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Questions related to Energy Conservation
According to the mass-energy equation [1], E = mc2, the rest energy of an electron is contained in its mass. When the positive and negative electrons annihilate [2], e+ e- = γγ, their rest energy is converted to photon energy and the total energy is conserved. The electron also carries an electric charge and has electromagnetic energy. When an annihilation reaction occurs, the mass disappears and so does the charge, where does the energy of the charge go? If all energy is contained in the mass-energy equation, does this mean that charge and mass are closely related? Therefore, all mass is electromagnetic mass [3][4][5]. If electromagnetic mass is only a part of mass, then what kind of mass is produced by the Higgs mechanism?
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2025.1.31
One can continue to ask, if the charge contains energy, what form of energy is it? If it is the same as the electric field energy, then when all the energy of the charge is contained in the electric field outside of it, what should the ‘charge’ itself be? And if not, which implies that the charge contains two types of energy, how is the electric field energy bound to the charge energy?
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Reference's References
- Is it possible to create a special optimization algorithm to improve energy efficiency?
2. Is it possible to develop an algorithm to become a hybrid algorithm based on energy efficiency parameters?
Dear respected researchers
I am grateful to you for taking the time to read this question and I hope to see your suggestions and answers about this question.
My greetings and respect to you
2025 International Conference on Renewable Energy and Energy Conservation (REEC 2025) will be held in-person on January 10-12, 2025 in Xinyu, Jiangxi, China.
Conference Website: https://ais.cn/u/2mMjEb
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The topics of interest for submission include, but are not limited to:
◕ Renewable Energy
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Should there be a cosmological constant Λ term in the GR field equations? Is the Λ term symmetric with Gμν?
"According to Einstein's theory of General Relativity, gravity should lead to a slowing of the cosmic expansion. Yet, in 1998, two teams of astronomers studying distant supernovae made the remarkable discovery that the expansion of the universe is speeding up. To explain cosmic acceleration, cosmologists are faced with two possibilities: either 70% of the universe exists in an exotic form, now called dark energy, that exhibits a gravitational force opposite to the attractive gravity of ordinary matter, or General Relativity must be replaced by a new theory of gravity on cosmic scales."[1] In order to match the phenomenon of cosmic expansion, the general theory of relativity introduced the cosmological constant term and various speculations on its cause have been made [2]. However, these studies have rarely addressed the possible solutions in the structural aspects of the universe [3].
If there is only gravitational force, it looks like there is a deficiency. We believe that if there is a gravitational force, there is a corresponding repulsive force. But who should cause it and under what circumstances? It is important to know that in electromagnetic interactions, both positive and negative forces are formed by charges, and our goal is to unify the electromagnetic and gravitational forces. Would dark energy be a repulsive force symmetrical to gravity? Where does their symmetry come into play? If the result is to be symmetrical, the cause must first have symmetry. According to the assumptions of modern physics, the dark energy that causes the expansion of the universe is background and not symmetrical with the energy in GR. Regular energies are floating above the dark energy background, so they cannot have symmetry. In Einstein's gravitational field equation, Gµν + Λgµν = G*Tµν, the energy Tµν leads to an unmeasurable intrinsic Space-Time Curvature Gµν [4] while Λgµν is assumed to be a measurable extrinsic Space-Time Expansion due to the universal energy [5]. Specific and background, intrinsic and extrinsic, curvature and expansion do not have any symmetrical meaning. It would then not be appropriate to arrange them in a GR field equation.
Philosophically speaking, there should be no difference with ‘existence’ at this time and the other time, this place and the other place, i.e., when space and time are considered as background *, ‘existence’ does not depend on space-time coordinates. Therefore, the equations of the universe should not require boundary and initial conditions. Physics, by analysing observational data, has proposed the ‘Big Bang Theory’ and the ‘Accelerated Expansion Theory’ of the Universe, both of which are inconsistent with this. Therefore, the hypothesis of dark energy based on this foundation is questionable.
Our Questions:
Does the existence of ‘energy’ necessitate the existence of ‘dark energy’ or ‘anti-energy’? The hypothesis of the existence of dark energy is based only on the observation of the expansion of the universe. Is it the only explanation for the expansion of the universe? [6]
The function of energy is to drive interactions, and energy is presented in discrete forms, which can be manifested in a variety of forms, including gravity. Is the function of dark energy only to cause negative gravity? Is there only one form of dark energy?
Conservation of energy is an important physical principle, is dark energy conserved?
If gravity and negative gravity cancel each other out, why can't energy and dark energy cancel each other out directly?
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Notes
* We believe that existence itself has a space-time parameter, but not a coordinate parameter.
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References
[1] Dark Energy Survey, Collaboration. https://www.darkenergysurvey.org/the-des-project/overview/
[2] Peebles, P. J. E., & Ratra, B. (2003). The cosmological constant and dark energy. Reviews of Modern Physics, 75(2), 559.
[3] Fan, C. (2023). Convergent and Disperse Cyclic Multiverse Model (CDCMM). https://www.preprints.org/manuscript/202309.0784/v2
[4] Doubts about General Relativity (7) - Is Space-Time Bend a Motion? https://www.researchgate.net/post/NO42Doubts_about_General_Relativity_7-Is_Space-Time_Bend_a_Motion；
Doubts about General Relativity (5) - Should there be "negative gravity" in General Relativity?，https://www.researchgate.net/post/NO40Doubts_about_General_Relativity_5-Should_there_be_negative_gravity_in_General_Relativity.
[5] Doubts about General Relativity (3) - Are Space-Time Curvature and Expansion Two Different Geometrical Mechanical Properties? https://www.researchgate.net/post/NO38Doubts_about_General_Relativity_3-Are_Space-Time_Curvature_and_Expansion_Two_Different_Geometrical_Mechanical_Properties.
[6] Is there a reasonable alternative to the theory of the expanding universe?
My exploration of the string Euler characteristic made me wonder if the Euler characteristic is related to energy conservation, then why not consider string thermodynamics. Not heat but free energy.
The Gibbs phase rule F = c - p + 2 for the string reads degree of freedom 1 = 1 component - 2 phases +2.
The rule is a tautology on one component because one degree of freedom implies two phases, and two phases implies one degree of freedom.
The string energy can only be defined under one degree of freedom.
So experimental evidence unequivocally shows two distinct energy phases: amplitude expansion and amplitude contraction.
Clearly the two phases are determined by the same closed system.
Note the 1 degree of freedom Lagrangian is E = T + U, not E = T - U
Phase I: When the deformed string is released, the baseline potential energy U is increases to U + U'(t). Energy conservation is the same as volume preservation, so the shape of the manifold minimizes surface area. This forces the excess potential energy U'(t) into kinetic action T(t) so that U + U'(t) > U + T(t).
Phase II When all excess potential energy is transferred to kinesis, the normal curvature of the smooth manifold is restored but with a surface that is moving. Then the kinetic energy T(t) runs down to zero. The base line potential energy cannot run down.
So the time-invariant standing wave has a covariant derivative which gives the string velocity, and therefore the invariant frequency, too.
This proves that the frequency and amplitude are both determined by the Gibbs free energy change which drives amplitude decay.
It is therefore proven that frequency and amplitude are dependent on the same closed potential system.
I have attached sketches of the string energy cycle at rest, deformed, expansion, and contraction.
If anyone would like to help write these equations better, I would appreciate it. My calculus has limits. I think someone could really do some interesting things here. The field is wide open for discovery and original research (in spite of what they tell me on Stack Exchange).
If you do write the string energy equations, go over and lay them on physics stack exchange for me.
CO2 Sequestration [CO2 Emission & Absorption]
Feasible to precisely estimate the annual production of CO2 from human activity?
What happens when it exceeds 10^14 kg?
How far the global CO2 emissions from fossil fuels and industry
is expected to grow
from its current value of
nearly 40 billion metric tons (GtCO2)?
And, when could (year) we expect
the point of inflection?
From the current values of CO2 emissions by
Coal (16 billion tons),
Oil (12 billion tons) and
Gas (8 billion tons),
how much do we expect
to get reduced by 2030, 2040 & 2050?
From the current values of CO2-emitting sectors by
Electricity and heat production (50%);
Transport (25%); &
Manufacturing & construction industries (20%),
how much changes do we expect by 2030, 2040 & 2050?
Why were the global CO2 emissions - mainly unchanged -
between 2014 & 2016?
