I don't think that the fields (E,H) of (single) photons are observables. It takes coherent many-photon states to have quasi-classical, observable fields, but for these the question is obsolete.

The non-observability of the fields put aside, I still think that the 'answer' to your question would not be unique. Photons are quantized modes of the em field and to me their "shape" depends on context - i.e. boundary conditions. Photons also can have rather well defined energies, and then the wave train must be much longer than a single wavelength.

Coming back to "observing a photon crossing some point of observation": what kind of observation would you suggest for revealing the presence of the photon? Absorption is a possibility. the length of the wave train then does not give the duration in time during which the presence of the photon is noticeable but rather an uncertainty with respect to the point in time at which moment you will observe the absorption to (instantly) take place in case it does.

Thanks Dr Fauth for your several points to think seriously.  

With the emergence of advanced technology, there are many companies which make single photon counters capable of counting a single photon at a time.  Presuming that this counter involves the process of absorption of a photon in the detection medium and this process is same that we learn from the theories of absorption of light, it appears  that even a single photon moves with electro-magnetic field around its location at a given point of time.  Now the question is if this field is existing well ahead of its location, then the field reaches the detection region before the photon itself; apparently, this seems to violate the principle of causality, -while I guess  so but may be wrong.  Similarly, if the field lags behind the photon then it would amount to have its interaction with detection medium even when the photon has moved beyond the detection region.  But since the field is still in the detection region for which the photon is keeping its interaction with detection material implies that the photon can be absorbed in the medium even when it has gone out of it.  This thought experiment  tells that the filed does move with photon and it neither travels ahead nor lags behind the location of the photon at a given instant;  the only region that could be relevant is of the order of wave length or possibly half of it which represents the wave packet size of the photon.  

However, in spite of the simple logic which seems o.k, I am not sure of its accuracy.  Perhaps  a sound discussion helps in underlining the truth. 

I have doubts on whether "location of the photon" is a valid concept. the photon is an electromagnetic quantum object.

For comparison, think of electrons. If you ask it ( each time by means of an appropriate single experiment)

a) "whats your charge ?", you'll always get the response "-e".

b) "where are you ?", you will always get an answer ("here") to within the precision of your apparatus. [in theory, measuring position is represented by applying the position operator. After doing that, the electron will be in an eigenstate of that operator, this happens to be the Dirac "delta function" at the measured position. this is not, however, a stationary state for the electron]

In case of b), you can't know from a single experiment, if that information was complete (giving you all "quantum information" on the electron). Ask question b) to trillions of electrons in hydrogen 1s states, and (despite them being identical) you shall get loads of different answers, which statistically are represented by the probability density function of the H1s electron wave function.

Ask the same question to an ensemble of electrons prepared in the H2s state, and you will get another set of answers, piling up to a different spatial distribution. This doesn't exclude getting the same answer from two electrons prepared in two different states.

So from this, what is the validity of the concept "location of the electron"? To me, the same applies for photons.

All of this is not against the existence of single photon counters ihmho. Now concerning the theories on absorption of light, it may depend on the level. What one usually gets exposed to in qm lectures is a semiclassical theory, using the em fields as a perturbation (of "classical" character) to the quantum system. This approach, while doing many things quite nice and providing an analogy to the entirely phenomenological approach of electrodynamics, cannot get the quantum aspects of em radiation right. Therefore, for a further discussion, it would be useful if you specified the desired theoretical context of the description of the absorption of light (or whatever detection scheme) - just to be sure that everybody is pondering the same subject.

http://phys.org/news/2015-03-single-photon-quantum-memory-diamond-optical.html

and related sidebar articles may help.  You can count single photon events by interacting with them but not by watching them passing by...

Even in semi classical approach, the em filed matter interaction is a necessary condition for detecting the photon or em field. Under bound conditions, the wavelength associated with photons and the Bohr radius of the system may play an important role in deciding the life times of photon decay and will set the limit for its detection. Even in the field theoretical approaches, the decay time or the detection limit for observing a photon will not be same for all kind of photon as the states broadening will depend on the associated wave length and interaction.

