Measure v_abs by width of photon?

[sahil5d]

A while back in the ACG forum we had a thread on the width of a photon. Not wavelength, but transverse width. There is some reason to expect that a pulse of light has a transverse width, because at a certain hole width, meshes will go from transparent to reflective (microwave meshes, radio telescope meshes).

Can this be used to determine v_abs, by measuring the width of a laser-emitted photon in all 3 axes, and confirming if there is a direction in which the photon has a smallest width?

The virtue of measuring a photon's width versus its wavelength is that the width (being perpendicular) wouldn't be Doppler-unshifted by the receiver moving at velocity.

• Is there such a thing as a photon width? If not, then what is that property of a photon that can be determined by trying to pass a photon thru meshes of varying hole width?
• Is this paper https://arxiv.org/abs/quant-ph/0506231 accurate in saying that the width of a photon is λ/π ?
• What is the fastest way to perform this experiment to measure a laser-emitted photon's width in all 3 axes and calculate v_abs?

[RedshiftDrift]

This was discussed in April 2022 on the ACG forum.

A single photon has no width, it's a plane wave.

Asking for the "width of a photon" is as absurd as asking for the "width of the A 440 tone".

[RedshiftDrift]

When you say "plane wave", is it plane-wave-infinite-no-bounds, or is it spherical-wave-expanding-around-emitter?

Which part of "plane" is not clear? Not 'spherical', plane as in 'flat'!

[sahil5d]

"A single photon has no width, it's a plane wave." - L. Marmet, 2023-10-02

"a plane has no bounds." - 2023-10-04

"The single photon is a plane wave of indefinite extent, with energy E = hν" - 2024-06-16

"An atom emits a spherical wave expanding at c around the emitter, as you wrote above." - 2024-08-06

"Which part of 'plane' is not clear? Not 'spherical', plane as in 'flat'!" - 2024-08-28

That is what is not clear. Your definition of an atom emitting a quantum of energy is inconsistent.

[RedshiftDrift]

"A single photon has no width, it's a plane wave." - L. Marmet, 2023-10-02

Since an infinite plane has no boundary, it has no width that can be measured or even defined.
To clarify: "no width" means "undefined width" (not "zero width").

"a plane has no bounds." - 2023-10-04

Same as the above statement.
Consistent with the above statement.

"The single photon is a plane wave of indefinite extent, with energy E = hν" - 2024-06-16

Same as above with the additional information that the energy given to that photon is E = hν.
This is consistent with all of the above statements.

"An atom emits a spherical wave expanding at c around the emitter, as you wrote above." - 2024-08-06

Here I was not talking about a photon but the spherical wave emitted by an atom.
The atom emits a quantum of energy in the shape of an expanding spherical wave. The spherical wave is represented by the usual quantum mechanical wavefunction given by a plane wave expansion as the sum of $N$ plane waves traveling in every directions as

$$ |\Psi \rangle = \frac{1}{\sqrt N} |dir_1 \rangle + \frac{1}{\sqrt N} |dir_2 \rangle + ... + \frac{1}{\sqrt N} |dir_N \rangle $$

with each plane wave (photon going in a given direction) having a probability $1/N$ equal to the square of the amplitude (and therefore an energy $E = h\nu/N$).
Then we let $N \rightarrow \infty$. The total energy of that spherical wave is always $E = h\nu$.

While plane waves do not have a measurable spatial extent (they are everywhere in space), multiple plane waves interfere constructively and destructively to produce a spatially localized wavefunction.
(The complete wavefunction also has a time dependence (not explicitly written in the above equation to keep it simple) that produces a localization of the wavefunction along the direction of propagation.)

For example, the spherical wave emitted by an atom has a well defined boundary, in the shape of a spherical shell with a radius $r = ct$, where $t$ is the time after emission of the quantum of energy.

This describes a different system, but is consistent with all of the above statements.

"Which part of 'plane' is not clear? Not 'spherical', plane as in 'flat'!" - 2024-08-28

Back to the description of a photon.
As above, this is the same description of a photon described by a plane wave: the wavefronts are flat.
This is consistent with all of the above statements.

Your definition of an atom emitting a quantum of energy is inconsistent.

