The detection process provides a crucial difference. When you detect ``whatever passes through the slits'' (which I, personally, would rather not call either a wave or a particle. I believe someone, whose name escapes me, suggested ``quanticle''. I think this to be excellent), at the screen, you will only ever perform *one* detection of the photon, at *one* reasonably well-defined position. The ``interference pattern'' only arises when you wait for many detection events to accumulate. On the other hand, when you detect sound (at ordinary amplitudes) the whole wave can be detected everywhere, with a continuously varying intensity.

Further, though this might in fact confuse your student, it is nevertheless true that if your sound wave is made to have low enough amplitude, it will, in fact, consist of isolated phonons. This is presumably a non-trivial experiment, and I doubt whether it has been done. But in principle, there is no doubt of the quantum nature of sound waves when these have sufficiently low intensity: the same thing happens as with the electromagnetic field. You would then detect your sound wave phonon by phonon, and you would be led, by the same argument as for the EM field, to the statement that every single phonon interferes with itself.

Further, modern experiments have shown that truly macroscopic objects can be made to pass through two slits and display an interference pattern: a C60 molecule, which is a huge object by any account (720 times the mass of a hydrogen atom, which itself is usually viewed as a classical object, also a radius of 710 nm, compared to about 0.12 nm for hydrogen). Of course, such objects are of necessity sent one by one, and they are detected, at some position on the screen, equally one by one. Contrary to sound, there can, obviously, never be any talk of detecting an ``intensity'' of, say,  0.0153 molecule at a given point.

I think there are no particles flying over space but only tuning modes of fields to measure. All other energy is as waves, the wave environment, which remains all signalling and all quantum states as opposite cycles (normal and anti-). The handedness is measuring-dependent and in a weird way so that you can delay the environment status (polarization) before measurement and the wave environment remain your moves for the entangled partner when checked causally. The entangled particles are at opposite states and the checking over environment reveals which state is which.

Something like that in a nutshell, still exploring...

If photons are fired one-by-one,  in sequence,  through a single slit,  a diffracted interference pattern still develops from the many “hits” on the detection screen.  Thus, an interference pattern doesn’t need to be attributed to the wave nature of light.

Dear Prof Leyvraz ,

The phonon description is a collection of molecule collisions, similar to the Swift description of sound in thermoacoustics where he uses the term packets.

The molecular level consists solely of particle collisions. Each collision has two particles (neglecting wall effects) with a velocity and mass. The velocities can vary from zero to a high number. So observation of a single collision does not convey macro information.  

In a thought experiment, one can aggregate the molecule collisions to compute gas temperature, or gas pressure or a sound wave. It is the observer that decides on the aggregation and hence which parameter is being measured.

So the undergrad asks, why are photons different? why do physicists make them somehow a special case, different to sound?

No one has yet managed to explain that.

Dear Dan,

with a single slit, diffraction occurs but not interference. If the experiment looks for waves then interference is observed, if the photon trajectory is known (by the experiment) then there is no interference.

The undergrad says that this is the same analogy to sound waves, whereby you have to aggregate collisions to look for temperature pressure or sonic effects. It is the observer that determines what is measured. (In the case of molecule collisions it is temperature pressure etc.)

Paul,  Below is a quote from this website:  https://en.wikipedia.org/wiki/Double-slit_experiment.

“…when this "single-slit experiment" is actually performed, the pattern on the screen is a diffraction pattern in which the light is spread out. The smaller the slit, the greater the angle of spread. The top portion of the image shows the central portion of the pattern formed when a red laser illuminates a slit and, if one looks carefully, two faint side bands. More bands can be seen with a more highly refined apparatus.”

The interference bands exist in the single slit but are not as defined as the double slit bands.  Here is an explanation that shows such interference patterns result from particle interactions in lieu of waves.

Reproduced below in italics is another wikipedia quote regarding Compton’s work.  “Compton's experiment convinced physicists that light can behave as a stream of particle-like objects (quanta)….”

