If the transition is instantaneous, the moment the photon appears must be superluminal.
In quantum mechanics, Bohr's semi-classical model, Heisenberg's matrix mechanics, and Schödinger's wave function are all able to support the assumption of energy levels of atoms and coincide with the spectra of atoms. It is the operating mode of most light sources, including lasers. This shows that the body of their theories is all correct. If they are merged into one theory describing the structure image, it must have the characteristics of all three at the same time. Bohr's ∨ Heisenberg's ∨ Schödinger's, will form the final atomic theory*.
The jump of an electron in an atom, whether absorbed or radiated, is in the form of a single photon, and taking the smallest energy unit. For the same energy difference ΔE, jumping chooses a single photon over multiple photons with lower frequency ν, suggesting that a single photon structure has a more reasonable match between atomic orbital structures**.
ΔE=hν ......(1)
ΔE=Em-En ......(2)
It is clear that without information about Em, En at the same time, generating a definite jump frequency ν is impossible. "Rutherford pointed out that Rutherford pointed out that if, as Bohr did, one postulates that the frequency of light ν, which an electron emits in a transition, depends on the difference between the initial energy level and the final energy level, it appears as if the electron must "know" the frequency of light ν. level and the final energy level, it appears as if the electron must "know" to what final energy level it is heading in order to emit light with the right frequency."[1].
Bohr's postulate of Eq. (1)(2) energy level difference is valid [2]. But it does not hold as axiomatic postulate. This is not just because all possible reasons have not been ruled out. For example, one of the most important reasons is that the relationship between the "wave structure" of the electron and the electromagnetic field has not been determined†. Only if this direct relationship is established can the transition process between them be described. It is also required that the wave function and the electromagnetic field are not independent things, and it is required that the wave function is a continuous field distribution, not a probability distribution [5]. More importantly, Eqs. (1)(2) do not fulfill the axiomatic condition of being axiomatic postulate, which is not capable of ignoring the null information‡.
Doing it as a comparison of questions is the same as when we ask how the photon controls its speed [3] and where the photon should reach next. They are both photon behaviors that must rest on a common ground.
Considering the electron transition as a source of light, it is equally consistent with the principle of Special Relativity, and the photons radiated must be at the speed of light c and independent of the speed of the electrons††. However, if the light-emitting process is not continuous, the phenomenon of superluminal speed occurs.
We decompose the light-emitting process into two stages. The first stage, from "nothing" to "something", is the transition stage; the second stage, from something to propagation, is the normal state. According to classical physics, if the light emission is instantaneous, i.e., it does not occupy time and space. Then we can infer that the photon from nothing to something is not a continuous process, but an infinite process, and the speed at which the photon is produced is infinity. We cannot believe that the speed of propagation of light is finite and the speed at which light is produced is infinite. There is no way to bridge from the infinite to the finite, and we believe that this also violates the principle of the constancy of the speed of light.
There is no other choice for the way to solve this problem. The first is to recognize that all light emitting is a transitional "process" that occupies the same time and space, and that this transitional process must also be at the speed of light, regardless of the speed of the source of light (and we consider all forms of light emitting to be sources of light). This is guaranteed by and only by the theory of relativity. SR will match the spacetime measure to the speed of light at any light source speed. Secondly, photons cannot occur in a probabilistic manner, since probability implies independence from spacetime and remains an infinity problem. Third, photons cannot be treated as point particles in this scenario. That is, the photon must be spatially scaled, otherwise the transition process cannot be established. Fourth, in order to establish a continuous process of light emission, the "source" of photons, whether it is an accelerated electron, or the "wave function" of the electron jump, or the positive and negative electron annihilation, are required to be able to, with the help of space and time, continuous transition to photons. This will force us to think about what the wave function is.
Thinking carefully about this question, maybe we can get a sense of the nature of everything, of the extensive and indispensable role of time and space.
Our questions are:
1) Regardless of the solution belonging to which theory, where did the electron get the information about the jump target? Does this mean that the wave function of the electron should span all "orbitals" of the atom at the same time.
2) If the jump is a non-time-consuming process, should it be considered a superluminal phenomenon¶ [4]?
3) If the jump is a non-time consuming process, does it conflict with the Uncertainty Principle [5]?
4) What relationship should the wave function have to the photon to ensure that it produces the right photon?
-------------------------------------------------------------------------
Notes:
* Even the theory of the atomic nucleus. After all, when the nucleus is considered as a "black box", it presents only electromagnetic and gravitational fields.
* * It also limits the possibility that the photon is a mixed-wavelength structure. "Bohr noticed that a wave packet of limited extension in space and time can only be built up by the superposition of a number of elementary waves with a large range of wave numbers and frequencies [2].
† For example, there is a direct relationship between the "electron cloud" expressed by the wave function of the hydrogen steady state, and the radiating photons. With this direct relationship, it is possible to determine the frequency information between the transition energy levels.
‡ If a theory considers information as the most fundamental constituent, then it has to be able to answer the questions involved here.
†† Why and how to achieve independence from the speed of light cannot be divorced from SR by its very nature, but additional definitions are needed. See separate topic.
¶ These questions would relate to the questions posed in [3][4][5].
-------------------------------------------------------------------------
References:
[1] Faye, J. (2019). "Copenhagen Interpretation of Quantum Mechanics." The Stanford Encyclopedia of Philosophy from .
[2] Bohr, N., H. A. Kramers and J. C. Slater (1924). "LXXVI. The quantum theory of radiation." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 47(281): 785-802. This was an important paper known as "BSK"; the principle of conservation of energy-momentum was abandoned, and only conservation of energy-momentum in the statistical sense was recognized.
[3] “How does light know its speed?”；
https://www.researchgate.net/post/NO3_How_does_light_know_its_speed;
[4] “Should all light-emitting processes be described by the same equations?”；
https://www.researchgate.net/post/NO11_Should_all_light-emitting_processes_be_described_by_the_same_equations；
[5] “Does Born's statistical interpretation of the wave function conflict with ‘the Uncertainty Principle’?” https://www.researchgate.net/post/NO13_Does_Borns_statistical_interpretation_of_the_wave_function_conflict_with_the_Uncertainty_Principle；
Dear Chian Fan.
