Let us recap what actually happen in the experiment: the llight, or the atoms, or molecules, are sent through two slits and they are detected on a screen rather distant from the slits. The detection is observed to occur in isolated events: one photon is detected one at a time, where by ``photon'' I simply mean that which causes a photomultipier to detect. The issue is then the following: if we accumulate many detections with both slits open, we wind up having a distribution of events on the screen which is smooth. If we proceed to make the same experiment with only one slit open, we have another distribution. The crucial point is then the one that is sometimes denoted by the word ``interference'': namely the compound distribution, the one arising from having both slits open, is not the sum of the two distributions resulting from having each slit open separately.

Clearly, the interference phenomenon is impossible to understand in terms of classical particles. Equally, the fact that each detection event is of similar intensity (we aways detect ``one unit'' of something, never 1/2 or  5/37) is unexplainable in terms of classical waves. It is also hard to imagine a purely wave explanation for the same experiment with atoms, or even heavy molecules: indeed, two-slit interference has been observed with C60, that is, a molecule consisting of 60 carbon atoms. It is hard to argue that these are intrinsically waves. They certainly behave as particles in most situations. It is handled as a quite ordinary particle by chemists. It can be seen with a microscope. It is, in other words, what we would call an ordinary object. Yet, if appropriate care is taken, it behaves just as light would in a double slit experiment. Again, one should emphasize that the detections at the screen are always made atom by atom, or molecule by molecule. The effect arises as a one particle effect and cannot thus be viewed as some kind of peculiar interaction.

The way quantum mechanics describes this is, at least nowadays, not by any kind of wave-particle duality, but rather via a notion of state: to each system configuration, one associates a complex amplitude. This association is the state, and from it one can compute the expected value of each proposed measurement, as the *square* of the modulus of some amplitude. The interference effects arise from the fact that, under appropriate circumstances, what must be summed are the amplitudes. A positive amplitude summing with a  negative one leads to one of the characteristic intriguing features of this experiment: some positions on the screen cannot be reached when both slits are open, but can be when only one is.

Note that these amplitudes must be associated to each configuration of the system. When the system consists of one particle, this can be made to look like a wave. When it consists of many particles, however, the difference becomes essential. This, of course, is important if we wish to understand why, on the screen, detections are discrete: this arises from the measurement interaction, which involves many particles, and which is such that no analogy between the quantum mechanical state and a wave can be made. Over all, I am not aware of a simpler explanation than the usual one of the phenomena I have summarized above.

Duality is a nice concept making easy to answer any question on the interference. Photon is only a quantum of electromagnetic wave. Wave is characterized, in particular, by the phase. Phase depends on the propagation path. Intensity of electromagnetic field. In case of two propagation paths  intensity depends on the relative phase of components of a superposition. Probability to detect photon in a given point is proportional to the intensity of a field in this point..........One may speak about the "phase of a photon" but rigorous quantum mechanicians will desecrate this concept....

Read the 1st chapter of Dirac's "The Principles of Quantum Mechanics" and Sakurai's "Modern Quantum Mechanics"...

regards,

ankur

Dear all thank you so much.

I want to understand this phenomenon from real time analysis point of view. if we assume there is an observer moving in the frame of the quantum particle how do you think will it see the events of this interference?

A similar idea is in superconductors: which way of choice for a single Cooper pair would be in the case, say, of two alternative conducting branches. Lot of reasechers ignore a single particle case (it's difficult, then cannot be written a paper to the time), and still devide the electric flow into two equal parts. But this decision is false, right following your ques, though being a such natural in the first sight.  

Since light has long been demonstrated to be an electromagnetic "wave" for which interference is unsurprising, the question should be why the energy of the photon manifests itself only at a point-like location which is small in comparison to the slits.  Sometimes this is called wavefunction collapse.  In any case, it is the primary effect of quantization of energy. 

So the question becomes why (and how) energy is quantized, does it not?  To "assume" the photon is a "particle" and try to explain from that is building a castle in the air (i.e. on that assumption which is unprovable).  Take the mystery at face value and try to understand it as it is, not as someone has mis-formulated it.

As long as the question is the relation between the wave and quanta - on both ends - then it is properly formulated for understanding.  If you assume you know what a photon is, you are making a mistake right there, because there is as much evidence for one thing as another.

I worked 40 years as an electrical engineer and have two degrees in it.  We build emitters which emit fields all the time.  It is no big trick.  In the modern age when kids are taught quantum concepts, the original dilemma gets lost ... and that was not how the emitter emits quanta.  It does so by Maxwell's equations.  The mystery is why the emitter does NOT emit at other times and thus why the hydrogen atom does not collapse.

This mystery is solved in QM by recognizing there is a kind of resonance, like a cavity, in the orbits and that transitions to a non-resonant state are not possible.  Once this is done, Maxwell's equations describe quite well how the emission propagates as a wave. 

