@ Sergey Shevchenko

I would like to add some comments to Sergey Shevchenko's answer. de Broglie's theory is a hidden variables theory, encompassing the idea that an individual particle is accompanied by a wave, more or less like a bow wave is accompanying a ship.

This idea can be compared to the idea of vacuum fluctuations in quantum field theories. There is, however, a fundamental difference between de Broglie's theory and quantum mechanics: whereas a de Broglie wave is thought to be a wave accompanying a single particle, is the Schroedinger wave a statistical description of an ensemble of particles (this has been experimentally corroborated e.g. by

Tonomura (see

http://www.hitachi.com/rd/portal/highlight/quantum/index.html#anc04

Videoclip 1).

Unfortunately, by physicists Schroedinger's wave function is often

confounded with a de Broglie wave, Heisenberg's uncertainties being

confounded with Bohr's `latitudes of definition of physical quantities'.

(see also http://www.phys.tue.nl/ktn/Wim/muynck.htm)

de Broglie matter-wave concept is coded in the Heisenberg uncertainty principle.

You ask about Heisenberg uncertainty principle?.. It directly follows from the de Broglie wavelength for a freely moving particle. Please start with differentiation...

It is unnecessarily long way. Moreover, I doubt whether this is the right way?..

Dear Murali, existense of de Brogli waves strictly follows from Schredinger equation without unneeded talks.

Dear Marat, you say "existense of de Brogli waves strictly follows from Schredinger equation without unneeded talks" - But you do not answer to the question.

Even Wikipedia gives the answer, see "de Broglie" and then for instance the subsection

Matter and wave–particle duality

Main article: De Broglie hypothesis

Please consider that dB published his thesis (of 23 pages) in 1923; that is 2 years before Heissenberg and Schroedinger's publications

His electron dualism was an analogy of the photon dualism of p and lamda/nu and used to explain electron beam diffraction

There is standard physical term: wave-particle dualism, which has no relation to Heisenberg uncertainty relations. The last represent relations between average value of argument of some function and average value of argument of its Fourier transform. Pure mathematics.

“…There is standard physical term: wave-particle dualism, which has no relation to Heisenberg uncertainty relations. The last represent…Pure mathematics…”

there cannot be in physics “pure mathematics”, in pure mathematics there are many things that have no relations to physics,

when in physics mathematics is nothing more then a very convenient language; which becomes be physical only with some verbal connotation. A formulae F=Gm1m2/r2  becomes be physical Newton’s gravity law only if it is pointed that F is a force, m1 and m2 are masses, r is a distance, G is gravitational constant. As well as Heisenberg uncertainty relations are just Heisenberg uncertainty relations only because of that there exist physical wave-particle dualism, which is realized in Matter just as these relations…

Cheers

de Broglie concept? u mean the de Broglie relation right?

Well, it is about the relation between the momentum and the wavelength of a single wave, while the Heisenberg relation is based on the concept of wave pockets. so it seems that the de Broglie relation is prior. in fact, if u want to do reverse, u must use some additional hypotheses...

The pages in this thread are so short...

Cheers

I repeat, Heisenberg relation is mere mathematical relation between average value of some function and and average value of its Fourier transform. This relation has no relation to usual wave-particle dualism, which sometimes is named de Broglie relation.

It seems interesting, where in pure mathematics the letter “ћ” is used? And if is used – what does it  [the letter] mean in such cases? besides – in physics the fundamental elementary action or angular momentum have dimension energy*time, including in the Heisenberg relation – what are energy and time in pure mathematics?…

Cheers

Dear Sergey, Fourier transform of the usual coordinate wave function is the same wave function in momentum representation. Its argument is momentum divided by h . All of this is answer to your question.

Dear Profs. Murali, Darabi, Shevchenko, Guryev, and other readers of this string,

                                                                                                                                               I would like to add, hoping to be relevant, that given our researches into lower dimensional systems, say for e.g. our proof of the P vs. NP problem listed on my website which we share, The DeBroglie relation can be calculated by experimentally creating the Higgs, Englert, Bosonic meanfield of single electron flow in a QM QFT by using electrons from suitable material molecules of information and energy (electromagnetic), and using the meanfield to obtain the above Kinetic Potential from quantum reservoirs and using the genetic quality arrow of time spaceXtime Dbranes String derivative actions in AGGN or AG'N Networks in zero gravity. Please also refer to some of our answers published on this site. In fact, in lecture notes submitted to the RSAS we have shown that the appropriate group homology of the string particles can be termed "green polarons" and "green gravitons" in this Field. Sorry if this answer is hedonic, this is String Theoretic Econophysics.