What happens when we fail to stabilize CO2 emissions
despite our focus on
energy conservation,
energy efficiency or fuel substitution and
alternative sources of energy
(apart from the occurrences of heat-waves & extreme-events of rainfall – which is quite a normal physical phenomena,
associated with the conventional earth’s climate change
that gets repeated over geological-cycle)?
OR
With the current world average temperature hanging around 15.031 deg C; and with world average temperature of 0.018927 deg C in 2024, and
with the weekly (in July 2024) world average temperature of 0.000627 deg C, what exactly it means, even,
if we end up exceeding 4+ deg C increase by 2100
as against the aim of Paris Agreement
to keep the rise of global temperatures to 2 deg C in this century?
With nearly 3 million hectares of forests cut down per month globally, whether, deforestation remains to be the major culprit
between the imbalance between
the emission from soil (525 billion tons of CO2 per annum) and
the absorption in the forest (485 billion tons of CO2 per annum)?
Suresh Kumar Govindarajan
Obvious, humans as a species, are unable to wean itself from fossil fuels quickly enough... to make any impact on Global Warming.
Also, countries are unwilling to shut down antiquated and useless sections of their economies, like investing in war making and standing armies, to transfer those funds to fight humanity's four greatest enemies-- Global Warming, Desertification, Meeting basic human needs, and Providing free health care and education.
The only reasonable solution, is to replant all of the desert lands with native trees, grasses and wildflowers, to cool the barren surfaces, so that the sun's heat will not get trapped by the CO2 and methane in the air.
That is what the Saudis and 24 countries are doing right now, planting 50 billion trees with their Middle East Green Initiative, which India is a member of, picture from the COP27 meeting which put that project together.
By planting back that insulating layer of local native vegetation on the barren desert soils, that will cool Global Warming immediately on that spot, whereas reducing or removing the CO2 will take decades to centuries to have the same amount of effect.
Energy Conservation Measure (ECM) analysis is a process that involves identifying and evaluating potential opportunities for reducing energy consumption in a building or facility. The objective of ECM analysis is to identify cost-effective solutions for reducing energy consumption, improving energy efficiency, and reducing greenhouse gas emissions.
Since nanoparticles can be used for redshift. How the energy conservation can be explained. Can this be related with downconversion phenomena, in which an energetic photon is splitted into two low energy photons.
“According to general theory of relativity, gravitation is not a force but a property of spacetime geometry. A test particle and light move in response to the geometry of the spacetime.”[1] Einstein's interpretation of gravity is purely geometrical, where even a free point particle without any properties and any interactions, moves in a curved spacetime along geodesics, but which are generated by the energy tensor Tµν [2]. Why isn't gravity generated directly by Tµν, but must take a circuitous route and be generated by the geometry of spacetime Gµν‡?
Gµν=G*Tµν
This is Einstein's field equation, and the Einstein tensor Gµν describes the Space-Time Curvature. We know that in classical mechanics and quantum field theory, it is the Hamiltonian, Lagrangian quantities that determine motion. Motion is essentially generated by energy-momentum interactions. Why is it irrelevant to energy-momentum in GR? Einstein had always expected the unification of electromagnetic and gravitational forces to be geometrically realized [3]*. Is such an expectation an exclusion of energy-momentum interactions in motion? Can the ultimate unification of forces be independent of energy-momentum and manifest itself only in motion in pure spacetime? If not, one of these must be wrong.
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Supplement: Gravity is still a force
Gravity appears to be a ‘spacetime gravity’, i.e., gravity caused by spacetime metric differences, the same as gravitational red shift and violet shift [1]. The current four-dimensional space-time ‘geodesic’ interpretation of gravity is to match the geometric appearance of Space-Time Curvature. Time and space are symmetrical, and geodesic motion is not initiated by the ‘arrow of time’ alone, but must be accompanied by equivalent spatial factors. Any interpretation that destroys the equivalence of space and time should be problematic.
[1] "What is Force, a Field? Where is the Force Field? How does it appear? Is the Force Field a Regulating Effect of the Energy-Momentum Field?"
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Notes
* "After his tremendous success in finding an explanation of gravitation in the geometry of space and time, it was natural that he should try to bring other forces along with gravitation into a “unified field theory” based on geometrical principles."
‡ If one thinks that it holds only at Tµν = 0, see the next question NO.37: Is there a contradiction in the Schwarzschild spacetime metric solution?
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References
[1] Grøn, Ø., & Hervik, S. (2007). Einstein's Field Equations. In Einstein's General Theory of Relativity: With Modern Applications in Cosmology (pp. 179-194). Springer New York. https://doi.org/10.1007/978-0-387-69200-5_8
[2] Earman, J., & Glymour, C. (1978). Einstein and Hilbert: Two months in the history of general relativity. Archive for history of exact sciences, 291-308.
[3] Weinberg, S. (2005). Einstein’s Mistakes. Physics Today, 58(11).
Can Physical Constants Which Are Obtained with Combinations of Fundamental Physical Constants Have a More Fundamental Nature?
Planck Scales (Planck's 'units of measurement') are different combinations of the three physical constants h, c, G, Planck Scales=f(c,h,G):
Planck Time: tp=√ℏG/c^5=5.31x10^-44s ......(1)
Planck Length: Lp=√ℏG/c^3=1.62x10^-35m ......(2)
Planck Mass: Mp=√ℏc/G=2.18x10^-8 kg ......(3)
“These quantities will retain their natural meaning for as long as the laws of gravity, the propagation of light in vacuum and the two principles of the theory of heat hold, and, even if measured by different intelligences and using different methods, must always remain the same.”[1] And because of the possible relation between Mp and the radius of the Schwarzschild black hole, the possible generalized uncertainty principle [2], makes them a dependent basis for new physics [3]. But what exactly is their natural meaning?
However, the physical constants, the speed of light, c, the Planck constant, h, and the gravitational constant, G, are clear, fundamental, and invariant.
c: bounds the relationship between Space and Time, with c = ΔL/ Δt, and Lorentz invariance [4];
h: bounds the relationship between Energy and Momentum with h=E/ν = Pλ, and energy-momentum conservation [5][6];
G: bounds the relationship between Space-Time and Energy-Momentum, with the Einstein field equation c^4* Gμν = (8πG) * Tμν, and general covariance [7].
The physical constants c, h, G already determine all fundamental physical phenomena‡. So, can the Planck Scales obtained by combining them be even more fundamental than they are? Could it be that the essence of physics is (c, h, G) = f(tp, Lp, Mp)? rather than equations (1), (2), (3). From what physical fact, or what physical imagination, are we supposed to get this notion? Never seeing such an argument, we just take it and use it, and still recognize c,h,G fundamentality. Obviously, Planck Scales are not fundamental physical constants, they can only be regarded as a kind of 'units of measurement'.
So are they a kind of parameter? According to Eqs. (1)(2)(3), c,h,G can be directly replaced by c,h,G and the substitution expression loses its meaning.
So are they a principle? Then who are they expressing? What kind of behavioral pattern is expressed? The theory of quantum gravity takes this as a " baseline ", only in the order sense, not in the exact numerical value.
Thus, Planck time, length, mass, determined entirely by h, c, G, do they really have unquestionable physical significance?
-----------------------------------------
Notes
‡ Please ignore for the moment the phenomena within the nucleus of the atom, eventually we will understand that they are still determined by these three constants.
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References
[1] Robotti, N. and M. Badino (2001). "Max Planck and the 'Constants of Nature'." Annals of Science 58(2): 137-162.
[2] Maggiore, M. (1993). A generalized uncertainty principle in quantum gravity. Physics Letters B, 304(1), 65-69. https://doi.org/https://doi.org/10.1016/0370-2693(93)91401-8
[3] Kiefer, C. (2006). Quantum gravity: general introduction and recent developments. Annalen der Physik, 518(1-2), 129-148.
[4] Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der Physik, 17(10), 891-921.
[5] Planck, M. (1900). The theory of heat radiation (1914 (Translation) ed., Vol. 144).
[6] Einstein, A. (1917). Physikalisehe Zeitschrift, xviii, p.121
[7] Petruzziello, L. (2020). A dissertation on General Covariance and its application in particle physics. Journal of Physics: Conference Series,
Gerard Reid (2020) stated about Energy: "The choices and approaches... are governed by the following paradoxes...: 1. The Utility Paradox; 2. The Market Efficiency Paradox; 3. Jevons Paradox; 4. The NIMBY Paradox 5. The Renewable Energy Paradox 6. The Philosophy Paradox. On the other hand, Adam Szymański (2020) showed that the Levelized Cost Of Energy (LCOE) definition is incorrect as it leads to an Economic Paradox. This discussion is intended to launch a scientific debate on these essential energy issues and related technical, socioeconomic, and environmental implications.
