurr. Conservation of matter , interprated locally, is a requirement of the quantum theory.( at least in Schrodinger like)

My Dear Sofia,

In my theory, if ε is the duration during which a moving particle exists before disappearing and if µ is the duration of the particle's disappearance then we have that:

µ

@ Thierry De Mees

"Louis de Broglie would certainly not say it like that. He would rather say: the appearance of a wave as a particle."

I feel that bthere is wisdom in this statement, but I don't work in plasm a domain.

Thierry, please be kind and read in my article

Deleted research item The research item mentioned here has been deleted

at least the sections 5 an d 6. They are very short. You'll see my arguments against a "particle". In short, this "particle" should undergo constructive and destructive interference".

What De Broglie has said about wave-particle duality have been highlighted with underline and Yellow colors in attached paper (Nobel lecture by De Broglie himself).

This question arises precisely because, the essence of the quantum phenomena is not understood, appreciated or accepted, even after more than a century of its practice. The fact is that it is a novel and revolutionary aspect of objective reality that no one could even anticipate in their wildest imagination before; and represents a point of departure for epistemology and for physics. The quantum phenomena is unintuitive to conventional world view of causality, continuity, certainty, determinism etc., because these concepts cannot be extended to the quantum level. But the force of habit and historical practice are so great that these concepts are taken for granted as a priori truths, because these are the only ones humanity experienced at macroscopic scale of its life and history! Only a materialist dialectical epistemology based on "chance and necessity" and on the exactly opposites notion of causality, can understand the quantum phenomena:

https://www.amazon.com/Philosophy-Space-Time-Whence-Cometh-Matter/dp/984041884X

Even the venerable uncertainty principle is interpreted as mere statistical uncertainty (only a measurement problem!) by all physicists of a false divide of the two polar opposites of causality, Einstein vs. Bohr. The effort to preserve “logical continuity” has pushed classical materialism (an opportunist mis-match) to extreme polarization – on the one hand to the crass French materialism of de La Mettrie (L’homme Machine) and by extension to the absurdity of "the infinite worlds” and on the other to the “Positivism” (theism) of Bishop Berkeley - the two extreme ends of causality!

The facts are that:

1. The conservation laws (of energy/mass) in physics and thermodynamics, including "Ex nihilo nihil fit" of philosophy and theology breakdown at quantum level and creation “ex nihilo” is practically feasible! https://www.scientificamerican.com/article/something-from-nothing-vacuum-can-yield-flashes-of-light/

2. Heisenberg’s “uncertainty principle” is not just a statistical problem as is commonly assumed, Nature at quantum level is fundamentally uncertain. This fact has both scientific and philosophical foundation: "Are you certain Mr. Heisenberg"?

https://phys.org/news/2012-01-heisenberg-deepen-quantum-uncertainty.html

Also, https://www.tuwien.ac.at/aktuelles/news_detail/article/7357/

3. It is possible to conceive of an explanation of the wave/particle duality and "the particle jump" of the quantum phenomena on the basis of the "Virtual Particles" of the quantum vacuum: Article Real/Virtual Exchange of Quantum Particles as a Basis for th...

@ Abdul Malek

I read your article. But I don't understand where from did you take the formula of the rate of exchange R?

Another issue: Assunme that the particles with which we have to do are not electrons or positrons, but big particles as atoms or molecules. Which virtual paticles do you think that exist for them? Does any theory say that there exist virtual huge molecules as fullerenes or porphyryn?

@ Gokaran,

Many thanks! The de Broglie theory is old, today not very accepted, but his Nobel prize article has to be in the database of articles of any physicist.

Again, thank you

Sofia D. Wechsler

Thanks for your response:

1. The exchange rate is explained in the article. it has to depend on the length of time of the existence of a quantum particle in the system under consideration, assuming that the excange rate with the virtual particles is very very high, compared to any other parameters. In other words, the distance or volume the quantum particle covers in unit time.

2. The real/virtual exchange strctly applies to fundamental particles - real or virtual. Though not related to your question, I would like to bring to your attention a fact, which I have asserted in my decade-long debate (as "futurehuman") in the Guardian, specially related to the LHC that the so-called "Higgs boson" (if it was really "discovered", which I doubt because I have pointed out how their conclusion is contrived), could be a virtual particle of the quantum vacuum.