The remaining mystery which we have not quite got at is how to invert this process.  It seems it would require that light either not be a wave, but particles, which creates the interference puzzle, or that some kind of FTL phenomenon is going on during wavefunction collapse, like Bohmian non-locality.

Dear Sadeem,

The following may help answer your question and highlights the need to deal with the photon (as well as other forms of matter) as having both wave and particle-like properties at the same time. I looked at this topic in my book “Physics in 5 Dimensions” in both Appendix B on page 486 – See Copenhagen Interpretation and in Chapter 8 Quantum Non-Locality on page 161. These pages are available via the Google book link at http://www.physics-in-5-dimensions.com/keyword.html using the link Click here for Keyword search and then entering the bold text names above to find the relevant pages.

In the case of the Copenhagen Interpretation look for “ ……. This poses some interesting questions. Suppose one were to do the double slit experiment and reduce the light so that only one photon (or electron) passes through the slits at a time. In performing the experiment, one will see the electron or photon hit the screen one at a time. However, when one totals up where the photons have hit, one will see interference patterns that appear to be the result of interfering waves even though the experiment dealt with one particle at a time. ……..”

In the case of Quantum Non-Locality look for “ ….. Experiments involving single electron diffraction and non-local single photons provide proof of the dual nature of matter and demand that we look at other important aspects of quantum mechanics. ………. In 1993 Elitzur and Vaidmann (EV) demonstrated that quantum mechanics permits the use of light to examine an object without a single photon of the light actually interacting with the object. The following text in is an edited version of the article "Interaction-Free" Quantum Measurement and Imaging by John G. Crame. ………………. In the interferometer shown in Fig 60, suppose that we use a light source L that can emit photons, one at a time, and on command …………….. One of the peculiarities of quantum mechanics, which distinguishes it from classical physics, is called the "collapse of the wave function". In a situation like the one described here, in which light waves that travel along two paths can interfere, the interference can take place only if we have no way of determining which path was taken. Any measurement that determines the path will "collapse" the wave function to that particular path, after which there can be no two-path interference. ………………..”

There is quite a lot to read about this subject in both classical physics as well as various aspects of ‘’Physics in 5 Dimensions. “Classical Physics” is defined in my book to refer to the current view of the fundamentals of physics including for example Quantum Mechanics and Einstein's Special and General Theories of Relativity.

In section 6.4.6 on 5-dimensional space and the Dual Nature of Matter we have ….. Matter can be considered to have reality in terms of both particles and waves. We have established the properties relating to both the wave and particle nature of matter and in section 6.4.4 reviewed the manner in which electromagnetic radiation can produce groups of matter waves with a particle-like-nature and energy…….

So your question is “knocking on the door” of some very important aspects of physics which relate to the creation of matter according to “Physics in 5 Dimensions”. However, whether you agree with this interpretation or not, the above references relate to the classical physics aspects of your question and so I hope the answer is of some interest.

Next week I hope to get written approval from the publisher to place the full text of “Physics in 5 Dimensions” on ResearchGate.

Why a single photon? Up to me, the most clear interpretation of many photon interference is that the each photon interferes with itself. I recommend The Feynman Lectures on Physics. In this book just the double slit experiment is chosen to explain the main principles of the quantum mechanics.

Let me add that it is the wave function that displays the interference.  The photon is not its wave function. The photon just does what its wave function tells it to do (statistically).

I know that this partially begs the question but then it partially doesn't.

Dear Johan,

If the photon is a coherent wave with a single frequency, then it is totally, temporally non-local and exists for all time. How to then to deal with the energy-time uncertainty relation? I believe that treating the photon as you suggest not only violates uncertainty relations but also fails to account for photon antibunching which is a well established phenomenon. 

Dear Johan,

I did not use the word temporarily in my comment.  I used the word temporally.  It was my way of saying that the photon depended on an extended range of time values rather than a single value of time.  I was using the term "non-local"  in time by analogy to the use of that term with respect to space. So I think that I am still doing physics.

Rather than pursue the role of uncertainty relations in this matter let me just again point out that if photons had the property that you assign them, then photon antibunching would not occur.  But it does.

Dear Johan,

at this point I will simply side with Einstein and Minkowski (a good group eh?).  

As far as antibunching is concerned: there is much literature on the subject and you can easily find discussions concerning the essential quantum character of the phenomenon.

Johan,

EM-wave travels at a finite speed.  In a Einstein-Podosky Rosen experiment two entangled photons can be kilometers from each other (I rather think that one single entity is kilometer extended) and if one interact than it has an immediate effect on the measured property of the other one.  Could an EM-wave change instantly accross space?

Gentlemen, now I almost understand nothing, so much ideas, if refer me to the initial question. I've just fixed the following:

How does quantum mechanics look for this interference?

- as an ordinary, basic effect.

Does the photon interfere with itself or are the waves accompanied with it interfering with each other?

- with itself, and, together with her wave friends, as well.

What's the relation of wave particle duality with this experiment?

