Momentum - Science topic

The conventional interpretation of the cosmic microwave background (CMB) anisotropies is that they represent the result of a primordial ‘minefield’ of Dirac-delta energy concentrations that has a characteristic comoving spatial distance between the mines. The mines all exploded at the time of the big bang, generating what evolved into spherical baryonic-matter pressure waves in the primordial plasma, and the time of recombination just happened to coincide with the time when the diameters of the pressure waves were approximately equal to the characteristic scale of the minefield. The observed CMB anisotropies are believed to reflect the spatial form of the universe’s matter at the time of recombination.

This concept appears to be purely speculative, with no underlying mechanism proposed for the existence and form of the ‘minefield’, other than generic allusions to quantum events.

Even if this conceptual model is valid, it doesn’t imply anything about the behavior of dark matter- dark matter doesn’t care about baryonic pressure gradients. A random field of dark matter particle concentrations would have initiated its gravitational collapse process as soon as the particles formed, presumably the time of baryogenesis. At that early time the universe was extremely small (and gravitational accelerations extremely rapid). The dark matter would have collapsed hierarchically: smaller dark matter concentrations would consolidate most rapidly, medium-sized concentrations would have taken longer to consolidate, and really-large scale concentrations would still be far from consolidated. The same process can be described as small voids forming initially, as particles were gravitationally drawn away from lower-density regions, and those small voids subsequently expanding and merging into ever-larger voids, eventually comprising inter-cluster space.

Initially, when the cosmic velocities of dark matter concentrations were small, the collapses would have been towards the centers of local regions of above-average dark matter density. These collapses would have led to the formation of black holes, comprised of dark matter, with a wide range of sizes. As time passed and medium-sized dark matter concentrations started to collapse, their components would have developed significant amounts of angular momentum. They would have collapsed into gravitationally-bound dynamic systems, the beginning of the cosmic web. Those systems would have contained both the first generation of black holes, still feeding, and substantial amounts of dark matter particles.

At any given point in time, the evolving cosmic web would have a characteristic scale, reflecting the overall progress of the gravitational collapse process. In general, voids smaller than the characteristic scale would be slowly growing and merging, but at larger scales there would not yet have been enough time for significant density changes and void-mergers to occur.

By the time of recombination, the evolving dark matter web would have been surrounded by local concentrations of baryonic matter, unable to collapse deeper into the web because of the primordial plasma’s pressure. However, in inter-cluster space the vacuum would have been almost perfect. Following recombination, the baryonic matter halos would have started to collapse gravitationally into the dark matter halos, and the baryonic matter would have tended to be drawn towards the largest dark matter black holes. Galaxies would start to form, and increasing angular momentum at all scales would stabilize the forms of both the dark matter web and of the galaxies and their contents.

This process is entirely different from the conventional model of massive and super-massive black holes: that they formed by the gradual consumption, by early post-recombination supernova-remnant black holes, of large numbers of stars, of other supernova-remnant black holes, and of competitors. In this model, there were no massive or super-massive black holes at the time of recombination. This conventional model is currently being challenged by the James Webb Space Telescope’s identification of numerous super-massive black holes at very high redshifts.

So, a proposition: that the current cosmic web of dark matter was largely complete by the time of recombination, and it included both dark matter particles and dark matter black holes of all sizes. The web has evolved further since then, with more of the dark matter more localized into sheets and filaments and super-massive black holes. The cosmic minefield, and the baryon acoustic oscillations, are illusions.

Do we need to find a motivation for symmetry: {?} → {invariance} → {conservation} → {symmetry} →

Should there be an ultimate symmetry that is identical to the conservation, structure invariance, and interaction invariance of the energy-momentum primitives and that determines all other symmetries?

Symmetry, invariance, and conservation are, in a sense, the same concept [1][2][3] and will generally be described in this order, as if symmetry were dominant.

As commonly understood, energy-momentum conservation was the first physics concept to be developed. It exists as a matter of course in mechanics, thermodynamics, and electricity. However, after physics entered the twentieth century, from quantum mechanics to general relativity, the conservation of energy-momentum has been repeatedly encountered with doubts [5][6][7][8][9][10], and so far it still can't be determined as a universal law by physics. Some of the new physics is insisting on "something out of nothing"[11][12][13][14] or spontaneous vacuum fluctuations[15], which equals to the rejection of energy-momentum conservation. The important reasons for this may be: First, Energy-momentum conservation cannot be proved† . Second, energy-momentum in physics has never been able to correspond to a specific thing, expressed by a unified mathematical formula‡, and it can only be the "equivalence" of various physical forms that are converted and transferred to each other [16]. Third, we have a biased understanding of the status of energy-momentum conservation, such as "These symmetries implied conservation laws. Although these conservation laws, especially those of momentum and energy, were regarded to be the most important of all. Although these conservation laws, especially those of momentum and energy, were regarded to be of fundamental importance, these were regarded as consequences of the dynamical laws of nature rather than as consequences of the symmetries that underlay these laws."[17]. Conservation of energy-momentum was relegated to a subordinate position. Fourth, it is believed that the Uncertainty Principle can be manifested as a " dynamics ", which can cause various field quantum fluctuations in the microscopic domain, and does not have to strictly obey the energy-momentum conservation.

"Symmetry" refers to the "invariance under a specified group of transformations" of the analyzed object [4]. Symmetry is always accompanied by some kind of conservation, but conservation does not only refer to the conservation of energy-momentum, but also, under different conditions, to the conservation of other physical quantities, such as charge, spin, or the conservation of other quantum numbers. Thus, "conservation" is usually the constant invariance of something at some level, and Wigner divided symmetries into classical geometrical symmetries and dynamical symmetries, which are associated with specific types of interactions, every interaction has a dynamical invariance group. "It may be useful to discuss first the relation of phenomena, laws of nature, and invariance principles to each other. This relation is not quite the same for the classical invariance principles, which will be called geometrical, and the new ones, which will be called dynamical."[1]. According to Wigner, we can define the "geometric invariance" of everything as the manifestation of interactions filtered through the absoluteness of the spatio-temporal background. This interaction exhibits itself whenever you assume an observer*. displacement invariance, Lorentz invariance are typical. We can define all "dynamical invariance" as manifestation when the background absolutes of the potential field are filtered out. gauge invariance, the diffeomorphism invariance are typical manifestations." from a passive role in which symmetry is the property of interactions, to an active role in which symmetry serves to determine the interactions themselves --a role that I have called symmetry dictates interaction." "Einstein's general relativity was the first example where symmetry was used" actively to determine gravitational interaction" [2]. This expresses the same idea, that the role of symmetry is elevated to the status of "force". Gross says that the secret of nature is symmetry. The most advanced form of symmetries we have understood are local symmetries-general coordinate invariance and gauge symmetry. The most advanced form of symmetries we have understood are local symmetries-general coordinate invariance and gauge symmetry. unified theory that contains both as a consequence of a greater and deeper symmetry of which these are the low energy remnants [18]. He regards the unification of general relativity and quantum field theory as a unification of symmetries. He regards the unification of general relativity and quantum field theory as a unification of symmetries. If we define generalized invariance as the completeness of the structure, properties, and laws of interaction of the analyzed objects when they interact, i.e., the undecomposability of the whole as a whole, the conservation of the properties (charge, spin, other quantum numbers, etc.), and the consistency of the interaction relations (laws), it is clear that the invariance in this case is special invariance, which means only the invariance of the laws of interaction.

While symmetry, conservation, and invariance are almost equivalent expressions at the same level, there are subtle but important differences. If unbounded, it is the order in which the three are expressed, who actually determines whom, and who ultimately determines the laws of physics. In any case, when we currently speak of symmetry, it must correspond to specific invariance and conservation, not to broad invariance and conservation. This in fact greatly limits the claim that "symmetry dictates interaction", since interaction is much more general. There is no such thing as a failure of interaction, but there is often a failure of symmetry, unless we decide that there will be an ultimate symmetry that determines all other symmetries.