As for the wave/particle duality of larger particles like atoms molecules like fullerings etc., I am not sure how authentic the claims are, even if very tenuous. In any case, would you admit that my interpretation of the wave/particle duality is relatively more realistic and credible than the "infinite path" formalism of Richard Feynman and the mathematical trick of renormalization? Paul Dirac said that "renormalization" is like sweeping and hiding the infinity dirt under the rug!

Those who have doubt on wave-particle duality, MUST explain these experiment without any "IF" and "BUT".... Here are the experiment:

(1) Photoelectric effect

(2) Compton Effect

(3) Davisson and Germer experiment

(4) Electron Diffraction from any Crystal structure

(5) Transmission Electron Microscope working principle (Why one get Images from electron transmission through thin film)

In Last, Science does not drives by FAKE THEORY and FAKE assumption like virtual particle, virtual photon (which violate conservation of energy and the second law of thermodynamics )propagated by Feynman and Dirac.... Science drives by HARD FACTS which can be proven repeatedly in any LAB without any "IF" and "BUT"....

Here is one experiments where uncertainty principle has been BROKEN DOWN ... https://phys.org/news/2012-09-scientists-renowned-uncertainty-principle.html

Imagine, if uncertainty principle turns WRONG, then what will happens to QFT/QCD ...

@ Gokaran Shukla

GK> “Imagine, if uncertainty principle turns WRONG, then what will happens to QFT/QCD ...”

I am sorry to say that you seem to have been carried away by the grossly misleading headline (quite common for science report in Physorg!) and misunderstood the essence of the article you cite. Also, either your comment is a humour or you seem to be confused about the quantum phenomena (wave/particle duality, Virtual Particles etc.) and the difference between quantum electrodynamics (QED), which consider discrete matter particles as the basis of objective reality at the most fundamental level vs the Quantum Field theories (QFT, QCD) etc., which consider “continuous field” (no discrete particles) as the basis of objective reality, like the “spacetime field” of general relativity (GR). Discrete particles and the uncertainty principle are of no or secondary importance to the “field based” theories, because field are continuous (no jump possible), deterministic, have certainty, follows the rules of cause and effect like we see in everyday life experience, etc. In wave concept, the particles are only wavelets, or (so to say) droplets of the field, like the relation of the Higgs boson to the Higgs field. The "field" concept was introduced into the quantum phenomena to nullify "uncertanty principle " and avoid "God playing with dice" and make it compatible to causality and GR.

QED, (the basis of my article referenced above) deals with the uncertainty principle, wave/particle duality, virtual particles etc. QED was developed mainly by Heisenberg and Dirac. The predictions of QED like the antiparticles, virtual particles etc., have been well established experimentally and are practiced in reality like the positrons in PET, Virtual Particles as Casimir force etc. Virtual Particles of the quantum vacuum can be made real particles (creation from nothing!), if enough energy corresponding to their mass equivalent is available like the report in Scientific American or the perported "Higgs boson" that I gave reference above. The presence of the virtual particles in the quantum vacuum affects the electronic energy levels for example in the hydrogen atom, causing a shift from the calculated energy level, known as the "Lamb Shift". The experimental measurement of the Lamb Shift represents one the most precise ever in modern physics.

The experiments reported in the Physorg articles did not prove that the uncertainty principle is “wrong” and/or doubtful. On the contrary, they proved the real essence of the quantum phenomena that I asserted in my comment above; this is not a simple measurement problem as was wrongly interpreted or assumed by Heisenberg and others; the objective reality itself at quantum level is uncertain. As one of the reports says as the final words (at the end), “The uncertainty principle is of course still true", the researchers confirm. "But the uncertainty does not always come from the disturbing influence of the measurement, but from the quantum nature of the particle itself."

Dear Abdul,

Have you read that Article that I have shared? Let me quote again ""Each shot only gave us a tiny bit of information about the disturbance, but by repeating the experiment many times we were able to get a very good idea about how much the photon was disturbed,"

(1) Do you know what does it mean that "How much the photon was disturbed" ?