In my understanding, in the semiclassical approach there are no photons, just fields. But then, if the fields are not observables with (single) photons, this is exactly where the different approaches disconnect and it gets easy to produce incoherent language.

{The connection to photon annihilation and hence absorption is somewhat artificial in the semiclassical description. What a (weak) classical excitation does [to a 2 level system] is to create Rabi oscillations (leaving aside damping and dephasing mechanisms for the time being). There are no such oscillations in single photon absorption.}

O.k. let us see the specific experimental reality.  experimental techniques can produce light pulse of pico and femto seconds which means that all photons in such a pulse are confined to a time span of 10^{-12} and 10^{-15} seconds which implies that all photons are confined to .01 and .00001 cm of space line.  This is how a lay man would think and this implies that location of photons can be determined the same way we determine the location of a moving electron.  One can see a light pulse coming towards a point in the space and passing by that point.   Since quantum mechanics defies lay man's perceptions, I want to understand how this observation is interpreted in wave mechanics.    

As far as the electrons moving around the atomic nucleus are concerned there are close loops; electron(s) move repeatedly on these loops and it is difficult to see them in terms of their locations as we can keep track of electrons moving on straight line or open loops.  For all practical purposes they can be replaced by density (mass/ charge) distribution and I wonder if it amounts to believing that electrons get fragmented into pieces to have a mass or charge distribution.  

Could we say that wave packet representation of a quantum particle is applicable or is not applicable to a photon ?    

You are right about the short pulses, these (and even shorter ones) can be produced. These pulses are coherent (laser) pulses, though, comprising a large number of "phase correlated" photons and correspond to a classical electrodynamic wave train, where em fields are now real and observable. The large number of photons in these pulses leads us to the realm of the correspondence principle, i.e. that quantum mechanics at high quantum numbers may yield correspondence to classical physics.

No, electrons cannot be point objects moving on closed loops around the nucleus in an atom. This Bohr picture is necessarily wrong, since the electron would in this case have to collapse into the nucleus very rapidly, emitting em radiation in that process. This does not happen - the classical image of a small kind of planetary system is therefore to be rejected at this microscopic scale. (The emission of radiation by accelerated charged particles is an extremely well-known phenomenon today - the many synchrotron radiation sources worldwide operate on exactly this principle. The classical picture is thus well verified in this regime of very high energy - the laws reigning at small energies [or quantum numbers] are necessarily different).

Notice that the orbital movement of lowest energy of an electron in the electrostatic field of the nucleus carries zero orbital angular momentum ("s-electrons") this is yet another aspect of the inadequacy of the idea of Bohr orbits (there is no mechanical circular or elliptical movement with finite radius and finite velocity and zero angular momentum).

So, for the electron to be stable in the lowest energy state of an atom, it is essential that its charge density be stationary, meaning time independent. It is not fractured. It's the quantum nature of the electron to adopt a state represented by a spatially extended "wave function".  The time evolution of that function is approx. given by the Schrödinger equation, and in terms of "where the electron is, when I do an experiment to find it out" this function represents a probability amplitude. (etc. etc.)

{It might be helpful to recall the capacity of single electrons to do diffraction - just as photons do. The electron thus has to have the capacity to probe electrostatic potentials at different locations at the same time - this is an aspect of its wave character.}

An ultrashort laser pulse is certainly adequately seen as a wave packet. In vacuum, the shape of the wave train is highly stable, since the velocity of light is the same for all frequencies (linear dispersion relation). This changes upon propagation in matter and is altogether different for particles with finite rest mass (such as electrons, parabolic dispersion relation at small energies).

Dear Prof Fauth,

Thanks a lot for your detailed discussion which has greatly helped me understanding issues related to my question. 