- one can observe a wave or a particle, both not the Janus at the same time in this leading role.

What are the most acceptable interpretations of this experiment?

- those following from the theory of linear monochromatic waves. 

Am I right?

Dear Johan,

To clarify your misunderstanding of the intent of my remark about Einstein and Minkowski: it was merely my way of disengaging from what I considered to be a non-fruitful and somewhat ridiculous conversation.

Regarding Antibunching,( the first approach to producing and observing of which was due to myself), my purpose was to point out that the phenomenon is inherently quantum mechanical and has no classical counterpart.  That means that in the classical limit a state displaying antibunching does not survive. Your concept of a photon is so heavily mired in classical theory that it would prevent you from deducing the possibility of antibunching. Try it and see.

DS

Johan,

How did you come to your theory?  I guess it is a long story.

There are experiments that depend in an essential way on the quantum nature of electro dynamics (the mentioned anti bunching is one of them), and it is often convenient to think of photons as particles, discrete "silvery marbles". Seductive as this may be, a quantum particle really is not like that and the picture of marbles can be highly misleading. It is more of a figure of speech to count field excitations. For a configuration with a double slit the excitations of the EM field excitations have to take this slit into account, so asking how the photon is interfering with itself is sort of beside the point: there are only interfering field configurations that can be excited. 

However, I have never understood where the quantum field nature of light itself even comes in in the double slit experiment. In fact  I think it is much easier to understand the double slit experiment as a classical electromagnetic field exhibiting all the usual diffraction phenomena, interacting with quantum matter in the form of a sliver crystal or better,  a CCD pixel.  The characteristic spotty picture that are usually shown as "proof" of the existence of photons is then simply the result of the intensity of light being so low and/or the exposure time so short, that the probability of a CCD pixel to contain an excited electron in the valence band is of the order of 1/the number of pixels. For a single crystal pixel this means that the energy deposited on the pixel is of the order of the energy required to create an  electron/hole pair in the the conduction band or about 2* 1eV (one electron and one hole) = hc/ 620 nm (colloquially, the energy of a photon of light with wavelength 620 nm).  By one of the standard limit laws in probability, a probability of the order of the inverse of the  number of "tries" (pixels)  gives that the distribution of excited electrons over the pixels is Poisson i.e. it looks like the ccd has been hit by marbles raining on the ccd. The probability to contain an electron in the conduction band (or more technically the intensity of the Poisson process of the number of electrons in the conduction band  as a CCD essentially counts excited electrons) is proportional to the intensity of the light shining on the pixel. The interference pattern of the classical EM field then emerges to better and better approximation as the exposure time or intensity is increased.

Johan:

It is one thing to be wrong, it happens to everyone sometime.

As far as "stupid" is concerned, I don't engage in name-calling in public. 

The conceptual formulations that you have put forward are not stupid.

They are not even wrong. 

PS: What about the antibunching issue that I raised?

DS

Sadeem Fadhil (PhD, University Lecturer) is asking: "What's the interpretation of single photon interference in a double slit experiment?". Me: Dear friend, a single photon produces a dot as the impact place on the screen. How from this single event a wise-man can deduce the interference? P.S. My deep respect of your scientific degree, I am just the Master of Science, thus can be very wrong.

Dear Dmitri

With all respect to you and to your degree, I'm not asking about the definitions of interference in waves I'm asking about the quantum mechanics view to this phenomenon which is still under argumentation. Even the basic physics, like what are photons are still under argumentation. But there are different level of understanding, the same phenomenon can be studied in undergraduate level and post graduate level. some times the questions are only a way to give your view about certain subjects,I'm not shamed to ask about anything in physics and discussing it with others. Nevertheless if this question bother you  there are many other questions that you can find in research gate or other websites just follow them

regards

Dr. Fadhil: "How does quantum mechanics look for this interference?"

Me: According to article John Polkinghorne FRS (the Templeton Prize, Fellow of the Royal Society), ``Physics and Theology'' (Europhysics News 45/1 (2014)) both Bohr's and David Bohm's theories are not excluded by empirical evidence. Do you mean Bohr or Bohm theory under QM? They are opposite, incompatible, like Verity vs. Delusion.

Dear John-Francis, experiments over the Vavilov-Cherenkov radiation has confirmed a single photon observation using a good human eye as a detector. I agree, the word "detection" by eye would be better, instead "observation", though any human cannot be as experimental set.

Dear Johan,

Since I do not pay you to teach me basic physic do not feel oblige in any way to answer my question.

 Everybody knows maxwell equations and before quantum physics and before Einstein's experiment everybody thought that light was an EM wave.  What is it that everybody could not explain the double slit experiment by using the EM wave explanation?    What was missing in their assumptions.  From what you explained above, I get that they neglected to take into account certain physical  constraints (minimum energy, etc)  for the absorption and emission of EM wave.    Why is it that a EM-wave that is not interacting can instantaneously change its form accross the whole space.  You said that it is just a consequence of changing the boundary conditions on the solution of Marxwell equations.  Is it controversial?   In short I do not understand why is there such a difficulty to convince the scientific community when you are not introducing exotic physics but simply using old physics with a few constraints? 