(2) Do you know that QFT/QCD break conservation of energy principle? Also, Do you know that Nature will never give you required amount of energy at equilibrium? There must be any sort of gradient (read my paper "Flaw in Maxwell-Demon Paradox", and "Flaw in Crooks Fluctuation theorems", if you have no clue about it ) between Surrounding and System for energy flow. This is nothing but the Second law of thermodynamics. QFT/QCD breaks these two soul principle which Nature follows absolutely. I have already proved in another thred that if conservation of energy break any short period of time, then it will break for every finite time period. Which means you WILL NEVER able to use conservation of energy principle in any experiments. Do you know the consequence of breaking of conservation of energy principle???

(3) Casimiri effect can be explained very well using Max Planck Black body theory... Seems you have no clue that why Max Planck body theory Nature follows absolutely..

(4) There is NO antiparticle in nature... Don't rely on fake experiments. Two particle move clockwise and counter clockwise due to SPIN, it has nothing to do positive charge or negative charge....

(5) Do you know that value of charge is as FUNDAMENTAL as Planck constant? See how the electric charge value has been deducted from SLOPE of the experimented data by Mulliken in 1911...

(6) Your DIRAC was FRAUD at highest scale. He even suggested that there will be monopole in nature, without knowing the fact that why magnetic lines forms close loop.....He even suggested that Nature constant such as permitivity, permeability, speed of light, Planck's constant, value of electric charge changes as function of time with millions year time period.... He was such a FRAUD that he thought that all Nature constant which is nothing but the SPACE property will change as a function of time...

(7) Uncertainty principle is WRONG... Quantum Mechanics is very Successful and Uncertainty principle , and ENTANGLEMENT has No role in this success... Live example are Density functional theory and BCS theory which is purely based on non-relativistic Schrödinger equation .. There are no role of Entanglement and uncertainty principle in DFT...

(8) QFT/QCD is a virtual theory only applicable to virtual particle..... So hold your horse and enjoy with your Virtual world... Any way these two (QFT/QCD) FAKE theory will die own natural death.... Wait few more year...

In last, GR is absolute CRAP theory.... The day Black hole will exist, your existence in this NATURE will be vanished... (Read my paper "Impossibility of Black holes in Nature" if you want why Black hole will NEVER exist)

Gokaran,

It is fully permitted to have doubts on whatever theory But I don't want in my thread calumnies. All the time you say "Fake theories". Please express your doubts in polite words, and it would be legitimate.

Now, what's your problem with the photoeletric effect? I doesn't prove much. The excited levels of an atom do not form a continuum, they are discrete.

About the Compton effect also, what's your problem? We have no wave-particle dualty, X-rays and gamma rays are small wave-packets, their movement can be considered AS A WHOLE i.e we deal with the movement of the center of the wave-packet.

But, I don't understand, why do you ask such questions? You are supposed to know these things. You see, you blame certain theories, but, on the other hand there are basic facts in QM that you do not understand. It's a common human sin to try to discredit things that one does not understand. But for a scietist, it's just low level. So, if you don't understand something and it seems to you wrong, ask questions, don't blame. Alternatively, prove that it is wrong, otherwise, saying that "fake theories" is just calumny. Stay away from such a behavior.

Dear Sofia,

(1) Do you know why Compton got Noble prize???

If you don't know then here is the answer:

He got Nobel prize because he showed Particle nature of light without any doubt... So hold your horse that these are the basic thing and I don't know.. I know much better than you (Sorry to say it)

(2) Do you know Why Einstein Got Nobel prize?

Here is the answer: He explained Photoelectric effect with the Particle nature of light (after Max Planck Black body discrete energy)

(3) Do you know why Davission and Germer got Nobel prize?

Here is the Answer: Both shows wave nature of Electron after performing electron Diffraction with single crystal. Later many scientist did same experiment with poly-crystal and found diffraction patter with electron beam .

(4) Do you know Why TEM works?

Here is the answer: Because of the wave nature of electron( De Broglie wave).

(5) You said that De-Broglie theory become old and cut no ice... Do you know why every matter have wave associated with themselves?

(6)Also, do you know "why" Atoms have stationary orbits?