Compton’s work is a formal proof regarding the makeup of light or radiation.  In our work,  it is shown how light can be viewed as a stream of individual entities that display both particle and wave characteristics without such entity actually being a wave or a particle.  For example,  such entity is consistent with the particle nature of light given by Planck, Einstein, and Compton;  and is consistent with Maxwell’s wave equations.  Meaningful explanations of the experimental results of slit experiments, and Compton’s work and mathematics can be addressed using the proposed models of light and the electron. 

First, we show how Compton’s work can be physically understood.  Generally,  in the Compton experiment,  the wavelength shift is zero when the scattered photon’s angle of departure (from the electron) relative to the direction of the incoming photon is zero degrees;  and the wavelength shift is maximum when the scattered photon’s angle of departure relative to the direction of the incoming photon is 180 degrees.  In between zero and 180 degrees,  the wavelength shift gradually increases as the angle of departure of the scattered photon gradually increases,  from zero to 180 degrees,  relative to the direction of the incoming photon.

We are all aware that an electron carries a cylindrical B-field as it translates.  For purposes of this post,  such bound B-field can be considered the electron itself,  since the electron is similarly constructed in our work;  for example, see Fig. 2 in the link.  Such cylindrical B-field consists of oscillating photon fibers that also rotate about their origins, all of which align along the longitudinal axis of the cylindrical B-field per Fig. 2;  Fig. 1 gives a view of the oscillating photon fiber.

A photon that enters the bound cylindrical B-field of the electron,  will interact with one or more of the photon fibers that make up such B-field per Maxwell’s calculus.  A spatial rate of change of “B” within the cylindrical B-field is increased due to the presence of the incoming photon fiber.  This,  in turn,  creates a radial inward-pulling force on the cylindrical B-field,  and a radial outward-pulling force on the incoming circularly twirling photon fiber.  Thus, one (or more) of the circularly rotating photon fibers of the cylindrical B-field undergoes a decrease in its diameter,  while the diameter of the incoming circularly rotating photon fiber increases before it departs the electron.  As a result,  one or more of the circularly rotating photon fibers,  that make up the cylindrical B-field,  have shorter oscillation strokes,  and the incoming circularly rotating photon fiber has a longer oscillation stroke as it departs the electron.  Due to this,  the frequencies of the oscillations of the photon fibers increase and decrease, respectively;  as such,  the wavelength of the scattered photon is greater than it was when it entered the electron’s cylindrical B-field.

Per Compton’s work,  the wavelength shift is zero when the scattered photon’s angle of departure (from the electron) relative to the direction of the incoming photon is zero degrees.  If there is no wavelength shift,  then the incoming photon must have entered the electron’s cylindrical B-field at 90 degrees to the longitudinal axis of the cylindrical B-field,  since this is the only orientation where the incoming photon doesn’t interact with the photon fibers of the cylindrical B-field.

Per Compton’s work,  the wavelength shift is maximum when the scattered photon’s angle of departure (from the electron) relative to the direction of the incoming photon is 180 degrees. This implies the incoming photon must have entered the electron’s cylindrical B-field in-line with (at zero degrees to) the longitudinal axis of the cylindrical B-field,  since this is the only orientation where the incoming photon will undergo maximum strength of interaction with one or more of the photon fibers of the cylindrical B-field.  This means the diameter of the circularly rotating incoming photon fiber increases the greatest in this orientation,  thereby resulting in smaller frequency and greater wavelength of the scattered photon.

In between the above extremes of scattered angles from zero to 180 degrees,  the wavelength shift gradually increases as the angle of departure of the scattered photon gradually increases,  from zero to 180 degrees,  relative to the direction of the incoming photon.  The angle of departure of the scattered photon is dependent on the angle of the incoming photon relative to the longitudinal axis of the bound cylindrical B-field of the electron, as implied in Compton’s work.  The strength of interaction between the incoming photon and the cylindrical B-field varies correspondingly with such angle, as well.