"A symmetry can be exact, approximate, or broken. Exact means unconditionally valid; approximate means valid under certain conditions; broken can mean different things, depending on the object considered and its context. different things, depending on the object considered and its context."[19] "It is not clear how rigorous conservation laws could follow from approximate symmetries"[1]. This reflects the uncertainty of the relationship between conservation currents ( charges) and symmetries, and if we know that conservation currents can still be maintained even with approximate symmetries, it should be understood that this must be a function of the fact that conservation currents have a more universal character. From a reductionist point of view, the conservation charge at all levels will gradually decompose with the decomposition of matter, until finally it becomes something that cannot be decomposed. Such a thing can only be the most universal energy-momentum and at the same time be the ultimate expression that maintains its conservation as well as the invariance of interactions. Otherwise, we will pursue the questions:

1) If energy-momentum conservation is not first, where does the power to move from one symmetry to another, symmetry breaking [11] [12], come from? How can symmetry violations [13] in physics be explained?

2) If symmetry fully expresses interactions, how do we evaluate "symmetry implies asymmetry", "imperfect symmetry", " approximate symmetry", " hidden symmetry"? hidden symmetry"?

3) One of the implications of energy-momentum conservation is that they have no origin, are a natural existence, and do not change with scale and energy level or temperature; symmetry has an origin, and is related to scale, temperature and energy level. How are they equivalent to each other?

4) Must there be an ultimate symmetry which will determine everything and be consistent with conservation and invariance?

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Notes

† We will analyze this separately, which is its most important physical feature [20].

‡ Can different forms of energy be unified?[16]

* We can define the actual observer to be the object of action and the abstract observer to be the object of action for analysis. For example, when we analyze the Doppler effect, we are analyzing it in the abstract; if you don't actually detect it, no Doppler effect occurs in the object of analysis.

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References

[1] Wigner, E. P. (1964). "Symmetry and conservation laws." Proceedings of the National Academy of Sciences 51(5): 956-965.

[2] Yang, C. N. (1996). "Symmetry and physics." Proceedings of the American Philosophical Society 140(3): 267-288.

[3] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[4] Brading, K., E. Castellani and N. Teh (2003). "Symmetry and symmetry breaking."

[5] 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.

[6] Dirac, P. A. M. (1927). "The quantum theory of dispersion." Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 114(769): 710-728.

[7] Carroll, S. M. and J. Lodman (2021). "Energy non-conservation in quantum mechanics." Foundations of Physics 51(4): 83.

[8] Bondi, H. (1990). "Conservation and non-conservation in general relativity." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 427(1873): 249-258.

[9] Maudlin, T., E. Okon and D. Sudarsky (2020). "On the status of conservation laws in physics: Implications for semiclassical gravity." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 69: 67-81.

[10] Pitts, J. B. (2022). "General Relativity, Mental Causation, and Energy Conservation." Erkenntnis 87.

[11] Hoyle, F. (1948). "A new model for the expanding universe." Monthly Notices of the Royal Astronomical Society, Vol. 108, p. 372 108: 372.

[12] Vilenkin, A. (1982). "Creation of universes from nothing." Physics Letters B 117(1): 25-28.

[13] Josset, T., A. Perez and D. Sudarsky (2017). "Dark energy from violation of energy conservation." Physical review letters 118(2): 021102.

[14] Singh Kohli, I. (2014). "Comments On: A Universe From Nothing." arXiv e-prints: arXiv: 1405.6091.

[15] Tryon, E. P. (1973). "Is the Universe a Vacuum Fluctuation?" Nature 246(5433): 396-397.

[16] Chian Fan, https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified

[17] Gross, D. J. (1996). "The role of symmetry in fundamental physics." Proceedings of the National Academy of Sciences 93(25): 14256-14259.

[18] Gross, D. J. (1992). "Gauge theory-past, present, and future?" Chinese Journal of Physics 30(7): 955-972.

[19] Castellani, E. (2003). "On the meaning of symmetry breaking." Symmetries in physics: Philosophical reflections: 321-334.

[20] https://www.researchgate.net/publication/369890893_Summary_Table_of_Light_String_and_Light_Ring_Properties_Supersymmetry

Until recently, practically no one was involved in the development of general relativity. Thousands of people are engaged in dead-end hypotheses. However, general relativity remains the only confirmed theory.

The last significant result in the theory of gravity was obtained in 1918. Then it was understood that the elements of the pseudotensor are not densities of energy or momentum.

A significant result was obtained recently (2021):

Studies (e.g., Ötting, Deutscher, Singleton, & De Angelis, 2023) showed that red cards are by far the most meaningful events to impact football match outcomes, and as a team receiving a red card reduces their chances of winning.

Is there study showing that red cards generate psychological momentum ?

We are trying to apply spectral quasi linearization technique to solve fluid flow stretching sheet problem in matlab. We can solve the momentum equation alone in this method. We are in need of help in matlab code for simultaneous equations. Thanks in advance

A body at rest has rest Energy, so it should also have rest Momentum.

Lao Tzu said, “Gravity is the root of lightness; stillness, the ruler of movement”(重为轻根，静为躁君)*. The meaning of this statement can be extended in physics to mean that "big-G determines how light or heavy an object is, and rest-m determines how easy or difficult it is to move".

According to the mass-energy equation** [1], E=mc^2, any object with mass m has "rest energy" [1], regardless of its inertial frame†. Note that E here is meant to be the energy lost when radiating the photon γ, which is absolute and unchangeable in any inertial frame. The mass-energy equation has been experimentally verified [2] as the correct relation.

According to special relativity [3], the mass of the same object is different in different inertial frames, m' = βm. Therefore, the energy of conversion of m of an object into photon γ is different in different inertial frames. This issue has been discussed in [4], but there is no consensus. Our view is that the "rest energy" is theoretically not Lorentz invariant, and the existence of a minimum value is a reasonable result. The most rational explanation for this is that the minimum corresponds to an absolutely static spacetime, i.e., absolute spacetime(Later we will show that absolute space-time and relative space-time are not in conflict). Analytically, this is one of the reasons why absolute spacetime should exist. The constant speed of light is another reason.

In all cases in physics, energy and momentum coexist and have a fixed relationship, not independent metrics. The energy-momentum ‡ of a photon, E=hν[5], P=h/λ[6]; the energy-momentum relation of Newtonian mechanics, E=P^2/2m; and the relativistic energy-momentum relation, E^2=c^2p^2+m^2c^4. Therefore, it is assumed that if there is a body of mass m that has "rest energy", then it should also have "rest momentum". There is a "rest momentum", and the rest momentum cannot be zero. The rest energy is not intuitive, and the rest momentum should not be intuitive too. The calculation of the rest momentum is the same as the calculation of the rest energy. The nature of mass looks more like momentum; after all, energy is a sign of time, while momentum is a sign of movement. Therefore, instead of calling it the principle of equivalence of inertial mass and rest-energy[1], it should be called the principle of equivalence of inertial mass and rest-momentum.

When positive and negative electrons meet and annihilate [7], -e+e→γ+γ, radiating two photons in opposite directions. Their energy is conserved and so is their momentum. Energy is a scalar sum, while momentum is a vector sum. It seems that the "rest momentum" inside the object should be zero. However, one could argue that it is actually the momentum of the two photons that is being carried away, but in opposite directions. The momentum of the two photons should not come out of nothing, but rather there should be momentum of the two photons, also in some balanced way, and probably playing a very important role, such as the binding force.

Our questions are:

1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum".

2) Elementary particles can be equated to a " energy packet ", and energy is time dependent. If an elementary particle is also equivalent to a "momentum packet", the momentum in the packet must be related to space. Does this determine the spatio-temporal nature of the elementary particles? And since momentum is related to force, is it the force that keeps the "energy packet" from dissipating?

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Notes：

* Lao Tzu，Tao-Te-Ching，~500 BCE. This quote is a translation of someone else's. There are some excesses that I don't entirely agree with. Translating classical Chinese into modern Chinese is just as difficult as translating classical Chinese into English.

** There is a historical debate about the process of discovery of the mass-energy equation, and digging into the history shows that there were discoverers and revisers both before and after Einstein, see literature [8][9]. Important contributions came from Poincaré, F. Hasenöhrl, Planck et al. Their derivations do not have the approximation of Einstein's mass-energy equation. And there is also a debate about the interpretation of the mass-energy equation. Notable debates can be found in the literature[10].

† There is a question here, i.e., is the rest mass Lorentz invariant? That is, is the rest mass the same in different inertial systems? Why?

