Is the Fine-Structure Constant the Most Fundamental Physical Constant?
The fine-structure constant is obtained when the classical Bohr atomic model is relativisticized [1][2]. α=e2/ℏc, a number whose value lies very close to 1/137. α did not correspond to any elementary physical unit, since α is dimensionless. It may also be variable [6][7]*.
Sommerfeld introduced this number as the relation of the “relativistic boundary moment” p0=e2/c of the electron in the hydrogen atom to the first of n “quantum moments” pn=nh/2π. Sommerfeld had argued that α=p0/p1 would “play an important role in all succeeding formulas,” he had argued ‡ [5].
There are several usual interpretations of the significance of fine structure constants [3].
a）In 1916, Sommerfeld had gone no further than to suggest that more fundamental physical questions might be tied to this “relational quantity.” In Atomic Structure and Spectral Lines, α was given a somewhat clearer interpretation as the relation of the orbital speed of an electron “in the first Bohr orbit” of the hydrogen atom, to the speed of light [5].
b) α plays an important role in the details of atomic emission, giving the spectrum a "fine structure".
c) The electrodynamic interaction was thought to be a process in which light quanta were exchanged between electrically charged particles, where the fine-structure constant was recognized as a measure of the force of this interaction. [5]
d) α is a combination of the elementary charge e, Planck's constant h, and the speed of light c. These constants represent electromagnetic interaction, quantum mechanics, and relativity, respectively. So does that mean that if G is ignored (or canceled out) it represents the complete physical phenomenon.
Questions implicated here :
1) What does the dimensionless nature of α imply? The absence of dimension means that there is no conversion relation. Since it is a coupling relation between photons and electrons, is it a characterization of the consistency between photons and charges?
2) The various interpretations of α are not in conflict with each other, therefore should they be unified?
3) Is our current interpretation of α the ultimate? Is it sufficient?
4) Is α the most fundamental physical constant**? This is similar to Planck Scales† in that they are combinations of other fundamental physical constants.
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Notes
* Spatial Variation and time variability.
‡ Sommerfeld considered α "important constants of nature, characteristic of the constitution of all the elements."[4]
† https://www.researchgate.net/post/NO30The_Relation_Between_Mathematics_and_Physics_6-Are_Planck_Scales_Constants_Parameters_or_Principles
** https://www.researchgate.net/post/No28The_Relation_Between_Mathematics_and_Physics_4-Could_All_Physical_Constants_be_Unified_to_a_set_of_Fundamental_Constants_of_Nature
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References
[3] 张天蓉. (2022). 精细结构常数. https://blog.sciencenet.cn/blog-677221-1346617.html
[1] Sommerfeld, A. (1916). The fine structure of Hydrogen and Hydrogen-like lines: Presented at the meeting on 8 January 1916. The European Physical Journal H （2014）, 39(2), 179-204.
[2] Sommerfeld, A. (1916). Zur quantentheorie der spektrallinien. Annalen der Physik, 356(17), 1-94.
[4] Heilbron, J. L. (1967). The Kossel-Sommerfeld theory and the ring atom. Isis, 58(4), 450-485.
[5] Eckert, M., & Märker, K. (2004). Arnold Sommerfeld. Wissenschaftlicher Briefwechsel, 2, 1919-1951.
[6] Wilczynska, M. R., Webb, J. K., Bainbridge, M., Barrow, J. D., Bosman, S. E. I., Carswell, R. F., Dąbrowski, M. P., Dumont, V., Lee, C.-C., Leite, A. C., Leszczyńska, K., Liske, J., Marosek, K., Martins, C. J. A. P., Milaković, D., Molaro, P., & Pasquini, L. (2020). Four direct measurements of the fine-structure constant 13 billion years ago. Science Advances, 6(17), eaay9672. https://doi.org/doi:10.1126/sciadv.aay9672
[7] Webb, J. K., King, J. A., Murphy, M. T., Flambaum, V. V., Carswell, R. F., & Bainbridge, M. B. (2011). Indications of a Spatial Variation of the Fine Structure Constant. Physical Review Letters, 107(19), 191101. https://doi.org/10.1103/PhysRevLett.107.191101
Dear Chian Fan,
According to me the value of the fine-structure constant comes from a cosmological parameter.