Next,  we show how Compton’s work can be built upon to provide insight as to how diffracted interference patterns of light develop in the ‘slit’ experiments.  Although,  Compton did scatter x-ray photons off a free or loosely bound electron,  there are similarities in the mechanism responsible for the Compton Effect and the mechanism that gives the interference patterns of light in slit experiments.

Previously,  regarding the Compton Effect,  it was mentioned that the angle of the direction of the scattered photon (from the electron) is dependent on the angle between the direction of the incident photon (into the electron) and the longitudinal axis of the bound cylindrical B-field that constitutes such electron.  This is implied in Compton’s work as was shown.

The primary difference,  between the two experiments,  is the electron is free in Compton’s work and the electron’s cylindrical B-field can have any possible orientation relative to an incident x-ray photon;  whereas in the slit experiment,  the orientations of the cylindrical B-fields of the electrons,  within the material along the edges of the slit,  have fixed orientations relative to the direction of the light photons that enter the slit.  Due to this difference,  the scattered photon in Compton’s experiment may depart at any angle from the electron;  whereas in the slit experiment,  the passing photon can only diffract at certain unique angles. 

As a result,  light diffraction with interference bands develops on the detection screen in single or double slit experiments.  Electrons fired through slits will also create diffracted interference bands similar to light photons since electrons consist of photons, as proposed.

Article UNVEILING of the ELECTRON (Post #1) [A Proposed Electron Structure]

Forget phonons: just a short summary of my answer: when you measure the EM field at low intensities, you get occasional clicks of detectors, saying a photon has been detected at position x on the screen. It is always one photon.

Similarly for C60 molecules: you find the C60 molecule you  sent through the slits at one position. There is no diffraction pattern unless and until you wait and accumulate all the measurements. These then yield a diffraction pattern.

So the crucial difference is in what you measure at the screen: in the sound case, you measure all over the screen a continuously variable intensity. In the case of quantum objects, you measure them each one at a time at one single position. Sound is in fact a global phenomenon with a continuous intensity, whereas each quantum particle is only measured in one position, but when these positions are put all together, they result in a diffraction pattern.

You seem to ask what happens, if you reduce pressure very much. I believe that when you have too few gas molecules, the concept of sound will disappear, and no sound waves can be detected, whereas the  molecules will be flying freely from one container wall to the other (this does happen at high vacuum). If, on the other hand, you decrease the sound intensity while leaving the pressure constant, you would, eventually, get into the limit of isolated phonons I talked about. But this I believe to be more confusing than anything else.

In summary, what prevents interpreting the diffraction of quantum objects as an ordinary wave phenomenon  is the nature of the detection at the screen.

Dear Prof Leyvraz,

yes you are correct interference patterns have been seen in buckyballs (C60) and other large molecules.

In the sonic case, one only sees the interference pattern if a specific set of measurements is taken; a traverse across a plane normal to the excitation source (a loudspeaker) , i.e. the analogue of a screen in the photon case. If one takes a different measurement, for example calculating the mean speed of all the molecules, then temperature results.

Sonic interference patterns form when pressure is low enough so that there is only one particle collision at a time.

In the case of a high vacuum, I have not seen this experiment done even though I have searched quite hard for evidence. Anyone fancy doing the experiment?

Dear Charles,

Yes, I agree that in sound engineering phonons are not very helpful. Am not sure I agree with your last statement about thermal motions drowning out the sound.

Yes, there is a signal to noise issue (noise having a thermal element) in detecting sound. However, in a typical audio setting, the mean velocity of the molecules due to thermal is ~300m/s, for low intensity sound the package velocity (as defined by Swift) is many orders of magnitude lower than this.

If we have structures which has resonance frequencies for sound to recharge and discharge some tension, the quantum effect is similar to tuning modes of photons: emitting and absorbing. The conservation of energy is more effective with electromagnetic phenomena.

Dear Remi,

I agree with your comment about Phonons etc. being mathematical conveniences and not fundamental particles.

Your comment about QM is not accurate on two counts. The twin slit experiment has been done with large observable molecules as mentioned previously in this thread (C60) . No twin slit experiment has observed interference with a single photon. See my previous post.