In wave mechanics a particle is recognised as a wave packet of size ~ $\lambda/2$  where $\lambda$ is related to momentum of the particle.  Even a particle trapped parabolic potential can be seen to have a spread of about $\lambda/2$ in its ground state if we use ground state energy equal to p^2/2m and use p to determine it $\lambda$.  What I mean is wave packet representation of particle is universal nature.  And in fact when wave mechanics assumed this premise I do believe that it was believed to be valid in every case.   Experiments also reveal that wave packet manifestation assume relevance only when we are dealing with situations of the size of $\lambda/2$,  In low energy states of an electron in atomic orbits we are dealing with such situations but in high energy situations $\lambda/2$ becomes much shorter than orbits radius hence correspondence principle is valid.  $\lambda/2$ of He-atoms in liquid helium compares or becomes larger than inter-atomic distances at a T such as few K  and these liquids really exhibit quantum effects at macroscopic level unlike other liquids where $\lambda/2$ is much shorter than $d$.   As such, what I perceive that electron moves around the atomic nucleus as wave packet not as point particle.  And to this effect your perception of electrons in different orbits and my perception do not differ significantly.  And whatever confusion remains I believe I will be able to resolve.  

As such in agreement with the packet manifestation of a particle as one of the basic premises of wave mechanics, it appears to me that packet representation should be valid to a pulse of many photons as well as to a single photon.  However, if I am not wrong in understanding your argument, it appears from your discussion that it is valid for the pulse of photons in their phase correlated state but not for single photon.  I tried to rationalise and thought about seriously but so far I could not help myself.  I would appreciate your helpful comment.    

Hello again,

I do not really agree with your description of what a wave packet actually is, and certainly not with the kind of restriction you give for its spatial extent. I won't have time to go in very much detail, but take my notions here.

To me, "a photon" essentially is "a quantized mode of the electromagnetic field". In free space these modes could classically be monochromatic plane waves. Such states have the nasty feature that they cannot be normalized in the qm sense. (Classically its not much different: a strictly monochromatic plane wave is unrestricted in spatial extent therefore carries infinite energy as soon as the amplitude of the fields is nonzero).

The mode spectrum of free space is continuous. Were we to deal with em radiation in a cuboidal box with metallic walls, then these boundary conditions would imply a discrete mode spectrum (of standing waves).

The modes have one well-defined quantity, its their frequency of oscillation. Moving to qm, we get eigenstates/quanta instead of classical modes, each of these being assigned an energy content \hbar\omega.

Spatially confining the em field  *in free space*  requires the superposition of a continuum of different modes. That to me is a wave packet. Its spatial extent depends on the superposition you choose.

There is an analogy to harmonic oscillators. Their basic spatial confinement is provided by an "external" potential. Therefore, already the eigenmodes are spatially confined. In the lowest energy state (could tale either the h.o. or the atomic 1s state) there is no way to talk about something like a wavelength at all - the shape of the "wave functions" is more pulse-like than wave like. In terms of the eigenstates of free space, these would be wave packets, but in their system, they're just the eigenmodes.

Wave packets are still a useful concept though: consider/construct a state in which the (h.o.) object is localized at some point in time (t=0, say) at a non-zero position (might look like the ground state function but displaced). This is then a non stationary state (it changes (center of mass) position & shape as time moves forward). Yet you can write down this displaced state at t=0 as a superposition of the functions representing the stationary states. This again is a wave packet to me.

So I have a stupid question for this thread: A flux in electric field produces a magnetic field which...with Maxwell's equations, and Faraday's law,  implies the induction of voltage within a circuit loop that you might have oriented around the path of the electron. Via quantum mechanics though, you can't simply act as if this induced field puts a force on electrons within the wire; QED tries to explain this, but it is still very weird. As far as I understand, some level of orthogonal force has to be exerted, and it would be done so by a virtual partical...can anyone expand on this?

Henry, I don't get the core of your question. What process are you pondering?

(consider opening an independent thread, we're more on wavepackets etc. here)

Well, Yatendra asked a question about a photon's electromagnetic field; in general this isn't a "real" question due to the nature of photons and quanta in general. If it were framed within the realm of an electromagnetic wave such as a directional (plane wave) wifi signal, it'd be a much easier question to answer - you can simply construct the em wave using Maxwell's equations, and note that different wave structures result in different wavefront arrival times. Is a wave packet truly the best perspective to approach a definitively quantum mechanical phenomena? I don't think so myself.