Regards

My stock answer to our students is the wave-particle duality poses a problem of understanding to us but not to behaviour of the particle/wave itself.

Light does what light does - waves and particles are just our language/concepts that we choose to (try) describe it.

The wavelike properties define the probability distribution of the particle-like behaviour.

To try and understand a deeper significance of "particle" or "wave" is (I think) just trying to force the natural world into a superficial description.

Dear Johan,

The following paper related an old scientific-religious controversy that has some relevance.

The Metaphysical Reach of Science, by Michael Polanyi

https://www.missouriwestern.edu/orgs/polanyi/Duke/Duke1.pdf

Dear Johan,

Miles? a betrayer of physics? I must  demur!

isn't it the case that the categories 'particle' and 'wave' are just mental constructs - devices we've found helpful in forming a causal model of the classical world? to force the microscopic world into this mould, surely, will always lead to apparent paradoxes?

I would describe Miles' statement as the 'rational sceptic' interpretation of science - and perfectly respectable it is too...all there are - really- are observations and measurements. Equations interpolate between observations, and can also extrapolate from them, up to a point. None of this actually requires the metaphysical concept of "understanding" .

Dear Stephen,

You are right to say that Miles is representative of certain way to conceive science that celebrated philosophers of science such as Popper, celebrated scientist such as Bohr have suscribed and this still continue to be the dominant conception.  But it is not the only one. A lot of great scientists of the past were realist, were not guided by doubt.  And one of these great scientist, Michael Polanyi even explicitly formalized an alternative realist position, one that is based on the feeling of finding the truth and that contradict the celebrated honorable dominant position of today.

The Duke Lectures of Michael Polanyi February-March 1964

https://www.missouriwestern.edu/orgs/polanyi/Duke-intro.htm

presents an alternative view.

If we take the Ptolemy model , we can mathematically transform it into the Corpernicus model, just by a few transformations.  So mathematically, the two models is near equivalent.  But physically they mean two different worlds and most importantly if you think in terms of the Ptolemy model you cannot understand tides, you cannot do what Kepler did and Galileo did.  They not equivalent phyical models.  But in this thread we are not discussing philosophy but a specific theory.  That theory offer a much simpler model that the current quantum models and even though the later make predictions that have been tested and have been usefull, if Johan's model make the same prediction but with a simpler way, a way that is easier to understand then it will be a much better physical model and one that can lead to discoveries that we cannot do with the other ones.  

In practice, experimentally one can construct an interference pattern photon-by-photon or atom-by-atom. In the last case it is easier, as atomic beam fluxes are generally less intense than laser ones. I have made experiments with metastable hydrogen atom beams where the average distance between each atom was of the order of 1km, and I used counting method to register the interference signal atom by atom. At each scan of the acquisition device there was less than one atom.

To get interference pattern suppose the accumulation of many realisations with a parameter that has to change. Even for the light what you see suppose a discretisation of the observation region. So the interference pattern can be constructed atom (particle) by atom and there is still one as the wave function, which is related to the repartition of the loci of arrival of the atoms. As a consequence it is more related to a macroscopic property of the system as it has to be for any wave problem (see Kirchhoff-Helmholtz theorem) than to a microscopic one.

People using neutrons have observed the same kind of construction of interference packet neutron by neutron.

One can also play with the statistic within the beam and count only atoms that arrive within a definite time interval by a bias on the detecting device. In that case the interference pattern can be totally modified. These experiments had been realised first with neutrons see H Rauch, and we have reproduced them quite easily.

As a conclusion when one makes the experiment the question gets another taste.

Read the paper of Charles Townes named "anti-photon", or  the paper he wrote later wirh Willis E. Lamb (both Nobel) and other good physicists: The photon results from quantization of "normal modes" of electromagnetic fields. You are not allowed to use it in free space. This your problem is meaningless.

Let us recap what actually happen in the experiment: the llight, or the atoms, or molecules, are sent through two slits and they are detected on a screen rather distant from the slits. The detection is observed to occur in isolated events: one photon is detected one at a time, where by ``photon'' I simply mean that which causes a photomultipier to detect. The issue is then the following: if we accumulate many detections with both slits open, we wind up having a distribution of events on the screen which is smooth. If we proceed to make the same experiment with only one slit open, we have another distribution. The crucial point is then the one that is sometimes denoted by the word ``interference'': namely the compound distribution, the one arising from having both slits open, is not the sum of the two distributions resulting from having each slit open separately.

