What is the size and shape of single optical photon?

[Duda Jarek]

Optical photon is produced e.g. during deexcitation of atom, carrying energy, momentum and angular momentum difference.
So how is this energy distributed in space - what is the shape and size of single photon?

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

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

Quote

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, experimental arguments?

 

 

Edited April 30, 2021 by Duda Jarek

[exchemist]

3 hours ago, Duda Jarek said:

Optical photon is produced e.g. during deexcitation of atom, carrying energy, momentum and angular momentum difference.
So how is this energy distributed in space - what is the shape and size of single photon?

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

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

Is it the proper answer?

Are there other reasonable answers, experimental arguments?

 

 

To be honest I have trouble seeing how asking what the "shape" of a photon is can possibly be a question with any meaning.

One could only define a "shape" if one could find a way to interact with it in a way that did not disturb it, which does not seem possible to me. It also seems to me the uncertainty principle would suggest its extent in space would depend on the degree to which its momentum was defined.  

This seems to be merely an academic exercise in exploring, for fun, the ramifications of the Bohr model -  which was abandoned as a model in the 1920s, due to its obvious inadequacies.  

I also note the paper is dated 2018, a decade after this George Hunter bloke, whoever he may have been, died. 

But I'm not a physicist. There are others that can comment more authoritatively, I'm sure. 

[Duda Jarek]

Photon is EM field, the basic question is energy density distribution of EM field for single photon - some rho ~ |E|^2 + |B|^2 ( https://en.wikipedia.org/wiki/Electric_field#Energy_in_the_electric_field ).

Can we say anything concrete about this energy distribution, preferably based on experimental arguments like mentioned above?

Ps. Paper by different author: https://arxiv.org/pdf/1604.03869

Quote

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

 

[exchemist]

2 hours ago, Duda Jarek said:

Photon is EM field, the basic question is energy density distribution of EM field for single photon - some rho ~ |E|^2 + |B|^2 ( https://en.wikipedia.org/wiki/Electric_field#Energy_in_the_electric_field ).

Can we say anything concrete about this energy distribution, preferably based on experimental arguments like mentioned above?

Ps. Paper by different author: https://arxiv.org/pdf/1604.03869

 

I'm sure you can say something about the distribution of probability of detecting the energy.   

[Duda Jarek]

"Detecting" by who, what? This is very subjective question, while I am asking for objective EM field configuration - telling anything concrete about it.

While this is a difficult question, there are at least these two articles, most importantly - providing experimental arguments (quoted in post above). What do you think about them?

[exchemist]

1 minute ago, Duda Jarek said:

"Detecting" by who, what? This is very subjective question, while I am asking for objective EM field configuration - telling anything concrete about it.

While this is a difficult question, there are at least these two articles, most importantly - providing experimental arguments (quoted in post above). What do you think about them?

My limited, chemist's understanding of QM is that you can't really speak of an "objective" EM field configuration for a single photon. If you could, it seems to me it would be a classical object rather than a QM one.  

But I think we probably now need a real physicist's input.

[Duda Jarek]

The basic difference between classical mechanics and quantum, is that in the former we have single trajectory optimizing action, while in the latter we have Feynman ensemble of trajectories, fields etc.

So the question can be seen: what is mean size of such photon's energy density - averaged over quantum ensemble.

QM cannot be used to completely neglect such a basic question of physics, and we have also experimental arguments like quoted above.

[swansont]

2 hours ago, Duda Jarek said:

"Detecting" by who, what? This is very subjective question, while I am asking for objective EM field configuration - telling anything concrete about it.

Detecting by who or what is a detail that gives you information.

 

2 hours ago, Duda Jarek said:

While this is a difficult question, there are at least these two articles, most importantly - providing experimental arguments (quoted in post above). What do you think about them?

Those are (largely) theory papers. The experimental results in the first one give summaries of some experiments, but the writing in the second one suggests the authors did not do any experiments. From my perspective there's a bit of a gap between a quoted observation and the conclusion they draw in most of their soliton section, which is in support of their own model, and not to be taken as a generally-accepted model of the photon.

[Duda Jarek]

I have just found another - 2021 with more sophisticated models: "The size and shape of single photon" http://dx.doi.org/10.4236/oalib.1107179

Sure, these might be just the beginnings ... but asking for EM field configuration of photons is valid question, also from quantum perspective: as Feynman ensemble of classical ones - we can ask for e.g. dimensions averaged over such ensemble.

[swansont]

53 minutes ago, Duda Jarek said:

I have just found another - 2021 with more sophisticated models: "The size and shape of single photon" http://dx.doi.org/10.4236/oalib.1107179

Sure, these might be just the beginnings ... but asking for EM field configuration of photons is valid question, also from quantum perspective: as Feynman ensemble of classical ones - we can ask for e.g. dimensions averaged over such ensemble.