Back to the description of a spherical wave (which is not a photon) emitted by an atom.
I've shown above that the description is consistent: the atom emits a spherical wave with a total energy equal to $N \times h\nu/N = h\nu$ that is composed of a superposition of photons (plane waves).

---

@sahil5d the source of your confusion may be that you think an atom emits a photon, which is not necessarily the case depending on the system being described. You've been switching between two different systems:
[atom emitting a spherical wave] and [free photon]
while using the properties of one to describe the properties of the other. This cannot work.

Here are some examples of different systems with increasing complexity that have very different properties. The quantum mechanical description must match the entire system, not be built from the sum of individual components of the system.

1. [A single photon] This is represented by a plane wave; it has no boundary in any of the three dimensions - it is everywhere in space and a "width" is not defined. (Mathematically, its width is infinite. "Infinity" does not have a meaning in science, hence the width of a photon/plane wave is not defined in physics.)

2. [An atom emitting a quantum of energy] This is represented by the wavefunction of the atom and a quantum superposition of plane waves (photons) propagating in every direction. The wavefunction of the light field is spatially localized on a spherical shell that expands at the speed of light. Because the plane waves are equally distributed in all directions, the total momentum of the spherical wave is zero and the atom does not experience any recoil.

3. [An atom E emitting a photon that is absorbed by another atom A] The direction of propagation of the photon is precisely defined by the direction $\vec{k} = \vec{E-A}$ defined by the position of the atoms. The photon had a momentum $h\vec{k}$ that was given as recoil to atom E and absorbed as recoil to atom A. The plane wave between the two atoms does not have a boundary, so its "width" as it was propagating between the two atoms is not defined.
   [Note that I did not write 'an atom emitting a spherical wave' because if atom A detects the photon, atom E could not have emitted a spherical wave! This system is described by a photon propagating in the direction of atom A.
   Again, it is important to remember that this quantum system
   [An atom E emitting a photon that is absorbed by another atom A]
   cannot be described as
   [An atom E emitting a quantum of energy] + [a quantum of energy absorbed by another atom A]
   In quantum mechanics, the entire system must be described as a unit, not as a sum of simpler systems.]

4. [An atom E emitting a photon that goes through a small hole before being absorbed by another atom A] Here the photon wavefunction is defined by the position of the atoms and the hole. If the atoms and hole are not colinear, momentum is also exchanged with the hole. The plane wave (photon) propagating between atom E and the hole does not have a boundary, so its width is not defined. The hole limits the spacial extent of the wavefunction which is therefore localized inside the hole, but the wavefunction inside the hole is a complicated superposition of plane waves ($N$ photons with various probabilities) which interfere with each other. One cannot talk about the width of a photon because the field inside the hole is a quantum superposition of many photons. The shape of the light field inside the hole has the same shape as the hole, so its width is the width of the hole. But beyond the hole we're back to plane waves (photons) that don't have a meaningful width.

I hope this progression in complexity gives an idea of the language used to describe light interactions. The thing to remember is that to measure a width, light has to interact with something. But then that interaction changes the shape of the wavefunction. Without slits and atoms, the photon itself is everywhere in space (this is the "excitation of an electromagnetic mode"), it has no shape that can give meaning to the concept of "width".

[sahil5d]

the source of your confusion may be that you think an atom emits a photon

What? Do you think that there's no such thing as an atom emitting a photon?

Also, you described the following model,
[atom emits a quantum of energy in the shape of an expanding sphere,
as the sum of N plane waves traveling in every direction,
with each plane wave having an energy E = hν / N, then we let N → ∞, and
the total energy of that spherical wave is always E = hν,
but the total energy hν only arrives at one point on that sphere].
Can you give that a name? (as you don't want to call that a photon)

That model ^ has a problem similar to what I articulated here,
https://github.com/orgs/a-cosmology-group/discussions/162#discussioncomment-10235768.
How does all that energy hν materialize at one point?
How does it immediately go from all over the sphere to one point on that sphere?

Here are some examples of different systems with increasing complexity that have very different properties. The quantum mechanical description must match the entire system, not be built from the sum of individual components of the system.