‡ Einstein questioningly emphasized that energy and momentum seem to be inseparable, but did not explain it.

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References：

[1] Einstein, A. (1905). "Does the inertia of a body depend upon its energy-content." Annalen der physik 18(13): 639-641.

Einstein, A. (1935). "Elementary derivation of the equivalence of mass and energy." Bulletin of the American mathematical society 41(4): 223-230.

[2] Rainville, S., J. K. Thompson, E. G. Myers, J. M. Brown, M. S. Dewey, E. G. Kessler, R. D. Deslattes, H. G. Börner, M. Jentschel, P. Mutti and D. E. Pritchard (2005). "A direct test of E=mc2." Nature 438(7071): 1096-1097.

[3] Einstein, A. (1905). "On the electrodynamics of moving bodies." Annalen der physik 17(10): 891-921.

[4] Is there a minimum value of m in the mass-energy equation E=mc^2? https://www.researchgate.net/post/NO7_Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2；

[5] Planck, M. (1900). " " Verh. Deutsh. Phys. Ges 2: 237.

[6] Einstein, A. (1917). Physikalisehe Zeitschrift xviii: p.121

[7] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.

[8] Ives, H. E. (1952). "Derivation of the mass-energy relation." JOSA 42(8): 540-543.

[9] Sharma, A. (0000). "The past present and future of the Mass Energy Equation DE =Dmc2." http://www.mrelativity.net/Papers/8/Sharma4.htm.

[10] Peierls, R., J. Warren and M. Nelkon (1987). "Mass and energy." Physics Bulletin 38(4): 127.

Does energy have an origin or root?

When Plato talks about beauty in the "Hippias Major", he asks: "A beautiful young girl is beautiful", "A sturdy mare is beautiful", "A fine harp is beautiful", "A smooth clay pot is beautiful" ....... , So what exactly is beauty? [1]

We can likewise ask, Mechanical energy is energy, Heat energy is energy, Electrical and magnetic energy is energy, Chemical and internal energy is energy, Radiant energy is energy, so what exactly is "energy"?[2]

Richard Feynman, said in his Lectures in the sixties, "It is important to realize that in physics today we have no knowledge of what energy is". Thus, Feynman introduced energy as an abstract quantity from the beginning of his university teaching [3].

However, the universal concept of energy in physics states that energy can neither be created nor destroyed, but can only be transformed. If energy cannot be destroyed, then it must be a real thing that exists, because it makes no sense to say that we cannot destroy something that does not exist. If energy can be transformed, then, in reality, it must appear in a different form. Therefore, based on this concept of energy, one can easily be led to the idea that energy is a real thing, a substance. This concept of energy is often used, for example, that energy can flow and that it can be carried, lost, stored, or added to a system [4][5].

Indeed, in different areas of physics, there is no definition of what energy are, and what is consistent is only their Metrics and measures. So, whether energy is a concrete Substance**, or is just heat, or is the capacity of doing work, or is just an abstract cause of change, was much discussed by early physicists. However, we must be clear that there is only one kind of energy, and it is called energy. It is stored in different systems and in different ways in those systems, and it is transferred by some mechanism or other from one system to another[9].

Based on a comprehensive analysis of physical interactions and chemical reaction processes, energy is considered to be the only thing that communicates various phenomena. Thus, "Energism" was born*[8]. Ostwald had argued that matter and energy had a “parallel” existence, he developed a more radical position: matter is subordinate to energy. “Energy is always stored or contained in some physical system. Therefore, we will always have to think of energy as a property of some identifiable physical system”. “Ostwald regarded his Energism as the ultimate monism, a unitary "science of science" which would bridge not only physics and chemistry, but the physical and biological sciences as well”[6]. This view has expressed the idea of considering "pure energy" as a "unity" and has assumed the process of energy interaction. However, because of the impossibility to determine what energy is, it has been rejected by both scientific and philosophical circles as "metaphysics" and "materialism"[10].

The consistency and transitivity of energy and momentum in different physical domains have actually shown that they must be linked and bound by something fundamental. Therefore, it is necessary to re-examine the "Energism" and try to promote it.

The relationship between energy and momentum, which are independent in classical mechanics, and their conservation are also independent. the momentum of the particle does not involve its energy. but In relativity, the conservations of momentum and energy cannot be dissociated. The conservation of momentum in all inertial frames requires the conservation of energy and vice versa. space and time are frame-dependent projections of spacetime[7].

Our questions are:

1) What is energy, is it a fundamental thing of entity nature**, or is it just a measure, like the property "label" of "beauty", which can be used by anyone: heat, light, electricity, machinery, atomic nuclei. Do the various forms of energy express the same meaning? Can they be expressed mathematically in a uniform way? Is there a mathematical definition of "energy"? ***

2) Is the conservation of energy a universal principle? How does physics ensure this conservation?

3) Why is there a definite relationship between energy and momentum in all situations? Where are they rooted?

4) If the various forms of energy and momentum are unified, given the existence of relativity, is there any definite relationship between them and time and space?

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* At the end of the nineteenth century, two theories were born that tried to unify the physical world, "electromagnetic worldview" and "Energism". We believe that this is the most intuitive and simple view of the world. And, probably the most beautiful and correct view of the world.

** If it is an entity, then it must still exist at absolute zero. Like the energy and momentum of the photon itself, it does not change because of the temperature, as long as it does not interact with each other.

*** We believe that this is an extremely important issue, first mentioned by Sergey Shevchenko（ https://www.researchgate.net/profile/Sergey-Shevchenko ）in his reply to a question on Researchgate, see https://www.researchgate.net/post/NO1_Three-dimensional_space_issue; SS's reply.

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Referencs

[1] Plato.

[2] Ostwald identified five “Arten der Energie”: I. Mechanical energy, II. Heat, III. Electrical and magnetic energy, IV. Chemical and internal energy, and V. Radiant energy. Each form of energy (heat, chemical, electrical, volume, etc.) is assigned an intensity. And formulated two fundamental laws of energetics. The first expresses the conservation of energy in the process of transfer and conversion; the second explains in terms of intensity equilibrium what can start and stop the transfer and conversion of energy.

[3] Duit, R. (1981). "Understanding Energy as a Conserved Quantity‐‐Remarks on the Article by RU Sexl." European journal of science education 3(3): 291-301.

[4] Swackhamer, G. (2005). Cognitive resources for understanding energy.

[5] Coelho, R. L. (2014). "On the Concept of Energy: Eclecticism and Rationality." Science & Education 23(6): 1361-1380.

[6] Holt, N. R. (1970). "A note on Wilhelm Ostwald's energism." Isis 61(3): 386-389.

[7] Ashtekar, A. and V. Petkov (2014). Springer Handbook of Spacetime. Berlin, Heidelberg, Springer Berlin Heidelberg.

[8] Leegwater, A. (1986). "The development of Wilhelm Ostwald's chemical energetics." Centaurus 29(4): 314-337.

[9] Swackhamer, G. (2005). Cognitive resources for understanding energy.

[10] The two major scientific critics of Energism are Max Planck and Ernst Mach. The leading critic of the political-philosophical community was Vladimir Lenin (the founder of the organization known as Comintern). But he criticized not only Ostwald, but also Ernst Mach.

To date, the SDGs have failed to reduce socioeconomic inequality within and between countries in the post-covid pandemic World. How can governments, civil society, and other stakeholders regain the momentum lost, to "leave no one behind?

Are annihilation and pair production mutually inverse processes?

p+p− → γ γ'

“Annihilation can happen when all the quantum numbers of two colliding particles add up to zero. It might be electron on positron, proton on antiproton, neutron on antineutron, quark on antiquark etc. The force responsible depends on the possible interactions of the annihilating particles.” “Annihilation does not require the presence of other fields.”[x]

“In particular, one concludes that the two photons resulting from the annihilation of slow positrons in matter always have their planes of polarization perpendicular to each other. This has been pointed out by Wheeler who also proposed a possible experimental verification.”[2]

γ γ' →p+p−

It is often assumed that the concept of pair generation was first introduced by Breit and Wheeler, ω1+ω2→e+e-; however, in their paper [1], "pair generation" appears as an old term and cites the paper by Weizsäcker, CF, Z (1934), and Williams' formula。

Perrin (1933) (in French) was probably the first to introduce the concept of 'pair production'. He had a paper entitled "The possibility of materialization by the interaction of photons and electrons."

