Just a quick answer, the fact you want to measure the time of flight require you to know the exact time of departure of the electron. Lets say you will have some error on this measure (Dt), this will lead to an spread of the electron kinetic energy (DE).

So that Dt*DE>hbar/2

So at the end you can not know if the electron arrives late, for example, beacuse took the longer path or because it was slower.

Your question is erroneous by principle : You have supposed that the electron is a corpuscle, and passes by ONE hole or slit.

An interference experiment succeeds because the electrons are all of the same energy, and therefore, of the same wavelength. The experimental device you will use to be sure of the date of the next electron will destroy this good definition of the wavelength, so destroying any cooperation of the repeated electrons to give you a good statistical pattern of interference..

“…Your question is erroneous by principle…”

- that is wonderful question. The problem indeed exists and practically isn’t discussed in existent scientific publications. And it is as follows:

- there is no problem when an interference of “classical” (i.e. – oscillations in some medium)  waves is observed . In this case the oscillations exist stabely and so there is no problem – when wave fronts from different slits reach an one point in a screen, forming the pattern depending on the phases difference that is determined by the difference of the fronts’ pathes.

But in the case with a particle – here electrons – this explanation doesn’t work – the “first” electron becomes be absorbed quickly and so there is no “interferating partner” for the next electron, which can be fired later.

But the interference is observed.

It seems here we have some version of the quantum entanglement, but what? Or  there is something very interesting else, when this something can relate to the entanglement, though.

And the problem should be studied experimentally again and again; including with “measure the time difference of electrons” by using, for example, a control of the discharges of particles from the gun.

Cheers

@Sergey Shevchenko. You are still under the corpusculist postulates.

There is a bilingual list of the Göttingen-København postulates we do not more admit :

http://jacques.lavau.perso.sfr.fr/Physique/postulates.html

Of course each electron interfers with itself and pass simultaneously by the two slits when there are interferences. How could the Aharonov-Bohm-type experiments succeed if the electron had anything in common with your mythic corpuscle ?

@Jacques Lavau

- “these Göttingen-København postulates” don’t claim that a particle, say – the electron – is only some “corpuscle”, they only account for the well established fact that particles, including photons, interact with other particles (atoms, etc) as some pointlike object.

Though indeed, just experiments with single particles that mentioned in the thread’s question  gave a lot of grounds to consider the version that “each electron interfers with itself and pass simultaneously by the two slits when there are interferences.” At that the obstacles as “…error on this measure (Dt) … will lead to an spread of the electron kinetic energy (DE)...” aren’t essential – the electrons energy is known / determined by the electron gun and so here is no necessity to be estimated.

So, again – the claim that  a particle interferes with itself has evident uncertainty also – seems nobody till now suggested a reasonable physical model for this process. Including

– taking into account that interactions, say – absorption, of some particle happens (rather probably)  practically instantly,

- how the interference, which requires seems no more then the time interval that is necessary to complete internal processes in the particle, i.e. - mc²/h -  can happen?

 - when in the interference patterns there are peaks that  relate to a number more then unity; i.e.  to happen such interference a particle  must “wait” somewhere – where and how?

That is especially evident for photons, where possible difference of paths of interference can be hundred and thousands wave lengths.

At that with a large probability  there is no principal difference in this case between photons and “massive” particles, Matter is built by a rather simple an universal scheme (see https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics )

So to study the possible “particle interference with itself” it would be  sufficient, at least on first stages,  to study more carefully the interference of photons…

Cheers

Article The Informational Conception and Basic Physics

@ Sergey Shevchenko :

All the work you wish is done and published years ago, but severely censured and ignored by the hegemonic chapel.

John Cramer published TIQM in 1986, and I rediscovered it in the 1997-1998 year (of course not with the same name nor the same vocabulary). Everybody in the IN2P3 (University Lyon 1) ignored that I was preceded by 12 years by Cramer.

That the Zitterbewegung is the key of the electron-photon Compton scattering, I demonstrated in 2011, but Erwin Schrödinger did it before in 1932. Who knows that ? Only P.A.M. Dirac mentions this, in his Nobel lecture, 1933.

http://jacques.lavau.perso.sfr.fr/Physique/Zitterbewegung_Bragg_Compton_english.html

http://deontologic.org/quantic/index.php?title=Calcul_diffusion_Compton_et_Zitterbewegung

http://deontologic.org/quantic/index.php?title=Interpr%C3%A9tation_transactionnelle

I disagree on the main thema of your enclosed paper : we came about 14 ou 15 milliards years too late to demand that the laws of nature are here to provide us information. And the theorem of the necessary variety, from W. R. Ashby is very cruel to such pretentions.

I bet that you did not even know that a team conducted by Michel Gouanère has measured the Dirac-Schrödinger intrinsic clock frequency of the electron : 2mc²/h.

Experimental observation compatible with the particle internal clock,

by M.Gouanère a/, M.Spighel a†, N.Cue b*, M.J.Gaillardb/, R.Genre b/, R.Kirsch b/, J.C.Poizat b/, J.Remillieux b/, P.Catillon c†, L.Roussel c/.

http://aflb.ensmp.fr/AFLB-331/aflb331m625.pdf

http://aflb.ensmp.fr/AFLB-301/aflb301m416.pdf

As far as I can see, one has the usual alternative: if the electron wave packet was emitted over a sufficiently short time, then you can indeed know through which slit the electron passed, but will not see interference.

Similarly, if the electron is sufficiently spread out, it will interfere with itself (contrary to other posts, there is strictly no problem with that), but its time of emission will not allow to conclude anything with certainty, as to the slit it passed through. Apart from that, it is well-known that one can have some (probabilistic) knowledge as to which slit the particle goes through, while not altogether destroying the interference: the alternative is not altogether rigorous.