Clearly, the interference phenomenon is impossible to understand in terms of classical particles. Equally, the fact that each detection event is of similar intensity (we aways detect ``one unit'' of something, never 1/2 or  5/37) is unexplainable in terms of classical waves. It is also hard to imagine a purely wave explanation for the same experiment with atoms, or even heavy molecules: indeed, two-slit interference has been observed with C60, that is, a molecule consisting of 60 carbon atoms. It is hard to argue that these are intrinsically waves. They certainly behave as particles in most situations. It is handled as a quite ordinary particle by chemists. It can be seen with a microscope. It is, in other words, what we would call an ordinary object. Yet, if appropriate care is taken, it behaves just as light would in a double slit experiment. Again, one should emphasize that the detections at the screen are always made atom by atom, or molecule by molecule. The effect arises as a one particle effect and cannot thus be viewed as some kind of peculiar interaction.

The way quantum mechanics describes this is, at least nowadays, not by any kind of wave-particle duality, but rather via a notion of state: to each system configuration, one associates a complex amplitude. This association is the state, and from it one can compute the expected value of each proposed measurement, as the *square* of the modulus of some amplitude. The interference effects arise from the fact that, under appropriate circumstances, what must be summed are the amplitudes. A positive amplitude summing with a  negative one leads to one of the characteristic intriguing features of this experiment: some positions on the screen cannot be reached when both slits are open, but can be when only one is.

Note that these amplitudes must be associated to each configuration of the system. When the system consists of one particle, this can be made to look like a wave. When it consists of many particles, however, the difference becomes essential. This, of course, is important if we wish to understand why, on the screen, detections are discrete: this arises from the measurement interaction, which involves many particles, and which is such that no analogy between the quantum mechanical state and a wave can be made. Over all, I am not aware of a simpler explanation than the usual one of the phenomena I have summarized above.

To Johan: do you really believe a C60 molecule can be fully modelled by a classical wave? In any case, however, your comaprison with antennas is misleading: Reeception of waves by antennas is not quantized: the size of the signal received varies continuously. And if you have many antennas receiving a classical wave, they will all simultaneously detect various intensities from the same wave. Antennas emphatically do nothing like collapsing radio waves. (If they did, my turning on the radio would make it impossible for my neighbour to receive anything).

On the other hand, in the quantum double slit experiment, you have a whole screen full of detectors, and each time only one detector fires. This is true for EM radiation, but also, less surprisingly, for atoms and molecules. The detectors only detect one atom at a time because there is only one atom. Similarly, they detect only one wave quantum at a time, because there aren't any more. In the case of classical waves, on the contrary, all antennas which are within the region occupied by the waves will respond variously and continuously. It is this difference which makes it impossible to accept a purely wavelike description of quantum mechanics.

Finally some questions as to what you could actually mean in your remark: you speak of ``Add to this that such an antenna cannot absorb more or less energy than hf; and it means that an impinging diffracted light wave with energy hf, can only collapse in one of the MANY atomically-sized antennas.'' Why can an ``atomic size antenna'' not absorb more energy than hf? first of all, why should EM energy *classically* be related in any way to frequency? If you follow the tack of classical EM, energy can only meaningfully be connected to intensity. Why does an EM wave ``collapse'' on an atomic size antenna, if we see that it fails to do so on another antenna? Again, why do you speak of ``an impinging diffracted wave with energy hf''? Once more a wave, whetther diffracted or not, has an energy determined by its intensity, not by its frequency. So in a way, the concept you seem, darkly, to be grasping for, is clearly that of a photon. Which is all well and good, but by no means classical. So in the final analysis, we may turn out to be saying the same thing :) !

To prof. Leyvraz,

Thank you for your clear and concise contribution! this one, I think, makes sense to me...on a side issue, you mention experiments with C60. Do you know if analogous experiments have been performed with anything larger? and if so, ho large, and what was concluded. I'm imagining an experiment with laser cooled nanoparticles, for example - is that unreasonable?

Regards, Stephen

Dear Johan,

In response to professor Lyvraz's question, "do you really believe a C60 molecule can be fully modelled by a classical wave?", you say, "The hydrogen atom is modelled in terms of waves, so why not the C60 molecule"

The original question concerned modelling hydrogen atoms as classical waves. Perhaps I'm misunderstanding you here, is it your position that the hydrogen atom, and a C60 molecule can be modelled as classical waves?

Regards,

@Stephen: I am not aware of work on larger molecules. The reference is Nairz, Arndt and Zeilineger, Am. J. Phys., Vol. 71, No. 4, April 2003 . However, there is work on interference effects in Bose-Einstein condensates, which may involve more atoms, but in stranger conditions. 

@Johan: the solution of the Schrodinger equation cannot be obtained from any wave equation, at least for a system having more than one particle. This followsfrom the fact that the solution of the  Schrodinger equation depends on all the particle positions simulatneously. If there are two particles and the system is three-dimensional, the psi function will depend on 2 times 3 = 6 space arguments and time. A wave of whatever constitution, however it may be connected to the Maxwell equations, only depends on time and position, that is on 4 arguments. I do not doubt one can imagine ways around this, but one then either will not be dealing with the Schrodinger equation as it is usually understood, or one will be extending the meaning of wave far beyond its ordinary acceptation.