Regarding pair production: 1）At first sight light-light scattering seems to be impossible because in classical electrodynamics (linear Maxwell equations) the process does not occur. The resulting wave is everywhere given by the sum of the two incoming waves. 2）In quantum mechanics however the situation is quite different. Due to the uncertainty principle a photon of energy E can fluctuate into states of charged particle pairs (with mass mpair.）Experimentally it is very difficult to collide high energy photon beams. A very elegant way of avoiding this difficulty is again to use virtual particles, this time the quantum fluctuation of an electron into an electron photon state.[3]

The identification of pairs is usually a result of statistical findings[4][5][7][8][9]. e.g.

The identification of γ γ → pp events is mainly based on three artificial neural networks, used to separate antiprotons from e−, µ− and h−, where h− represents either a π− or K−[4]

QCD predictions for large-momentum transfer cross sections of the type ‘γγ→ BB' are given, for B and B' any members of the baryon octet or decuplet, and all possible helicity combinations for photons and baryons[8].

An electron enters the laser beam from the left, and collides with a laser photon to produce a high-energy gamma ray. The electron is deflected downwards. The gamma ray then collides with four or more laser photons to produce an electron-positron pair [9].

1) The process of "pair production" and the process of annihilation of positive and negative particles are not mutually invertible. Just as the mass-energy equation is not reciprocal (E=mc^2, which is irreversible for photons), p+p- → γ γ' and γ γ' → p+p- are not γ γ' = p+p-. This is one of the differences between the mathematical equations and the physical equations.

(2) The process of "annihilation" does not require special conditions, while the process of " pair production" must require auxiliary conditions, the presence of other particles being necessary. What is the essential function of these auxiliary conditions? What are the conditions under which photons can "collide" and not just interfere?

3) Is the process of "pair production" one or two processes? Must the " pair of particles" be produced in pairs at the same time, or with equal probability for positive and negative particles? Or is it both. The literature [6] describes pairs of positive and negative particles as being produced simultaneously. This question is very important because it determines the mechanism of the "photon-particle" transition and even their structure.

(4) The colliding positive and negative particles do not necessarily annihilate into photons, but essentially depend on whether the magnitude of the energy reaches the energy value of a certain particle, e+e-→µ+µ-. Here is the root of the problem of the level difference of the three generations of particles implied, just as the energy level difference of orbiting electrons. Can quantum field theory give a concrete, or directional, explanation?

5) Where do the properties of the original positive and negative particles go after annihilation occurs? Charge, spin-magnetic moment, mass, and the spacetime field of the elementary particle. Can the origin of the properties be inferred from this? That is, if the properties are somehow conserved, then by reversibility, do the annihilated photons imply all the properties of the elementary particles. The total charge is conserved after the annihilation of the positive and negative electrons. But where does the positive charge go and where does the negative charge go? The following issues are involved here: https://www.researchgate.net/post/How_Fermions_combine_four_properties_in_one

[1]【Breit, G. and J. A. Wheeler (1934). "Collision of two light quanta." Physical Review 46(12): 1087】

[2]【Yang, C.-N. (1950). "Selection rules for the dematerialization of a particle into two photons." Physical Review 77(2): 242】

[3]【Berger, C. and W. Wagner (1987). "Photon photon reactions." Physics Reports 146(1-2): 1-134】

[4]【Achard, P., O. Adriani, M. Aguilar-Benitez and etl. (2003). "Proton–antiproton pair production in two-photon collisions at LEP." Physics Letters B 571(1-2): 11-20】

[5]【de Jeneret, J., V. Lemaitre, Y. Liu, S. Ovyn, T. Pierzchala, K. Piotrzkowski, X. Rouby, N. Schul and M. V. Donckt (2009). "High energy photon interactions at the LHC." arXiv preprint arXiv:0908.2020.】

[6]【Michaud, A. (2013). "The Mechanics of Electron-Positron Pair Creation in the 3-Spaces Model." International Journal of Engineering Research and Development 6: 2278-2800】* Researchgate Link：

Minimum mass issues are involved here:

https://www.researchgate.net/post/Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2

[7]【Klein, S. R. and P. Steinberg (2020). "Photonuclear and two-photon interactions at high-energy nuclear colliders." Annual Review of Nuclear and Particle Science 70: 323-354.】

[8]【Farrar, G. R., E. Maina and F. Neri (1985). "QCD Predictions for γγ Annihilation to Baryons." Nuclear Physics B 259(4): 702-720】

[9]【SLAC. (1970). "SLAC Experiment E144 Home Page." from https://www.slac.stanford.edu/exp/e144/.】

【Burke, D. L., R. C. Field, G. Horton-Smith, J. E. Spencer, D. Walz, S. C. Berridge, W. M. Bugg, K. Shmakov, A. W. Weidemann, C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. J. Boege, T. Koffas, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, D. A. Reis and W. Ragg (1997). "Positron Production in Multiphoton Light-by-Light Scattering." Physical Review Letters 79(9): 1626-1629】

【Schwarzschild, B. (1998). "Gamma Rays Create Matter Just by Plowing into Laser Light." Physics Today 51(2): 17-18】

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2023-06-25

For the "pair production" experiment, the 2021 STAR Collaboration collectively published a paper "Measurement of e+ e- momentum and angular distributions from linearly polarized photon collisions" [4].

"At RHIC, scientists accelerate gold ions to 99.995% of the speed of light in two accelerator rings. If the speed is high enough, the strength of the circular magnetic field can be equal to the strength of the perpendicular electric field," Xu said. perpendicular electric and magnetic fields of equal strength is exactly what a photon is-a quantized "particle "So, when the ions are moving close to the speed of light, there are a bunch of photons surrounding the gold nucleus. As the ions pass one another without colliding, two photons (γ) from the electromagnetic cloud surrounding the ions can interact with each other to create a matter-antimatter pair: an electron (e-) and positron (e+) [5]. [The headline of the media report is more interesting [5][6][7]]

The history of the discovery of the physics of particle production and annihilation is presented in paper [1]; paper [3] is an analysis of the experimental phenomena by Anderson, the discoverer of positrons, in which four possibilities are proposed for each result, "pair production" being one of them. He finally determined that "pair production" was the real case. The results provided by André Michaud [9] should be similar [see his replies for details].

Comparing the STAR experiment [5] and the E114 experimental method [8], they produce photon "collisions" in a very different way. These two experiments are in turn different from experiments [2] and [3]. It is commonly believed that there are three possible interactions [4]: the collisions of two virtual photons (as calculated by Landau and Lifshitz, giving the total cross section for e+e- production predominantly at the pair threshold), of one virtual and one real photon (Bethe-Heitler process ), or of two real photons-the Breit-Wheeler process.

Question: Yang[1] and Andeson considered that Chao [2] and Anderson [3] are both electron pair generation processes, so is this a "photon-photon" collision "γγ → e+e- " process? If so, are the photons real or virtual, and what is the difference between them and the experiments [4][8]? If not, then there are no "photon-photon" collisions in the experiments of Chao [2] and Anderson [3], but only "photon-particle" collisions?

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Reference：

[1] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.

[2] Chao, C.-Y. (1930). "The absorption coefficient of hard γ-rays." Proceedings of the National Academy of Sciences 16(6): 431-433.

[3] Anderson, C. D. (1932). "The apparent existence of easily deflectable positives." Science 76(1967): 238-239.

[4] Adam, J., L. Adamczyk and etl. (2021). "Measurement of e+ e− momentum and angular distributions from linearly polarized photon collisions." Physical Review Letters 127(5): 052302:

[5] "Collisions of Light Produce Matter/Antimatter from Pure Energy": https://www.bnl.gov/newsroom/news.php?a=119023

[6] "Colliding photons were spotted making matter. But are the photons 'real' ? ": https://www.sciencenews.org/article/colliding-photons-matter-particle-physics#:~:text=In%20a%20demonstration%20of%20Einstein%E2%80%99s%20E%3Dmc%202%2C%20collisions,colliding%20particles%20of%20light%20create%20matter%20and%20antimatter.