I have a short post published in LiveJournal in 2018: https://vida-louca.livejournal.com/15863.html with a very similar title "How do electrons know everything?". There, an "anomaly" in the excitation energy of an electron in the Na atom among other alkali metals is considered. Surprisingly, the same anomaly is found in the thermal expansion coefficient of Na in the solid state. This amazing result and some others obtained in the work https://www.researchgate.net/publication/370058256_Thermal_expansion_of_solids_or_how_the_space_in_crystals_is_born_Detection_of_fermionic_excitations_of_electrons_in_atoms_during_thermal_expansion_of_solids allow us to conclude that
1) inside the atoms there are small thermal excitations of electrons, which are impossible within the framework of Schrödinger equation;
2) these excitations are proportional to the energy of nearest transition between energy levels in atom;
3) and their energy, in the first approximation, is equal to the value h/Nτ, where h is the quantum of action, N is the total number of electrons in atom, τ is the time of transmission of action quantum to the all atomic electrons at once. That is, the crystal heats up exclusively due to the transfer of action quanta, and not by the energy quanta, as one might think.
Unfortunately the post in the first link is written in Russian. And if Google translator does not help you, I will try to translate it into English after a while and publish it here. I am very busy at the moment as I am going to speak in Novosibirsk next week at a conference on thermal physics.
Or here is another post in Russian: "Birth and death of photon" (https://vida-louca.livejournal.com/29165.html), which may be of interest to you. It tells how photon is absorbed and emitted by an atom.
Yours, Mikhail.
“…How do Electrons in Atoms Know the Transition Level difference in Advance?….”
- to answer really scientifically to this question it is necessary before to know scientifically concretely what are “electron” ,“photon”, and “atom”, however for this it is necessary to understand scientifically what are the fundamental system “Matter”, for what it is necessary before to understand scientifically what are at least the fundamental phenomena/notions “Space”, “Time”, “Energy”, “Information”, which in mainstream philosophy and sciences, including physics, are fundamentally completely transcendent/uncertain/irrational.
The fundamental phenomena/notions above can be, and are, scientifically defined only in framework of the really philosophical 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
- more concretely relating to Matter in the SS&VT informational physical model
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, which is based on the conception, and
- more concretely relating to the thread question in SS&VT 2007 initial model of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
In the whole physical model it is rigorously scientifically, first of all in complete accordance with all reliable experimental data, it is shown that the informational system “Matter” is based on a simple binary reversible logics, and so the ultimate base of Matter are the primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4+1]4D dense lattice, which is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- and so everything in Matter is/are some specific disturbances in the lattice.
Utmost typical disturbances are “particles”, which are created at impact of 4D momentum, P, [“bold” means 4D vector in 4D space with metrics (cτ,X,Y,Z)] on some the lattice’s FLE, what causes cyclic propagating along 4D “helix” of FLE-by-FLE “flipping point”, the “helix” so has radius, λ, so the flipping point has momentum P and “angular momentum”, “M=Pxλ”, and, in parallel, the creating momentum P in 4D direction of this momentum. Here is principal nuance that the cross-product in 4D space don’t exist as 4D vector, however that isn’t essential in this case.
The cyclically flipping point so always moves in the lattice with the speed that is completely determined by the main properties of FLE , i.e. FLE “size” and “FLE binary flip time interval”, which are equal to Planck length and Planck time, lP and tP, Vhelix=√2x(lP/tP), however along the creating P-direction the speed of the flipping point is c= lP/tP, i.e. all particles constantly move in 4D lattice – and, of course, in 4D space – with velocities that have identical absolute values be equal to the observed 3D speed of a particle “photon”, which is created by some only3D space directed P momentum – i.e. to standard speed of light.
Note also, that the sequence of FLEs in the cycle is the particle’s close-loop algorithm that cyclically runs , and on the algorithm’s FLE-sequence other particle’s properties/parameters are written in the space dimensions (g,w,e,s).
Correspondingly all particles have momentums P=mc and energies E=Pc=ћω; ћ and ω are reduced Planck constant and frequency the particle-algorithm ticks with which.
Matter is absolutely rigorously based on the set of ultimately fundamental and universal laws/links/constants, which are written in every FLE – every FLE knows physics completely, and so always knows what it must concretely do at every concrete impact.
Including, returning more concretely to the thread question, every an atom state is a special configurations of FLE-systems [particles], which transforms under impacts from a given state into other state in complete accordance with the laws, etc.;
- and at transitions of electrons between an atom shell levels, when some photons are radiated/absorbed, that can happen really practically instantly – again, particle “photon” exists, including at creation, as particle-[flipping]point, though here can be some other nuances that complicate the picture.
But, again, there is no any problem in that “photons know its speed” – again that know every FLE, that is written in FLE’s size and flip time, and any FLE by no means can change something in this case.
Correspondingly, say, that
“…Then we can infer that the photon from nothing to something is not a continuous process, but an infinite process, and the speed at which the photon is produced is infinity. ….”
- really is too vague claim, in Matter no infinities exist.
That [relating to the speed of light] was already explained in SS posts in https://www.researchgate.net/post/NO3_How_does_light_know_its_speed , however in this thread also a few other posters rather vividly took part, answering the thread question by telling how “Roman empire European clerics/scientist tried to translate the old documents of the Greece and Roman culture eide”, etc., so in this thread the note exist
“…Doing it as a comparison of questions is the same as when we ask how the photon controls its speed [3] and where the photon should reach next. They are both photon behaviors that must rest on a common ground.…[3] “How does light know its speed?”；
https://www.researchgate.net/post/NO3_How_does_light_know_its_speed ….”
- let’s hope that such posters will not appear here.
Cheers
Mikhail N Dulin
What do you think of the idea that space-time is built by wave effects of the causal velocity c nature, basically neutrino-type standing and transmitting waves, and electromagnetic wave is the antipodal coherent pair of such a foundation waves? The supersymmetric counterpart of photonic and gluonic bosons would indeed be a fermionic space-time background of separation potentials, which would have the same antipodal phases known from time-like fermions, i.e. the measurable reality actually constantly varies between matter and antimatter, left and right, even and odd distances.
In my model, the neutrino oscillation would be explained by gravitational terms, not by mass terms.
Dear Esa Säkkinen.
Unfortunately, I cannot give you a substantive answer. I am very far from the topic of your research, but in every possible way I welcome the construction of classical space-time by means associated with wave excitations. To which photons also belong, since I consider them as an excited state of some discrete elements of the surrounding space, which are in the ground state and represent fermions in a surprising and incomprehensible way for me.
As for neutrino oscillations, I have so far only limited ideas. But they tell me that neutrinos are a hollow double shell like a soap bubble that has a spatial curvature similar to the particles that have mass. Therefore, I really like your desire to explain the neutrino oscillations by some gravitational terms.