SKM

for NH, SM, SKM

 Heisenberg himself at some point defined his uncertainty principle as 1, which is the same as 2, while 3 is the original de Broglie relation, if this is what you mean by the de Broglie concept.

 Aren't 2 and 3 the very same equation adapted by Heisenberg as 2 to account for a precision drift of the chosen velocity, thus the length of the ground orbital, on either side of the selected velocity value on the hydrogen ground orbital, since the only variable is v?

Since de Broglie equation came first, it seems to me that the Heisenberg equation can only have been drawn from it.

"It directly follows from the de Broglie wavelength for a freely moving particle. Please start with differentiation." -  As I have wrote 6 days ago.

Thank you, Mr. Michaud. Now, I hope it is clear to everyone.

Andre

1 2 and 3 are NOT equivalent

de Broglie is a certainty relation equating the impulse and wavelength of a moving electron along a defined path

Heisenberg is an Uncertainty relation in the sense that impulse and place are only defined with this uncertainty combination

“…de Broglie is a certainty relation…Heisenberg is an Uncertainty relation in the sense that impulse and place are only defined with this uncertainty combination…”

yea,  de Broglie didn’t know about the quantum uncertainty.

But this uncertainty value is near the de Broglie wavelength value. Besides, the quantum uncertainty is inevitable – that is a manifestation of fundamental self-inconsistence of the notion/phenomenon “Change”; every change of everything is quantized and “when is quantizing” is uncertain. But it isn’t  arbitrarily uncertain,  and so evolution of a quantum material system proceeds in accordance with fairly well defined the system's [just "wave-"] Ψ- function…

Cheers

And as always in Research Gate the questioner does not answer at all?

Harry,

If you read again, you will see that I did not say that 1 2 and 3 were equivalent.

I wrote that 1 and 2 were the same.

Since the area of most probability of the wave function applied to the hydrogen rest orbital averages out at the classical Bohr orbit, then obviously, even at the limit, the de Broglie equation represents the certainty of a set among the most probable locations of the wave function statistical spread allowed by the generalized Heisenberg equation as applied to the hydrogen rest orbital.

Since the de Broglie equation was established first, I certainly am not the only one observing the similarity of both 2 and 3, and that it seems impossible that Heisenberg would not have heard or read about the de Broglie equation before establishing his generalized version.

“And as always in Research Gate the questioner does not answer at all?”

- the answer was done in the thread already, probably not too clear, though: de Broglie hypothesis  that any particle is also “a wave”, at that wavelength is equal λ=h/P, and Heisenberg’s uncertainty relations are

on the one hand – different, because of  “de Broglie wave” was some “spatially deterministic” object, when Heisenberg’s relation for momentum and spatial position relates just to fundamental QM uncertainty [and there are a number of other relations between other physical parameters at changes of quantum objects/systems]; and

on the other hand the relation was obtained in fact basing on the de Broglie hypothesis. So if somebody will attempt to prove the de Broglie concept using Heisenberg uncertainty principle, she/he will at that use some circular argumentation.

Cheers

It seems rather strange already, but the pages in this thread remain be so short…

@ Sergey Shevchenko

I would like to add some comments to Sergey Shevchenko's answer. de Broglie's theory is a hidden variables theory, encompassing the idea that an individual particle is accompanied by a wave, more or less like a bow wave is accompanying a ship.

This idea can be compared to the idea of vacuum fluctuations in quantum field theories. There is, however, a fundamental difference between de Broglie's theory and quantum mechanics: whereas a de Broglie wave is thought to be a wave accompanying a single particle, is the Schroedinger wave a statistical description of an ensemble of particles (this has been experimentally corroborated e.g. by

Tonomura (see

http://www.hitachi.com/rd/portal/highlight/quantum/index.html#anc04

Videoclip 1).

Unfortunately, by physicists Schroedinger's wave function is often

confounded with a de Broglie wave, Heisenberg's uncertainties being

confounded with Bohr's `latitudes of definition of physical quantities'.

(see also http://www.phys.tue.nl/ktn/Wim/muynck.htm)

@Willem Marinus de Muynck

you noted indeed very important and very interesting feature of the QM particles/waves motion – if there is some ensemble of particles then there is some interference of the waves in the ensemble, which, though, doesn’t differ practically from the case when EM photons/waves interfere, when this interference is well described by classical ED, without relation to the QM stochastics.