[7] "Scientists Generate Matter Directly From Light – Physics Phenomena Predicted More Than 80 Years Ago": https://scitechdaily.com/scientists-generate-matter-directly-from-light-physics-phenomena-predicted-more-than-80-years-ago/?expand_article=1

[8] SLAC. (1970). "SLAC Experiment E144 Home Page." from https://www.slac.stanford.edu/exp/e144/.

[9] the FERMILAB experiment E632 bubble chamber picture;

Recently I asked a question related to QCD and in response reliability of QCD itself was challenged by many researchers.

It left me with the question, what exactly is fundamental in physics. Can we rely entirely on the two equations given by Einstien? If not then what can we say as fundamental in physics?

A pendulum bob oscillates between potential energy maxima at the top of its swing through kinetic energy maxima at the bottom of its swing. The potential energy is given by the mass times the height of the arc times gravitational acceleration and the kinetic energy maximum is given by the mass times the maximum velocity times the average velocity. Energy may be treated as a scalar in many phenomena, but here both energies are products of two vectors, fall direction and gravitation for potential energy and momentum times average velocity for kinetic energy. This nature of the pendulum is important.

The potential energy of the pendulum is equal to the work it can do under gravitational acceleration until its string is vertical. That work accelerates the pendulum bob to its maximum velocity. The kinetic energy of the pendulum is equal to the work it can do against gravitation to bring the pendulum bob to the top of its arc. It is posited that the shape of the atoms and molecules in the bob is the cause of its acceleration in the refraction gradient of a gravitational field, like a light path bending when passing a star. When the bob is free to move, their asymmetrical oscillations change the position of the bob as the process of falling. The response of the atoms and molecules in the bob to motion is to adjust their shape in order to remain in harmony with themselves, that is they shorten to enable complete oscillations despite translation. These shape changes together transfer potential energy to kinetic energy in the bob which is then available for the work of lifting the bob by reversing the changes in shape while decelerating. The key to this speculation is that reversible refraction or translation compensation actually move the location of internal oscillations in matter.

Hi all,

I am currently working on simulating a water jet problem, where water is injected from the left boundary and exits the domain through the right boundary. However, I am facing a challenge of keeping both momentum and mass conservation at the same time. In order to ensure mass conservation in the scenario where a single two-dimensional jet evolves into multiple droplets, it is necessary to enforce the condition that the outlet flux, represented by the product of the cross-sectional area of the droplets (S2) and their velocity (u2), is equal to the inlet flux, represented by the product of the initial cross-sectional area of the jet (S1) and its velocity (u1). Since S2 is typically greater than S1, it follows that u2 must be smaller than u1 to maintain mass conservation. However, this approach alone does not guarantee momentum conservation.

ps: I am using my own code for the simulation and it is an incompressible flow solver， which has been validated in many benchmark cases. The physical properties in my code jump across the interface without any diffusion.

Best regards,

Min Lu

The energy of light is E=hf, and the momentum is P=h/λ. The energy of light excites the momentum of light; the momentum of light carries the energy of light as it travels. If we observe from the perspective of momentum conservation, as long as the initial speed of light is c, it will always maintain this speed c in free space. but it is not that light knows this speed, it's that we know this speed.

If light does not cooperate with space-time (i.e., space-time is not involved in the control of the speed of light), how can it control itself to travel a wavelength of distance forward per unit time? And maintain the same speed in different inertial systems (with different spacetime measures)?

If spacetime is involved in the control of the speed of light, does the definition of energy-momentum of light have the supremacy?

During metadynamics calculation, Desmond gives error:

--

Allowed momentum exceeded on 2 particles.

7187:

force = (-3.0580500e+04 4.4492168e+04 -7.2957642e+03)

momentum = (-2.9018593e+01 4.8549679e+01 -7.0306296e+00)

7183:

force = ( 3.0668949e+04 -4.4422215e+04 7.3239116e+03)

momentum = ( 3.0992996e+01 -4.4353527e+01 7.6161938e+00)

RECORD EXCEPTION in: dessert_localhost.localdomain.90864

::: DESSERT (short form) :::

Exception: Desmond::Failure

Context:

Momentum overflow; see stdout for information. @src/mdlib/dynamics/gpu_momentum_step.cu:116 in (unknown)

Checked in license.

Calling user-specified exit_callback() from desres::dessert::terminate_with_output

--------------------------------------------------------------------------

MPI_ABORT was invoked on rank 0 in communicator MPI_COMM_WORLD

with errorcode 1.

--

This problem can't be solved with Nvidia driver replacement (as described in Schrodinger KB).

Who have some problem and probably who knows how to fix this bug.

The energy operator ih∂/∂t and the momentum operator ihΔ or ih∂/∂x play a crucial role in the derivation of the Schrödinger equation, the Klein-Gordon equation, the Dirac equation, and other physics arguments.

The energy and momentum operators are not differential operators in the general sense; they do play a role in the derivation of the equations for the definition of energy and momentum.

However, we do not find any reasonable arguments or justifications for the use of such operators, and even their meaning can only be speculated from their names. It is used without explanation in textbooks.

The clues we found are:

1) In the literature [ Brown, L. M., A. Pais and B. Poppard (1995). Twentieth Centure Physics (I), Science Press.], "In March 1926, Schrödinger noticed that replacing the classical Hamiltonian function with a quantum mechanical operator, i.e., replacing the momentum p by a partial differentiation of h/2πi with position coordinates q and acting on the wave function, one also obtains the wave equation."

2) Gordon considered that the energy and momentum operators are the same in relativity and in non-relativism and therefore used in his relativistic wave equation (Gordon 1926).

(3) Dirac also used the energy and momentum operators in the relativistic equations with electron spins (Dirac 1928). Dirac called it the "Schrödinger representation", a self-adjoint differential operator or Hermitian operator (Dick 2012). (D).

Our questions are:

Why can this be used? Why is it possible to represent energy by time differential for wave functions and momentum by spatial differential for wave functions? Has this been historically argued or not?

Keywords: quantum mechanics, quantum field theory, quantum mechanical operators, energy operators, momentum operators, Schrödinger equation, Dirac equation.

Poynting's vector theorem P = ExH is one of the universal laws of physics that applies to electromagnetic fields in AC and DC circuits. A rigorous analysis of the electromagnetic fields of DC and AC circuits shows that Poynting's law P = ExH applies to both stationary and time-varying electromagnetic fields.

Keeping the generality It can be shown that Poynting's theorem P = EXH represents EM power flow per unit area is quite valid for direct current electrical circuits and its stationary electromagnetic fields.

It is theoretically and experimentally verified that optical EM radiation has linear pressure and momentum.

It now follows that the momentum density flux of an electromagnetic wave is given by

P=E x H /c

where c is the speed of light, E is the electric field, H is the magnetic field, and P is the Poynting vector.

The question is valid:

Is it true that this is just the limiting case of time-varying EM fields as the frequency f tends to zero or some other new concept may be missing?

In the theory of superconductivity, it is argued that superconductivity is associated with a positive coupling constant, i.e. with particle attraction. This conclusion is based essentially on the Fermi statistics (anticommutation of creation and annihilation operators) and the Fermi momentum p_F explicitly built into the theory. Fs a result, the model can be resolved only at the coupling constant g<0. See, for instance §39 in L. D. Landau, E. M. Lifschitz, Lehrbuch der Theoretischen Physik (Statistishe Physik, Band 5, teil 2 ), in German, 1st edn. edited by H. Escrig and P. Ziesche (Akademie-Verlag, Berlin 1980) [or an English translation]. Is there a similar derivation for superfluidity based on Bose statistics?

Freestyle swimming is a highly technical sport that requires a great deal of skill and coordination. One of the key components of efficient freestyle swimming is the use of proper leg technique. While the primary focus of freestyle swimming is on the arm stroke and breathing technique, the legs also play a critical role in generating forward momentum and maintaining balance and stability in the water.

Recent research has shown that incorporating backstroke leg exercises into a swimmer's training regimen can have a significant impact on improving freestyle technique. Backstroke leg exercises involve working the legs in a similar way to how they are used in backstroke swimming. This includes kicking with a straight leg, pointing the toes, and engaging the hips and core muscles.

By incorporating these exercises into their training routine, swimmers can develop better balance and stability in the water, as well as increase the strength and endurance of their leg muscles. This can lead to improved propulsion and a more efficient freestyle stroke.