Mikhail.
Dear Chian Fan
Schrödinger's equation was only meant by him to represent the resonance volume within which the electron axially oscillates when captive in one orbital of the hydrogen atom, as a development of the discovery of this resonance state by de Broglie as described in his 1924 thesis.
The integer sequence of the wave function relates to the sequence of resonance frequencies corresponding to the ground orbital (integer 1) at mean Bohr radius distance from the proton, and the higher integers corresponding to the further away metastable orbitals to which the electron can be excited to move to, and from which they almost instantly jump back to the rest orbital (integer 1) at which point a bremsstrahlung photon is released, corresponding to the energy difference between this further away orbital and the ground orbital.
All of these emitted photons, with frequencies all being multiples of the Planck constant, as discovered by de Broglie to correspond to one orbit in orbital 1 at theoretical Bohr radius distance, were already known from spectral recordings, and it is this integer relation between their frequencies that caused de Broglie to discover the related resonance sequence.
De Broglie and Schrödinger had as a main project to establish the mechanical process by which these photons are emitted when returning to the ground state, but the almost immediate focus of the community on the Heisenberg statistical method and the advent and dominance of the Copenhagen Interpretation completely overshadowed their project, that was abandoned at that time due to total lack of interest in the community, as related by Schrödinger in these 1952 references:
Einstein, A., Schrödinger, E., Pauli, W., Rosenfeld, L., Born, M., Joliot-Curie, I. & F., Heisenberg, W., Yukawa, H., et al. (1953) Louis de Broglie, physicien et penseur. 2. Éditions Albin Michel, Paris. Page 18.
and
Schrödinger, E. (1952) Are there quantum jumps? Brit. J. Philos. Sci. 3 109,233.
https://philpapers.org/rec/SCHATQ-3
However, the mechanics of these photons emission and absorption processes have now been established from the electromagnetic perspective, and nowhere in the process is the velocity of light exceeded, and neither can these processes be instantaneous.
The related analyses are available in Sections 28 and 29 of this article:
Article Emphasizing the Electromagnetism according to Maxwell's Init...
All historical formal references are provided.
The resonance states of the electron in the hydrogen atom are analyzed in this other article:
Article An Overview of the Hydrogen Atom Fundamental Resonance State...
Best Regards, André
Dear Mikhail N Dulin
Many thanks to Vad Pérez for his translation work for all of us. I'm sad that I can't use ChatGPT. Also curious, is it ChatGPT itself that recognizes (как в Великой Китайской Стене) and excludes the underlining?
Mikhail N Dulin made a good observation and offered a good insight. Even though I don't understand thermal physics, I can sense that it touches on profound truths. If we take out the concept of higher dimensional space, it almost satisfies the need for reality.
Van_dak, who commented on the Russian original (https://vida-louca.livejournal.com/15863.html), used the Chinese character "易" as his profile image. This is interesting. "易" is the name of the ancient Chinese book “Yi Jing”. “Yi Jing” is a philosophical book that explains the theory of change in all things. The character 易 is made up of two characters, "日”（sun） on top and "月”（moon）on the bottom, representing the unity of yin and yang，and change of motion. The core idea is that "yin and yang is the Tao". The Tao here is the "Tao" in Lao Tzu's Tao Te Ching.
Back to the point. 易 is the way of change, the electron transition is change [1]. So, is the electron also one with yin and yang? Why and how does it change?
If we say that the electron is one of yin and yang, what is "yin" and what is "yang"? Is the negative electric field the "yin", the positive electric field the "yang", or the "electric charge" the "yin" and "magnetic charge" as "yang"? The question of whether there is a "magnetic monopole" [2], what "electric charge" and "magnetic charge" are, whether they must be accompanied by each other, and how to accompany each other, will be drawn into deeper consideration[3][4].
Best Regards, Chian Fan
----------------------------------------------------------
[1] Milonni, P. W. (1984). "Why spontaneous emission?" American Journal of Physics 52(4): 340-343.
[2] Dirac, P. A. M. (1931). "Quantised singularities in the electromagnetic field." Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 133(821): 60-72. This is an important paper on magnetic monopoles.
[3] Dirac, P. A. M. (1948). "The theory of magnetic poles." Physical Review 74(7): 817；It is a paper on the relationship between electric and magnetic charge.
[4] MoEDAL-Collaboration and V. A. Mitsou (2022). "MoEDAL, MAPP and future endeavours."；. "MoEDAL (the Monopole and Exotics Detector at the LHC) ".
：MoEDAL is designed to fully exploit the energy-loss mechanisms of magnetically charged particles in order to optimise its potential to discover these elusive particles. Various theoretical scenarios foresee the production of magnetic charge at the LHC: (light) ’t Hooft-Polyakov monopoles , electroweak monopoles, global monopoles , monopoles in Born-Infeld theory and monopolium, a monopole-pair bound state. Magnetic monopoles and dyons — the latter possessing both magnetic and electric charge — are fascinating hypothetical particles. Even though there is no empirical evidence for their presence, strong theoretical reasons motivate their existence and many theories, including grand unified theories and superstring theory, predicted them.
Dear André Michaud
It was a period worth studying why physicists immediately accepted the Copenhagen interpretation which should not have been readily accepted. At a time when Einstein, A., Schrödinger, E. De Broglie had enough influence as well as the advantage of philosophical reality, the physics community fell back on Copenhagen, which has become an article of faith up to the present day. Personally, I went through very difficult thinking to understand the ideas that the Copenhagen school easily popularized. I am concerned that the psychological and spiritual issues that exist here go beyond what is conceptually right or wrong in physics. I am particularly interested in knowing the final answer to this question, whether it is a breakthrough in physics, a turn away from physics, or whether physics has taken a fork in the road.
In addition, your paper discusses an extremely important issue. “Maxwell considered that both fields had to mutually induce each other cyclically for the velocity of light to be maintained while Lorenz considered that both fields had to synchronously peak at maximum at the same time for this velocity to be maintained, both interpretations being equally consistent with the equations.”
Best Regards, Chian Fan
Dear Chian Fan ,
Yesterday, I have unswered to your question in a better way, but somthing went wrong with my internet connection... The comment was lost...
Now the short answer to your question:
1) 'Regardless of the solution belonging to which theory, where did the electron get the information about the jump target? Does this mean that the wave function of the electron should span all "orbitals" of the atom at the same time. - in case of stabile atom: from exterior in non stabile elemnt from both direction: exteriors interior: should good be good here study of BEC..