The scenarios 2 and 3 in your list
[An atom emitting a quantum of energy]
[An atom E emitting a photon that is absorbed by another atom A]
are arbitrary divisions. (Also, it's strange you write "An atom E emitting a photon" when you said earlier that's a source of confusion.)

The explanations for whether there's recoil of the emitter are not logical and they seem like post-facto (knowing whether the photon reached another atom) excuses, like the MOND wide binaries where what is defined as a "system" is post-facto decided.

[sahil5d]

More on the Nvidia raytracing paper that reproduced the photon single-slit and double-slit diffraction/scatter patterns..

The ray diffraction/scatter might be caused by something like a van der Waals force on photons or some second order van der Waals force. Another possible explanation is an electro-optical effect like the effect_Pockels or effect_Kerr, or something similar, in which an electric field affects refractive index.

[sahil5d]

I think waveguides prove the conjecture about radiation having a transverse width, because the radius of a circular waveguide (informally, a metal pipe) is proportional to the max wavelength of a photon that can go through the pipe without significant attenuation.

https://www.everythingrf.com/rf-calculators/circular-waveguide-calculator

I'm looking into the 1.8412 value, and if anyone has some insight on that, that would be appreciated.

[AngelBlanco19]

@sahil5d

Another point in favor of the photon having a width (specifically a radius of λ/(2π)) is that it is consistent with effective antenna aperture in antenna theory.

The EXACT diameter of a photon (1•10^-34 m) does not depend at all on the frequency of the wave disturbance that it perceives through 6 dimensions (eternally hidden) and retransmits through other 6 dimensions (the “3” ours). The "wavelength” does not paint anything here – the important thing is only the frequency. It is a universal Invariant. Whatever its state of relative rest, it has exactly the same diameter in each of the infinite and IMMOBILE frames of an infinitesimal Time and Length duration of our phenomenological Reality. It is a fact, it does not admit any discussion. In every infinite and IMMOBILE frame of our phenomenological and therefore sensitive, erroneous, misleading, false and not exact Reality, absolutely all Positions, Times and Lengths, Distances, are absolutely defined, determined, regardless of the relative rest state of any particle - none moves. The movement occurs only and exclusively in the Absolute, to which for obvious reasons we have no access. The Absolute is in charge of the permanent and eternal succession of these IMMOBILE frames of our phenomenological Reality with an EXACT frequency of 1•10^44 Hz. This is what the physical process of Time, the most important of infinite and eternal Matter, is responsible for. This Absolute Truth has an approximate age of between 2518 and 2486 years more or less. Between any two consecutive infinite and IMMOBILE frames of infinitesimal Time and Length duration of our phenomenological Reality, there exists a Quantum of Time (1•10^-44 s) and its corresponding Quantum of Length (1/6•10^-34 m), both EXACT values, which are a Universal Constant, a Universal Invariant and does not depend on any unit of measurement that can be invented. These are open secrets. Now calculate the frequency spectrum of visible light and you will realize every what exact time a visible light wave event occurs and transmits. I am writing all this to you, because I suppose that like many, you will want to know the Truth.

[AngelBlanco19]

I forgot to mention the Quantum of Action, which is the name of each of the 6 wave events that an elementary particle of Matter emits at each infinitesimal instant of time and length of our phenomenological Reality and that has the same infinitesimal duration of Time and Length as the Phenomenon. Each of the 6 Quantum of Action emitted is the result of the physical and mathematical differentiation of the Phenomenon and the Phenomenon is the result of the physical and mathematical integration of the 6 Quantum of Action received. They are both separated by exactly 3 Quantum of Time and their corresponding 3 Quantum of Length, which means that a certain set of 6 Received Quantum of Action will be converted into Phenomenon after that time, and likewise, a certain Phenomenon will be converted into 6 emitted Quantum of Action after that time. This is a permanent and eternal process, the result of the physical process of Time. It is obvious that there are only 12 possible states of a Photon, called in quantum mechanics, quantum states. Each of the 6 Quantum of Action is emitted to a different Photon, and likewise, each of the 6 Quantum of Action received is received from a different Photon. Having all these EXACT data already, you will be able to put them in your formulas and get exact results.