In addition to improving leg strength and technique, backstroke leg exercises can also help prevent injury by promoting proper alignment and reducing strain on the lower back and hip joints. This can be especially important for swimmers who may be prone to overuse injuries or who have a history of lower back pain.

Overall, incorporating backstroke leg exercises into a swimmer's training regimen can have numerous benefits for improving freestyle technique and overall performance. By developing better leg strength and coordination, swimmers can achieve greater efficiency and speed in the water, while also reducing the risk of injury.

The GPT CHAT is starting to gain momentum on the web, everyone is talking about it, and we have all, or almost, tried it.

Should we see this technological advance of the I.A is an opportunity to go fast or on the contrary it will be a threat to human intelligence?

Hello everyone

I have read Lundgren(2002) article "Linearly forced isotropic turbulence" which by adding a linear forcing to momentum equation, he was able to get forced isotropic turbulence. I did the same thing(I had initial HIT velocity field) and after a while flow filed start to make mean flow which theoretically must be zero. Also, TKE oscillates very dramatically which is not my desire. Now, my question is that, is there any other Linear forcing method or any other simple method to keep forcing to initial HIT and make it Forced HIT?

Thanks,

Farzad

So-called "Light with a twist in its tail" was described by Allen in 1992, and a fair sized movement has developed with applications. For an overview see Padgett and Allen 2000 http://people.physics.illinois.edu/Selvin/PRS/498IBR/Twist.pdf . Recent investigation both theoretical and experimental by Giovaninni et. al. in a paper auspiciously titled "Photons that travel in free space slower than the speed of light" and also Bereza and Hermosa "Subluminal group velocity and dispersion of Laguerre Gauss beams in free space" respectably published in Nature https://www.nature.com/articles/srep26842 argue the group velocity is less than c. See first attached figure from the 2000 overview with caption "helical wavefronts have wavevectors which spiral around the beam axis and give rise to an orbital angular momentum". (Note that Bereza and Hermosa report that the greater the apparent helicity, the greater the excess dispersion of the beam, which seems a clue that something is amiss.)

General Relativity assumes light travels in straight lines in local space. Photons can have spin, but not orbital angular momentum. If the group velocity is really less than c, then the light could be made to appear stationary or move backward by appropriate reference frame choice. This seems a little over the top. Is it possible what is really going on is more like the second figure, which I drew, titled "apparent" OAM? If so, how did the interpretation of this effect get so out of hand? If not, how have the stunning implications been overlooked?

I have used in my current paper the pressure-based solver for air distribution inside the control room, I would like to ask which governing equation determines the velocity field and also the continuity and momentum equations for which purpose work in CFD calculation if there is an explanation

Quadratic form of energy and momentum are well proven in accelerator experiments.

E² =(mc²)² +(pc)²

Also energy is the sum pf potential and kinetic where gravity is part of the potential.

E = T + K

E² = T² + 2TK + K²

Comparing the two quadratics at high speed it appears that (mc²)² and (pc)² must be related to each other, for a quadratic equation to be necessary.

Taking (mc²) as T, K is calculated

K = - (mc²) + SQRT( (mc²)² + (pc)² )

Implication is that momentum increases faster than expected from applied thrust field, from conversion of mass to kinetic energy caused by acceleration.

A graph of my creation is attached. The top line slope is the total energy gain including conversion of mass to kinetic energy in this representation. The maximum point is a critical condition that occurs inside a kinetic wormhole. Farther right shows mass conversion continuing without need of engine power.

The vehicle and contents may convert to gamma rays at the point where three lines meet if acceleration continues to the extent that reverse engine power is not able to stop it.

This is the alternative representation to infinite energy needed to reach light speed in the well accepted equation.

E²(1-v²/c²) = (mc²)²

Mass decreases as speed increases, going to zero at light speed in agreement with observation that massless objects travel at light speed.

The bottom line is momentum.

Why is Energy A Quadratic equation?

Several scientists pointed out a paradoxical consequence of the application of the Lorentz Force as an addendum to Maxwell's equations in the form given by Heaviside. There is at least one case where the momentum is not conserved...

From the script of 1911 Einstein and Laub to Coleman, Shockley, Furry, Boyer, Babson, Reynolds, Bjorkquist, Griffiths, and Mansuripur till 2012 it was pointed out such an issue.

See the link for details http://people.exeter.ac.uk/sh481/shockley-james.html

-----------

Einstein A and Laub J "Über die im elektromagnetischenFelde aus ruhende Körper ausgeubten pondermotorischeKräfte"

Ann. Phys. 26 541 (1911)

--------------

Coleman, S. and Van Vleck, J. H. "Origin of Hidden Momentum Forces on Magnets"

Phys. Rev. 171 1370 (1968)

------------

Shockley W "Hidden linear momentum related to the α,E term for a Dirac-electron wave packet in an electric field"

Phys. Rev. Lett. 20 3434 (1968)

-------------

Furry, W. H. "Examples of Momentum Distributions in the Electromagnetic Field and in Matter",

Am. J. Phys. 37 621 (1969)

--------------

Boyer, T. H. "Concerning hidden momentum",

Am. J. Phys. 76 190 (2008)

---------------

Babson, D., Reynolds, S. P., Bjorkquist, R. and Griffiths, D. J. "Hidden momentum, field momentum, and electromagnetic impulse",

Am. J. Phys. 77 826 (2009)

-----------------------------

Mansuripur M. Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation.

Phys. Rev. Lett. 108 193901 (2012)

------------------------------

"The size of the plus pin for S-parameter port 1 is electrically large above 15.8126 GHz, S-parameters may become unphysical." -

To mitigate this issue, I added 0.05 mm x 0.05 mm stub in each of the port and did 0Hz to 32GHz simulation without this warning. But if I go for higher and higher frequency I get this warning when the port length crosses lyambda/10 (according to momentum port theory in ADS) electrical length.

But in the lower frequency range, the result (without stub added to port) is not matching with the added stub one.

Hello,

What is the difference between the simulation on ADS schematics and layout simulation for S parameters?

In layout simulation the Momentum is used to get the S parameters, in schematics how ADS calculate the S parameters? And why it fast than Momentum ?

I am simulating the flow of super-critical CO2 over a circular cylinder in FLUENT. I am using NIST real gas model to calculate the thermo-physical properties of sCO2.

The residual for continuity, momentum and energy equations have been set to 10^-6, 10^-7 and 10^-8 respectively. Discretization for density, momentum and energy is set to second order accuracy.

Now I am having problem regarding the convergence of the continuity. Could anyone suggest me any solution strategies for this case ??

LIGO and Virgo consortium has published results in which the mass of a merged black hole is always less than the sum of masses from the binary black holes.

GR can predict this mass loss in the Bondi-Sachs Formalism, often in the range of 5% loss while the merged event horizon is not spherical.

Not everyone agrees with published mass loss. See Tables 5.2 and 5.3 for no mass loss.

References are given for mass loss.

In my publications I compare the LIGO mass loss to theory of Polarizable Vacuum extended for high speed with reasonable agreement. In other threads I asked the question if high speed might cause part of mc² energy to convert to pc energy. It is not widely accepted, but is allowed in the popular energy momentum equations for GR situations where curvature cannot be ignored.

In Black Hole Mergers Does Part Of Mass Energy mc² Convert To Momentum Energy pc?

What is the minimum energy required to change the orbital angular momentum or orbital energy?

I would like to explain my question with the following illustrative situation. In general, when we apply external perturbation such pressure, and temperature to the crystalline materials, the atomic orbital energy levels are modified. In precise, how much minimum required temperature or pressure is needed to get the significant changes in orbital?

Your valuable explanation, suggestion, and guidance will be very useful to our research works. Thank you very much in advance.

It's said “this case is another effect of relativity", but actually I can't fully understand it.

original text from 𝙏𝙝𝙚 𝙁𝙚𝙮𝙣𝙢𝙖𝙣 𝙡𝙚𝙘𝙩𝙪𝙧𝙚𝙨 𝙤𝙣 𝙥𝙝𝙞𝙨𝙮𝙘𝙨

I am running a simulation with ansys for flow in an aircraft intake. The flow is transient and when I setup FLUENT for getting the solution, the momentum residuals are very low like the x-velocity starts at 1e-10. And the same goes for y-velocity and z-velocity. Then they drop down to 1e-18, and restart from 1e-10 at the beginning of the time-step.