2.)'2) If the jump is a non-time-consuming process, should it be considered a superluminal phenomenon¶'- The Is there no jump the it happening change in wave character of the lelctron. '[4] “Should all light-emitting processes be described by the same equations?”；'- I haven't looked into the question! nevertheless, my answer is as follows: Yes, sould, all light-emitting processes should be described by the same equations.
'3) If the jump is a non-time consuming process, does it conflict with the Uncertainty Principle [5]?' See previous answer... however you interpret it: it does not conflict with the Uncertainty Principle [5].[I have not looked in 5]
'4) What relationship should the wave function have to the photon to ensure that it produces the right photon?' De Brogle wave function and to these consider André Michaud 's response: 'Schrödinger's equation was only meant by him to represent the resonance volume within which the electron axially oscillates when captive in one orbital of the hydrogen atom, as a development of the discovery of this resonance state by de Broglie as described in his 1924 thesis.' and:'De Broglie and Schrödinger had as a main project to establish the mechanical process by which these photons are emitted when returning to the ground state,(...) With concept of the graviton:
only abstract:
Research Proposal Physico-metaphysical proof of the existence of graviton (Fiz...
Conclushion:
Chapter Physico-metaphysical proof of the existence of graviton
can be resolved:
Regards,
Laszlo
'
Dear Chian Fan
You wrote: "It was a period worth studying why physicists immediately accepted the Copenhagen interpretation which should not have been readily accepted."
Yes. My personal analysis of the behavior of the leaders of opinion of this era led me to conclude that it was the hubris of a single man, Heisenberg, which is at the origin of the so ready adoption of the Copenhagen interpretation as an outcome of the 1927 Solvey Congress.
He was in reality a pure mathematician, and not a practising experimentalist, so he was looking at the subatomic level from a strict mathematics perspective. He was apparently personally convinced that if he could not understand the atomic and subatomic levels more clearly than what his method allowed, then nobody else could. He wrote so himself.
The thing is that, given that his statistical method mapped over Schrödinger's wave equation allowed precisely determining the various levels of momentum energy of the electron in their possible orbitals in the hydrogen atom, if the idea that no further understanding could be reached about these magnitude levels as Heisenberg proposed was accepted, then this offered an easy way out to everybody to stop spending any more efforts in trying to understand further.
This was the psychological "easy way out of not having to needlessly waste any more effort at trying to understand what was deemed impossible to understand" trap that the Copenhagen interpretation formally offered at the 1927 Solvey that was then intensely promoted to generation after generation of students mainly by Sommerfeld and Wheeler, according to an analysis carried out by Franco Selleri in his book (1983/1990 Die Debatte um die Quantentheorie (The Debate on Quantum Theory))
https://www.amazon.ca/GRAND-DEBAT-THEORIE-QUANTIQUE/dp/2082111652/ref=sr_1_2?crid=3OQS88RX9NB2K&keywords=franco+selleri&qid=1693139167&s=books&sprefix=franco+selleri%2Cstripbooks%2C297&sr=1-2
To my knowledge, this book, available in French and German, never was translated to English.
You wrote: "At a time when Einstein, A., Schrödinger, E. De Broglie had enough influence as well as the advantage of philosophical reality, the physics community fell back on Copenhagen, which has become an article of faith up to the present day."
In retrospective, we observe that their influence, as well as that of Planck, who was in agreement with them regarding the nefarious influence on research of the budding Copenhagen interpretation philosophy, as he formulated in an exposé he made in 1930, just recently translated to English by the Minkowski institute, was not as important as we tend to believe. I even read a comment by a French physicists, a student of Wheeler, on the internet, that his opinion was that de Broglie had received his Nobel prize for political reasons!
(Planck, M. (1931) Positivismus und reale Aussenwelt. Akademische Verlagsgeselschaft M. B. H., Leipzig. https://catalog.princeton.edu/catalog/2057791)
https://www.amazon.ca/Positivism-Real-External-World-Realism/dp/1927763843/ref=sr_1_36?crid=3NO65F0VQVT5O&keywords=Max+Planck&qid=1693140278&s=books&sprefix=max+planck%2Cstripbooks%2C396&sr=1-36
Other historical publications of Planck's works are available in English from the Minkowski Institute that clearly expose his rational research philosophy.
On his part, Einstein, despite his role in history, was soon considered as not being in phase with mainstream, now completely swallowed up by the Copenhagen interpretation philosophy, to the point that when he concluded in his last years in the 1950's that gravitation follows the pattern of electromagnetism, his conclusion was rejected without a second look, as reported by Wheeler in his 1995 book (
Ciufolini I & Wheeler JA (1995). Gravitation and Inertia, Princeton University Press.)
"A distinguished physicist even published in his very last years' works, the main point of which is to claim that gravitation follows the pattern of electromagnetism. This thesis, we cannot accept, and the community of physics, quite rightly, does not accept." Archibald Wheeler, 1995, p. 391)
The consequences of the advent of the Copenhagen Interpretation are presented in the Foreword of my second book on electromagnetism, available in free access here:
Article Introduction to Electromagnetism According to Maxwell
You wrote: "In addition, your paper discusses an extremely important issue. “Maxwell considered that both fields had to mutually induce each other cyclically for the velocity of light to be maintained while Lorenz considered that both fields had to synchronously peak at maximum at the same time for this velocity to be maintained, both interpretations being equally consistent with the equations.”
Indeed, I found that this conclusion by Maxwell turned out to be the key to understanding Einstein's conclusion about electromagnetism as applicable to quantized electromagnetic energy at the subatomic level, which does not in any way contradict electromagnetic wave treatment at our macroscopic level, according to the Lorenz gauge. It is this avenue that I have been following for the past 25 years. My analysis and synthesis of the subatomic level grounded on all historical formal sources is now complete and available for the upcoming generation.
In other words, I analyzed what the Copenhagen interpretation captive mainstream community considered for the past hundred years as impossible to understand.
Best Regards, André
Dear Chian Fan and André Michaud ,
My opinion on this question is electron does not know what path to follow. It just stochastically takes a random path downward energetically. Electron energy is not quantized but photon energy is quantized. The quantization of electron energy in a confined space such as an atom is to satisfy a resonance state that can last a longer time in the stochastical process, which is then observed by an observer with a much larger probability than those non-resonant states. As such my humble opinion is quantum mechanics has nothing to do with statistics, disagreeing with the Copenhagen interpretation and agreeing with André Michaud . Statistics comes after quantum mechanics as a separate process in the statistical thermodynamics calculation and description of the quantum phenomena. That is, I don't believe in super-position at the single particle level.