(7) If any theory breaks the second law of thermodynamics then that theory MUST be fake.. "Great Scientist Arthur Eddington has said it . Let me Quote again : “The second law of thermodynamics holds, I think, the supreme po-sition among the laws of Nature. If someone points out

to you that your pet theory of the universe is in dis-

agreement with Maxwell’s equations-then so much the

worse for Maxwell’s equations. If it is found to be con-

tradicted by observation, well, these experimentalists do

bungle things sometimes. But if your theory is found to

be against the second law of thermodynamics, I can give

you no hope; there is nothing for it but to collapse in

deepest humiliation"

QFT/QCD breaks the second law of thermodynamics. You might be emotionally attached with QFT/QCD/GR , but don't expect other rational thinkers will also do the same

Dear Gorakan,

I am sorry; I cannot afford the time to deal with all the issues you have raised. I assume that these are your personal views and there is no point in arguing about personal opinion or belief! If you see my RG profile, my comments in RG and the Guardian (as “futurehumn”), my published articles and books; you would see that I am the most consistent (and also probably the most hated) opponent of the “Field” based theories like GR, QFT, Higgs field etc. For me as a dialectical materialist; discrete/particulate "matter" and "motion" (and not "continuous field") are the primary attributes of objective reality. There can be no matter without motion and no motion without matter!

My comment here is based on what is experimentally established and used in practice. You still did not understand what the reports in Physorg says. The uncertainty principle was previously interpreted as a measurement problem only; Heisenberg and others did not consider the possibility (fact) that the quantum phenomena is a new (previously unknown) attribute of objective reality and that Nature at microcosm is inherently uncertain.

Heisenberg in his thought experiment assumed that to view the position of a quantum particle like an electron for example, you need a microscope with a very high energy (gamma ray) photon beam; photons with high momentum, such that they will knock (displace) the electron from its supposedly fixed position, which will bring an error in the measurement of the position of the electron. He did not think that the position of the electron (because of its quantum nature) is inherently uncertain by itself (even without being displaced by a high energy photon!)!

What the experimentalists in these reports have done, is to show that they can minimize the disturbance (assumed by Heisenberg) to be negligible, but the uncertainty of the position of the quantum particle still remains! This means that Heisenberg’s interpretation based on measument disturbance is not valid. The uncertainty problem is much more fundamental! Nature (objective reality) is inherently (for no reason or cause at all) uncertain at quantum level.

Unfortunately, this will be my last comment in this forum for now.

Gokaran,

It's YOU wo probably do not understand what is this duality. Here is a citation from Wikipedia

"De Broglie himself had proposed a pilot wave construct to explain the observed wave-particle duality. In this view, each particle has a well-defined position and momentum, but is guided by a wave function derived from Schrödinger's equation. . . . . the wave-particle duality vanishes, and explains the wave behaviour as a scattering with wave appearance, because the particle's motion is subject to a guiding equation or quantum potential. "This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored",[19] J.S.Bell. "

The duality means that the quantum object propagates as a wave, but on a photographic plate it leaves a single spot, as a particle. This is why de Broglie and Bohm supposed that INSIDE a wave-packet there is some small particle and that it's this particle that leaves the spot on the photographic plate.

The duality is not a issue in some high energy experiments, where the whole wave-packet is small, and can be taken in en tirety for a particle, without looking for a particle inside the wave-packet.

Dear Abdul,

You said that nature is uncertain at quantum mechanical level...

Do you have any experimental evidence?..

But I do have theoretical evidence ( Bands analysis) using DFT that nature is very certain at each level...

You wrote that experiment done by neutron spin did not break the uncertainty principle because of experimental limitation ..

Please tell why any rational mind does not assume that uncertainty arises due to the pure experimental limitation of measuring two non commutative variable, and it has nothing to do with Nature uncertainty? Listen what De Broglie said about the uncertainty.. https://www.youtube.com/watch?v=stRrf4DB_3Y

Dear Sofia,

You could have read De Broglie Nobel lecture to get his view from his mouth directly., Why you depend on Wikipedia?..

(2) De Broglie proposed and derived pilot wave in 1921, whereas Schrödinger derived his equation in 1926... TDe Broglie was way ahead in his thought experiment which Nature Follows Absolutely.. (It can be proven using Max Planck Black body idea that every matter MUST have the wave associated with themselves)

Gokaran,

I am having very hard days and I am not young, as you kn ow. Then, please think well on what you write. You are a Ph.D., your logic level has to be high.

What's our business that de Broglie preceded Schrödinger? You estimate the truth of a theory by chronological precedence? What happens with you?

