#162 Measure v_abs by width of photon?
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?
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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”.
Plane waves have a cross section, right?
And what about the practical reality of a pocket laser emitting a beam, a beam of some number of photons, and that beam evidently having a cross section less than 1 cm^2 and greater than 0 cm^2, and therefore each photon must having a cross section in that range?
There could be other forces at work creating the illusion of proton width
No, a plane has no bounds.
A narrow light beam is necessarily the sum of multiple photons propagating in different directions. None of the photons have a width, but their assembly does. The more photons you use, the better the “width” becomes defined. (Heisenberg uncertainty principle for a coherent state.)
Some call this an “emergent property” 1. Back to my analogy, it’s the combination of notes that makes a melody; each note taken separately has no melody.
Although I disagree with this term used in the sense of a property that could not have been predicted from the individual components.
I disagree. A narrow light beam is multiple photons in the same direction. Why do you think they are going in different directions?
Also, what about this section in page 4 of the paper https://arxiv.org/abs/quant-ph/0506231? This sounds reasonable to me.
RedshiftDrift is right with is based on multiple photon assembly, width is better defined
@RedshiftDrift Does this video somewhat depict your idea of a laser? https://www.youtube.com/shorts/Lb2w4g4Dko8
It’s not something I think, it’s a consequence of the Fourier transform relationship between position and momentum. The relationship $\Delta x \ \Delta p \ge \hbar/2$ holds for every wave. If the beam is narrow, $\Delta x$ is small and the momentum spread $\Delta p$ must be larger. Therefore the photons are not going in the same direction.
The video is wrong, the emitters in a laser don’t have to be regularly spaced. In the HeNe laser, the emitters are the moving atoms of a gas; they are not regularly spaced apart. In a semiconductor laser, the atoms are spaced by a few Å, a distance much smaller than a wavelength. Note however that the beam spreads outside of the focal point, which shows that the photons are not all going in the same direction.
@sahil5d the narrator is incorrect in saying “this ensemble of emitters together sends out its total wave energy almost exclusively in the vertical direction”
Also, that is not how laser beams are made. His energy is still going out in all directions, whereas laser beams are focusing all waves/photons into one direction.
In the beginning he even shows each emitter emitting waves in all directions. What happened to this energy going horizontal? Emitters cannot bend the waves of other emitters, so how does this happen? Not the way he describes.
It is a common misconception to say destructive interference is a point of zero energy. There is energy. For sure there is energy. It is just not making itself visible, but 2 waves destructively interfering are still 2 waves worth of energy travelling through space. I prefer to think in photons terms, then, coupling 2 photons out of phase is like sending them off with a cloaking device over them. If you could somehow decouple their phase again, you may harvest the energy of both.
In the video the half-wavelength spacing in the horizontal direction ensures destructive interference in the horizontal direction. The energy does not ‘disappear’, it is merely undetectable in that state.
If we took a single (horizontal) line of his emitters, there would be an dark band to the left and right and the rest of space will be filled with shaded intereference patterns, with a hint of constructive interference directly vertical. By stacking them one wavelength apart he creates a strong constructive interference vertical, and now also has a band of destructive interference horizontal next to the array. You can see this immediately begins to break down at the corners of his construct.
@RedshiftDrift
Sure, a beam can diverge by a degree or so, but this debate was about whether a photon is more like a ray or an infinite plane.
I still don’t understand how you conceive of a photon as an infinite plane. A similar alternative to that is photon as an expanding sphere (a sphere of probability expanding at c around the emitter atom, where the photon energy has a chance of materializing at a point on the expanding sphere), but I think that model has issues too.
Is your idea of a photon an infinite plane, or an expanding sphere of chance, or neither?
@Francois-Zinserling
Good question. That would be a lot of energy not going into the beam!
Lasers have reached an efficiency of 85% (https://ieeexplore.ieee.org/document/4628740), which is far more than 50%, so that’s a reason to doubt the destructive-interference depiction. Also, Louis’s points, “the emitters in a laser don’t have to be regularly spaced. In the HeNe laser, the emitters are the moving atoms of a gas; they are not regularly spaced apart. In a semiconductor laser, the atoms are spaced by a few Å, a distance much smaller than a wavelength.”, refute the destructive-interference depiction.
Check out this recent work from Nvidia. Diffraction in simulation is possible by modeling a photon as a ray with width. https://www.youtube.com/watch?v=5jfVn2ABxTo&ab_channel=NVIDIADeveloper
You are not alone to not understand. Perhaps this ‘question and first answer’ can help? Or perhaps a review of a Fourier series would help? The Fourier series expansion of the electromagnetic field is expressed as a sum of photons. I don’t know how to break this down in even simpler terms.
It doesn’t help explain, because it doesn’t address the issue of how once a quantum of energy is emitted from an atom, that quantum of energy somehow becomes an infinitely wide wavefront, which would mean that energy has transferred from the atom to sections of the wavefront faster than c. (Since the midpoint of the wavefront is radiating from the atom at c, the shoulders of the wavefront have radiated faster than c.)