And at that EM wave don’t “accompany” photons – photons are simply rather wIde waves themselves and, besides, that seems as such a wave lives in Matter’s aether rather long time after “its front” had interacted with a screen – and that is true for any other particle as well.

But that is the main puzzle of the QM…

Cheers   .  

@Marat Guryev. You juste violate the history. Louis de Broglie published in 1923 and 1924. And Joseph Fourier in 1824-1827.

The first of the de Broglie's relations is the most heavily censured by the hegemonic sect  : intrinsic spinorial frequency = m. c² / h.

In 1930, Erwin Schrödinger put the evidence from the Dirac equation of a second intrinsic frequency : 2 mc² / h. The electromagnetic one.

This one has been experimentally proved :  aflb.ensmp.fr/AFLB-301/aflb301m416.pdf 

Already in his Nobel lecture, P.A.M. Dirac noticed that the Zitterbewegung frequency fully explains the Compton's scattering of photons by electrons. So nor the photon nor the electron have to transmute into corpuscles...

I have demonstrated it again in 2011, but Schrödinger came before :

http://jacques.lavau.deonto-ethique.eu/Physique/Zitterbewegung_Bragg_Compton_english.html

Dear  Jacques, I remind you about Schwarz inequality for Fourier transforms and its consequence - Heisenberg unequalities.

@Marat Guryev. Only the corpuscular hypothesis could justify the relabelling of the Fourier's results by Heisenberg.

Oh ! Ah ! Cruel uncertainty on the position of the corpuscle ! Drama !

But 92 years later, it is still to be experimentally proved that corpuscles exist. Against thousands of proofs that they never exist in microphysics.

Only in macrophysics the concept of corpuscle may be relevant.

“…Only in macrophysics the concept of corpuscle may be relevant….”

- yeah,  for example photons, indeed propagate in space as waves; and so, for example,  after a diffraction grating  photons’ diffraction patterns  have well macrophysics sizes, which are well relevant to macrophysics. But at that photons appear and interact as practically pointlike corpuscles [particles], in space volumes near atoms’ sizes, which aren’t relevant…

 Cheers             

@Sergey Shevchenko. Maybe you are confusing with the often tiny size of the absorber.

{ Tiny size of the absorber + tiny size of the emitter } do not imply that the intermediate diameters remain so small. Proofs are so many, and a sum is at 

https://www.researchgate.net/publication/313309517_La_microphysique_que_l'on_vous_conte_est-elle_bien_la_bonne_La_physique_quantique_transactionnelle_expliquee_pour_tous

Book La microphysique que l'on vous conte est-elle bien la bonne ...

@  Jacques Lavau : “…Maybe you are confusing with the often tiny size of the absorber…”

- photons indeed move  by unknown way in the space as [being] waves and interact – by analogously unknown way, as waves with macro regions of  absorbers [for example creating diffraction patterns]. But eventually they excite at interaction with  and are radiated at creation by singled out atoms of absorbers/emitters, i.e. as pointlike particles…

Cheers

And – seems it would be useful if at least abstracts in your papers were in English

Here is our transactionnal definition of the photon :

A photon is a successful transaction between three partners :

an emitter, an absorber, and the space or (at least half-transparent) medium or optical devices between them,

which transfers by electromagnetic means a quantum of looping h,

and an impulsion-energy that depends on the respective frames of the emitter and of the absorber.

End of definition. 

It does not matter whether the emitter and the absorber are separated, in our human frame, by tens or hundreds of milliards of human years. The human point of view does not matter at all.

Dear Murali, Heisenberg unequality is derived in detail from Schwarz unequality in "Quantum Mechanics" of  F. Schwable. At the end of his derivation he has accepted that squared absolute value of wave function is probability of particle to be at given point. There is answer to your question.

@Willem Marinus de Muynck. You wrote : "the Schroedinger wave a statistical description of an ensemble of particles".

Er... It is exactly the contrary of the point from Schrödinger.  It is only what the ennemies of Schrödinger have taught since. They could no more erase the equation of Schrödinger : it was already too known. So they energically un-Schrödinger-ized it, to cover again their corpuscular surrepticious postulates.

@Jacques Lavau,

You are completely right that it is quite different from Schroedinger's view. Unfortunately, Schroedinger could not profit from the measurement results by Tonomura (and others) I referred to in my earrlier comment. I could. You could too, This has nothing to do with any enmity. I am a great admirer of Schroedinger.