We are all in great debt to the fathers of QM, and the greatness of de Broglie is indisputable. His theory was revolutionary at its time. But now, we have clear proof that QM has no substructure of particles floating inside the wave-packet and following trajectories guided by the wave-function.

Do you want a simple proof? See sctions 5 and 6 from

Deleted research item The research item mentioned here has been deleted

Section 5 proves that "particles" have either to disappear in certain situations - which is impossible because particles do not disappear, they are not waves to undergo destructive interference. Or, they have to jump from a region in space to another one, without passing through the space in between - the point of the present thread. Again, it is problematic to assume that particles disappear "here" and re-appear "there". One ca easily find a frame of coordinates by which the particle disappears "here" at a time t1, and re-appears "there" at a time t2 > t1, i.e. in the in terval t2 - t1 it disappeared from the universe.

Dear Thierry,

You read my section 5 as you say. It is shown there that a particle is bound either to jump over some space, or to disapear. De Broglie didn't have to do with such sitations s.t. what he said des not solve my case.

". . . . the additional introduction of an antiparticle will provide a gamma ray, and the removal of the antiparticle elsewhere from this gamma ray can provide it. This process however requires a technique that we don't know yet."

Where freom should I take the anti-particle? And what can help me the gamma ray? Neither such a ray won't disappear "here" and re-appear "there".

I was pleased with your riginal idea - a particle behaving as a wave - i.e., in fact, a wave. It has no problem to disappear "here" because of destructive interference and re-appear "there" because constructive nterference.

If the electron meets with positron, both anhialate into a gamma ray, and the gamma ray creates a pair on the other side,?

zero wave function in normal quantum theory,

means an infinitely high potential barrier, so it cannot pass.From the expresion of quantum current, zero wave function, zero current,

Local matter conservation boild down to a form

div(J) + partial derivative of rho with respect to time equals zero.

I understand that bound quantum states carry no current J, but you still could have a quantum current bouncing around. The momentum p for emission would not automatically give you the right wave length for a bound state from p=h divided by lambda.(de Broglie wave length). That means electrons could still not be excluded...if I understand you correctly....in the experiment. Maybe only electrons with certain energies excluded from entering the region. (J=0)...an electron could be already inside.(the case of a single well region)-

Not too many ways to exclude electrons!

one way

Periodicities create gaps in a continuous spectra, no electrons with the right energies for gap states. ie an alternating stack of two different semiconductors.

No wave, no particle

Both wave and particle always ocurr suspiciously together, I grant that

However there are build up experiments where you see both dots on the screen

and the wave pattern of the dots. This points to both together, as separate logical entities. Particles and probability density pattern (the wave).

Otherwise you have to admit one wave for each dot, much too intricate for me. No collapse for each dot, the dots describe the wave.

Yes, Juan, if you do the experment as Feynman said, i.e. one single wave-packet at a time i the apparatus, you get one particle per wave-packet. The pattern of fringes or of whatever form is obtained from many dots, but each dot came with a separate wave-packet.

You cannot afford more than one particle in a wave-packet, otherwise the particles within one wave-packet become entangled and you get another pattern at all.

In 4D such an observation is possible when considering higher dimensional systems. The particle can go through some other dimension that is not observed by the same researcher.

Particle in a box is this type of situation. The barrier can be made so strong and thick that adding more barrier does not decrease the rate of micro particles passing through. The conclusion is that the particles bypass the barrier in some other dimension allowed by sum over paths method. Only the smallest particles do this.

At very high energy there is a possibility that space time of 4D becomes folded into layers and sheets within 6D or higher dimensions. In such case there is a chance of making a short path from one sheet to another. TGD theory is like this, one of the high energy extensions of GR, where limitations of space time result in squeezed quantum states and scale relativity. Folding makes the basis wormhole theories.

Hi sofia

Yes, I think that is Feyman opinion, probably usuall opinion.

However the waves for each separate dot have to be all coordinated, same phase.

Also I never like the idea that a wave carries mass. I prefer particles swimming in in a wave as separate entities.(more de broglie bohm)

@ Thierry,

Yes, so it seems.

With kind regards,

Sofia

Juan, my friend,

Thierry De Mees made a proposal who reminded me of Feynman's way of referring to particles in the path integral theory. Feynman spoke of a particle that may follow all sort of paths, but these paths had phases and intefered. No need to remind how successful was Feynman's path-integral theory.