If we want good quality physicists for future generations, we need people that question and understand the theories. Asking them to believe in a theory is a religion not science as was mentioned earlier.

If you think that there is no analogy with sound waves in a gas, then please give your logic. Think about what happens at the molecular level, not a group of particles.

Dear Charles,

your referenced paper give some useful insights to QM and I thank you for sharing it on this post.

Von Neuman's Mathematical Foundations of Quantum Mechanics paper in 1932 described QM phenomena not sonic.

Let me re-iterate. Sound induced interference can be seen in a system where there are only particle collisions (gas molecules) where only one collision takes place at any point in time. So before one can use the argument in QM that only one particle at a time transverses the experiment therefore the particle (or wave function or whatever construct one wants to use) passes through both slits, one has to be able to explain the sonic case. Which I still maintain has not been done. I look forwards to and encourage such a description that can be understood by an undergraduate with an enquiring mind.

@ Charles: ``If your sound wave amplitude is low enough, then it will be drowned by thermal motions (effectively white noise).''

I guess I agree, at least under conditions in which the temperature is high enough. So it is  not enough to lower the amplitude, it would be necessary to have a system with very low dissipation.

I think that shows that you cannot readily go to the quantum limit in the case of sound.

@ Paul: ``Sound induced interference can be seen in a system where there are only particle collisions (gas molecules) where only one collision takes place at any point in time.''

There is a problem here with ``particle'': if the analogy is to hold, then this concept should be used in the same way in both cases. Now the particles in the case of light (or electrons, or C60 molecules) are just that: they go one by one through the slits, and their *position* is recorded on the screen.

On the other hand, in a sound wave, very few particles actually go through the slits: and the particles that do go through the slits do not hit the screen. Sound is not, in that sense, something that belongs to particles. It manifests itself as excess density or excess speed that communicates itself through collisions from one part of the gas to the other. What you detect on the screen is a continuous intensity distribution. Were you to attempt to detect isolated atoms, you would be overwhelmed by a huge number of atoms all hitting the screen almost simultaneously. And decreasing the pressure, as was said before, will lead to all molecules flying around freely, with no sound wave and no interference present.

Dear Remi,

In your crookes tube example, you say "record the scintillations as a time lapse", hence you measure multiple photons. As I say, only one photon goes across the aparatus at once, but to see interference, you need many photons.

In your referenced paper, look at figure 2, it shows photon count rate, which would be pointless if these was only one photon :-).

Junior researchers often take the colloquial "single photon ... experiment" literally. whereas it means that only one photon at a time passes through the slit (or other experimental setup). The screen (or detectors) requires many photons to build up the pattern and show interference.

If we look at the emitter itself, the book "single-photon generation and detection edited by Migdall, Fan and Bienfang  shows how single photons are produced. However, if one looks more closely, the internals of the emitters have many photons producing the required frequency of emission, they then describe how one is selected for emission.

Paul,   It is not necessary for a single photon to pass through both slits and interfere with itself to obtain interference. I used to work with laser radar systems. It is possible to stabilize two different lasers so well that their frequencies only differ by a few Hertz. If these two stabilized beams overlap on a diffusing surface, the scattering surface mixes the two beams and they will produce interference even though no photons are interfering with themselves. Even if two laser beams differ in frequency by several GHz, the interference (beats) between these beams can still be observed if they are combined in a beam splitter and observed with a fast detector.

Therefore, it is wrong to think of photons interfering with themselves. Electric fields from different photons add and subtract to produce beats and interference patterns. The particle properties of photons only is required to explain emission and absorption. Otherwise the wave properties dominate. Even when a single photon passes through a double slit, only the wave properties are important. The waves pass through both slits and the interference pattern is a wave effect. Any experiment which determines which slit the photon has passed through is the equivalent of an absorption and reemission from one of the two slits. Therefore there is only a single slit diffraction pattern. The mystery becomes how to explain the fact that the photon is a wave when it is propagating but a quantized unit of energy when it is emitted or absorbed.