I have updated a new version preprint proposing to connect quantum mechanics with classical mechanics. I was very confused with the Copenhagen interpretation when teaching an undergraduate quantum course so gave it a try to explain it differently. For those who have read the previous versions, this new version adds a discussion on helium energy levels:
Preprint From Particle-in-a-Box Thought Experiment to a Complete Quan...
Dear André Michaud
Admire your keen observations and thank you for the time and effort you put into this ["One hundred times on the loom review your work"]. Thanks for the reference links, I will try to read more.
"needlessly waste any more effort at trying to understand what was deemed impossible to understand". In China, the norm in the teaching of quantum mechanics is the one who says "Shut up and calculate!
It is undoubtedly the mainstream physics community will benefit most from the re-examination of the Copenhagen interpretation. Basing all research on an inaccurate foundation is perhaps the reason why there have been no fundamental breakthroughs in theoretical physics for half a century (you wrote, "the absence of progress that we have been observing for decades now in fundamental physics research. fundamental physics research."). Younger physicists, in particular, are not always aware of the historical details and do not realize that many theories of physics were accepted without resolution of the controversy and then became taken for granted with the passage of time.
"A distinguished physicist even published in his very last years' works, the main point of which is to claim that gravitation follows the pattern of electromagnetism. This thesis, we cannot accept, and the community of physics, quite rightly, does not accept." I think that Einstein will still be Einstein after all. And will eventually confirm that his efforts to combine electromagnetic and gravitational fields are in the right direction. This is also the direction of your "Our Electromagnetic Universe".
Best Regards, Chian Fan
Dear Vad Pérez
Thank you for your kind offer. But unfortunately, I've tested it over and over again and I'm not able to access the link, https://www.perplexity.ai/. This is probably also blocked by "The_Great_firewall". I'll use a different tool，desite the limitations..
Best Regards, Chian Fan
Chian Fan and André Michaud,
Thanks and congrats for the conversation. Very interesting!
Dear Chian Fan
You wrote: "Thanks for the reference links, I will try to read more."
I particularly encourage you to read the historical formal references that are provided. All assertions that I made in my analyses come from these sources, that date back from before the Copenhagen interpretation warped the general mindset of mainstream, and from more recent formal accounts of experiments that are never referred to by mainstream because they contradict the Copenhagen interpretation, many originally written in German or French, that never were translated to English – until recently – through neglect of mainstream, and that consequently were never referred to in standard reference work initially written in English by authors who do not understand these languages and consequently never read them.
You wrote: " In China, the norm in the teaching of quantum mechanics is the one who says "Shut up and calculate!"
The same mantra is repeated in all institutions worldwide with regards to Quantum Mechanics. Feynman is the one, to my knowledge, who first said that.
This is not the only nefarious recommendation that he made. In 1949, he specifically recommended to his admiring followers to refrain from exploring the only remaining unexplored frontier in fundamental physics:
"In many problems, for example, the close collisions of particles, we are not interested in the precise temporal sequence of events. It is of no interest to be able to say how the situation would look at each instant of time during a collision and how it progresses from instant to instant."
Ref: Richard Feynman (1949), Space-Time Approach to Quantum Electrodynamics, Phys. Rev. 76, 769 (p. 771).
Exploring this last frontier is what allowed finally understanding the reason for the stationary action stability of all unexcited electronic orbitals in atoms.
Now that this complete set of historical formal references, untainted by the Copenhagen interpretation philosophy, is available to all for the first time since the early 1900's, I am convinced that the upcoming generation will again start grounding their research on this more consistent foundation.
Best Regards, André
The thread question “How do Electrons in Atoms Know the Transition Level difference in Advance?” is rigorously scientifically enough clarified in the SS post on page 1, if briefly:. it is scientifically explained, that Matter is rather simple logical structure, and so absolutely everything in Matter is/are specific disturbances in the Matter’s fundamental, universal, and ultimate base– 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], the lattice is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct);
- and that everything that happens in Matter, including, say, when electrons in atoms, quite specifically radiate/absorb photons, is determined by logical FLE structure, by fundamentally different [now known 4] fundamental Nature forces, charges of which are specifically written in particles’ algorithms “Forces’ charges” sections, and a set of fundamental and universal laws/links/constants, that also are written in FLE stricture.
At that particles, including photons, are specific disturbances that are created at transmission to some FLE in the lattice some 4D momentum, P, what causes in the lattice propagating of “FLE-by-FLE binary flipping” of precessing FLEs, while this “FLE flipping point” propagates in the lattice along some 4D “helix” trajectory.
Correspondingly any particle ay every given time moment exists as “FLE flipping point” that has size be equal to Planck length, and always exists in Planck time interval.
That above is, though well better than first, some approximation of what particle is; the picture is more complex, but that isn’t too essential in this case; and, so, say, a photon that is radiated at relaxation of some excited electronic shell level, is radiated in ~ Planck time interval, however that is completely concrete photon; that is another thing that further in the precessing photon’s algorithm FLEs some “electric” and “magnetic” properties appear in whole the algorithm N FLEs sequence, N=λ/2πlP, lP is Planck length, λ is the photon wave length;
- though that doesn’t mean that the whole atom’s shell relaxation happens in Planck time, the shell is rather complex system of charges/masses/spins/orbital momentums, etc.
More see the SS post on page 1 and links in the post, here only note again: Matter is a completely perfect automaton, where everything in Matter knows physics absolutely completely, so where, including, particles and closed enough systems of particles, say, atoms, are completely identical, i.e. are identical algorithms, and so the same structures in the same initial conditions behave identically.
Though a note else relating to claimed in a few posts here as quite wrong “Copenhagen interpretation” - this QM interpretation really looks as utmost rational among other ones, say, “pilot wave”, “Multiverse”, etc.
https://www.researchgate.net/post/Time_and_Gravity/2
Cheers
Dear Jixin Chen
"It just stochastically takes a random path downward energetically."
Randomness is uncausal, and it implies the destruction of the "conservation of energy and momentum", and the destruction of the "principle of least action". Energy-momentum itself is not probabilistic, and if the electron does not choose the path of least energy, what is the reason?
choosing energy levels and choosing paths should be different. This is possible if there are symmetric multiple paths with equal downward energies. But can we prove that there must be such a case, with absolutely symmetric paths?