The StackExchange answer ventures into mathematics, but forgets major aspects of the physical situation. And Fourier series or the ability to approximate a function as a sum of various cycles don’t prove the [infinite plane model of a photon].
I have been on the hunt for a photon wavefunction for a while but the one presented in the link above is somewhat simplistic. However, from Euler we can show the same wave function as $ψ(x,t) = Ecos(x-wt) +iBsin(x-wt)$ (I added the E and B) This simply describes a wave function where E and B may be the amplitudes of the orthogonal electric and magnetic fields. It also defines it well as to where it is to be found on the x and t axes. I don’t know where the jump comes in to say
and the rest of the discussion is not clear on this either.
Constantin Meis in this link gives what I determine the most understandable wave function for a photon I have yet to see. See equation (70). (Please keep in mind ‘understandable’ for me is quite a low bar to cross.)
But it’s not just a bare wave function. From it can successfully be derived energy E=hf and momentum P= h/λ, and spin +/- h. The take-away is that a photon is a particle (wave corpuscle as he calls it) that is localised within its wavelength.
The one thing I don’t quite understand is how he includes for polarisation, except by saying >where the polarization can be either left (L) or right (R) circular.
@RedshiftDrift not sure if you find this paper to your liking, but if you were to write eq(70) as e.g. R circular only, how would you write it? (sorry, this is for me, not for this discussion necessarily)
That’s not what happens. An atom emits a spherical wave expanding at c around the emitter, as you wrote above.
The Fourier series is not meant to prove anything, it’s just a tool used to calculate an answer. You could decompose electromagnetic waves using any set of orthogonal mathematical functions (e.g. Legendre polynomials) and get the same answer. The Fourier series is convenient because it is a transformation between wavelength and frequency.
@Francois-Zinserling the paper is standard QED up to Eq. (17). After that I’m not sure what the author does, but Eq. (70) is not as general as he claims and the epilogue has no reference to support the claims…
In any case, Eq. (70) is a set of two equations, one for R-circular and another for L-circular. For R-circular polarization the equation is written with the index ‘R’ only
$$\Phi_{k, R}(\vec{r}, t) = \left( \frac{\varepsilon_0 \omega_k}{\hbar} \right) ^{1/2} \left[ \alpha_{0k}(\omega_k) \left( \hat{\varepsilon}_{k, R} e^{i(k \cdot r -\omega_k t)} + c.c. \right) \right]$$
In other words $\hat{\varepsilon}_{k, L}$ is another variable (a complex vector) for left-polarization.
Ok. Earlier you wrote “A single photon… it’s a plane wave” and “a plane has no bounds”.
So now the model under examination is [photon as a sphere of probability expanding at c around the emitter atom, where the photon energy has a chance of materializing at a point on the expanding sphere].
Here are some issues with the [expanding sphere of chance] model:
When a “sphere of chance” is diffracting and reflecting at slits and walls and sensors, how is it changing direction without transferring momentum? Is it transferring momentum? If not, how is it changing direction? That’s why there’s a weakness in analogizing one photon to a water wave, because with a water wave, the full wavefront has momentum, and diffraction and reflection are actual momentum transfer between molecules.
When a “sphere of chance” expands, what is its gravity to the rest of the universe? Is the photon’s hf/c^2 contributing to gravity? At what position?
What is the emitter atom’s position and velocity as the emitted “sphere of chance” expands?
i doesn’t fit with conservation of momentum. ii is absurd. iii is not possible with the expanding “sphere of chance”. That’s a ray model.
You’ve changed the model, these two descriptions don’t correspond to the same physical problem. The first one only has an atom emitting a spherical wave. The second one has an atom emitting light and interacting with slits and matter.
…
This conversation follows the pattern of the Bohr–Einstein debates. Bohr claimed (like I am doing here as the devil’s advocate) that quantum mechanics could calculate the result of any quantum experiment, but Einstein (like you @sahil5d) was not convinced and designed a large number of Gedanken-experiments, trying to force Bohr to admit quantum mechanics was incomplete. Einstein published the famous EPR paper…
It “is absurd” you say, echoing Einstein’s question: “Is the moon there when nobody looks?” Of course this is absurd! The moon is there even if nobody is looking! But nobody has been able to break quantum mechanics and nobody has been able to break Einstein’s arguments. “Nobody understands quantum mechanics”, that’s where we’re at.
@sahil5d I won’t live ling enough to repeat the 90-year long conversations between Einstein, Bohr, Bell, Renninger, Feynman, etc. All I know is that the ‘quantum mechanics tool’ works well1, but I don’t know why the tool works so well. To my knowledge, there is no satisfying physical picture that describes what happens between atoms and light2 (although I believe Sabine is on the right track with superdeterminism)
Physical objects have a width, but since ‘photons’ are mathematical objects, asking for their transversal width makes no more sense than asking for the width of the polynomial $x^2 + 3x -1$. On the other hand, given a wall with holes in it and a description of the light beam hitting that wall, it is possible to calculate how much light will get through the holes and where it will end up on the detectors.