“Applying scattering theory and classical electrodynamics is the most reliable way to solve this problem.”

I don’t see how this gives a QM result

 

[SergUpstart]

From those lectures on quantum mechanics that I looked at on YouTube, it follows that the photon has no shape or trajectory. A photon has only two points, where it was born and where it was absorbed. Thus, the photon is a "black box", as it is arranged from the inside, we do not know.

[exchemist]

3 hours ago, Duda Jarek said:

I have just found another - 2021 with more sophisticated models: "The size and shape of single photon" http://dx.doi.org/10.4236/oalib.1107179

Sure, these might be just the beginnings ... but asking for EM field configuration of photons is valid question, also from quantum perspective: as Feynman ensemble of classical ones - we can ask for e.g. dimensions averaged over such ensemble.

I'm still struggling to see what the "dimensions" of a photon, or even expectation values for a set of dimensions for an ensemble of them, can mean.

According to my understanding, QM only describes how quantum objects are expected to interact (usually expressed in terms of probability distributions) and is deliberately silent on what they "do" in between. Do any of these authors suggest that the "shape" or "dimensions" of a photon predict how it will interact with other QM objects?  If not, then it seems to me to be just building castles in the air.  

[SergUpstart]

32 minutes ago, exchemist said:

According to my understanding, QM only describes how quantum objects are expected to interact (usually expressed in terms of probability distributions) and is deliberately silent on what they "do" in between. Do any of these authors suggest that the "shape" or "dimensions" of a photon predict how it will interact with other QM objects?  If not, then it seems to me to be just building castles in the air.  

Imagine that a photon hits a semi-transparent mirror. What, it will split into two "ellipsoids"? But in the end, only one half will be absorbed, and the other half will disappear. And which specific half will be absorbed will be known only at the time of absorption.

[Duda Jarek]

Sure such photon dynamics is extremely complex, but it doesn't mean we should just neglect this fundamental problem of understanding physics.

For example while naively quantum processes are instant, reaching such measurement possibility, turns out e.g. that photoemission takes a few dozens of attoseconds: https://science.sciencemag.org/content/328/5986/1658 - there is some concrete hidden electron dynamics leading to EM field wave of the photon, we should at least try to understand.

The ellipsoid view is probably only an approximation of energy density shape, to understand e.g. Mach-Zehnder there should be also some pilot/theta wave flying the second path, like from http://redshift.vif.com/JournalFiles/V16NO2PDF/V16N2CRO.pdf  :

[studiot]

Have you considered how far a 'photon' will (must) have moved in one second or even one attosecond, in relation to any reasonable 'size' one might attribute to it ?

[Duda Jarek]

EM field as consequence of electron dynamics travels with speed of light: ~0.3 nm per attosecond.

Here is some paper trying to model emission of photon from hydrogen: https://link.springer.com/chapter/10.1007/0-306-48052-2_20

[swansont]

25 minutes ago, SergUpstart said:

Imagine that a photon hits a semi-transparent mirror. What, it will split into two "ellipsoids"? But in the end, only one half will be absorbed, and the other half will disappear. And which specific half will be absorbed will be known only at the time of absorption.

Photons don't split*, and they can't be half absorbed. You either have the photon or you don't.

 

*You can create two photons from one in certain interactions, but these are not being described here.

4 minutes ago, Duda Jarek said:

EM field as consequence of electron dynamics travels with speed of light: ~0.3 nm per attosecond.

Here is some paper trying to model emission of photon from hydrogen: https://link.springer.com/chapter/10.1007/0-306-48052-2_20

"This question has been answered by modeling photon emission by an atom in terms of classical radiation theory"

 

You keep citing works that are using classical theory, and yet you and they use the term "photon" which is not classical.

[SergUpstart]

It seems to me that trying to describe the shape of a photon is trying to explain quantum physics from the standpoint of classical physics. But this is impossible, on the contrary, classical physics is derived from quantum physics in the limiting case.

[Duda Jarek]

5 minutes ago, swansont said:

Photons don't split*, and they can't be half absorbed. You either have the photon or you don't.

Many nonlinear optics effect kind of split photons e.g. SPDC: https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

Regarding absorption of half of photon, I would say that it happens e.g. in spin echo: photon rotates spin by pi, here they are rotated by pi/2:

https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#Pulsed_electron_paramagnetic_resonance

 

SergUpstart, quatnum physics is built on classical e.g. through quantization, Feynman ensembles of classical scenarios.

So we can ask what are dimensions of energy density of photons averaged over such ensemble.