Dear Jamil Kooli
If the fine-structure constant comes from some cosmological constant, we need to correlate that cosmological constant with the electric charge e, the Planck constant h, and the speed of light c. This is equivalent to turning back. And it is not obvious that the cosmological constant has to be correlated with e and equally dimensionless.
However, we believe that the fine structure constant must be affected by some cosmological constant, e.g. through the spacetime metric (spacetime expansion). Atomic structure parameters can be different at different spacetime metrics, unless there happens to be a canceling effect.
The fine structure constant reflects the physical phenomena inside the atom, and it is a microscopic constant. Usually we think that cosmological phenomena are built up from microscopic accumulations, therefore, in the causal relationship, cosmological parameters should be the effect, not the cause. Probably many people disagree with this view.
Best Regards, Chian Fan
Dear Chian Fan,
Planck constant has according to me an equation not the one E/f but an equation a function of cosmological parameters. in other side its ok e is a function of fine-structure which depends on a cosmological parameter. But be carreful I insist to the fact that speed of light is not a function of any cosmological parameter and the Newtonian constant is also not a fuction of any cosmological parameter but they have another special link.
“[NO.33】 What Does the Dimensionless Nature of the Fine-Structure Constant Mean?”
- the rigorous scientific answer to the question above
– as that is in every case when some physical answer really relates to any really fundamental problem, while in mainstream physics all really fundamental phenomena/notions, first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fundamental Nature forces” – and so “charges”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are fundamentally completely transcendent/uncertain/irrational, and so in every case when the mainstream addresses to any really fundamental problem, then result is completely inevitably is transcendent/mystic something
- is possible, and more 30 fundamental questions, including in the quote above, are answered, only in framework of the Shevchenko-Tokarevsky’s Planck scale informational physical model, 3 main papers are
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics
https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics
https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force
More concretely the answer is in the 2007 SS&VT initial Planck scale model of fundamental Nature Gravity and Electric forces, see 2-nd link above, section 6. “Mediation of the fundamental forces in complex systems”, though to understand completely what is in this section is necessary, of course, to read and understand both the first papers.
So more see the links above, here only a few notes:
“…c) The electrodynamic interaction was thought to be a process in which light quanta were exchanged between electrically charged particles, where the fine-structure constant was recognized as a measure of the force of this interaction. [5]….”
- that is an example of some – and in this case even evidently transcendent/mystic – mainstream “thoughts”. Indeed in mainstream QED and Standard particle Model photons are postulated as mediators of Electric Force, despite the evident fact – if there are two or more charges in statics, then the charges are quite really interact, but at that quite evidently no any photons are observed. Etc., that isn’t an unique mainstream mystics in this case, though.
Really, as that is completely rigorously scientifically shown in the SS&VT whole model above, the Matter’s ultimate base is the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct).
FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP, andeverything what exists and happens in Matter is/are only some disturbances in the lattice, that are created if some the particle FLE is impacted, and propagate/move on the lattice only with 4D. (cτ,X,Y,Z) speeds c=lP/tP.
Particles are created if to a FLE some no-zero 4D space (cτ,X,Y,Z) momentum P [bold means 4D vector] is transmitted, corresponding disturbances are some close-loop algorithms that cyclically run with frequency ω=Pc/ћ on “FLE hardware” as sequential FLE-by-FLE flipping; say, electron’s algorithm is sequence that has “logical length” [number of FLEs] N0~2.4x1022FLEs.