To @Paul and to the other users:

You cannot explain that one photon goes through both slits, because we don't know this. We don't know what is the wave-function. The standard quantum mechanics tells us only what we can get if we measure. All the rest is speculations.

What you can tell the students is that in order to get interference, both slits should be open. If only one slit is open we don't get interference. Therefore, whatever we can infer is that something passes through both slits, and in consequence we get interference. But what passes and through which slit, we don't know.

This is exactly the domain of research named fundaments of QM. We try to investigate these issues but for the moment we don't have answers. We don't know what we have in our apparatus before we measure.

About water waves that pass through two holes, what adds up generating maxima and minima is the amplitude of vertical oscillation of the water molecules.

About sound waves, they need a medium for propagating, and what propagates is the oscillation of the molecules of the medium, transmitted from one molecule to the other by collision. Beyond two slits the amplitude of this oscillation adds up constructively or destructively. There is no question if a molecule passes through the slits, both slits should be filled with molecules. If one slit is empty, along that slit the vibration won't be transmitted and there won't have interference beyond the slits.

Firstly, one photon cannot produce an interference pattern. It produces a single scintillation on the screen from which no conclusion about the pattern can be made. The pattern only appears as a result of many photons passing the slits, or, theoretically speaking, from an ensemble of single-photon measurements.

Secondly, the statement that photons only interfere with themselves is plain wrong. The counter-example -- two independent coherent laser sources -- has been discussed above by John Macken. This misconception emerged in the pre-laser era, when such coherent sources where unavailable, and, as all misconceptions, survived far beyond its correctness.

Thirdly, I would rather refrain from lecturing this audience on the concept of coherence in quantum electrodynamics. Roy Glauber did it much better than I can ever hope to do.

Dear Paul,

I did not feel comfortable with my post so I deleted it. 

Kind regards,

Vu.

@Charles is VERY correct.

Why people downvote without asking questions when they disagree with something? Maybe the comment is correct and the downvoter didn't understand it.

So, I will explain: we have no right to believe that the wave-function is ontic, i.e. a high-fidelity model of what runs in our apparatuses. For the moment, what we know is that the wave-function is a tool for calculating different probabilities, correlations, etc. Of course, we are trying to get a deeper understanding. If experiments will teach us new things about the wave-function, we will have the right to say more. But for the moment we can talk only in base of what we know now.

To start with, I wholly agree with Lev Plimak: there is no "single photon or electron interference"  in Young two-slit experiment. None.

Funny, this is an almost ancient subject discussed I guess zillion times by each new generation of physicists... Most recent known to me authoritative statement on the subject was made by Joseph H. Eberly, a prominent expert in quantum mechanics & nonlinear optics, in  June'2013 issue of  OPN (Optics & Photonics News) , who stated that  "electrons can only interfere with themselves and ... not each other". That statement was supported by his reference to Dirac's book "Quantum Mechanics", 1930. A LOT of people sent in their letters arguing against that statement, but the editorial board apparently decided that the subject is  too hot potato for an optical magazine, and shut down any further discussion. 

As you may guess, I was one of those with dissenting views, and I've got sort of evasive letter from OPN, but decided to just drop the matter -- no point for the fight; it is mostly the matter of interpretation , and anyway who cares... But I thought that this is an appropriate forum to post my old unpublished (and sort of humorous) piece here, see the file attached.

@Charles Francis,

You are right and rigorous in what you explain, just you have to be a bit more explicit in the following statement of yours:

"but as the consequence of a probabilistic calculation of where the particle will be found, modeling the behaviors of probability densities by using abstract mathematical properties of Hilbert space."

For avoiding confusion you have to say that the QM mathematical apparatus goes with amplitudes of probability of different contributions, i.e. the probability of an event is the absolute square of the sum of all the complex amplitudes which contribute to that event. That, to the difference of classical mechanics were the probability of some event is the sum of the probabilities of the contributions.

I know that in the QFT the calculus goes differently, it involves the creation and annihilation operators - you are right in everything you say - but for an undergraduate I would stay at the level of QM not of QFT.

Kind regards!