Can anyone tell me why is this happening? I have attached a picture for reference.

I'm currently working in OpenFOAM as part of my research on two-phase viscoelastic flow. OpenFOAM version 9 supports viscoelastic flow models such as Maxwell, giesekus and PTT, listed under momentum transport models(Laminar). I don't know how to implement these models in the case file. If some case files of benchmark problems related to these(Twophase Visco elastic flow) exist, could someone guide me through those?

Separate Laminar flow physics used in each layer. I tried different conditions in Wall node.

Experiments conclude that electron is point like and stable. Spin angular momentum suggests that electron has a structure extended in space, although occupying small volume.

Does Electron Have Component Parts With Fractional Charges?

Research in education is based and is validated by test groups involving students. However, teachers are not unified in their outcome. Some consistently produce higher average scores given uniformly allocated student capabilities classes and some reasonable time frame to gather data.

These teacher's methodologies bear a causal role to these results but these results they may not be explained by standard explanations i.e. cognitive or behavior focus or lesson plan delivery and quality.

These kind of research scenarios might also be use to downplay the actual contribution to learning of popular ideas like student engagement or the popular conceptions of engagement i.e. 1/3 of class time, 1/2 of student population participating or surface types of participation or teacher-led participation based on class momentum rather than authentic understanding. Cognitive models with little engagement might prove to contribute more than believed.

MOOCs are gaining momentum and popularity day by day owing to their unique features of overcoming the challenges and Problems of Traditional Education. It becomes pertinent for 21st Century Educators to have knowledge of various philosophical and psychological considerations while designing and developing MOOCs. Kindly share your information regarding the said query.

The orbital angular momentum of a planet yields a repulsive force from a central mass. Why the spin angular momentum of a planet does not yield a similar effect? How can one include a spin angular momentum potential term?

At the beginning of the 20th century, Newton’s second law was corrected considering the limit speed c and the relativistic mass. At that time there has not been a clear understanding of the subatomic particles and basically there was little research in high energy physics.

According to particles of matter transfer discrete amounts of energy by exchanging bosons with each other and energy has mass and momentum, we can recorrect relativistic Newton’s second laws directly by using conservation law of momentum.

Why expectation value of angular momentum square operator <J_x²> = <J_y²> ? How can we prove this?

How to use Ansys software to solve nonlinear equation in fluid mechanics ( Nanofluid).

Since during the nonlinear analysis, we have so many equation such as equation of momentum, equation of energy, equation of nanoparticle flux. How to solve these equation in Ansys software.

Please give your valuable suggestion.

Doesn't the angular momentum of a BH indicate that it is not a singularity, but an extended object?

If angular momentum is conserved, where does the moment of the BH accretion disk go?

The answers I have found do not explain what rotates.

Saying that it is the black hole what rotates does not explain it.

I have read that Kerr metric black holes don't have point singularities, but this refers to mathematical equations, not physical reality.

Thank you.

If you are using application software or code that is fine but you are not really learning much as all you do is learning how to enter the input data and produce the output results. The inside details such as knowing how the governing differential equation is treated mathematically or numerically, how the domain of analysis is represented, and how the code is written using a computer programming language are not really known. This problem is overcome here by offering computer source codes, where all the steps from A to Z in solving many engineering, applied math, physics and mechanics problems are presented. If you are interested or have a question please contact me at youssefhafez995@gmail.com.

The computer codes and numerical models listed herein represents over 25 years of hard work in the field of applied mathematics, numerical methods and computer programming in FORTRAN. They have been used in many large scale projects and validated against analytical solutions and field data.

1- WAVES-2D Model: A two – dimensional unsteady Finite Element (FE) hydraulic model for calculating the two dimensional (2D) horizontal velocity components and the water depth in lakes and river channels. It does 2D flood modeling and overland flow. It also does 2D river, lake, and channel hydrodynamic flow modeling.

2- TurbFlow: A three-dimensional velocities (U, V and W velocity components) and pressure distributions in the cross section of a fully developed flow region. It uses Finite Element (FE) numerical model for solving Navier-Stokes equations in ducts, pipes, closed conduits and open channels using a non-linear K-E turbulence modeling (used in Ph.D. Dissertation, CSU, Fort Collins, CO, USA). This program constitutes the ultimate modeling of transport phenomena and finite element modeling of highly non-linear convective flows. It does model very accurately secondary currents in ducts and open channels at corners and roughness discontinuity areas. In addition it simulates effects of the free surface on turbulence (dampening effect of the free surface).

3- NERVE–1D Model:A one–dimensional hydraulic and morphologic model for calculating water levels, velocity, and scour and deposition in river Channels. This program has an advantage over other models in that it does the roughness coefficients calibration process automatically without need for the commonly used trial and error approach.

4- Non-Linear-Networks: Non-Linear Discrete FE model for network analyses such as water distribution systems and flow of polymer melts through processing units. It is validated for New York and Hanoi water networks.

5- Water/Soil Quality – 1D: A one –dimensional unsteady water quality FE transport model used in predicting the spatial and temporal distributions of BOD TDS and CI along the stream channel. It does soil quality modeling of the transport of Radon gas in soils.

6- SUITE-3D: A three-dimensional unsteady FE model for simulating the three-dimensional momentum transport. It solves the three-dimensional advection-diffusion transport differential equation. It uses Finite Element (FE) numerical model for solving the full Navier-Stokes equations in three-dimensions. It does air pollution dispersion modeling, and heat transfer analysis.

7- SUITE – 2D: A two – Dimensional Hydrodynamic and transport FE model incorporating turbulence for detailed flow and large scale eddy structures around hydraulic structures. It also solves for the heat and mass transport equations.

8- Poisson/Laplace 2D: Finite Element 2D model for solving Poisson’s PDE and Laplace’s PDE, application to ground water flow in porous media, heat transfer, and viscous flows.

9- ODE2: General Differential Equation Solver for Second Order Ordinary Differential Equation using the Finite Element method applied to heat transport in pipe flows, deflection of tight wires, and beams on elastic foundations.

10- Heat 1D: One dimensional Finite Element Model for solving the heat partial differential Equation applied now to simulate Radon gas transport in porous media.

11- Wave 1D: FE one-dimensional model for the Wave PDE used for non-linear Fourier heat analyses in Skin tissues.

12- Networks: Discrete FE model Solves network problems as water pipes networks, electrical networks & spring systems.

13- Continua-2D: solves 2D stress-strain analysis for deformations of elastic solids.

14- Nonlinear Dynamics: It solves nonlinear dynamical equations such as the pendulum differential equation including also resistance forces such as friction and form drag forces in addition to electromagnetic forces.

15- Local scour prediction: It calculates bridge pier scour, plunge pool scour, scour downstream of barrages and grade control structures, and abutment scour.

Hi guys, I am simulating an horizontal axis wind turbine using Ansys Fluent (steady state simulation). To get more accurate results I use second order upwind momentum discretization scheme, but unfortunately the results don't agree with the experimental ones. Meanwhile with the 1st order upwind momentum discretization scheme, the solution match better with the experimental one. What must I do in this case ?

The original MOMENTUM INTEGRAL EQUATION

The derivation should include the following terms

1. time rate of increase in momentum within the element

2. momentum flux through the surface normal to x

3. momentum flux through the sloping face of the element.

4. pressure gradient

method: approximate solution involving satisfying the boundary layer equations at the wall and at the edge of the boundary layer and considering the momentum relation applied to some plausible velocity distribution.

Hello everybody, I highlighted somewhere in this pdf (attatched file) under the title, the momentum representation of the tight binding Hamiltonian for the Bravais lattices with one atom in each point of the lattice, in which the author says that "... the factor of 1/2 is to avoid double counting".I do not understand what the author means. An other problem is that the factor of 1/2 is not seen on the LS of the equation (29). Is this related to the equivalency of the sites in the Bravais lattice, as well as the presence of one atom on each lattice point? I appreciate anyone that answer me.