Compare this with a model in which two negative electrons B and C are connected by a line centered at O, and far away in the direction of the line across O and down the vertical line, there is a positive electron A. A is attracted down by both B and C and eventually oscillates up and down at O. In the case of absolute symmetry, A will not fall to either B and C. However, with infinitesimal interference, A will favor one side over the other. In real physical systems, there are various symmetry-breaking factors, all of which appear to be random, but must actually be caused by tiny non-random factors that cannot be determined.
In a box filled with hot moving particles, will there be an absolutely symmetrical path after particles collide? Physics must avoid such a situation. We start with the symmetry of the smallest region, and whenever a locally symmetric state is composed, there is always the possibility that a symmetry-breaking external factor exists, unless that external factor is also symmetric. In this way, its symmetry in turn requires that the more external factor must also be symmetrical. This situation extends indefinitely. When the symmetry-requiring factors keep extending outward, it is as unattainable as the requirement to match an infinitely long codeword. It becomes even more unattainable when motion symmetry is considered. Considered microscopically, substances like crystals can only be considered quasi-symmetric, or dynamically quasi-symmetric, at any given time. The actual growth process of a cell must be statistically significant if there is an equal probability of a two-choice state. Mathematically, there are multivalued functions, e.g., square roots in the case of complex numbers, and roots of logarithmic functions. However, physically there will be no solutions that are simultaneously greater than 1. Is this likely to rise to a principle? It should be analyzed further. We should consider that there can be only one thing in physics that is absolutely symmetrical. That is the symmetry of the base element of all things.
Best Regards, Chian Fan
Chian Fan
I agree with you that in a deterministic point of view, randomness is strange. But chaotic and randomness of any many body system is a natural property to an observer due to the infinite amount of information in such a system. There is infinite amount of paths that are fundamentally symmetrical to follow in such a system with a infinitesimal perturbation. For example, the perfectly still ball can feel a photon passing by, can be hit by a dust, can follow some internal vibrational cycles, can be affected by the gravitational wave. It is beyond our current ability to calculate any of these probabilities. Rather we put all these unknowns into a random function and calculate their average effects on the stability of the ball. The same for the solar system hitting by many asteroids. Thus we correlate the randomness such as the lifetime of the ball to an statistical average value such as temperature.
In my opinion symmetry is not the law it is a beauty carried by conservation laws. If we upgrade it to a law then careful confinement is needed. Least action is neither the law it is a path defined by laws happened to carry the property in some special systems compared to the paths we thought were equally possible. But nature does not think so, i.e. a gap between our theory and reality.
For the electron paths, as well as it goes downwards energetically, symmetry holds. If it goes upwards absorbing a photon or collided, symmetry holds as well. The problem is how to calculate the lifetime. For which we need correlate with its energy needed to break the state and the incalculable thermal fluctuations or excitation beam to get a probability of its lifetime. Let’s admit that we don’t have the god computational power and memory and will probably never have it. And statistics has enabled us to narrow down a range between boundaries we have estimated. for quantum my complain is we give up too early by factoring randomness at the fundamental lays rather than decoupling it to statistical thermodynamic layer.
Dear Jixin Chen ,
'I agree with you that in a deterministic point of view, randomness is strange. But chaotic and randomness of any many body system is a natural property to an observer due to the infinite amount of information in such a system. There is infinite amount of paths that are fundamentally symmetrical to follow in such a system with a infinitesimal perturbation.'
- That kind of reasoning It can deceive a person. deterministic prediction of certain earthquakes has been solved. on the basis of that, it can be said that there is the phenomenon itself, which follows a certain basic law of nature. Others are incidental and somewhat follow Hegel's dialectics. In the computer age, you don't have to work with functions but with algorithms and artificial intelligence. The electron is not a flea to jump here or jump there. has a well-defined interval position. between which the changes of state occurring in it cause it to change its position relative to the centre. Here we come to an interesting conclusion, but this totally original idea has not been tested... Therefore it may be wrong.
Regards,
Laszlo
László Attila Horváth ,
Agree that "Therefore it may be wrong." I believe every theory is wrong but there are things less wrong or meet an application quality control, specifically, cheap and fast at the required significant figures.
If the theory happens to be beautiful or easy to understand, that is a plus even if it is wrong at the higher standard of quality control.
The idea that an electron can be jumping between states is totally functional in explaining the observations of quantum jump and also cheaper and easier to understand than the quantum equation. The simple version of Bohr model does fail to explain the finner structures of the spectrum but it is still fixable by adding wave, spin, and vibrational properties to the electron orbitals, which was not possible before the computer age but totally possible now.
AI does not have any model to go with it other than a regression model of the complicated convolution of many Taylor expansions. As such, it is a fitting method whose accuracy is dependent on the accuracy of data. "Garbage in garbage out."
We are discussing here how to get high-quality simulated data which is a problem this thread raises.
Dear Jixin Chen ,
I can't really go against your recent answer.
'We are discussing here how to get high-quality simulated data which is a problem this thread raises.' - If you know what you're looking for, where to find it, how-in what form you can get it, you can easily buy good food, then you can easily achieve a high-quality simulated data. That's why it's important to have a more natural concept that is as simple as possible... Then comes the testing... detection of errors (trying to see what caused the error, solution, and new test... and so on... In the meantime, if possible, the best possible theory must be formulated... If the theory is right, the world opens up showing the secrets of nature...
I know that science is not poetry: but knowing is like creating a poem, only then will it succeed if it is intertwined, through you with your environment.
Regards,
Laszlo
“…Randomness is uncausal…..”
- randomness can be quite causal; say, when a coin flies in the air, its “Ψ-function” collapses “heads” and “tails” probabilities values after the coin halls into a palm are (1/2, 1/2); and, though in a M collapses series Nheads and Ntails are random, this randomness is quite causally determined by the coin construction,
- and electron jumping between an atom electronic shell levels states is quite causally determined by the atom construction,
- while everything in Matter, including randomness of all states and jumps in all atoms is completely causally determined by FLE constructions and the set of specific logical conditions “fundamental Nature forces” …
More see the SS posts above and links in the posts.