@Sergey Shevchenko : "photons indeed move by unknown way in the space". Unknown ? Really ?

However astronomic optics exists. Atmospheric turbulence exists. Polarization and polarizers exist. Gravity lenses exist. The 21 cm hydrogen ray is well studied.

Chemical analysis by ray absorption is practiced as well in industry as in astronomy... So we are not so ignorant. By Scherrer Law, we can evaluate the size of the crystallites on which our X-photons diffract. So we are not so ignorant of the width of each of these photons where they diffracted on the crystal.

Very very far from the magnitude postulated by the corpuscularists.

@Jacques Lavau 

“…Unknown ? Really ?

However astronomic optics exists. Atmospheric turbulence exists…, etc.”

That isn’t the knowledge, that is a phenomenology. It describes “how”, but doesn’t answer “why” – and essentially “how” also, though.

Cheers

So the magnitudes of widths and lengths of various photons, depending on the experimental conditions, are known, and all these experimental facts are fully compatible with Maxwell's equations, never with corpuscularist ideations. The geometry of Fermat's spindles is known and confirmed.

What is quite outside of electromagnetics are the laws of the Dirac-de-Broglie noise, preceding and following each successful transaction. This is another story, surely not in the Newton time.

@Willem Marinus de Muynck : sure you are not the ennemy of the defunct Schrödinger, but Niels Bohr was. See the letter from W. Heisenberg, reported by Emilio Segrè.

@Sergey Shevchenko. Your request of translated abstracts.

The abstract of the book https://www.researchgate.net/publication/313309517_La_microphysique_que_l'on_vous_conte_est-elle_bien_la_bonne_La_physique_quantique_transactionnelle_expliquee_pour_tous

is now translated into english.

Maybe poor english...

Book La microphysique que l'on vous conte est-elle bien la bonne ...

Dear Murali:

Proof of Heisenberg Uncertainty Principle using de Broglie concept is possible. See the attached file. However, proof of de Broglie concept using Heisenberg Uncertainty Principle is not possible. This shows the superiority of Wave Mechanics over Dirac Heisenberg picture. Wave Mechanics is a wholesome theory.

de Broglie's wavelength concept (1923) was proved by Davisson Germer's experiment (1928). This experiment also showed quite clearly that wavelength and momentum of a subatomic particle can be measured simultaneously.

One can however have an intuitive  glimpse of de Broglies idea (not a proof) even starting from the uncertainty principle. For a subatomic particle as we go below the atomic length scale it looses well defined position and momentum. Then we can look at them as waves, not particles. If it is a pure sinusoidal monochromatic wave it's wavelength will be fixed but position will be completely uncertain. Then to have some localisation in space we start superposing a bunch of sinusoidal waves of different wavelengths; thus an uncertainty in wavelength creeps in but a degree of localisation is achieved in position. This uncertainty in wavelength is equivalent to an uncertainty in momentum, which is formalised by de Broglie hypothesis, which did hypothesize an one to one deterministic relation between wavelength and momentum, λ=h/p .

"Uncertainty" is an egotist and anthropocentric concept, based on human subjectivity.

Such an egocentric fraud is the basis of the public success of this mistake, as a revenge on the huge butchery of the world war.

Impersonnaly it is just a matter of undefinition. But "undefinition" does not sell as well as "uncertainty". Heisenberg was denying waves, and selling corpuscles, so he told about "uncertainty" on the position of the pretended corpuscle.

No.  There does exist a corresponding ``uncertainty principle'' for classical waves; this doesn't imply anything about the existence of corresponding particles, for instance.

de Broglie's concept refers to spacetime properties, Heisenberg's uncertainty principle to phase space properties. The two are logically independent. A lot of confusion when discussing quantum mechanics is due to to identifying the two. 

de Broglie introduced the idea of wave-particle duality before Schrödinger had written his equation-which, also, refers to phase space, not spacetime. 

No. In his papers in 1926, Schrödinger refutes duality, as he refutes anything corpuscular. That is why Niels Bohr personnally, and more generally speaking, the whole Göttingen-København sect, concentrated their violence on Schrödinger.

While Louis de Broglie persisted in believieng in corpuscles, and in the whole macrophysic geometry, with position coordinates... So he remained with the two feet in a 300 kg concrete clog for the remaining of his life.