At that some parts of algorithms have some Forces “marks”, and when a particle algorithm runs, its marked by the Force FLEs cause propagating in 3DXYZ space disturbances “Force mediators”, which, if hit into other particle’s also flipping and marked by the same Force FLE, cause a momentum that impacts on the “irradiated” particle and at statics is directed to the first [radiating] particle.
Electron’s – and other electrically charged particles’ [besides quarks] algorithms have the part of E-marked FLEs that is relative, and is equal to √α. Just that is the physical sense of the fine structure constant.
I.e. number of E-marked FLEs is always ~ 8% of N0, in electron NE~2x1021FLE, in proton algorithm in ~1000 times lesser, but since proton’s algorithm ticks in ~1000 times faster, proton also has charge e, etc.
Nothing more, so Electric Force [particles] strength constant e=(αћc)1/2.
More see the links above, , note also, though, that at least 3 – Gravity, Electric, and Nuclear, Forces act by the same – the above – scheme.
Cheers
Dear Jamil Kooli
Without clarifying the microscopic origin of the cosmological parameters, your argument firstly negates reductionism. Secondly, it also denies the foundations of modern physics. I think any attempt to establish a completely new physics is dangerous.
Best Regards, Chian Fan
Dear Chian Fan,
I find that for example if someone begins to make researches in physics using dimensionless Planck unities as I'm curretly doing I'm formel that soon or late he can as me find new equations for known cosmological parameters and also he can identify at minimum a new equation of a new cosmological parameter not yet well known. I want to say that till now constants of physics are not all identifief and this is the real big problem in modern physics. I also want to say that such people working in this way should arrive to proove to discover how cosmology uses some calculus means of the quantum world and this same people could proove how quantum calculus uses cosmological parameters. I hope that I can soon post my new equations for the exact hydrogen radius using a purely relativistic method as well as my new formulas for both the Rydberg constants and the classical electronic radius which I have just test them using the results of the experiments in muonic hydrogen and deuterium. According to me these results represents a tresor of information in same time for cosmology and for the quantum word because we can identify a dimensionless ratio which is good for the calculations both for the quantum world and in cosmology.
Dear Jamil Kooli
"..... ...make researches in physics using dimensionless Planck unities."
It is an interesting idea to start the research from here. but such a constant must not be the most fundamental physical constant, it is more likely to embody a fixed relationship, similar to a fine structure constant. Any constant embedded in physical behavior should have a dimension, just as π is meaningless unless it is embedded in a circle.
"I want to say that till now constants of physics are not all identified and this is the real big problem in modern physics."
I don't quite agree with this view. One reason is that physical constants are not well defined concepts in modern physics*; the other reason is that modern physics has been able to describe physical phenomena relatively accurately in both the macroscopic and microscopic domains, which means that important physical constants already exist in the list of physical constants. What we need is to discover which are the fundamental physical constants.
The above is only a personal opinion, and I look forward to new discoveries in your paper.
Best Regards, Chian Fan
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* Here are some references and different points of view: https://www.researchgate.net/post/No28The_Relation_Between_Mathematics_and_Physics_4-Could_All_Physical_Constants_be_Unified_to_a_set_of_Fundamental_Constants_of_Nature
https://www.researchgate.net/publication/377566579_The_Relationship_Between_the_Theory_of_Everything_and_the_Constants_of_Nature_English_Version
Dear Chian Fan
I have already written to you that there are only two fundamental spaces. The first is an electromagnetic space composed of discrete photons (with spin s=1ћ). The other is nuclear, composed of protons and neutrons, as well as electrons (with spin s=½ћ). The maximum speed of excitation of photons is the speed of light c. This is nature's choice. The maximum speed of excitation (movement) of fermions is equal to αс. That is, the fine structure constant α is the ratio of the two maximum possible speeds in two fundamentally different spaces. This is also nature’s choice, and you have to come to terms with it.
With best regards, Mikhail Dulin.
Dimensionless speed ratio: the speed of movement of spatial matter towards the nucleon (the cause of gravity) to the speed of light in space near the nucleon.