You say that you don't like the idea of a wave carrying mass. But Feynman's trajectories that interfered, constructively or destructively, carried the particle, as Feynman said. So, if the waves interfered destructively they cancelled one another WITH the particle INSIDE and all its properties, mass, charge, etc. For a wave-function with a fix number of particles, e.g. one single particle, the number of particles is conserved, s.t. the particle should reapeared in another place where the interference is constructive.

@ Jerry,

What you say about a particle passing through a potential barrier inside which the linear momentum is imaginary is very interesting, but I understood nothing from the part about other dimensions. How can a physical object be projected into other dimensions than the physical space with 4D, i.e. into a non-physical space?

Sofia

Maybe you partly agree with me.

You have then perhaps a micro wave function associated with each single particle, but this does not count with destructive interference. Its with a macro wave function, constructive interference, that you see with many electrons in the experiment forming an interference figure. (which are all nearly independent).

The Feyman path containing an action weight is bit more mathematical. Perhaps you are saying that far from a classical path the probability of finding any electron is low. The clasical path has the minumum action.(constructive interference of many paths) Feyman then mixes some Classical with quantum concepts. This is a similar idea.

Saludos, juan

It just ocurred to me, you will have aproblem with two waves pi out of phase,otherwise identical. Before interference they each carry one particle,

after interference, puf! no particle left at all.

Dear Juan,

Ahhh! Usually, I don't get announcements when people place answers to my questions. Now, what you talk about? I do not understand. Which micro wave-function and macro wave-function? There is no such thing.

It seems to me that you don't have the concept of single-particle wave-packet. If you do what we call single particle interference, you have to create wave-packet after wave-packet, and in each wave-packet one single particle, or, putting it more rigorously, occupation number = 1. You don't allow many particles in one single wave-packet, otherwise you get an entanglement, and you can't get anymore single particle interference.

I want to see whether you understood this issue. Only then I can go on. Just in general, your "puf" is lovely, but contains a mistake.

Saludos, peace, and with kind regards!

(P.S. Did you relax a bit about the economical problems you told me? Tell me in a private message. I am also having these days big troubles and worries.)

I definitely have heard about the macroscopic wave function, most often in superfluids or superconductors. (my specialty is solid state physics)

Something like a total wave function for collective phenomena,from a bunch of wave functions (the micro) all together.

Waves add, interfere, just like you say....create new waves.

Again, you cannot always assume that you have single particle interference. It depends.

I would not put more than one particle in a single particle wave function.

My image is a coherent mix of single particle wave functions, which carry many particles. Quantum coherence as opposed to decoherence. There are also many particle wave functions.

Resume discussion?

Juan, you cannot argue aginst the QM. YES, single particle interference requires ONE single particle in the aparatus at a time. One particle per wave-packet.

Two particles per wave-packet is an entanglement. You won't be able anymore to get single particle interference. The things are a bit more complicated, but you need the concept of pair coherence length vs. single particle coherence length.

Actually a true two particle wave function is either even or odd under the exchange of the two. There is similar rule for many particle wave functions.

Yes, Juan, it's true. So, you see, a couple of particles in the same wave-packet may form an entanglement. To get single particle interference we need to separate very well between the wave-packets and have ONE particle per wave-packet. For interference we send this wave-packet onto a beam-splitter and make the two emergent wave-packets cross one another. We repeat the procedure very many times, and thus, we get the pattern.

If you have a beam of electrons with sharpley defined momentum, it will be better described by exp(ikx) than a wave packet. Just the same, you fit one electron per

wave.

I do not think it is a packet just because it carries a particle.

When you talk about a wave packet containig many electrons, maybe you think about the Fourier analysis of the packet?

Juan,

what's the problem? I explained clearly, IF you want to obtain single particle interference, you need one particle at a time in the apparatus, and to take all the measures to avoid entanglements.

A wave-packet of many electron is not a single particle wave-packet, it is a multi-particle entanglement EVEN if you do Fourier analysis or any other analysis.

exp(ikx) is an idealization. If you want to do interference with very long wave-packets you have to accumulate data along days, because a long wave-packet has a long duration. I remind you that the experiment has to be repeated many times for obtaining a clear pattern.