Dear Professors Johan Frans Prins  and F. Leyvraz and all others:

Thank you for your excited discussions...I really enjoy the physics that you are displaying in your discussions. I just want to add: that the Schrodinger's solution is actually derivable from Lorentz transformations which already agrees with Maxwell's equations, but in a condition that the transformations become complex when made between the elementary particles and classical observers. I already used my new complex transformations in deriving the complex form of wave function from the complex transformations that are given in the following reference:

https://www.researchgate.net/publication/259996539_Solving_the_instantaneous_response_paradox_of_entangled_particles_using_the_time_of_events_theory

This fully agrees with Quantum mechanics, special relativity and Maxwell's equations. So, the equations from these theories can be combined together easily through these transformations.

Article Solving the instantaneous response paradox of entangled part...

Sometimes ago I responded to a question almost identical to this one. There is no mystery in this single-photon double-slit experiment! So long as interaction between photons is neglected, there is no difference, whatever, between the interference pattern corresponding to many photons released over a short period of time and that corresponding to a long-time observation associated with a single-photon; in both cases the underlying physics is described by the same equation. The situation changes when we take into account photon-photon interaction, the quantitative difference depending on the strength of the interaction.

Dear Prof Behnam

Usually in double slit experiment the interference pattern is yielded from the interference of waves according to classical theory of waves interference. In single photon the quantum effects arise more clearly that the pattern is rebuilt again but this time with multiple measurements. So the interpretation is still under argument in single photon case.

Dear Sadeem, I expressed my view on the basis of my personal understanding; for me personally, there is no argument as yet to be produced on the subject matter. As I indicated above, the interference pattern is there even for a single photon, the only problem with this being observational/instrumental of nature, and hence the necessity for observation over a sufficiently long period of time. This requirement can be relaxed by increasing the number of photons -- so long as the interaction between these photons is negligible, the two type of observations yield exactly the same outcome. 

A laser is NOT a single photon source by definition: it is stimulated light thus the result of a stimulating light source:

Here is the latest on REAL single photons

http://arxiv.org/pdf/quant-ph/0410112.pdf

This study combines the particle (anti-bunching) and wave nature (interference) of one PHOTON.  N.B.: the interferometer works in the same way as a double-slit

http://freespace.virgin.net/ch.thompson1/People/CarverMead.htm

Now, in the opening years of the new millennium, Mead believes that it is time to clear up the philosophical and practical confusion of contemporary physics. He revisits the debate between the Copenhagen interpreters of quantum physics--Niels Bohr, Alfred Heisenberg, John von Neumann, Richard Feynman--and the skeptics, principally Albert Einstein and Erwin Schrodinger. Pointing to a series of experiments from the world of microelectronic and photonic technology that still lay in the future when Bohr prevailed in his debates with Einstein, Mead rectifies an injustice and awards a posthumous victory to Einstein.

During a lifetime in the trenches of the semiconductor industry, Mead developed a growing uneasiness about the "standard model" that supposedly governed his field. Mead did not see his electrons and photons as random or incoherent. He regarded the concept of the "point particle" as an otiose legacy from the classical era. Early photodetectors or Geiger counters may have provided both visual and auditory testimony that photons were point particles, but the particulate click coarsely concealed a measurable wave.

Central to Mead's rescue project are a series of discoveries inconsistent with the prevailing conceptions of quantum mechanics. One was the laser. As late as 1956, Bohr and Von Neumann, the paragons of quantum theory, arrived at the Columbia laboratories of Charles Townes, who was in the process of describing his invention. With the transistor, the laser is one of the most important inventions of the twentieth century. Designed into every CD player and long distance telephone connection, lasers today are manufactured by the billions. At the heart of laser action is perfect alignment of the crests and troughs of myriad waves of light. Their location and momentum must be theoretically knowable. But this violates the holiest canon of Copenhagen theory: Heisenberg Uncertainty. Bohr and Von Neumann proved to be true believers in Heisenberg's rule. Both denied that the laser was possible. When Townes showed them one in operation, they retreated artfully.

In Collective Electrodynamics, Mead cites nine other experimental discoveries, from superconductive currents to masers, to Bose-Einstein condensates predicted by Einstein but not demonstrated until 1995. These discoveries of large-scale, coherent quantum phenomena all occurred after Bohr's triumph over Einstein.

…..

So early on you knew that electrons were real.

The electrons were real, the voltages were real, the phase of the sine-wave was real, the current was real. These were real things. They were just as real as the water going down through the pipes. You listen to the technology, and you know that these things are totally real, and totally intuitive.

But they're also waves, right? Then what are they waving in?