Cheers
Dear Chian Fan ,
The questions raised by you are quite valid and fundamental. However, giving direct answers to your four questions will not serve the desired purpose. For example, my answer to your second and third question is that the electron transition time in hydrogen atom is of the order of 10-16 seconds. But that answer will raise many more questions. So to begin with, we must first ask, "What is the shape, size, structure and field of an elactron? Can we mentally visualize it? Is it a particle or a wave? Can we mentally visualize the instant to instant motion of an electron in a Coulomb force field, say that of a proton?" In my opinion our inability to visualize a physical entity or phenomenon will show our ignorance about that entity or phenomenon.
The next step is to understand how exactly the electric and magnetic fields are induced by motion of an electron.
Best Regards
Gurcharn
“…So to begin with, we must first ask, "What is the shape, size, structure and field of an elactron? Can we mentally visualize it? Is it a particle or a wave? Can we mentally visualize the instant to instant motion of an electron in a Coulomb force field, say that of a proton?……”
- all that is essentially clarified already in the SS&VT 2007 Planck scale initial model of Gravity and Electric Forces, see
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
- and really more can be made really scientifically only as development of this initial model, first of all basing on the principle that really fundamental physics is possible only at considering physical problems on Planck scale,
- including in this case first of all it must be clarified – what are and how really they act – the “informal”, but really existing, acting, and really fundamental, Nature forces that determinate spin-spin and spin-orbital interactions; for what first of all it is necessary to clarify – what is 4D spin of particle..
Cheers
Dear Gurcharn Singh Sandhu
Thank you for bringing an inspirational point of view.
I believe that all physical structures and behaviors are picturable. It should not be true that there is no physics that any human mind can visualize, just as there is no physics that any computer can simulate. The human mind is a great creation of nature, and it should have the ability to map the physical, as long as the physical world is four-dimensional.
You touched on the question of waves or particles. This will trigger each of us to think of "wave-particle duality". I have never seen an exact definition of "wave" and "particle" in physics, and it doesn't seem to be needed. Usually we say that the double-slit interference experiment confirms the wave property of light; Einstein's photoelectric effect and Compton scattering experiment confirm the particle property of light. If the former confirms the concept of the field of light, and the field is a wave, we have no objection to the wave property of light. But does the particle property have to be the concept of "point particle"? Shouldn't there be a scale if it is a point? Can't a spatially distributed wave packet be considered a "point" as a whole? Must an "elastic collision" be considered a "point-to-point" impact? In fact, as long as we recognize that the momentum of a photon is P=h/λ, all momentum exchange behaviors that follow the conservation of momentum can be reduced to "collisions", elastic, inelastic, although the λ information must be reflected by the photon scale. Abandoning the concept of "point particles" should be necessary for us to recognize the nature of microscopic behavior.
Best Regards, Chian Fan
Dear Chian Fan ,
Regarding Wave-particle duality I understand that in QM, an electron in motion is regarded as a wave and Heisenberg's uncertainty principle becomes applicable to its motion. In classical mechanics, electron is treated as a particle and the motion of the center-of-mass' of the electron will be governed by Newton's laws of motion as well as Coulomb's laws of electrostatics.
In my opinion, an electron consists of a central spherical core surrounded by an intrinsic electrostatic wave field which contains about 35% of the total mass-energy of the electron. In motion, overall electron will behave as a particle while its intrinsic electrostatic field will behave as a wave. However, there is an ambiguity in the notion of electrostatic field itself.
Intrinsic Electric Field
Consider one electron located at an isolated point P in space - far removed from all other charges. This isolated electron will produce an (intrinsic) electric field around point P that spreads everywhere in surrounding space. This intrinsic electric field or the electrostatic field of an electron is an integral part of the electron charge and does not depend upon the presence or absence of any other charge in its vicinity - not even any test charge. In Maxwell's terminology of 'deformations of aether' we might call it 'strain field' or 'strain wave field' around the electron and consider it as an integral part of the electron structure - whatever it be.
Coulomb Field
However, for practical applications we quantify this electric field of the electron by measuring its interaction with a positive test charge positioned at a certain point Q at distance r from point P. The force on second charge or test charge is caused by the mutual interaction between the electric fields of the two charges and is governed by Coulomb's Law of electrostatics. The intrinsic electric field of an electron when quantified with a test charge, using Coulomb's law, may now be termed as Coulomb electric field of the electron. This Coulomb field of the electron will map the force acting on test charge located at Q as well as map the interaction energy released due to the mutual interaction of the superposed intrinsic electric fields of the electron at P and test charge located at Q. A significant point to be noted here is that a completely isolated electron will possess only an intrinsic electric field and there will be no potential energy or potential field physically existing around the electron.
Ambiguity
Mapping of the forces and energies for different locations Q of the test charge through the Coulomb field has introduced a major ambiguity in the notion of Electric Field of the electron. Ambiguity is in the lack of distinction between the Intrinsic electric fields of isolated electron and isolated test charge and the Coulomb electric field of their interaction forces and energies. Moreover, this mapping of interaction forces and energies cannot represent a physical field since the forces and energies mapped at different field locations Q1, Q2, Q3 etc. do not physically exist when the test charge is physical located at Q. Unfortunately, in Modern Physics the Coulomb electric field is de-facto treated as the Intrinsic electric field of the electron and potential energy is assumed to be physically existing around the electron.
Best Regards
Gurcharn
“…You touched on the question of waves or particles. This will trigger each of us to think of "wave-particle duality". I have never seen an exact definition of "wave" and "particle" in physics, and it doesn't seem to be needed. …..”
- what is "wave-particle duality" it is explained, say, in SS post, August 15, in https://www.researchgate.net/post/NO12_Should_an_Object_at_rest_have_Rest_Momentum/1
To read yesterday SS post on page 2 in https://www.researchgate.net/post/What_underlying_rules_might_have_lead_to_dual_nature_of_light/2it is useful as well.
Cheers
It might be that the electron has to wait for an appropriate virtual photon to come into existence to transfer certain energy. The electron does not know in advance; it depends on how much energy that particular virtual photon close by can absorb. Virtual photons have an energy range of about 10^-100 to 10^-10 ergs. https://www.linkedin.com/pulse/view-virtual-particles-ground-state-vacuum-2nd-booklet-warren-frisina/?trackingId=zAVyY6yWSJuKeDDZ7Yx6Wg%3D%3D
“…It seems odd to me that the photoelectric effect is seen as evidence of photons….”
- the photoelectric effect is too well observed at interactions of just photons with electrons in matter to have some doubts in this case.
The thread question is rigorously scientifically answered/commented in SS posts on pages 1-4, so for readers who really want to know the answer, and not only - see these posts and papers that are linked in the posts.