So I thought it might be pertinent to take the topic elsewhere in order to more fully address his question; quantum electrodynamics handles this exact sort of thought experiment too, so...here I am :) considering all this though, I'd be happy to take the topic elsewhere if Yatendra is looking for a more classical answer.

Agreed. Lets have Yatendra decide whether we have reached a point of kind of an answer to his original question which justifies moving on. I am not sure at all. We'd still have to deal with the single/multi photon issues properly.

In QED I'd be moving on very thin ice, however, and prefer listening to those who know more and better than myself!

Perhaps there are some confusions in understanding my question and my concerns.  I find Kai's last but one post reasonably informative.   However, there are certain confusions because light has finite velocity.   I am trying to rationalise all these information by considering different experimental possibilities which help me in re-framing my question with desired clarity. 

@ Dr. Kai,

I pondered on several points that came during this mode of communication.  I think we can take each point separately.   As you said in your first post that you don't think that the fields (E,H) of (single) photons are observables.  I tried to understand this point in relation to Young's double slit experiment with single photon.  I do not know if I rightly understood it but to me this experiment implies that single photon exists and moves from one slit to another and finally reaches at the detector.   I would appreciate your comments on the apparent disagreement between your statement and this experimental reality.   This would greatly help me in learning some interesting points of  physics since in physics we accept things that are supported by experiments.       

Dear Yatendra,

it makes a difference to say "I can observe a photon" or to say "the electric or magnetic field of a single photon is observable".

How can you "observe" a single photon? If you do it by absorption, then you have observed that it was there, because the absorption has destroyed the photon!

Now, can we observe the electric field of a photon? [If yes, how large would you expect it lo to be, anyway? One could try to make an estimate by assigning 1/2 \hbar\omega to the classical field energy and some volume to the photon (but how much space would you give to it?]

So, how to answer that question? Say you had an apparatus which could sensitively detect electric fields with high spatial & temporal resolution. Assume also you were able to prepare single photon states in a reproducible way, so that at given time t0 the q-m photon state is known (and you can reproduce this). Assume now you do that many tues and apply your field measurement apparatus to detect the electric field at some location and time t1>t0. You should be disappointed! The expectation value of the field is zero for all (x,t) despite all the effort. (The expectation value is what you obtain as the statistical average of a huge number of measurements.)

This iis what I meant by saying that the field is not an observable. Maybe the sentence itself is not correct, I would have to check. (In the theory, an observable is associated with a Hermitian operator. This operator can probably be constructed for the electric field in general).

I remember the above no well because I wasI was actually asked for it in my last examination when I studied. If I remember right, this should be treated in one of Messiah's books.

To construct a q-m state of light with "observable" fields, you have to do superpositions. Not just of single photon states but also of many photon states. A classical plane wave is represented in q-m by a so-called Glauber state. Its phase (and hence field vector) is well defined but its number of photons is totally indetermined.

This is just yet another variant of Heisenberg's uncertainty principle. If you turn it around it says that when you know the number of photons then you can't know the phase. The electric field vector cannot be known or determined.

with respect to the double slit experiment:

Actually the photon has to be in both shits at the same time. (What could make the photon from 0 he slit to the other...?!) For iinterference to occur, what is required is that the phase difference between the locations is well defined. The absolute phase does not matter.

These kinds of considerations are not unique to the q-m of the e-m field but always arise in the context of harmonic oscillators. Take the case of vibrations in a diatomic molecule. You will probably know that their energy is quantized. In an eigenstate you cannot know the distance between the nuclei. A state where you know it (at some given time, say) is not a stationary state, but a wave packet. (we had that one earlier). The wave packet is a superposition of many different states. In what do these states differ? In their energy, i.e. the number of excited quanta of vibration. The better you know how far the guys are apart, the less you (can) know in what vibrational state they're in (how many quanta there are).

Photons are quantized modes of the electromagnetic field. Replace "internuclear distance" by "electric" or "magnetic" field. Swap numberof quanta of vibrations by number of photons. You can't have both pieces of the cake at the same time. (what a piece of luck that cakes are classical objects most of the time...)