It's interesting, isn't it? That has hung people up ever since the time of Clerk Maxwell, and it's the missing piece of intuition that we need to develop in young people. The electron isn't the disturbance of something else. It is its own thing. The electron is the thing that's wiggling, and the wave is the electron. It is its own medium. You don't need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn't something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That's what waves do.

So how big is an electron?

It expands to fit the container it's in. That may be a positive charge that's attracting it--a hydrogen atom--or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That's what all waves do. If you try to gather them into a smaller space, the energy level goes up. That's what these Copenhagen guys call the Heisenberg uncertainty principle. But there's nothing uncertain about it. It's just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that's ten feet across, there's no problem with that. It's its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.

A ten-foot electron! Amazing

It could be a mile. The electrons in my superconducting magnet are that long.

A mile-long electron! That alters our picture of the world--most people's minds think about atoms as tiny solar systems.

Right, that's what I was brought up on-this little grain of something. Now it's true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one's positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there's a place where they are just right, and that's what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation.

Dear Johan [Johan Frans Prins], I did not utter a word about the coherent state of photons (e.g. laser light). Please re-read my relevant comment: I just said that where the photon-photon interaction can be neglected, from the theoretical perspective it matters not a bit whether one considers the interference pattern of a bunch of photons or of one photon at a time. In your comment you ascribe things to me that I have made no statement about. (I certainly did not make any general statement with regard to the phenomenon of interference -- I just focused on the main question on this page).

I agree with Johan Frans Prins and with:

Willis E. Lamb, Jr.,  Nobel for the  exact computation ofenergy levels of H atom . Look at his paper “Anti-photon.” [Appl. Phys. B 60 77-84 (1995).].  Look also at  [W. E. Lamb, Jr., W. P. Schleich, M. O. Scully, C. H. Townes, “Laser physics: Quantum controversy in action.” Rev. Mod. Phys. 71 S263-S273 (1999).

The theory of photon is quantum electrodyamics which quantizes "normal modes" of electromagnetic field which exist only in perfect resonators. Photon  may be useful in almost perfect resonators, but not in free space.

Use of photon leads to neglect optical coherence in nebulae, so that elementary explanations of a lot of observations can only be obtained introducing a lot of fantastic and absurd theories (big bang, dark things, MOND, and so on. For instance, the redshift is simply an impulsive stimulated Raman scattering which uses the incoherence of usual light to transfer energy from light to background.

No problem Johan. Incidentally, the "ee" should be "i".

I had always thought that the best answer was this: There are no particles. There are no waves. There are only excitations of a quantum field (think field quantization) which already fill all space. The vacuum state already knows about the "interference"  (think the mode expansion) before you even excite it. Putting photons in is just banging the vacuum with an a^\dagger, so of course a single photon looks like it interferes with itself because you light up the whole field at the same time. Propagation in this sense is rephasing among the components of a mixed state. So for me I had always thought that the field notion was more primitive than the particle or wave notion, and therefore more powerful for a logical narrative of what is going on.  Did I misunderstand the question? What am I missing here?

Johan:``The resaon why you see a spot on the screen is that the DETECTOR in the screen is of atomic size: A SINGLE wave like a laser-wave, thus has to disentangle the amount or energy that such a detector can absorb, and this is exactly equal to h*f.'' Putting this together with your insistence on using classical waves, I simply fail to see what you mean. It is an obvious mistake to say that there is sucha a thing as a ``single wave''. Waves do not comoe in bundles (I mean, of course, classical waves). Rather they have a continuously variable intensity. Speaking of energy of a single wave being h*f has nothing to do with classical behaviour and cannot be obtained from Maxwell's equations: these are linear, so if you diminish the intensity, all the penomena get scaled down proportionally. A wave that had a given energy, proportional to its intensity, will not ever become ``a single wave'' with energy h*f. To start with, in your approach, where does h cmome from? Perhaps I need to remind you that h does not occur in Maxwell's equations, and that it is thus close to a contradiction in terms to say ``Maxwell's equations as interpreted by the constanccy of the speed of light within all inertial reference frames prove that ANY moving entity with mass m, from Jupiter to C60, has a de Broglie wavelength''!

Might I end with the respectful suggestion that studying quantum mechanics might be a useful step previous to criticizing it?

Johan

There is no CW-laser producing light with a ONE single frequency.

BTW: ever heard of a PULSED (Nd YAG) laser?

But that is not the issue in this question here: the question is about single photon interference. As discussed in the link that I included there are sources of single photons. The proof for discrete photons is the antibunching behavior.

(There is a single photon source based on your specialty (nano) diamonds molecules.)

Bottom-line: the double-slit experiment has been done with single photons

My beef is

single frequency light does not exist

single photons do exist

We have gone beyond the question but it makes some fun.

In order to add some positive input on these question’s answer, I would like to mention the way measurement of observables is explained in “quantum statistical properties of radiation” by W.H. Louisell John Wiley ed 1973. This point of view both operational and conceptual can also be found in the book of E. Schrodinger “statistical thermodynamics” and of J. von Neumann and D. Bohm (written before his re-examination of quantum mechanics).