Heisenberg uncertainty principle was initially proposed for position-momentum conjugate pair. It states that the concurrent precise measurements of position and momentum of a subatomic particle are not possible. This idea has been extended to another pair of quantities, time and energy, without proper justification. Therefore, there has been an endless debate on the validity of the uncertainty concept for the second pair, such as:

· Can time be considered as an observable quantity?

· Are these variables dynamically conjugate, both in classical and in quantum mechanics?

· Does this pair exhibit similar principle as the position-momentum?

· The mathematics of the uncertainty of energy-time pair is not well defined as standard deviation of time does not make sense.

Furthermore, if a certain duration of time is necessary for the accurate measurement of some quantity like energy then we should consider it for momentum too. However, in the latter case, it has been accepted during the history of uncertainty principle, that the measurement of the momentum of any particle can be taken with an arbitrary accuracy irrespective of the duration of the measurement.

If momentum should be treated like energy then it is better to separate Heisenberg’s uncertainty principle from the inevitable measurement inaccuracy of some physical quantities within short interval, which is well understood in science. They seem to be completely different issues, which are kept under the same title.

I am working on the multi-dimensional spacetime. I realized that we can describe and expand the relation between the energy, mass and momentum of the particles from one dimensional spacetime and create their relationship formula in the higher dimensional spacetime. I realized that dimensional analysis is not valid in this method. I didn't find any source for discussing on the dimensional analysis when some terms of the equation belongs to n-dimensional spacetime and other terms are belong to the m-dimensional spacetime. For instance, does the unit of the measurement of the energy of the a one-dimensional particle is equal to the unit of the measurement of the three-dimensional particle?. these are my preprint paper and equations that not supported by dimensional spacetime.

These Preprints are under review, I don't know that could I use natural system of units for overcoming consistency.

The fundamental physical constants, ħ, c and G, appear to be the same everywhere in the observable universe. Observers in different gravitational potentials or with different relative velocity, encounter the same values of ħ, c and G. What enforces this uniformity? For example, angular momentum is quantized everywhere in the universe. An isolated carbon monoxide molecule (CO) never stops rotating. Even in its lowest energy state, it has ħ/2 quantized angular momentum zero-point energy causing a 57 GHz rotation. The observable CO absorption and emission frequencies are integer multiples of ħ quantized angular momentum. An isolated CO molecule cannot be forced to rotate with some non-integer angular momentum such as 0.7ħ. What enforces this?

Even though the rates of time are different in different gravitational potentials, the locally measured speed of light is constant. What enforces a constant speed of light? It is not sufficient to mention covariance of the laws of physics without further explanation. This just gives a different name to the mysteries.

Are the natural laws imposed on the universe by an unseen internal or external entity? Do the properties of vacuum fluctuations create the fundamental physical constants? Are the physical constants the same when they are not observed?

Hi everyone, I need to get the momentum representation function of this function

ψ(r,θ,φ)=(ⅇ^(-ar) (1-ⅇ^(-br) )^d Cos(θ))/r I used a Fourier transformation as φ(p)= ∫_0^∞▒ ∫_0^π▒ ∫_0^2π▒〖ψ(r,θ,φ) e^(-ip.r) r^2 sin⁡(θ)dφdθdr〗 such that -ip.r= -iprcos(θ) and, I have tried to solve it by Matlab and Mathematica but no result I could get. Any ideas about that??

The BCS is based on the concept of Cooper pairs (or pairons), which was actually conceived before the BCS. The concept of pairons is widely known and accepted even from researchers who think the BCS is not adequate to describe all types of superconductors. In the BCS, pairons are though to form from singlet electron pairs (with single state and total spin=0) whose total momentum is zero (-k, +k). Is there any cause that prevent triplet spin electrons (with 3 states and total spin=1) to form pairons or even other combinations of multi-pairons in superconductors?

see Attachment.

while studying the longitudinal momentum distribution for any halo nuclei during a reaction in lab frame .I want to change this distribution into the center of mass(CM) frame .is it possible change it directly? What factor I need to multiply or divide so that momentum distribution became according to the CM frame. Any suggestion or method or any reference ?

I would like to recap all the conditions needed in order Raman scattering occours. I have collected some but i do not know if some of the are equivalent or i am missing some. Here there are:

- conservation of the energy

- conservation of the momentum

- variation of the polarizability along one normal mode

- if harmonic potential, the transition is allowed only for adjacent energy levels

do i am missing some?

Please can anyone help with COMSOL. I am trying to simulate gas storage in a porous media but I am at a loss on how to go about it especially how to input my mass balance, momentum and energy balance equations. Any helpful links, resources or tips will be highly appreciated. Thank you

Can you help me to solve this example

In reactive exothermic collisions (A+B-->C+D) masses of the reactants change after collision and some heat is released. Let's assume that the heat released is used in accelerating products (i.e. C and D). How can we compute the post-collision velocities of C and D such that the momentum is conserved. Please note that the masses of C and D are not the same as masses of A and B, however, their sum is.

The Huygens–Fresnel principle has every point on a wavefront become the source of spherical waves, and different points mutually interfere, and they sum to a new wavefront. This seems to conserve the momentum for a beam of photons. What happens to the momentum during diffraction? Same question for electrons in the double slit experiment when interference pattern appears, is the momentum conserved in some way?

We understand from Special Relativity that the speed of light is an upper limit on the relative speed between moving objects. This concerns the rate of change of position, and constant momentum.

Is it a useful question to ask: Why is there no upper limit on angular speed; concerning the rate of change of orientation, and constant angular momentum?

Dear friends, I am simulating spray injection in a pipe. My model is multiphase/ DPM/ K-W and the step size is 0.0001 with 350 iteration per step time. by now, I can get convergence in continuity(10e-4)/ u(10e-6)/ v(10e-5)/ w(10e-5)/ k(10e-5)/ and omg(10e-5) at about 3 time steps and it will continue till 30-35 time steps but the continuity then starts to fluctuate . I have already decreased URF ( momentum, Turbulent kinetic energy and specific dissipation rate to 0.3, 0.3, 0.3, respectively).

Any suggestion on what can I do to get continuously convergence at each time step?

I attached the text file of residuals.

Thank you all in advance,

Taha

Hi there,

I am simulating a hypervelocity impact between a sphere and a thin plate in ANSYS Autodyn. I need to be able to tell the mass, velocity and hence momentum at any given moment of each SPH particle. I have tried adding the gauge points interactively but it just takes far too long. Is there any way of selecting all of the particles to be gauge points?

Thanks

Conor

The standard description of superconductivity states that first electrons form cooper pairs, and then cooper pairs form a condensate. Electrons being fermions can't condense, but cooper pairs being bosons can. Two thing I don't get.

1. Cooper pairs are bosons, but electrons they are made of are still fermions and still can't occupy the same state more than twice. How can it happen that bosons are all in a same state (and all have, let's say, the same coordinate), but still every boson consists of fermions in unique states (all having different coordinates)?

2. Okay, let's say that somehow happened, and now a bunch of bosons condensed into a same state (now let's say into a same momentum state), like a gas condense into liquid, and high binding energy prevents that bunch from disintegrating again. Now why does this bunch keep its momentum unchanged? Why does not it gradually slow down as a whole and loose its momentum, like a boat in the water, making the superconductive current cease? What makes the current stable? Why a single electron can't do the same trick?

when we study plasma waves (plasma oscillations, electron waves and ion waves) we study perturbation in density, velocity and electric field and use momentum, continuity and poison equation to start with.

after introducing perturbation in each quantity we do linerization of non-linear (or higher order terms).

Please explain why is it necessary at all to do it? what if we do not linearlize the quantity ?

Thank you in advance,

Purvi Dave

I will be using blade element momentum theory (BEMT) code to design the turbine blade.

I'm trying to model a combined sinusoidally pitching and plunging oscillating hydrofoil, with just the pitching as a mesh movement, while adding a velocity source term to the fluid in the opposite direction of the plunging motion to mimic the effect of plunging. The units of a general momentum source term in CFX are kg m^-2 s^-2, dimensionally equivalent to density * acceleration, so I created an expression to calculate the foil acceleration and used it to create a momentum source term with those dimensions. Using the term in a transient simulation however produces velocity fields in the fluid domain that don't make any sense, and certainly aren't consistent with the plunging motion expected. Are there any ways to formulate a general momentum source term so that it results in the addition of a purely velocity component to the fluid?