Gerard Reid (2020) The Six Energy Paradoxes that slow the sector’s progress. Available on: https://energypost.eu/the-six-energy-paradoxes-that-slow-the-sectors-progress/
Szymański, A. (2020). Levelized cost of energy definition–An economic paradox. The Electricity Journal, 33(7). To be requested on:
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries[1].
In SR, force-free motion in an inertial frame of reference takes place along a straight-line path with constant velocity. Viewed from a non-inertial frame, on the other hand, this path of motion will be a geodesic curve in a flat spacetime. Einstein made the plausible assumption that this geodesic motion also holds in the non-flat case, i.e. in a spacetime region for which it is impossible to find a coordinate system that leads to the Minkowski metric in SR[2].
All spacetime models can be expressed in terms of the gμν = {4x4} matrix, differing only in the distribution of matrix elements. The gμν of Minkowski spacetime is the unit diagonal matrix {1 -1 -1 -1}; the gμν of Riemann spacetime is { X }. If a new spacetime model is introduced gμν={a0,-a1,-a2,-a3}, which is a non-unit diagonal matrix. (ds)^2=(a0)^2+(a1)^2+(a2)^2+(a3)^2, always holds, interpreting it as a non-uniformly flat spacetime, generalised Minkowski spacetime, and no longer a curved spacetime. Should Noether's theorem maintain its validity in this case.
----------------------------------
References
[1] Marvian, I., & Spekkens, R. W. (2014). Extending Noether's theorem by quantifying the asymmetry of quantum states. Nature Communications, 5(1), 3821. https://doi.org/10.1038/ncomms4821 ;
[2] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.
According to the principle that force is an exchange of "virtual particles", the "graviton" appears only when an object enters the gravitational field, how does it appear? Where is the "graviton" when only isolated matter carries its own gravitational field?
According to the principle that space-time is "curved" by matter, and curved space-time is gravity, is the "graviton" a part of matter? Does it also participate in the bending of space-time? Or is it the bending of space-time that produces the "graviton", and must the graviton also propagate along the geodesic?
a) Space-time is a kinetic "background medium "* that we should consider as a universal energy-momentum form. It can be transferred and exchanged like any other form of energy-momentum, and thus has the ability to change, and to be changed. Any elementary particle possesses an intrinsic spacetime parameter, which is where SR's "Length Contraction and Time Dilation" manifests itself, and why GR matter is able to change spacetime. Any interaction must be transmitted and exchanged through spacetime.
b) Different forms of energy-momentum can cause spacetime "bending", which must reflect the unity of energy-momentum [1]. The only thing that can cause spacetime to bend is spacetime. That is to say, energy-momentum, matter can only rely on its own spacetime to change other spacetime. Therefore, one of the properties that matter carries is the "curved" state of spacetime around it [2].
c) The essence of the "curvature" of spacetime is the unequal change of the components of the four-dimensional spacetime intrinsic metric Δs={Δt,Δx,Δy,Δz}† . This can be expressed as (ds)^2=-(a0*dt)^2+(a1*dx1)^2+(a2*dx2)^2+(a3*dx3)^2, with a0~a3 unequal. Such a definition is concise and physically complete, and is able to unify all spacetime-related concepts under the Minkowski spacetime framework. Consider spacetime as consisting of arbitrarily small-sized elements ΔV, which are of the same size, but in which the metric components Δt,Δx,Δy,Δz can be different. This requires the existence of two different properties of spacetime, an absolute positional coordinate and a relative metric between positions. This is equivalent to giving spacetime the concept of "metric density". Obviously it presents the media role of spacetime in a more vivid way.
d) This kind of definition of curvature can bring many convenient and reasonable explanations:
It guarantees the continuity of the whole spacetime and the global orthogonality of the three-dimensional space; it perfectly matches the "Length Contraction and Time Dilation" effect of SR and the Riemannian spacetime concept of GR✧.
Light does not change spacetime in free space, but participates in energy momentum to change spacetime in curved spacetime. Light changes spacetime in the same way that it is changed, e.g. gravitational redshift [4], violet shift, cosmological redshift, what actually happens is that its spacetime metric {Δt,Δx,Δy,Δz} is changed.
According to GR's causality, and reversibility, the energy-momentum causes the spacetime {Δt,Δx,Δy,Δz} to change, and then the energy implied by spacetime itself should be a function of Δt, and the momentum a function of Δx,Δy,Δz. This is the most direct and final expression, and the only possible choice!
Since the "geodesic" is the shortest path caused by energy-momentum L=∫ds=∫√gμν-dxμ-dxν, it is of course equivalent to the expression of energy-momentum. Therefore, this metric expression of distance has only a nominal meaning. In reality it should be the lowest "metric density" (lowest energy) path.
It is commonly believed that gravity is not a real force [5][6]. Objects move instinctively along geodesics, just as force is not required for inertial motion in free space. This interpretation is not in place††. It is the maintenance of energy-momentum conservation of the interacting system in a changing spacetime metric {Δt,Δx,Δy,Δz} that is the root cause of the "gravitational force" that leads to accelerated motion!
Criterion: What can change spacetime can only be spacetime. To change Δs={Δt,Δx,Δy,Δz}, another Δs'={Δt',Δx',Δy',Δz'} must join it, whether it is carried by a mass or arrives by a gravitational wave [7].
e) If the force is still defined according to the concept of exchanging virtual particles [10], then such a "graviton" does not exist‡. We must find a direct correlation between the so-called exchange of virtual particles and the exchange of energy-momentum. A "graviton "** exists if one considers the smallest unit of spacetime metric change due to the smallest unit of energy-momentum to be a "graviton". It consists only of the smallest spacetime metric {Δt,Δx,Δy,Δz} and must be dispersive. This is unlike any other elementary particle.
f) One of the symmetry manifestations of gravity should be the existence of positive and negative. If the theory has only gravity and no repulsion, then it must be deficient. Even if the repulsive force does not normally exist, a reason for its absence should be given.
g) When an interaction occurs, the energy-momentum involved is strong, the force presented is strong. In contrast to the electromagnetic force, the gravitational force is weak because it is not the main body of energy-momentum, but rather a spatio-temporal concomitant of the energy-momentum of matter, or an " residual " ♬.
Questions
1) How to define the concept of orthogonality of " intrinsic curvature " of spacetime between three spatial dimensions? How to realize its rationality?
(2) In the "curved spacetime", the "geodesic" is the shortest path, is its metric process essentially different from the "Length Contraction and Time Dilation" of SR?
3) Is the "graviton" currently sought by physics a detectable entity with a fixed form?
4) Doesn't it make sense that the positive or negative spacetime metric gradient determines whether an "attractive" or "repulsive" force is generated?
4) Photons are quantized, mass is quantized, and mass-induced "spacetime bending" should certainly be quantized. "Space-time bending" is equivalent to gravity. Doesn't the cause of space-time bending tell us what a "graviton" is? Aren't gravitational waves a collection of gravitons? Why do we have to search for "quantum gravity" through various assumptions，structures that are more fundamental than elementary particles [11]? Why should GR match the quantum framework and not the other way around?
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Notes
* "The main insight of Einstein's general relativity was the change of the role of space and time from a passive 'arena', in which physics takes place, to an active dynamical entity that is shaped by matter and acts back on it; but space-time remained a sharply defined classical object"[9]. However, space-time is not the same as matter in many ways, for example, it is universal, flat free space-time contains no energy-momentum, it can only be modified by the addition of energy, it can change nothing else. g = g0 + h, g0 is background metric (coordinate spacetime), contains no energy-momentum; h is modulation metric (relative spacetime), with energy-momentum. Therefore, it is appropriate to call this view of spacetime an upgraded version of the "Aether" doctrine [3].
✧ Einstein never argues for the spacetime bending premise in GR, but takes Gaussian coordinates directly, which seems to be the only option. In fact, in SR, point-particle states vary equally in each component of the measure, g00 = g11 = g22 = g33, and the other gμν = 0; when there is a scale for the object, it changes only in the direction of motion. In GR the static Schwarzschild spacetime g00, g11, g22, g33 is not 0, and the other gμν = 0. Forcing the other gμν = 0 does not lead to complete failure of GR.