@Jacques Lavau :

“…the laws of nature are here to provide us information.”

-         it seems that you didn’t read the paper “The informational conception…” (the link in the SS post above). Though here would be useful to read the paper “The information as Absolute” https://www.researchgate.net/publication/260930711_the_Information_as_Absolute

also.

The papers of the French group that you pointed in your post are interesting for me.

Thanks.

Cheers

Article the Information as Absolute

This stupid question draws stupid answers, as the hegemonic believing is quite stupid. If the electron is not wide enough to see the two slits, then you know there is no interference. If you accelerate electrons at 6 GeV, you will not be able to do radiocrystallography with them : their wavelengths are far too small.

For instance in an apparatus designed for an Aharanov-Bohm experiment, you must have a "beam splitter", which is reallly an electron splitter : a negatively charged wire. And you must use a low voltage, under 100 V.

http://deontologic.org/quantic/images/2/27/Aharanov_bohm_perspective.jpg

If you have an interference, then the quanton, electron or else, uses two or more branches of path.

There is no physics at all, to perform the magic transmutation of an electron into a corpuscular something. It never ceases to be undulatory.

Each electron arrives on the detector plane and is measured at a point. These points build up over successive events to give the interference pattern. If the path lengths through each slit are different, what you will eventually see is a displaced interference pattern, due to a phase difference over each path. At most, this will give information about the difference of the path lengths, not which slit each electron went through. Gaining this information would destroy the interference pattern.

@ M. K. Olsen. So is the standard believing, taught everywhere.

However the slogan "measured at a point" takes the place of the physical description : "absorbed by an absorbing reaction, which diameter is not negligeable, though small compared to the distance between the two slits".

"which slit each electron went through" uses the surreptitious postulate that an electron is something corpuscular, even punctual. However the observed optics is still the Fresnel's one, 1821.

With electrons instead of X-rays, one still can do radiocrystallography, though less precise. And the valid optics is still the Fresnel's one, 1821. With diffractograms, we can say the size of the crystallites ; with clays, we obtain much broader diffraction peaks than with silts. I shot down an international crook in an international court, by this observation : http://deonto-ethics.org/impostures/index.php?board=26.0

How an electron could have a phase, if it was not an intrinsic clock ? But the standard believing (in the Göttingen-København heirs) rejects its two intrinsic frequencies with horrified horror : they are not compatible with the corpuscularist believings. I suggest you to read the Nobel lecture of P.A.M. Dirac, 1933.

Which particular part of Dirac's lecture should I pay special attention to? I am familiar with the lecture, as well as with his relativistic equation.

Dear Prof. Hourani,

                                   Each electron should not violate the uncertainty principle which in this case will be restricted to all the possible paths divided between the two slits. There is time and space. Please, if you wish to go by econophysics experiments and applications of String Theory, , you can take a look at my Haag's Theorem paper on my RG page. SKM Earl QC PhD EPS Fellow (Indirect)

@M.K. Olsen :

"The variables \lapha also give rise to some rather unexpected phenomena concerning

the motion of the electron. These have been fully worked out by

Schrödinger. It is found that an electron which seems to us to be moving

slowly, must actually have a very high frequency oscillatory motion of small

amplitude superposed on the regular motion which appears to us. As a result

of this oscillatory motion, the velocity of the electron at any time equals the

velocity of light. This is a prediction which cannot be directly verified by

experiment, since the frequency of the oscillatory motion is so high and its

amplitude is so small. But one must believe in this consequence of the theory,

since other consequences of the theory which are inseparably bound up with

this one, such as the law of scattering of light by an electron, are confirmed

by experiment."

Erwin Schrödinger was too timid and intensively disheartened by Bohr and Heisenberg, that he did not said himself these results, so Dirac mentionned them, and he was the last to know them. Nobody else noticed.

I have rediscovered it in 2011.

http://jacques.lavau.perso.sfr.fr/Physique/Zitterbewegung_Bragg_Compton_english.html

@Jacques Lavau,

“…As a result of this oscillatory motion, the velocity of the electron at any time equals the velocity of light…”

- that isn’t totally correct. Indeed all / every particles as a whole always move in the 4D Euclidian spacetime in different 4D directions with identical by the absolute value speed that [the absolute value] is equal to the speed of light. That is claimed in the SR also, therefore, probably, Dirac has said what you quoted.

Some example – a "massive" particle, say an electron, if it is at 3D rest in the absolute space, moves along the ct-axis with the speed of light. If it also moves along, say, X-axis with  gamma>>1, it moves with the spatial speed that practically is equal to the speed of light and along ct-axis practically with zero speed [but always >0].

The motion  of internal components of the electron (what realizes as “Dirac-Schrödinger intrinsic clock frequency”) is an additional [to the particle’s motion as a whole] motion, so these components must “move” with a speed that is greater then the speed of light [rather probably with a speed  = c.sqrt(2)].

That is another thing that in the reality all particles are, with a rather great probability, some disturbances of a dense 4D lattice (“Aether”) that fills the Matter’s spacetime, when all the lattice’s elements (FLEs) remains on their [points and a particles motion is a specific sequential circular “flipping point” of the FLEs.

More – again see the paper “The Informational Conception and Basic Physics” (the link in the SS post on 1-th page of this thread).

Cheers

Curiously, Sergey Shevchenko never sees a frequency, nor spatial, nor temporal.

How to have interference in a double slit experiment without the de Broglie spatial frequency, or wavelength ?

How to have diffractograms of crystals, without wavelength ? X-ray or electrons or neutrons wavelengths.

How to have the Compton scattering of gammas, without the Dirac-Schrödinger wavelength of the electron ?

Without frequencies, how to have a spin ?