@Charles Francis

> "both single photon and single electron interference are both very well established empirical phenomena"

Do you mind to cite any "established" experimental evidence of the above? 

@Charles and Aleš,

let me help. (Charles, you explain the things a bit too much abstractly.)

Of course that we have single-photon interference, i.e. sending a single photon to a screen with two slits, the two outputs that are obtained beyond the slits interfere with one another.

Let me justify that as follows: it is NOT possible to have a class of students that passed the QM exam, without each student and student having passed the exam. Similarly, in order to obtain an interference pattern from a beam of photons, each photon and photon has to obey the same rules: avoid the positions of the darkest fringes, let be detected with the highest probability at the position of one of the brightest fringes. From a single photon we won't get the pattern of fringes, for that purpose we need many photons. But each photon will behave according to the rules above

A clearer picture than a fringe pattern, is obtained if we bring the two outputs from the slits, on a beam-splitter (BS). Assume an ideal experiment, i.e. the slits are identical, the BS is non-absorbing, with R=T=1/2, and placed exactly in the middle of the distance between the slits and perpendicularly to that distance. If on one of the outputs from the slits we place a phase-shift of 3π/2, then each photon and photon will leave the BS through the side illuminated by that output.

Bottom line, the rules that produce an interference pattern, govern each photon and photon.

Aleš Kralj: "single photon interference" is understood as the interference of a photon stream, going through the two slits one by one.

A photon stream do not mean that a photon flies physically as a particle over air. No, we can only say that there seem to be waves between emission and absorption.

Dear Prof. Riley,

                             If the image formed on a X-Ray plate is of coherence and interference and there is no change in temperature in the closed box of the experiment so that no new particles have been created then it has to be the case that the particle beam has behaved as a string only to be integrated heterotically at the plate by integration of the meanfield. Please refer to my String Theory papers done Econophysically on my RG page. Earl Chair Prof. Dr. SKM QC EPS Fellow (In) MRES MES MAICTE

Spreading links to articles on the experience interference with single photons and quantum eraser, as well as to work with the C60 molecules. It may prove helpful to those articles:

- P. Grangier, G. Roger, A. Aspect, Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon Interferences, Europhys. Lett. 1, 173, 1986,

- M. O. Scully, K. Drühl, Quantum eraser: A Proposed photon correlation experiment conceming observation and "delayed choice" in quantum mechanics, Phys. A 25, 2208, 1982,

- O. Nairz, M. Arndt, A. Zeilinger, Quantum interference experiments with large molecules, Am. J. Phys. 71 (4), 319, 2003.

Problems of interference with the individual particles, atoms, molecules are considered in my book "The mysterious quantum mechanics. Experiments show the corpuscular-wave nature of matter" ŁośGraf Publishing House, Warsaw 2011 (book in Polish).

Regards,

Paul Pęczkowski

The misunderstanding is, a wave consists of many particles and it is a disturbance of energy that transferred from one point to another in a medium--- like wind, sound, and water waves. A wavefront encounters with a barrier (which is double-slit in this case), and elementary spherical waves occur, thanks to Huygens' principle which is an explanation of the diffraction phenomena with the wave theory. This wavefront consists of many particles, some of them pass through one slit and some of them another, which leads interference pattern. This interference pattern consists of dark and bright regions, in the dark regions waves cancel themselves (destructive interference), and in the bright regions waves amplify themselves (constructive interference). This interference is the superposition of waves, and due to superposition energy distribution of one wave is distributed upon another.

A beam of particles passes through slits, not one particle. To observe the interference phenomena, wave sources must be coherent and monochromatic, and the resulting wave must be governed by superposition principle. If one particle passes through slits and becomes a wave--- which is not, it might be possible to ask do we need coherent and monochromatic sources in order to achieve a wave? It is trivial that sound is a wave, but I can still hear the sound of an aircraft despite of the temperature differences between the engine and aircraft's position and my position. A 30-min review of wave, diffraction, interference might convince them, more important one is understanding wave. Actually the undergraduates are better to do follow waves and optics lecture well.