† Expressing spacetime bending in a deformed "3D mesh" animation [14], although more graphically expressing Δs={Δt,Δx,Δy,Δz}, may result in definitional conflicts: can spacetime be locally and infinitely stretched or extruded, resulting in spacetime tearing, or overlapping? Can the bending directions of neighboring spacetimes conflict? Does the endowed bending of spacetime conflict with the external bending of the overall spacetime? How is the orthogonality of the overall 3D spacetime manifested? How do field representations reflect spacetime curvature when other fields are in curved spacetime?
§ As when light passes through a medium with different refractive indices n, resulting in a decrease in the speed of light. This actually reflects the change in spacetime density in the path.
†† We need to focus on why there is motion, not whether there are "forces". An ant and a bee both know the shortest path to their nests, but if the ant loses its legs, it will not be able to return to its nest, and if the bee loses its wings, it will fall free along the geodesic and will not return to its nest.
‡ The essence of exchanging "virtual particles" is to exchange fields; the essence of exchanging fields is to maintain the conservation of energy-momentum; maintaining the conservation of energy-momentum is manifested as "force".
¶ The energy-momentum itself is a function of space-time and manifests itself internally. When energy-momentum is exchanged with the outside world, there must be external motion to balance the exchange. In fact, the relationship between energy-momentum and space-time is reflected in both rest and motion.
** Defined in this way, the essence of the graviton is the minimum spacetime metric. Because the constituents of matter and energy-momentum that lead to the curvature of spacetime are different, the metric of spacetime curvature they lead to is also different. We need to note one thing, energy quantization is derived from the theory of blackbody radiation. It is not correct to generalize that the photon is the smallest energy quantum, it is simply the smallest energy quantum at a particular frequency E=hν. the same is true of the graviton.
♬ Wilczek said, "The apparent feebleness of gravity results from our partiality toward the perspective supplied by matter made from protons and neutrons ." [13]. Concerning the question of the order of magnitude of forces, why don't we first see that different forces are located in different structures, and why don't we analyze them structurally?
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References
[3] Whittaker, E. (1910). A History of the Theories of Aether and Electricity, Courier Dover Publications（1989）;
[4] Will, C. M. (2018). Theory and experiment in gravitational physics, Cambridge university press.
[5] Ashtekar said,“Gravity is a manifestation of spacetime geometry”：Ashtekar, A. and E. Bianchi (2021). "A short review of loop quantum gravity." Reports on Progress in Physics 84(4): 042001. “”
[6] Kiefer said,“All manifestations of the gravitational field known so far can be understood from a classical theory—Einstein's theory of general relativity (GR), also called geometrodynamics. It is defined by the Einstein–Hilbert action." Kiefer, C. (2007). Lecture Notes in Physics-Approaches to fundamental physics, Springer. Why quantum gravity?: 123-130.
[7] Abbott, B., S. Jawahar and etl. (2016). "LIGO scientific collaboration and virgo collaboration (2016) gw150914: first results from the search for binary black hole coalescence with Advanced LIGO." PHYSICAL REVIEW D Phys Rev D 93: 122003.
[8] Why Should We Study Quantum Gravity? What Are Prima Facie Questions? Isham, C. J. (1994). Prima facie questions in quantum gravity. Canonical gravity: From classical to quantum, Springer: 1-21.
[9] Kiefer, C. (2007). Lecture Notes in Physics-Approaches to fundamental physics, Springer. Why quantum gravity?: 123-130.
[10] Cowan, G. (2012). "Review of particle physics." Phys. Rev. D 86(010001): 390.
[11] Mielczarek, J. and T. Trześniewski (2018). "Towards the map of quantum gravity." General Relativity and Gravitation 50(6): 68.
[13] Wilczek, F. (2005). "Nobel Lecture: Asymptotic freedom: From paradox to paradigm." Reviews of Modern Physics 77(3): 857.
[14] Schutz, B. (2009). A first course in general relativity. China, Cambridge university press.
I have a question regarding energy momentum tensor.
God said, "Let there be light."
So, did God need to use many means when He created light? Physically we have to ask, "Should all processes of light generation obey the same equation?" "Is this equation the 'God equation'?"
Regarding the types of "light sources", we categorize them according to "how the light is emitted" (the way it is emitted):
Type 0 - naturally existing light. This philosophical assumption is important. It is important because it is impossible to determine whether it is more essential that all light is produced by matter, or that all light exists naturally and is transformed into matter. Moreover, naturally existing light can provide us with an absolute spacetime background (free light has a constant speed of light, independent of the motion of the light source and independent of the observer, which is equivalent to an absolute reference system).
Type I - Orbital Electron Transition[1]: usually determines the characteristic spectra of the elements in the periodic table, they are the "fingerprints" of the elements; if there is human intervention, coherent optical lasers can be generated. According to the assumptions of Bohr's orbital theory, the transitions are instantaneous, there is no process, and no time is required*. Therefore, it also cannot be described using specific differential equations, but only by probabilities. However, Schrödinger believed that the wave equation could give a reasonable explanation, and that the transition was no longer an instantaneous process, but a transitional one. The wave function transitions from one stable state to another, with a "superposition of states" in between [2].
Type II - Accelerated motion of charged particles emitting light. There are various scenarios here, and it should be emphasized that theoretically they can produce light of any wavelength, infinitely short to infinitely long, and they are all photons. 1) Blackbody radiation [3][4]: produced by the thermal motion of charged particles [5], is closely dependent on the temperature, and has a continuous spectrum in terms of statistical properties. This is the most ubiquitous class of light sources, ranging from stars like the Sun to the cosmic microwave background radiation [6], all of which have the same properties. 2) Radio: the most ubiquitous example of this is the electromagnetic waves radiated from antennas of devices such as wireless broadcasting, wireless communications, and radar. 3）Synchrotron radiation[7]，e+e− → e+e−γ；the electromagnetic radiation emitted when charged particles travel in curved paths. 4）bremsstrahlung[8]，for example, e+e− → qqg → 3 jets[11]；electromagnetic radiation produced by the acceleration or especially the deceleration of a charged particle after passing through the electric and magnetic fields of a nucleus，continuous spectrum. 5）Cherenkov Radiation[9]：light produced by charged particles when they pass through an optically transparent medium at speeds greater than the speed of light in that medium.
Type III：Partical reactions、Nuclear reactions：Any physical reaction process that produces photon (boson**) output. 1）the Gamma Decay；2）Annihilation of particles and antiparticles when they meet[10]: this is a universal property of symmetric particles, the most typical physical reaction；3）Various concomitant light, such as during particle collisions；4）Transformational light output when light interacts with matter, such as Compton scattering[12].
Type IV: Various redshifts and violet shifts, changing the relative energies of light: gravitational redshift and violet shift, Doppler shift; cosmological redshift.
Type V: Virtual Photon[13][14]?
Our questions are:
Among these types of light-emitting modes, type II and type IV light-emitting obey Maxwell's equation, and the type I and type III light-emitting processes are not clearly explained.
We can not know the light-emitting process, but we can be sure that the result, the final output of photons, is the same. Can we be sure that it is a different process that produces the same photons?
Is the thing that is capable of producing light, itself light? Or at least contains elements of light, e.g., an electric field E, a magnetic field H. If there aren't any elements of light in it, then how was it created? By what means was one energy, momentum, converted into another energy hν, momentum h/λ?
There is a view that "Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways"[15]. What then are the actual things that can fulfill this interpretation? Can it only be energy-momentum?
We believe everything needs to be described by mathematical equations (not made-up operators). If the output of a system is the same, then the process that bridges the output should also be the same. That is, the output equations for light are the same, whether it is a transition, an accelerated moving charged particle, or an annihilation process, the difference is only in the input.
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* Schrödinger said：the theory was silent about the period s of transition or 'quantum jumps' (as one then began to call them). Since intermediary states had to remain disallowed, one could not but regard the transition as instantaneous; but on the other hand, the radiating of a coherent wave train of 3 or 4 feet length, as it can be observed in an interferometer, would use up just about the average interval between two transitions, leaving the atom no time to 'be' in those stationary states, the only ones of which the theory gave a description.
** We know the most about photons, but not so much about the nature of W, Z, and g. Their mass and confined existence is a problem. We hope to be able to discuss this in a follow-up issue.
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Links to related issues:
【1】"How does light know its speed and maintain that speed?”;
【2】"How do light and particles know that they are choosing the shortest path?”