Dear Mikhail N Dulin
Some misses are missed by the eyes, some misses are missed by the brain, and some misses are missed by the heart. I'm not sure where I missed your point. However, I remember we discussed causality between constants. α = e2/ℏc, is left equals right, not right equals left. In any case, it's wonderful to now see your unique and illuminating perspective. It exhibits an irresistible symmetry: "The maximum speed of excitation of photons is the speed of light c; The maximum speed of excitation of fermions is equal to αс." and the axiomatic thought: "This is nature's choice!"
However, there is still a lack of understanding of your idea of "only two fundamental spaces". I hope to be able to add to it in the future.
My current experience with fine structure constants is twofold:
1）According to QED, the fine structure constant，α=e2/ℏc，is not dimensionless, but the dimensions cancel out on both sides of the interaction. On one side is the charge e2, representing the electron, and on the other side is ℏc, representing the photon. This is hard to disprove.
2）There are many sources and different interpretations of the fine structure constant, almost all of them are correct, and we cannot doubt that they are the same constant. Then, these different interpretations must be unified, whether it's your point of view, @Preston Guynn's point of view, or Vladimir A. Lebedev 's point of view, and so on. That's the biggest problem.
Then, what physical meaning is implied behind this? Can all sources be attributed to electromagnetic interactions? Especially Relativity. It would appear so.
My conclusion: The Nature of Relativity must be Electromagnetic Interactions according to the behavior of the fine structure constant.
Dear Chian Fan
If only you knew what the electron in the Dirac equation does in response to the “compression” of EM space at a speed close to the speed of light.)) Not only does it use its spin so as not to emit photons during its uniform and linear motion, but also “ turns inside out" to level out the relativistic distortion of the surrounding space. However, this is just my personal opinion.
With best wishes, Mikhail Dulin.
Chian Fan While you rightly state that FSC alpha has many variants of (widely known typically metric multiple unit canceling) representations, by identifying the most important not widely known single metric unit cancellations (of both magnetic flux and electric resistance) it is clearly shown that FSC is not only a constant of the quantum domain, but bridging the quantum world and cosmology in the form of directly showing a physically likewise quantized spacetime based of a fully discredited (think LEGO) hexagonal structured vortex cell arrangement just as already Max Planck has envisioned is real:
Article New novel physical constants metric and fine structure const...
Conference Paper iSpace - Deriving G from α, e, R∞, μ0 and Quantum of Gravita...
Conference Paper iSpace - Exact Symbolic Equations for Important Physical Con...
The thread question “What Does the Dimensionless Nature of the Fine-Structure Constant Mean?”, more correctly “What is the Dimensionless Nature of the Fine-Structure Constant?”, is rigorously scientifically answered in SS post on page 1, 5 days ago now.
So for readers, , who really want to know what the fine structure constant is see this post and papers that are linked in the post.
Cheers
Dear Mikhail N Dulin
"If only you knew what the electron in the Dirac equation does in response to the “compression” of EM space at a speed close to the speed of light.)) Not only does it use its spin so as not to emit photons during its uniform and linear motion, but also “ turns inside out" to level out the relativistic distortion of the surrounding space. However, this is just my personal opinion."
Seems like a very valuable perspective. I need to study and comprehend your points carefully.
Best Regards, Chian Fan
We can understand e²/(2cε0) or e²√(µ0/ε0)/2 as an action quant related to the elementary static charge. We als know h as a fundamental action quant.
The relation e²√(µ0/ε0)/h therefor can be understood as a relation between a quant of physical action and an action quant, which corresponds to an elementary charge.
The Planck constant stands for a dynamic property and the charge quant stands for something static. Therefor this relation compares elementary static and dynamic actions. It seems that static actions are dominant by a factor of about 137.
Dear Vladimir A. Lebedev,
Could you provide me the value of this dimensionless ratio and also the two speeds separately.