Cheers
The thread question is rigorously scientifically answered/commented in SS posts on pages 1-4, first of all on page 1; so for readers who really want to know the answer, and not only - see these posts and links in the posts; here only to
“…Elementary particles know nothing.….”
- to write something it is necessary before to understand scientifically what the used in the text terms mean, in this case what are “Elementary particles”, “know”, and “nothing”, though.
In the mainstream philosophy and sciences, including physics, all really fundamental phenomena/notions, first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Inertia”, “Information”, are fundamentally completely transcendent/uncertain/irrational, and so any mainstream texts, if the texts address to some really fundamental points, logically inevitably are so only some strange mental constructions [“Higgs field”, “holes in spacetime”, etc., etc.].
Really scientific understanding of what exists and happens in humans, including, of course, what is “human” at all, and what is “know” is possible only in framework of the really philosophical Shevchenko-Tokarevsky’s 2007 “The Information as Absolute” conception, recent version of the basic paper
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed , where, including, the phenomena/notions above are rigorously scientifically defined/explained, and the last questions above are scientifically answered,
- and at application to the informational system “Matter” in the SS&VT informational physical model, where, including, it is rigorously explained what is “particle” – see
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics,
- what are fundamental Nature forces and the Forces’ fields – see initial Planck scale models [really fundamental physics can be only on Planck scale, in other case, i.e. in mainstream physics till now - see above ] of Gravity and Electric Forces in https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
- and of Nuclear Force in https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force
Matter is rather simple logical system, and so well probably all, and practically for sure at least the 3 ones above, Forces act by the same scheme, where all – particles and fields – and everything in Matter, first of all the FLEs – know completely all basic Matter’s fundamental and universal laws/links constants, what they must do in every concrete situation in matter, and always behave at existence and interactions in complete accordance with these laws/links/constants.
More relating to the thread question see the SS posts above in the thread; SS posts in https://www.researchgate.net/post/Do_extraterrestrial_aliens_really_exists/154, first of all the recent one, are relevant in this discussion as well.
Cheers
Chian Fan
Your thought experiment is controlled by stationary action, which as you probably know is a quantity integrated typically over time. Not by conservation laws, no matter how irresistable hf=ΔE may seem. The electron "knowing stuff" is akin to a teleological quality some attribute to the action principle. Another take is that from the photon's perspective, there is no interaction at all - there is a conserved quantity coupled to the action, but no conservation law.
Dear Frank van den Bovenkamp
Thank you very much for your reply, which brings a different perspective.
"Knowing" in this context means that there is relevant "information" and there is access to it. Although this is not human consciousness, it is the same at the level of information.
Throughout history, the laws of conservation have been challenged at many critical moments, only to be reaffirmed in the end. As long as there is a lack of conservation, even a "temporary" lack of conservation, causality is destroyed.
Best Regards, Chian Fan
Dear Chian Fan
I think the problem you describe is legit. However the idea is not that conservation laws are violated, but that they are subordinate - there is an aspect of the interaction that is not controlled by conservation laws.
Perhaps you could view your experiment in the light of the Euler-Lagrange formalism. Not sure though if it applies (probably involving momentum rather than energy), but it might help take away some controversy. Or perhaps use the Dirac delta, or path integral.
A somewhat more speculative idea is that photons also contain a Goldstone mode, but obviously not coupled as in fermions or EW bosons. These k=0 modes imo represent the action more naturally.
Dear Frank van den Bovenkamp
Thank you for your reply with new surprise.
I'll start by clarifying my point. "However the idea is not that conservation laws are violated, but that they are subordinate - there is an aspect of the interaction that is not controlled by conservation laws." The idea that conservation of energy-momentum is subordinate was also my earlier view, and I believe it is also the view of most people. I have since realized that there is no way to distinguish between "dominant" and "subordinate" relationships. We defaulted to "subordinate" because we never knew what energy-momentum was, or thought it was just a property of matter. This naturally makes it impossible for them to be considered dominant. However, both Lagrangian and Hamiltonian quantities depend on the definition of energy-momentum, as does any other physical equation, including the Einstein field equations. As long as you give a reasonable definition of the energy-momentum of matter, space-time, then there is essentially，"The conservation of energy-momentum determines the Einstein field equations, not the Einstein field Equations determining the space-time energy-momentum." Or, explaining the principle of the field equations in terms of energy-momentum, i.e., the reason why matter changes spacetime, removes the need to go into the description of gravitational field energy-momentum and the question of whether or not it is conserved.
Spacetime acts far beyond our conventional knowledge; they are the basis of all existence and the master of all. When we fully understand the nature of spacetime, the explanation of physical phenomena is not limited to the usual physical theorems. What I mean here can be explained by the apple falling to the ground. Q: Why did the apple fall to the ground instead of rising to the sky? First layer explanation: It was determined by Newton's law of gravity. Second layer explanation: it was determined by Einstein's geodesic equation. Ultimate answer: it was determined by the Energy-momentum equation.
I think the more important point is that you wrote "A somewhat more speculative idea is that photons also contain a Goldstone mode." My point is, as long as we recognize the reality of physics, and that all physics must be intuitively understandable, then it is certain that photons are and are uniquely so-called "Goldstone bosons", and that zero mode is the rest form of photons. So, as long as the "object", the rest form of photons, is moving, mass must be manifested ....... This also means that the Higgs potential does not need to be an external coupling, but a potential of its own.
Looking forward to your further thoughts on photons.
Best Regards, Chian Fan
Chian Fan
Good that you bring up the E-p-equation in this connection, and we should also recall that it is Dirac's departure point.
My take on what you're saying is that even though E and p itself are conserved, the E-p-eq. itself does not represent a conservation law.
Let's write it down: E2 = p2c2 + m2c4
The apparently central role of the E-p-e is not easy to understand. Perhaps you like the idea that it represents a Pythagorean triangle, i.e. implies a 2-manifold and so does spin [kg∙m2/s]. This imo touches on WHY Dirac discovered that spin solves the relativistic wave equation.
Expanding this further, one could argue that quantum spin and general relativity are two sides of the same paper. Recall the Hilbert-Einstein action here.
"it is certain that photons are and are uniquely so-called [uncoupled] "Goldstone bosons", and that zero mode is the rest form of photons"
This goes a step further than my intuition, but it makes sense. Note that both these 2 ideas fly at the outer rim of physics, but in my view are entirely within reason. Is "rest form" your term?
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