【3】"light is always propagated with a definite velocity c which is independent of the state of motion of the emitting body.";
【4】“Are annihilation and pair production mutually inverse processes?”； https://www.researchgate.net/post/NO8_Are_annihilation_and_pair_production_mutually_inverse_processes;
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Reference:
[1] Bohr, N. (1913). "On the constitution of atoms and molecules." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 26(151): 1-25.
[2] Schrödinger, E. (1952). "Are there quantum jumps? Part I." The British Journal for the Philosophy of science 3.10 (1952): 109-123.
[3] Gearhart, C. A. (2002). "Planck, the Quantum, and the Historians." Physics in perspective 4(2): 170-215.
[4] Jain, P. and L. Sharma (1998). "The Physics of blackbody radiation: A review." Journal of Applied Science in Southern Africa 4: 80-101. 【GR@Pushpendra K. Jain】
[5] Arons, A. B. and M. Peppard (1965). "Einstein's Proposal of the Photon Concept—a Translation of the Annalen der Physik Paper of 1905." American Journal of Physics 33(5): 367-374.
[6] PROGRAM, P. "PLANCK PROGRAM."
[8] 韧致辐射；
[9] Neutrino detection by Cherenkov radiation：" Super-Kamiokande(超级神冈)." from https://www-sk.icrr.u-tokyo.ac.jp/en/sk/about/. 江门中微子实验 "The Jiangmen Underground Neutrino Observatory (JUNO)." from http://juno.ihep.cas.cn/.
[10] 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.
[11] Schmitz, W. (2019). Particles, Fields and Forces, Springer.
[12] Compton, A. H. (1923). "The Spectrum of Scattered X-Rays." Physical Review 22(5): 409-413.
[13] Manoukian, E. B. (2020). Transition Amplitudes and the Meaning of Virtual Particles. 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment. E. B. Manoukian. Cham, Springer International Publishing: 169-175.
[14] Jaeger, G. (2021). "Exchange Forces in Particle Physics." Foundations of Physics 51(1): 13.
[15] Are virtual particles really constantly popping in and out of existence? Or are they merely a mathematical bookkeeping device for quantum mechanics? - Scientific American.
In energy conservation situations where the transient probability is additive, irrational numbers such as 2^1/2 have no place.
However, especially in QM as I understood it, the probability amplitude is multiplicative rather than additive.
The question is why in particular is 2^1/2 so important in QM?
Regarding the importance of using Metals (single atom, nanoclusters) as an active sites on a support (Metal Oxides, Metal sulfides, etc.) for enhancing the photocatalytic chemical reaction (H2 evolution / Water splitting/ CO2 reduction), which active sites will be good ; Metal single atom or Metal Nanoclusters or Mixture of them?
We assume that any N-dimensional space can have an (N-1)-dimensional "boundary". However, if the boundary is limited to points, lines, and surfaces, and not to bodies, then three-dimensional space will be the maximum spatial dimension that satisfies this condition. What is the mathematical concept involved here?
It is commonly believed that the concept of electron spin was first introduced by A.H. Compton (1920) when he studied magnetism. "May I then conclude that the electron itself, spinning like a tiny gyroscope, is probably the ultimate magnetic particle?"[1][2]; Uhlenbeck and Goudsmit (1926) thought so too [4], but did not know it at the time of their first paper (1925) [3]. However, Thomas (1927) considered Abraham (1903) as the first to propose the concept of spinning electron [5]. Compton did not mention Abraham in his paper "The magnetic electron" [2], probably because Abraham did not talk about the relationship between spin and magnetism [0]. In fact, it is Abraham's spin calculations that Uhlenbeck cites in his paper [4].
Gerlach, W. and O. Stern (1921-1922) did the famous experiment* on the existence of spin magnetic moments of electrons (even though this was not realized at the time [6]) and published several articles on it [7].
Pauli (1925) proposed the existence of a possible " two-valuedness " property of the electron [8], implying the spin property; Kronig (1925) proposed the concept of the spin of the electron to explain the magnetic moment before Uhlenbeck, G. E. and S. Goudsmit, which was strongly rejected by Pauli [9]. Uhlenbeck, G. E. and S. Goudsmit (1925) formally proposed the concept of spin[3], and after the English version was published[4], Kronig (1926), under the same title and in the same journals, questioned whether the speed of rotation of an electron with internal structure is superluminal**[10]. Later came the Thomas paper giving a beautiful explanation of the factor of 2 for spin-orbit coupling[11]. Since then, physics has considered spin as an intrinsic property that can be used to explain the anomalous Seeman effect.
The current state of physics is in many ways the situation: "When we do something in physics, after a while, there is a tendency to forget the overall meaning of what we are working on. The long range perspective fades into the background, and we may become blind to important a priori questions."[11]. With this in mind, C. N. Yang briefly reviewed how spin became a part of physics. For spin, he summarized several important issues: The concept of spin is both an intriguing and extremely difficult one. Fundamentally it is related to three aspects of physics. The first is the classical concept of rotation; the second is the quantization of angular momentum; the third is special relativity. All of these played essential roles in the early understanding of the concept of spin, but that was not so clearly appreciated at the time [11].
Speaking about the understanding of spin, Thomas said [5]: "I think we must look towards the general relativity theory for an adequate solution of the problem of the "structure of the electron" ; if indeed this phrase has any meaning at all and if it can be possible to do more than to say how an electron behaves in an external field. Yang said too: "And most important, we do not yet have a general relativistic theory of the spinning electron. I for one suspect that the spin and general relativity are deeply entangled in a subtle way that we do not now understand [11]. I believe that all unified theories must take this into account.
What exactly is spin, F. J. Belinfante argued that it is a circular energy flow [12][15] and that spin is related to the structure of the internal wave field of the electron. A comparison between calculations of angular momentum in the Dirac and electromagnetic fields shows that the spin of the electron is entirely analogous to the angular momentum carried by a classical circularly polarized wave [13]. The electron is a photon with toroidal topology [16]. At the earliest, A. Lorentz also used to think so based on experimental analysis. etc.
Our questions are:
1) Is the spin of an electron really spin? If spin has classical meaning, what should be rotating and obeying the Special Relativity?
2) What should be the structure of the electron that can cause spin quantization and can be not proportional to charge and mass?
3) If spin must be associated with General Relativity, must we consider the relationship between the energy flow of the spin and the gravitational field energy?
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* It is an unexpectedly interesting story about how their experimental results were found. See the literature [17].
** Such a situation occurs many times in the history of physics, where the questioned and doubted papers are published in the same journal under the same title. For example, the debate between Einstein and Bohr, the EPR papers [18] and [19], the debate between Wilson and Saha on magnetic monopoles [20] and [21], etc.
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Reference：
[0] Abraham, M. (1902). "Principles of the Dynamics of the Electron (Translated by D. H. Delphenich)." Physikalische Zeitschrift 4(1b): 57-62.
[1] Compton, A. H. and O. Rognley (1920). "Is the Atom the Ultimate Magnetic Particle?" Physical Review 16(5): 464-476.
[2] Compton, A. H. (1921). "The magnetic electron." Journal of the Franklin Institute 192(2): 145-155.
[3] Uhlenbeck, G. E., and Samuel Goudsmit. (1925). "Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons." Die Naturwissenschaften 13.47 (1925): 953-954.
[4] Uhlenbeck, G. E. and S. Goudsmit (1926). "Spinning Electrons and the Structure of Spectra." Nature 117(2938): 264-265.
[5] Thomas, L. H. (1927). "The kinematics of an electron with an axis." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 3(13): 1-22.
[6] Schmidt-Böcking, H., L. Schmidt, H. J. Lüdde, W. Trageser, A. Templeton and T. Sauer (2016). "The Stern-Gerlach experiment revisited." The European Physical Journal H 41(4): 327-364.
[7] Gerlach, W. and O. Stern. (1922). "Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. " Zeitschrift f¨ur Physik 9: 349-352.
[8] Pauli, W. (1925). "Über den Einfluß der Geschwindigkeitsabhängigkeit der Elektronenmasse auf den Zeemaneffekt." Zeitschrift für Physik 31(1): 373-385.
[9] Stöhr, J. and H. C. Siegmann (2006). "Magnetism"(磁学), 高等教育出版社.
[10] Kronig, R. D. L. (1926). "Spinning Electrons and the Structure of Spectra." Nature 117(2946): 550-550.
[11] Yang, C. N. (1983). "The spin". AIP Conference Proceedings, American Institute of Physics.
[12] Belinfante, F. J. (1940). "On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields." Physica 7(5): 449-474.