[AngelBlanco19]

It is obvious that there are only 12 possible states of a Photon, called in quantum mechanics, quantum states.

Explanatory note. The 12 different states of a photon refer to its adjacent neighbors, with respect to its own, so in total there are 13 different possible states, called quantum states. The Time and Length duration of each state is infinitesimal (1/∞), and therefore it is an indeterminate and non-countable magnitude. Everything is determined by the Dot-Dash-Dot rule. This rule works the same within each infinite and IMMOBILE frame of our phenomenological Reality, as between successive frames. Without Phenomenon there are no Quantum of Action, just as without Quantum of Action there is no Phenomenon at all.

[Francois-Zinserling]

https://www.everythingrf.com/rf-calculators/circular-waveguide-calculator

I'm looking into the 1.8412 value, and if anyone has some insight on that, that would be appreciated.

@sahil5d From your link:
$f_c = 1.8412c/2πr$ (1)
Don't know why this would be written so weird, because wavelength
$λ = c/f$ (2)
then if you rewrite (1)
$r = 1.8412c/2πf$ then insert (2)
$r = 1.8412λ/2π$
$r = λ/3.41$ ... this took too many steps :)

That number below the line is less than 4, meaning the size r is bigger than for $r = λ/4$ because at a quarter wavelength sized gap the waves do not go through. None of it. The grid on a microwave door has holes sized to ~1/4 of the output wavelength of the magnetron and it blocks 100%.

The number 1.8412 may have a mathematic significance, but I think possibly from experience keep increasing the size (from 1/4) until the wave attenuation is minimum and get to $r = 1.8412λ/2π$ because for a waveguide you don't want to block the waves, you want it to go through.

Not sure if you're still looking for this answer but I've seen elsewhere a photon could roughly be considered to fit into a cylinder of length = λ and diameter ~ λ/4. And I'm sure Louis will pop a hernia when he sees this :)

[sahil5d]

Hi @Francois-Zinserling, there might be a connection to the Nvidia raytracing idea
https://github.com/orgs/a-cosmology-group/discussions/162#discussioncomment-10687676.

Waveguide cutoff might be single-slit diffraction, or really, single-slit scattering with a circular aperture (see Airy pattern). A photon entering a narrow waveguide pipe might experience a [van der Waals force on photons] and scatter and not make it straight through, thus attenuation.

In the hypothesis that a photon has a width (diameter λ/π and radius λ/(2π)), a photon's narrowest, non-attenuating circular waveguide would have a radius of (the photon's radius * some value larger than 1), so that the photon has some room.

The 1.8412 comes from a theory involving a sin(x)/x-like function, a Bessel function, and that's another thing to examine..

[AngelBlanco19]

@sahil5d
The EXACT diameter of a Photon, as well as of any of the 28 possible different elementary particles of Matter, or elementary UNITS of existence, or Noumena, or Observers, or Individuum is 1•10^-34 m, and is a Universal Constant, a Universal Invariant and does not depend on any unit of measurement that can be invented. “Science” has “known” it for a long time, but it doesn't know that it “knows” it. It's an open secret. Take a look at this work of mine: https://github.com/orgs/a-cosmology-group/discussions/253#discussion-6983433. If you still have any questions, do not hesitate to ask.

[AngelBlanco19]

@sahil5d

Are you familiar with the claim that large molecules such as buckyballs display quantum interference (Arndt, Zeilinger, et al.)? I am looking into it, and I've realized a few things so far.