One can find on chapter 1§11 on page 43 of Louisell: If we measure an observable L a large number (actually an infinite number) of times, each time with the system in the same state ⎜ψ〉, and average all these measurements, we shall assume that the average is 〈L〉=〈ψ⎢L⎢ψ〉/〈ψ⎢ψ〉, All physically realizable states ⎢ψ〉 are represented by vectors of finite norm. And idem for a function f (L). Then it is written” the quantum averages are ensemble averages; that is, it is assumed that there is an infinite number of identical quantum systems, each prepared in an identical way, with non interaction between them. Each system is called an element of the ensemble. And two lines after. It should never be overlooked that a quantum average is an ensemble average with every element of the ensemble in state ⎢ψ〉.

So there is no mention of particles but of quantum system each of them prepared in an identical way. That is the experimental conditions have to remain the same during the all run of the experiments. And there are a huge number of realizations of this state (that can also be represented by a state operator i.e. a density matrix). So you have to register many “clicks” to get the average of the desired observable. And to detect an event somewhere can (should be explicitly) be represented by a projection operator. To compare the number of events in one point to the number of events in another point allows obtaining a curve. If you want to know the expectation value of the fluctuations you have for each location to compute the fluctuation of the related projection operator. You have also to take care of the number of particles you use. For a one-particle state (wave function) you get an average curve each point of the curve corresponding to the measurement of the projection operator on this point, but you have also to compute the fluctuation at each point. This gives you the probability to get one click somewhere. And you do the same for a two-particle wave function, which gives you the probability to get two, clicks somewhere, etc. .

Doing so avoid the voodoo formulation but imply some computational work. It is the way that one should use the quantum formalism for any experiment and it is reliable for the two slits or one slit experiment as diffraction and interferences are of the same physical origin.

What I have written in my first answer followed and pictured these more formal lines.

I agree that what precedes is a little boring, but the way used in the 70’s has proven to be efficient, if not flashy.

I add a precision to my preceeding answer I should have used a "one system state" instead of a "one particle state" the statistical independence is between teh measurement events, the measured systems can be interacting systems with Bose-einstein or fermi-dirac statistics used to define the symetry prpoperties of the quantum state. but once again each measurement process, that is each "click" has to be independent of the others so that to realize a Gibbs ensemble for the measurement process.

Wave-particle duality answers by an absurd concept a problem of mathematics that Louis de Broglie failed to solve because he had not convenient mathematics. This problem is the problem of "solitons", that is of non-linear waves. It remains a nearly impossible to solve problem.

The lack of convenient mathematics became an absurd physical concept.

Johan

You apparently refuse to read / study recent literature about single photons. You continue with your own idea of a source that emits single frequency light: WHICH source does so, in your OPINION?

It emits EM, not particles.

Johan

A laser with a single frequency and single photon: show me where in literature you encountered this.

Which atomic line is of a single frequency? Heard of lifetime-broadening?

Johan

I (re)iterate: a laser is by definition not a single-photon source because it is STIMULATED light, meaning stimulated by a source of photons

A real single-photon source emits concrete bunches of light in time/space as proven by the anti-bunching; THE evidence that a photon is not a continuous wave

I give you another famous early reference for single photons

https://www.haverford.edu/physics/love/teaching/Physics302PJL2009Recitation/03%20Hanbury%20Brown%20Twiss/PhotonAntiCorrelation-Grangier-Roger-Aspect.pdf

And where in the single-photon story do your usual QM culprits fit in?

A single photon is a single photon by whatever name you call it and single frequency photons do not have anti-bunching:

 http://scienceblogs.com/principles/2010/08/20/why-antibunching-equals-photon/

The photon beeing a wave alone does for me not conclusively explain why it can collapse at absorption into exactly one h*f or how it transfers correlation instantaneously between entangled parts. Something keeps track of it, that only one photon will be absorbed after one has been emitted. With catching a part of a wave on a shore I cannot cancel the whole wave along the shoreline. It will only create a small wave that expands with "wave velocity". "Beeing in instantaneous contact with itself" is a vaque concept that deserves more explanation. If there is no croupier watching the game and counting photons in and photons out than the photon must be some entity, maybe resting in one point in a certain space. Call it particle in common space or not.

Dear Johan,

Since the electron wave orbits in atoms or stable spatial electron wave configuration in atoms have specific energy levels, that there are no energy in between, then the emission of the photon wave by the transition of an electron wave to a lower energy level can only be instantaneous and so the photon-wave creation can only be instantaneous and for it to happen without reaching infinite density near the atom that energy has to be instantaneously transmit to the full photon-wave volume.

Although what I describe is vague, is it a correct interpretation?

Johan

A single frequency wave has no boundaries and therefore is not a physical entity.

A moving electron is the product of the TIME-DEPENDENT Schroedinger equation and a wave-packet is a solution of that equation