[13] Ohanian, H. C. (1986). "What is spin?" American Journal of Physics 54(6): 500-505. 电子的自旋与内部波场结构有关。
[14] Parson, A. L. (1915). Smithsonian Misc. Collections.
[15] Pavšič, M., E. Recami, W. A. Rodrigues, G. D. Maccarrone, F. Raciti and G. Salesi (1993). "Spin and electron structure." Physics Letters B 318(3): 481-488.
[16] Williamson, J. and M. Van der Mark (1997). Is the electron a photon with toroidal topology. Annales de la Fondation Louis de Broglie, Fondation Louis de Broglie.
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[17] Friedrich, B. and D. Herschbach (2003). "Stern and Gerlach: How a bad cigar helped reorient atomic physics." Physics Today 56(12): 53-59.
[18] Bohr, N. (1935). "Can quantum-mechanical description of physical reality be considered complete?" Physical review 48(8): 696.
[19] Einstein, A., B. Podolsky and N. Rosen (1935). "Can quantum-mechanical description of physical reality be considered complete?" Physical review 47(10): 777.
[20] Wilson, H. (1949). "Note on Dirac's theory of magnetic poles." Physical Review 75(2): 309.
[21] Saha, M. (1949). "Note on Dirac's theory of magnetic poles." Physical Review 75(12): 1968.
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].
My questions:
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:
[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;
The Green training increases the knowledge, skills and competencies of the employees to achieve the environmental goals, and equips employees with working approaches that ensure adequate resource utilisation, reduce waste, energy conservation, and environmental degradation cause reduction, and encourag them to adopt sustainable practices.
Dear all,
I am simulationg a CNT in water using Dissipative Particle Dynamics with energy conservation. I can find most of the parameters for Carbon (like repusion parameter...)from the related DPD papers, but I could not find any work done on CNT using eDPD. Does any one know of a work that has been done on CNT using eDPD package? I am looking for the thermal cutoff of carbon.
If not, Does any one know how to calculate that parameter?
Best Regards,
Delaram
How does light know its speed and maintain that speed?
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?
We have shown that the Lorentz transformation diverges to infinite energy at zero volume approaching a relative velocity of c. In the limit of small velocities the Lorentz transformation gives a three times higher field energy increase than the kinetic energy equation. The Galilean transformation does not transform field energy or volume if the relativistic invariant field transformations are considered. The Euclidean transformation allows a description of kinetic energy as a pure relativistic effect of increasing experienced volume. In the limit of small velocities the Euclidean relativity transforms field energy in the same relation as the kinetic energy equation.
Is the invariance of energy density a necessary rule in physics and the violation of this rule a reason to refute Lorentz transformation?
hello everyone
I am modeling an impact problem via Abaqus. and my model consists of an impactor and a solid ball.
The impactor impacts the ball through three different forces. and I extracted energy plots for all of these forces but I think they are not true because internal energy and kinetic energy didn't show an ending at the end of the plots.
does anyone know if these plots are true or not and what should I do to have a better plot?
I have started using Aspen Plus software, but I found it very difficult.
Dear researchers,
I am currently working on the development of a Low Mach Number multi-species solver (a system similar to that used in LMN combustion, but with no reactions at present ...) I am having issues with deriving the exact temperature equation (note that c_p varies for each species...) I emphasize that I am looking for having an equation expressed as a function of the temperature (not enthalpy, not internal nor total energy !)
- Can you please help by providing some references that can help to derive this equation ?
- Shall I start from the conservation equation of the internal or total energy ? should I neglect specific terms ?
- From your experience, is the inter-species diffusion term important and should be taken into account in such a system of GE ?
- Same for the term div(Pu) ? any ideas
- Same for the viscous tensor (u Tau) ... this is so complex to code in fact ....
Thanks for your comments and recommendations !
Regards
Elie
Energy conservation can be expressed in different ways, such as the temperature equation and the enthalpy equation. However, the two equations do not behave the same way when used in Computational Fluid Dynamics (CFD) simulation (finite difference method and finite volume method). My question is: why? If someone can give me a brief explication.
Circular Economy and Triple Bottom line are two main tools in achieving sustainable development goals. But many academics, professionals and stakeholders are finding difficult to distinguish the difference between them and also fail to interconnect them. In this aspect, how they are inter related in terms of construction industry and technological applications?
I would very much appreciate thoughts about drivers and barriers for development of ESCOs in Africa. Maybe this particular question should be firstly considered on the more limited markets. Eventually assessing of the situation with drivers and barriers should be done on the level of the regions or even on the level of particular countries. Furthermore, maybe it will be promptly bundled with several more questions including one as Whether SuperEsco may assist in overcoming key barriers?
For example ants that developed thermoregulation of their nest. Bees that generate heat through movement and the storing of energy in other forms such as in honey or wasps that just protect their queen long enough to start a fresh in spring. Maybe there is other more exotic and complex or simple examples out there?
Dear colleagues,
I need your help. The law of energy conservation in fluid dynamics is associated with Bernoulli equation or, in more general case, with Lagrange-Cauchy equation. I am interesting in the paper were this association was first declared. It is not Bernoulli own thesis, since the law was formulated in the middle of XIX c. I would like to know first arguments and definition of energy of the pressure term in the equation. As far as I know, Rayleigh was first who noted energy of pressure in fluid in his paper "On waves" (1876). But he did not give any definition what is the energy and how it has to be calculated. I am interesting in first definition.
In powder metallurgy, energy is consumed in powder production, ball milling, powder compaction, and sintering. Whereas in casting, the energy is consumed only in melting the ingot. In some of the papers, I have read that energy consumption is lower in powder metallurgy. How? Can anyone explain, please?
Redshift of radiation energy density has been taking place since the early universe due to the expansion of the universe. How much energy has been lost? How does our cosmological model account for it?
Case example: Author A stated an equation 'Dk= 4/3K (8RT/M)' in their report.
Author B cites this equation and writes in her/his report as "... the equation of xyz can be expressed as Dk=48 (RT/M) { ref:Author A}."
which probably have the same meaning but in different form. Any opinions?
Hello everyone,
I'm studding thermal properties of amorphous SiO2(a-SiO2) via molecular dynamics(LAMMPS) using Tersoff potential( ). But I'm experiencing a continuous temperature increasing issue in nve ensemble with a time step of 0.5fs. Problem can be solved by reducing the time step to 0.1fs. But my calculations are kinda time consuming ones so I really need to have the energy conservation with the 0.5fs time step. Anyone who experienced a similar issue with Tersoff potential (for a-SiO2)? Hope someone could give me an advice on my issue.
Stay safe.
Thank you
Chamara Somarathna
Dear Anže Hubman
First, thank you very much for your kind reply.
Back to my problem, I tried to create amorphous silica by melting and quenching method. Initially I tried to equilibrate Beta-Cristobalite at 1800K in NPT and NVE ensembles respectively. However, in the NVE ensemble, system temperature begins to increases as shown in the Fig. 1.
Then I skipped the NVE equilibration and used NPT for the melting and quenching process following http://dx.doi.org/10.1063/1.4983753. However the resultant amorphous silica also not able to handle the NVE ensemble keeping a stable temperature. My timestep size is 0.5fs and used the SiO.tersoff potential file which comes with LAMMPS.
I have attached my input script (SiO2.in) and the SiO.tersoff files herewith. I'm guessing that my initial atomic positions are the issue here since I have borrowed it from the LAMMPS mailing list. I have also attached the initial structure (SiO2.data lammps data file format) of my system herewith.
Can you please tell me about your procedure of creating amorphous silica, such as the initial crystal structure used, timestep size, whether is it ok to use the SiO.tersoff from LAMMPS or did you used a different potential file. I would be really grateful if you could help me out.
Over the years I have repeatedly encountered the problem that NVT dynamics of simple liquids and solids with a Langevin thermostat do not manage to keep the desired temperature. I have observed this behavior for several atomic and molecular liquids with VASP as well as with ASE. Sometimes this can be fixed by reducing the timestep and/or increasing the coupling constant (within reasonable limits), but in some cases, even this does not help.
My current system is pre-equilibrated liquid pentane at T = 300 K at its experimental volume with all masses set to 10 amu and a semi-empirical GFN0-xTB Hamiltonian. I have tried increasing the coupling constant from 0.02 au (suggested value) to 0.05 au and 0.10 au and decreased the time step from 4 fs to 2 fs and 1 fs, but even after 20 ps of simulation time and a pre-equilibration of 10 ps with an even higher coupling constant the average T of the simulation remains at ~290 K instead of the desired 300 K.