The complete cycle of a Photon consists of 6 semicycles, or successive 6 Quantum of Action or 6 infinite and immobile frames of our phenomenological Reality, after which, the Photon returns to the initial spatial position, making two equatorial turns and three polar turns and consequently, the set of 6 Quantum of Action received, after being integrated into a Phenomenon, is differentiated again and then another 6 Quantum of Action are emitted that correspond to those initially received. This is executed by the physical process of Time.
An infinite and immobile frame of our phenomenological Reality, has an infinitesimal time and space duration (1/∞), therefore it is an undetermined and non-countable magnitude. Between any two infinite and immobile consecutive frames of our phenomenological Reality, there is always a Quantum of Time (1•10^-44 s) and its corresponding Quantum of Length (1/6•10^-34 m), both of which are finite, determinate and countable quantities.
In each infinite and immobile frame of our phenomenological Reality of infinitesimal time and space duration, the Photon emits 6 Quantum of Action to another 6 different Photons (one Quantum of Action to each different Photon) and receives another 6 Quantum of Action, each of a different Photon (6 in total).
There are no empty spaces, no absolute emptiness, there is an infinite quantity of elementary particles of Matter, discrete and uninterrupted.
The Photon is the Universal boson, the building block of EVERYTHING, the main, fundamental and the most abundant elementary particle of Matter in the infinite and eternal Universe, being the ONLY elementary particle of Matter that has the complete set of 6 charges, or 6 spatial dimensions or 6 intrinsically different types of waves, as you want to call it.
The Photon emits 6 Quantum of Action in two sets of 3 Quantum of Action arranged at 180º from each other: (+X, +Y, +Z) + (-X, -Y, -Z). Each Quantum of Action is arranged at 120º of its two adjacent Quantum of Action within each set.
The Graviton also emits, like every elementary particle of Matter, 6 Quantum of Action arranged at 180° from each other, but of a different type: (+Z, +Z, +Z) + (-Z, -Z, -Z). For this reason it does not emit visible light. Each Quantum of Action is arranged at 120° of its two adjacent Quantum of Action.
The sign (+) or (-) is not the polarity of the charge or the type of wave, it is only to represent the direction of emission. There are no intrinsic differences between positive and negative charges, they are waves of the same type, only emitted in opposite directions.
There are only 28 different types of elementary particles of Matter. The Photon is a unique and exclusive product of the physical process of Time. The rest of the 27 elementary particles of Matter, are obtained from the transformation of the Photon, through the physical process of Gravity, including the Graviton, the “heaviest” boson of Matter, without which there is no and cannot take place the physical process of Gravity.
Among the 28 elementary particles of Matter, there are 4 different types of bosons, the fundamental ones being the Photon and the Graviton, from the interaction of both the physical process of Gravity occurs.
Every elementary particle of Matter is an elementary UNIT of existence, a Noumenon, an Observer, an Individual, as you like to call it.
Only the Noumena generate and emit and receive Quantum of Action. Only the Noumena can therefore transform, by integration, the received 6 Quantum of Action, into a Phenomenon and then differentiate it, in order to then generate and emit new 6 other Quantum of Action. It is an eternal process. Therefore only the Noumenon sees, observes, perceives, thinks, reasons, feels, suffers, has Consciousness and makes use of Reason. It should never be confused with «the thing itself».
The so-called and very well defined by Kant «the thing itself» is a unique and exclusive product of the physical process of Gravity and is its main function – the permanent and eternal synthesis of chemical substances, starting of course, with the hydrogen atom, which is the first product of the so-called hot "nuclear" synthesis.
Each atom of chemical substance is «the thing in itself» and is formed by strong, not so strong and weak bonds between different or no elementary particles of Matter, except bosons, as is obvious.
Therefore it is obvious that any union by strong, not so strong and weak bonds between atoms of chemical substances, separated from each other by a colossal amount of photons, is «the thing itself» and can never be a Noumenon, being constituted by Noumena. The human biological body, is «the thing in itself» and not a Noumenon.
It is also obvious that the true atom of chemical substance is what is considered today “the atomic nucleus“ and the so-called ”electrons" around them are photons that separate some atoms from others.
The characteristics and properties of a certain atom or isotope of chemical substance are determined by the type and arrangement of elementary particle of Matter on its external surface.
Each elementary particle of Matter can only receive the Quantum of Action emitted by the neighbouring elementary particles of Matter and can only emit the type of Quantum of Action according to the type of charge it possesses: either +/-X, +/-Y or +/-Z of the possible existing combinations. Now it is easily understandable the intrinsic nature of the absorption and emission spectra of each atom, of each isotope of chemical substance, it is its own unique fingerprint.
I had to make this long story, to demonstrate how some chemical substances work as a mirror, relaying the complete set of Quantum of Action of a Photon, depending on the direction of emission.
Surely now the so-called “quantum interference” of some substances is understood. A large part of the Quantum of Action received are absorbed, transformed internally, and only those that emit the Noumena on the surface and only 6 Quantum of Time and their corresponding 6 Quantum of Length are emitted after having received them. The phase difference between the received and the re-emitted light is always full cycle of Photon, although the direction reversal occurs (supposed "polarity" change).