 

Edited April 30, 2021 by Duda Jarek

[SergUpstart]

5 minutes ago, swansont said:

Photons don't split*, and they can't be half absorbed. You either have the photon or you don't.

That's what I mean

[swansont]

2 minutes ago, Duda Jarek said:

Many nonlinear optics effect kind of split photons e.g. SPDC: https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

If you hadn't truncated my post you would see that I said there are interactions that allow this. Reflection isn't one of them.

 

 

[exchemist]

3 hours ago, SergUpstart said:

From those lectures on quantum mechanics that I looked at on YouTube, it follows that the photon has no shape or trajectory. A photon has only two points, where it was born and where it was absorbed. Thus, the photon is a "black box", as it is arranged from the inside, we do not know.

Yes I suspect you touch on something important here. I'm halfway through Carlo Rovelli's book "Helgoland" at the moment. He points out that Heisenberg's approach to QM was based on deliberately restricting the model to accounting for the behaviour of systems in interactions - and not making any assumptions about what goes on in between. It is the classical mindset that assumes something goes on in between that can be defined and tracked. QM gives up that assumption. Or so I am led to understand.   

I feel it is not a coincidence that @Duda Jarek's posts and links continually refer to classical or semi-classical models. I suspect this is all an exercise in semi-classical modelling and should not be taken seriously as the way nature really behaves.

Edited April 30, 2021 by exchemist

[beecee]

A number of interesting facts/data came to mind when I saw this question. [1] Scientific theories are models we use based on known data...[2] The dual nature of light/photons...[3] the fact that light/photons have no rest mass...a photon is a quanta of light or a bundle of the smallest amount of energy we can measure.

Considering all that data, I came to the average sensible lay person's  conclusion that a photon would have no shape. But like any good sensible lay person, I did some checking...https://physicsworld.com/a/how-to-shape-photons-using-a-trapped-atom/#:~:text=A photon is a quantum,photon's temporal shape or mode.

"A photon is a quantum of light that can be described as a packet of waves that travel through space. A photon’s wavefunction is spread out over time and the specific nature of that distribution is the photon’s temporal shape or mode".

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then this.....https://cosmosmagazine.com/physics/what-shape-is-a-photon/

What shape are photons? Holography sheds light: 

Hologram of a single photon reconstructed from raw measurements (left) and theoretically predicted (right). Credit: FUW

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https://www.mat.univie.ac.at/~neum/physfaq/topics/shape.html 

The shape of photons and electrons:

extract:

 

"A free photon can have the shape of an arbitrary solution of Maxwell's equation in vacuum. But only very special solutions are controllable and hence useful for experiments or applications.
Upon production in a laser, photons are more or less localized (not precisely, this is impossible, as photons cannot have an exact position, due to the lack of a unique position operator with commuting coordinates); often only in the transversal direction of the beam - then you don't know where it is in the beam, except probabilistically.
For photons on demand (that you can program to transmit information) you need to know when and where you transmit the photon, so it must be well-localized.
Of course, a slit or a half-silvered mirror delocalizes a photon, and only a measurement (or decoherence along the way) relocalizes it. This enables interference effects. In these cases, the photon stops being particle-like and behaves just like an arbitrary excitation of the e/m field, i.e., like a wave.
The particle picture of light is good only in the approximation where geometric optics is applicable. This has been known for almost 200 years now.

The paradoxes and the alleged queerness of quantum theory both have their origin in misguided attempts to insist on a particle picture where it cannot be justified"

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Hope that helps............

Edited April 30, 2021 by beecee

[studiot]

2 hours ago, Duda Jarek said:

EM field as consequence of electron dynamics travels with speed of light: ~0.3 nm per attosecond.

Here is some paper trying to model emission of photon from hydrogen: https://link.springer.com/chapter/10.1007/0-306-48052-2_20

In Fig 2 seems to be suggesting that the photon travels the distance between distance between two wave peaks in the same time the electron makes one orbit of the atom.

Since the orbit circumference is much larger than that of this distance it seems to be suggesting that the electron (with mass) is travelling at many times the speed of the photon.

 

How can this happen either classically or quantally ?

 

5 minutes ago, beecee said:

The particle picture of light is good only in the approximation where geometric optics is applicable. This has been known for almost 200 years now.

This is a key statement.  +1

 

If you illuminate a barrier with one slit and direct the output  light from the slit onto a screen on the other side from the source what will you observe as the size of the slit is reduced  ?

Edited April 30, 2021 by studiot

[studiot]

14 hours ago, studiot said:

If you illuminate a barrier with one slit and direct the output  light from the slit onto a screen on the other side from the source what will you observe as the size of the slit is reduced  ?

I am referring to this issue.

The most relevent paragraph is indicated by the pink bars.