I have made similar observations in countless VASP simulations of atomic liquids and solids (DFT Hamiltonian), so I'm starting to think this is a fundamental problem of the LV thermostat? If I'm not completely mistaken that behavior means that the thermostat can not put energy into the simulation fast enough. But where is the energy going? With such a short time step energy conservation should be really good but obviously it isn't.
What is my misconception, what am I doing wrong, and how can I fix that behavior?
Any help would be greatly appreciated.
Jan
The smaller, the better? What can we benefit from using mini/micro channel heat exchangers in refrigeration and air-conditioning systems? Any thoughts shared here will be much appreciated. The following are my bits for your comments.
1. Compact from high heat transfer area-to-volume ratio (e.g., the ratio ~ 1/d for a cylindrical flow channel while d is the channel diameter)
2. Reducing refrigerant charge from small refrigerant-side volume with small OD tubes
3. Maximising capacity/COP with trade-off between decreasing pressure drop and increasing heat transfer coefficient by effective refrigerant flow distributing/circuiting
4. Air-side heat transfer coefficient increase from enhanced air flow disturbance with small OD tubes and narrow spacing tube banks
5. Low air flow pressure drop from using small OD tubes so both fan power and noise may be decreased
The smaller, the better for heat exchanger fluid flow channel size? This is one of the hot topics with users of our Refriglab cloud eTools ( www.refriglab.com being available for free trials). For developers and designers, an interesting question is how we can benefit more from a single mini/micro channel air coil design.
This post is a follow-up to my previous ones at LinkedIn:
The 3D Taylor-Green vortex problem is a well-established adademic test problem for decaying turbulence. For a careful comparison of two discontinuous Galerkin-FEM for the incompressible
case at Re=1600, I refer to N. Fehn et al in arXiv:1905.00142 (or IJNMF 2019). Results for under-resolved TG flow at higher Re numbers can be found in the Ph.D thesis by P.W. Schroeder "Robustness of high-order divergence-free FEM for incompressible CFD", Göttingen 2019, Sec. 9.1.3. For the inviscid TGV at Re=\infty, one observes for the method without any stabilization for
the fully turbulent flow for t \ge 10 a simple redistribution of kinetic energy., see Fig. 9.14. This unphysical behavior is sometimes called "thermalization" or "white noise".
To the best of my knowledge, the currently best numerical simulation of the incompressible 3D Euler TGV can be found in N. Fehn et al. in arXiv:2007.01656. The authors show that the kinetic energy evolution does not (!) tend towards exact energy conservation which implies an energy dissipation anomaly. The proper representation of the Reynolds stress tensor requires an appropriate numerical dissipation. In my opinion, it would be good to share the experience of other colleagues regarding the given problem and a proper choice of numerical dissipation which does not perturb the divergence-free constraint.
When we derive differential equations for flow, i.e. the mass, momentum, and energy conservations, we use Taylor's series to determine the relationship between the 2 points. Are there no other series that produce a more precise equations?
Dear respective researchers, please give your reply.
Thank you very much.
Kind regards.
Energy conservation is the result of several processes, such as productivity increase in terms of technological progress. However, energy efficiency is measure of energy intensity in a specific process.
Hello Researchers,
Energy is one of the most influential sectors in recent years. So, optimal management of this sector will be of great importance. In your opinion, what will be the energy management issues, in the future?
Arakawa(1966)'s Jacobian(his eq. 46) is a mean of 3 components: J++(eq.36), J+x(eq.37), and Jx+(eq.38), which have different conservation properties. I am trying to show the difference when using different version of Jacobian in the simulation of two dimensional turbulence, which can be formulated as the stream funciton(\psi)-relative vorticity(\zeta) equation:
\frac{\partial \psi}{\partial \t}=-J(\psi,\zeta)
The model was initialized with \zeta(\psi), such that the relative vorticity is a function of the stream funciton and J(\psi,\zeta)=0, therefore the flow field does not change with time. My result shows that energy/enstrophy remains almost conserved for a while but blows up anyway(for the accumulation of round-off error?), no matter which Jacobian implementation was employed, I am confused.
The Fourier-spectral method was emplyed for spatial differencing( so continuous form of J++ , J+x , and Jx+ were used in the code) and I know that the conservation property of Arakawa Jacobian, 1/3*( J++ + J+x + Jx+), should be independent of the sptial differencing technique. So I supposed that 1/3*( J++ + J+x + Jx+) should be better than using any of the 3 alone, in terms of energy/enstrophy conservation. However little difference was observed when different initial condition was used. In the simulation, horizontal diffusion in contained in a wavenumber filter to remove the shot waves beyond 2/3 of the maximum wavenumber. Highly possiblely it is an uneducated question, but would be appreciated if someone can explain.
We know that the energy density of the gravitational field around masses is negative.
This fact is a consequence of the analogy to the electrostatic attraction of different charges. If different charges come closer, the electrostatic field energy becomes converted to kinetic energy. In the electrostatic case this is obvious, because the electric field around both charges becomes weaker.
But in the gravitational case, the situation is just reverted. Approaching masses gain kinetic energy and the surrounding gravitational field becomes stronger. The only possibility, matching to energy conservation, is that the energy density in the gravitational field is negative.
But this fact has consequences. We also know that gravitational waves exist and that they have a positive energy contents. If gravitational waves are pure oscillating gravitational fields, the same fields which surround masses, then their energy content also would be negative. Therefore a gravitational field component, oscillating with normal gravitational fields but with positive energy density must exist.
Further consequences concern the generation of gravitational waves. Large heavy celestial bodies encircling each other generate gravitational waves, which are detectable light years away. The emission of gravitational waves costs kinetic energy. Obviously a mechanism exists, which converts the kinetic energy of moving masses to gravitational waves.
But what happens to the gravitational waves travelling through space? The oscillation amplitude becomes smaller and smaller and the energy density is reduced proportional to the square of the covered distance. What finally remains is a tiny contribution to positive gravitational field energy density.
We then come to the question, is the universe an infinite flat space with giant clouds of galaxy clusters inside or is it a closed S3-sphere. Let us assume it is a closed S3-sphere. In this case all gravitational waves finally would add up to a positive gravitational field energy, surrounding us in the background. In an infinite flat space the gravitational waves irrecoverably would escape together with fast particles and electromagnetic radiation.
What are the consequences of a positive gravitational field density surrounding us? The answer is simple, as long as there are no gradients we would not feel anything. If there are gradients, they cannot be steep, because they would be equalized by a gravitational wave flow, moving with the speed of light. But if there aren’t consequences all the arguments above wouldn’t be relevant.
This leads us to the final considerations. If giant moving masses produce gravitational waves, detectable light years away, tiny moving masses may also produce gravitational waves but with a small amplitude far beyond our detection capabilities. Even quants of electromagnetic radiation then could become a source of gravitational waves. The key point is, that stars contain fast moving particles and a high level of radiation. They therefore must be a considerable source of incoherent non detectable gravitational waves. But this flow actually would lead to a permanent gradient in the density of the positive gravitational field energy in the environment of stars. Dark energy therefore could be the same as the energy density resulting from flows of incoherent gravitational waves out of stars. The influence on galaxy dynamics and the details of the interaction between negative and positive gravitational energy must be investigated.
In general by strict mathematical definition of conservative fields, no magnetic vector field in any case even static can be conservative thus path-independent since it has no zero curl which is necessary for a field to be conservative [1]. In addition all conservative vector fields must be also irrotational (i.e. vortex, spiral). Even if a magnetic or other field special case, is found to be with zero curl that does not mean necessarily that it is conservative if it does not satisfy the condition in 3D space,
F:R3→R3 is continuously differentiable in a simply connected domain W∈R3 and its curl is zero:
Nevertheless, it is a mystery why the static magnetic field of magnet for example exhibits all the effects of a conservative field without having its properties?
No energy is consumed when a single charge particle is introduced forcing it to a circulation where equal amount of potential energy is converted to kinetic energy and vise versa. Energy is conserved thus no real work is done by the field thus conservative in effect!
Therefore a correct answer of time invariant static magnetic fields being conservative or not? Is I believe that they are virtual conservative fields by absence of any better explanation of this phenomenon and contradiction.
What are your thoughts and experience about this phenomenon?