[AngelBlanco19]

The Photon is the Universal boson, the building block of EVERYTHING, the main, fundamental and the most abundant elementary particle of Matter in the infinite and eternal Universe, being the ONLY elementary particle of Matter that has the complete set of 6 charges, or 6 spatial dimensions or 6 intrinsically different types of waves, as you want to call it.

Explanatory note, because such redaction may create doubts.
There are only 12 spatial dimensions in the Absolute, of which always, in every infinitesimal instant of time and space of our phenomenological, infinite and eternal immobile Reality, only 6 are manifested, which create the Phenomenon of our 3 spatial dimensions and the other 6 are and remain eternally hidden in the Absolute. Of course, they are not always the same, they take turns, so that each of the 12 spatial dimensions actively participates in our Reality.
Those that can be called charges, which are a type of wave intrinsically different from the rest of the other two and that end up forming our usual 3 spatial dimensions (the Phenomenon), are in total of three intrinsically different types: the +/-X, the +/-Y and the +/-Z, which I have called respectively electric, magnetic and torsional charges, but that's the least, it's just a name.
The charges or type of wave +/-X, complete a complete cycle, in each complete cycle of a Photon, that is, every total 6 consecutive half cycles any of a Photon, as the complete cycle of a Photon is composed of precisely 6 consecutive Quantum of Action or 6 consecutive infinite and immobile frames of infinitesimal Time and Length duration of our phenomenological Reality. This type of wave creates the bonds or weak forces between Noumena that possess them.
The charges or wave type +/-Y, complete a complete cycle, in each of the 6 half cycles of a Photon, that is, they have 6 cycles in a any complete cycle of one Photon. This type of wave creates the bonds or not so strong forces between Noumena that possess them.
The charges or type of wave +/-Z, complete 12 complete cycles, in each complete cycle of a Photon, that is, they have 12 cycles in any complete cycle of a Photon (they have a jump in each of the 6 half cycles of a Photon). This type of wave creates the bonds or strong forces between Noumena that possess them. It is the largest of the existing binding forces in Matter. It holds together the Gravitons of what is today erroneously considered a ”black hole", which is nothing more than a naked star (it only has the Graviton Core), the oldest in its immediate environment, without any of the chemical substances that it permanently synthesises and are expeled at high velocity and that opposes the centrifugal forces created by the rotation of the Graviton core until it reaches its finite, determined and countable limit.
Taking into account that the frequency of our phenomenological Reality, of the infinite and immobile consecutive frames of it, is 1•10^44 Hz, then the full cycle frequency of each charge or type of wave is as follows:
The full cycle frequency of the charge or type of wave +/-X is 1/6•10^44 Hz.
The full cycle frequency of the charge or type of wave +/-Y is 1•10^44 Hz.
The full cycle frequency of the charge or type of wave +/-Z is 2•10^44 Hz.
It is well known that the links or forces depend on the frequency. So we have the three types of possible bonds, as far as charges or type of wave is concerned.
The Noumenon always receives the 6 Quantum of Action through the 6 spatial dimensions hidden in the Absolute and can only receive the type of Quantum of Action (charge or type of wave) that has been emitted to him, it does not depend on him. It's obvious.
The Noumenon always emits the 6 Quantum of Action through the 6 spatial dimensions that, being as they are in the Absolute, can only be manifested through the Phenomenon of 3 spatial dimensions that we perceive as Noumena that we are in our Reality and they do depend on the type of Quantum of Action (charge or type of wave) that he himself possesses.
In this way, the objective origin of each of the three usual spatial dimensions of our phenomenological Reality is perfectly understood, which are located orthogonally at 90º, being as they are, in the Absolute orthogonally at 120º, forming an isometric image.
Our phenomenological Reality is not a simulation, it is impossible, it is just the manifestation, the Phenomenon of the Absolute.