If you read Mermin’s 1985 article, know that there are loopholes in Aspect’s experiments and every experiment demonstrating a violation of Bell’s inequality. This is still true today. Also, I am a “Type I” physicist as defined on p. 41.
Momentum is transferred to a slit when a photon passes through, the photon is transferred from one plane wave to another.
… and there is no theory of quantum gravity, so no answer can be given to your question.
I disagree. I was talking about the same photon as “expanding sphere of chance” and asking what happens to it in a given situation, specifically how it diffracts at a wall slit when it’s very unlike a water wave.
I agree. That’s why I’m listing these issues. Through an accounting of the issues, we’re more likely to conceive of an accurate, understandable model.
Also, many of the physics greats of the 1900s didn’t figure out that superluminal galactic recession is false, the BB is false, LCDM is false, SR is false because the Sun doesn’t go around the Earth, Maxwell’s Retarded Potential EM is false, and QED Renormalization is “hocus pocus”, so all that considered I’m inclined to expect they’ve whiffed with [photon as expanding sphere of chance where the photon energy has a chance of materializing at a point on the sphere].
We don’t have to repeat them! Have any of them had conversations probing these exact ideas?
Oh, this is interesting. Does that redshift the photon?
Well we have somewhat satisfying pictures and renders of atomic orbitals, waveguides (which have a cutoff frequency), and antenna apertures (which have an effective area), so we’re almost there.
Also raytracing technology today (see the Nvidia research above) is simulating single-slit diffraction.
Quantum mechanics (the so-called Copenhagen or wavefunction-only version) is incomplete because it does not describe the physical mechanism that produces the statistical output that the wavefunction successfully models. Theoretical physicists make up for this shortfall by spouting quantum babble: Superposition of states! Wave-particle duality! The measurement problem!
The situation with QM is analogous to that of a bookie (tout) before the start of a horse race. The bookie can give you the statistical probability for each horse to win the race but they cannot reliably predict the outcome of any particular race. Why? Because a horse race is a chaotic event with too many variables for the outcome to be scientifically or mathematically predictable.
The only difference between a QM experiment and a horse race is that you can observe the race itself and see how it plays out but you cannot observe the QM process without disrupting it. This characteristic of QM experiments is a hard physical limitation imposed by the quantum scale - an observation is tantamount to a measurement and concludes the experiment; the process cannot be observed only the outcome.
The alternative QM interpretation, Bohmian mechanics, does not have the quantum babble baggage because it describes the process in realistic terms as the interaction of a particle and a guiding wave induced on a chaotic subfield. It produces the same results as Copenhagen. It cannot predict the outcome of individual experiments either but the situation is again analogous to a horse race - the statistics cannot and do not predict the outcome - because of the chaotic elements. There is however a coherent explanation that does not require the metaphysical handwaving of quantum babble.
Of course it does, the new photon in the other plane wave is redshifted w.r.t. the initial photon. But the redshift is inversely proportional to the mass of the slit, so the effect is relatively small. Since it doesn’t matter if the photon is scattered by a slit or an electron, the equation for the redshift is the same as the Compton formula; the redshift $\Delta\lambda$ is always positive.
Hmm, redshift happens in so many ways. Recently I realized that redshift also happens when a photon reflects off a mirror (photon’s momentum reverses, mirror mass gains momentum, mirror mass has new kinetic energy, so the photon’s energy actually decreased).
When you say “plane wave”, is it plane-wave-infinite-no-bounds, or is it spherical-wave-expanding-around-emitter?
What do you think about Figure 4 in this paper? https://research.nvidia.com/labs/rtr/publication/steinberg2024diffraction/steinberg2024_fsd_paper_lowres.pdf.
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.
If the photon single-slit and double-slit diffraction patterns can be explained by the raytracing research, and if the buckyball grating pattern can be explained by van der Waals and polarizability, then QM is no longer unique in its calculated outputs, and QM probability wave and matter wave theory, with all its accompanying “collapse of wave function” mystery and nonsense, can be considered false.
Which part of “plane” is not clear? Not ‘spherical’, plane as in ‘flat’!
“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.
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”).
Same as the above statement. Consistent with the above statement.
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.
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.
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.
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.
[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.)
[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.
[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.]
[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”.
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?
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.
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.
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.
Follow through on your idea,it might lead to something
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.
https://en.wikipedia.org/wiki/Aperture_(antenna)#:~:text=must%20also%20be-,given%20by
The equation holds if you plug in πr^2 for A_eff, and 2πr for λ.
Going in the right direction
@RedshiftDrift writes: >it’s the combination of notes that makes a melody; each note taken separately has no melody.
But if notes are not limited in width (duration) then you get cacophony instead of melody.
@sahil5d
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.
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.
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.
@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 :)
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..
@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.
@sahil5d
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).
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.