Emmanouil
p.s The above virtual description of static conservative magnetic field begs a definitive better answer I believe and is a mystery proving how much more we have to investigate on this matter of Electromagnetism.
References
As my PhD work, I am working on underwater sensor networks and need a suitable simulator for designing in terms of effective routing and energy conservation.Among all available such as NS2, NS3, OPNET, OMNET, QUALNET, which is the best one to work with?
I am trying to make a smart phone charger by converting the wasted heat while cooking our food using thermoelectric generator (TEG).The main issue is I need to add a 5 V DC cooling fan along with a heat sink in one part of TEG in order to make that part cooler than the other one. If the DC fan is powered from the generated electricity using TEG, then will there be enough remaining electrical energy to charge a smart phone?
Some researchers consider rotation variables as work-conjugate with moments, others think that the displacement derivatives is, and others use semi tangential rotation as work-conjugate to conservative moments
Any explanation or more references?
What you say about, the idea of integration of SPV with an electrolzer and PEM fuel cell, how much energy we will lost?
Is it possible to combine together electrolyzer and fuel cell without external energy source?
As electrolyzer is used to produce hydrogen by splitting water into hydrogen and oxygen by using electricity and hydrogen fuel cell uses hydrogen as a fuel to converts chemical potential energy into electrical energy. And it’s common that people use extra waste energy produced by SPV (solar voltaic system) in electrolysis to produce hydrogen and in the absence of sunlight they use this fuel hydrogen to produce electricity by using a fuel cell. And my question is it possible that electrolyzer and fuel cell work together supply each other electricity and hydrogen fuel? If we already lost energy due to heat and always get less energy by fuel cell than we have spent on electrolysis, so maybe these processes are only for energy storage.
Sorry for my bad English as I didn’t explain a very simple question very well.
SPV, Solar voltaic system
PEM, Proton-exchange membrane
phosphoric acid plant energy conservation and quality control
There are different proofs that the quantum nechanics (QM), more exactly the quantum formalism (that was NEVER contradicted by experiment), does not admit a substructure of particles following continuous trajectories. As two rigorous proofs I recommend my article
and section 5, "Does a quantum objecthave a 'particle' ? ", in my article
Deleted research item The research item mentioned here has been deleted
However, with all my efforts until now, I didn't succeed to prove a stronger statement: that the quantum object, which travels in our apparatus(es) does not possess a weird 'particle' which jumps accross disjoints regions, separated by a space in which the wave-function is null. This problem arises very strongly when we have to do with a wave-function consisting in two or more wave-packets traveling through isolated regions, e.g. : |ψ> = |a> + |b>.
In my last article mentioned above, I used as assumption the idea that a particle cannot do such a jump. i.e. cannot jump from the wave-packet |a> to the wave-packet |b>. The motivation is that an instant jump between two disjoint regions would mean, in a suitable frame of coordinates in movement with respect to the lab, that the particle disappears for a while from the universe. That would contradict the energy conservation, which has to be respected in any frame of coordinates.
Could there be a NO-GO here? Could it be that it is impossible to prove that there is no such weird particle? Could it be that it though exists?
The Hamiltonian function H is defined as the total energy of a system, the sum of kinetic and potential energy. Lagrangian function L is defined as the potential energy subtracted from the kinetic energy.
Both functions are essential in solving for predicted movement in a many bodied problem of celestial mechanics. The Hamiltonian is conserved, while the change of Lagrangian with time is minimized in each interval.
That energy is conserved is intuitive. Minimizing the change of Lagrangian takes a bit of explanation that is usually not given. It has to do with the way the action S is calculated from L. One explanation is that in the nature of objects in a group moving under their combined gravities and individual momentums, the path of least resistance is the one in which the least possible conversion of energy between kinetic and potential occurs. This is the simplified explanation for the non specialist.
It's a bit of mystery why a physical system in vacuum space time would be biased against conversion of energy between kinetic and potential. The Lagrangian is suggesting the potential and kinetic energies compete with each other for control of curvature.
In an extreme high gravity the space curvature is tending to enclose the source in an event horizon, like a concave curvature. The opposite must be a convex curvature with respect to the source of kinetic energy. This difference may be a physical cause of bias against conversion between potential and kinetic energy. It is inconvenient in the mechanisms of stress energy and is avoided when another path is available.
In the present question it is recognized and well known in publications that a Legendre transformation is able to compute the Hamiltonian from the Lagrangian subtracted from the change of Lagrangian with logarithm of velocity, for a fixed location. Maybe some additional character can be deduced of space time and the objects it processes, especially how velocity and acceleration relate H to L. Conventional GRT has no such bias, but classical Celestial Mechanics does.
Why Can The Hamiltonian Be Computed From The Lagrangian?
I have done a couple of calculations with this dispersion corrections and range separated functionals. The complex under study is Cinnamic---DMSO from XRD studies, where the ethylene group is 3.4 Angstroems from the S of DMSO (dimethylsulfoxide). The LMO-EDA ends up with reasonable energies, except for polarization energy that is way out of range
-------------
ALL BASIS SET HARTREE KCAL/MOL
------------- wP57X-D / TZV
ELECTROSTATIC ENERGY ES= 35.155915 22060.69 kCal/mol ??
EXCHANGE ENERGY EX= 0.001502 0.94
REPULSION ENERGY REP= 0.020100 12.61
POLARIZATION ENERGY POL= -35.152773 -22058.72 kCal/mol ??
DFT DISPERSION ENERGY DISP= -0.008141 -5.11
TOTAL INTERACTION ENERGY HF OR DFT E= 0.016604 10.42
However using MP2 I get reasonable energies.
-------------
ALL BASIS SET HARTREE KCAL/MOL
-------------
ELECTROSTATIC ENERGY ES= -0.006687 -4.20
EXCHANGE ENERGY EX= -0.015563 -9.77
REPULSION ENERGY REP= 0.025771 16.17 kCal/mol
POLARIZATION ENERGY POL= -0.002422 -1.52 kCal/mol
MP2 DISPERSION ENERGY DISP= -0.005410 -3.40
TOTAL INTERACTION ENERGY HF OR DFT E= 0.001099 0.69
TOTAL INTERACTION ENERGY MP2 E= -0.004312 -2.71
Can anyone suggest a reason for that? Does anybody have a reference for H-bonds?
Thanks.
Consider the one-particle wave-function
(1) |ψ> = α|a> + β|b>, with |α|2 + |β|2 = 1.
where a and b are eigenvalues of some operator, e.g. path- operator.
Then, the amplitudes of probability α and β are usually defined as giving, theough their absolute square, the probability of obtaining the result a or b. We get a detection on path a with probability |α|2, or on path b with probability |β|2 .
But α and β have an additional phenomenological meaning. For instance, in interference experiments, they determine the contrast of the fringe pattern and the position of the pattern.
Though, my question goes further: in each trial and trial of the experiment, what do the amplitudes α and β? Let the detectors be ion-chambers, and let our particle be electrically charged. The detection is due to the ionization of the gas in the chamber by the charge of the particle. But, which effect have α and β in a given trial of the experiment? These amplitudes are not physical properties of the particle, as charge, energy, linear momentum, etc. Then, how do they influence the material in the detector?
No doubt there is an influence, since along the run of the experiment the detection on path a occurs with probability |α|2, and the detection on path b occurs with the probability |β|2. Therefore, it's due to these amplitudes, that in a given trial of the experiment a detector fires, or remains silent, and only one detector fires. But, how does it work, how does a detector interact with an amplitude?
I want to know the share of coal for producing electricity and steel production
With the Energiewende, the German government pursues a long term energy strategy which aims to transform the energy sector by mid-century. To achieve this it has implemented a comprehensive, long term policy framework which receives broad support across the political spectrum. The United States lacks a similar approach. The reasons are likely manifold. My question is how the character of each country's federalism impacts the long term energy approach of both countries and might help to explain differences?
i am taking an ieee 14 bus system.i consider an outage and i apply demand response on mostly loaded bus.taking 8,4,10 hrs as valley,peak,off peak periods respectively i want the price variations with respect to demand.
Recent research has delved into many aspects of aviation fuel consumption. In some ways the analogy with a personal automobile is apt: you fill up, and you drive until the tank is nearly empty, repeat. The difference for aviation is that the weight of the fuel itself significantly adds to the power needed to fly ("it takes fuel to fly fuel"). So, although the equations and ideas are well known, I would appreciate pointers to industry standard methods. Our goal is analytical shortcuts that would allow this idea to be built into a model of a major airlines network.
