Experimental suggestions for size and shape of single optical photon (wavepacket)?

Question

Optical photon is an electromagnetic wave produced e.g. during deexcitation of an atom, carrying energy, momentum and angular momentum difference.

So how is this electromagnetic energy distributed in space (rho~|E|^2+|B|^2) - what is the shape and size of a single photon? What is the position distortion of such wavepacket?

Looking for literature, I have found started by Geoffrey Hunter, here is one of the articles: "Einstein’s Photon Concept Quantified by the Bohr Model of the Photon" https://arxiv.org/abs/quant-ph/0506231

Most importantly, he claims that such single optical photon has a shape similar to an elongated ellipsoid of length being wavelength λ, and diameter λ/π (?), providing reasonably looking arguments:

1. Its length of λ is confirmed by:

– the generation of laser pulses that are just a few periods long;

– for the radiation from an atom to be monochromatic (as observed), the emission must take place within one period [10];

– the sub-picosecond response time of the photoelectric effect [11];

2. The diameter of λ/π is confirmed by:

– he attenuation of direct (undiffracted) transmission of circularly polarized light through slits narrower than λ/π: our own measurements of the effective diameter of microwaves [8,p.166] confirmed this within the experimental error of 0.5%;

– the resolving power of a microscope (with monochromatic light) being “a little less than a third of the wavelength”; λ/π is 5% less than λ/3, [12];

Is it the proper answer?

Are there other reasonable answers, preferably experimental arguments?

Update: similar conclusions from the different author: https://arxiv.org/pdf/1604.03869

the length of a photon is half of the wavelength, and the radius is proportional to the square root of the wavelength

Update: 2021 "The size and shape of single-photon" http://dx.doi.org/10.4236/oalib.1107179

Attosecond chronoscopy brings hope to verify e.g. photon models experimentally - gathered: https://scholar.google.pl/scholar?cites=15193546925951882986&as_sdt=2005&sciodt=0,5&hl=en E.g. 2020 "Probing molecular environment through photoemission delays" https://www.nature.com/articles/s41567-020-0887-8

Attosecond chronoscopy has revealed small but measurable delays in photoionization, characterized by the ejection of an electron on absorption of a single photon. Ionization-delay measurements in atomic targets provide a wealth of information about the timing of the photoelectric effect, resonances, electron correlations and transport.

Answer 1

One must understand what theories are in physics. They are mathematical models , i.e. depend on solutions of differential equations usually, that are used to map existing data and predict new data. BUT the theories region of validity is different for different models.

Maxwell equations united electricity and magnetism and gave a road map for unification for theories, but it could not explain the photoelectric effect, the spectra of atoms or black body radiation.. These forced quantum mechanics to be proposed and accepted.

The Bohr model, which is the basis of your link, was the beginning of quantum mechanics, a phenomenological model, superseded by the solutions of Schrodinger's equation that explained the same data in a mathematically more rigorous manner.

Schrodinger's equation had to be modified because of special relativity, and quantum field theory gave a more rigorous prediction of the fine structures seen in the data.

At present the main stream model of physics accepts that the under lying nature is quantum mechanical, from which all other theories/models emerge. This is called the standard model of particle physics. This has axiomatically the table of elementary particles that is used for fitting all existing data and predicting future measurements in particle physics. You will see that the photon is a point particle, it has no extension in space only spin +/- 1, mass zero and energy correlated with the frequency of the classical Maxwell wave a large number of such photons make, E=hnu,h the Heisenberg constant.

The fact that this is the mainstream theory, does not mean that other quantum mechanical models , for particular studies, cannot be successful in describing particular data, as the quantum field theory used for quantum optics. Or superconductivity, or...

The paper you quote though is from a conference "Quantum Theory: Reconsideration of Foundations, Vaxjo, Sweden, June 6-11, 2005" , which by its title is attempting to find theories beyond the mainstream one. That is why it has few citations also and has no peer review link. Such a theory, even if the mathematics is correct, can only be for a special region of the variables, because it cannot be incorporated in the standard model, which needs the particles in the table to be point particles.

So no, it is not the proper answer for a photon of mainstream, and I suspect it is not a proper answer for quantum optics, which in material have "photons" , because it talks about the Bohr model, not photons in material.

P.S. When I am in doubt I have found the MIT open courses useful., there is one for atomic and optical physics, from what I see. There are book recomendations

At the point where physics research is now, in mainstream physics , the photon is a point particle. To see how the interference pattern arise from point particles, see this experiment, it is all about quantum mechanical probabilities.

Answer 2

So how is this energy distributed in space - what is the shape and size of single photon?

Energy is never properly localized because it depends on a difference of potentials, for exemple the gravity force of the earth depends on the mass of the earth and the mass of the object it pulls. Energy is bound to "systems" of objects interacting with each others through "fields".

Most importantly, he claims that such single optical photon has shape similar to elongated ellipsoid of length being wavelength λ, and diameter λ/π (?)

What makes the shape of a photon ? What does it mean to say that it has a diameter of λ/π and yet can be "attenuated" by going "through slits narrower than λ/π" ? So if it can squeeze through such slit does it mean the size is elastic ? How do you define the meaning of "size" in that instance ?

Light has properties of wavelength, amplitude and polarization, a photon is a concept that boils down to "it's the light that a single electron emits or absorbs when changing atomic orbitals" meaning a photon is only defined in regard to its interaction with an electron bound to an atom. So each time you try to talk about photons in mid flight, you're in trouble because the only way to detect a given photon is by absorbing it with an atom, and then this photon is no more

Answer 3

There are really two meanings to "photon". One is the detection of a quantum of electromagnetic radiation, which always occurs at a point. The other is the probability distribution: the likelihood of detecting the quantum at each point. The probability distribution is spread out and can have pretty much any shape.

Answer 4

It makes sense to talk about the “physical nature of an object” only in the context of a defined observation, for two primary reasons. One, the “physical nature” of every object is dependent on the context of observation, or maybe better called the “context of physical manifestation,” where “physical manifestation” means an object has the capacity to interact with other ontic/physical objects, ie, it is not just an epistemic abstraction. Thus to ask, “What is the physical nature of an object without measurement?” is not an answerable question without a defined context - even analytically, there must be a defined context. Two, the condition “without measurement” is physically unrealizable anyway, as every object is always interacting with its context, or environment, and so is undergoing “measurement.” (See environmental decoherence theory.) Perfect isolation / non-measurement of an object cannot be physically realized. There is no meaning to “the physical nature of an object” without defining a context - manifest physical reality literally is context dependent. One may imagine, at least an abstract, comprehensive operator, C, that includes all elements of a defined context. This operator defines the associated eigenvalue equation possible solutions that may become physically manifest after measurement, ie, the eigenspace of C, and the observed object wave function, ψ, modulus squared, from ψ expansion in this eigenspace, defines the probability of each solution becoming physically manifest. Without a defined C, there is no eigenspace, no defined possible solution set, no ψ expansion, and no defined probabilities of outcomes - under these conditions, “the physical nature of an object” has no meaning.