Dear RG community members, this pedagogical thread is related to the most difficult subject among the different fields that physics uses to describe nature, i.e. the physical kinetics (PK). Physical Kinetics as a subject is defined as a “method to study physical systems involving a huge number of particles out of equilibrium”.
The key role is given by two physical quantities:
- The distribution function f (r, p, t), where r is a vector position, p is a linear momentum and t is the time for the function f which describes a particle in an ensemble.
- The collision or scattering term W (p, p¨) gives the probability of a particle changing its linear momentum from the value p to the value p¨ during the collision.
If the following identity is satisfied for the distribution function df (r, p, t) / d t = 0, then we can directly link PK to the Liouville equation in the case that the distribution function does not depend on time directly. Physics students are tested on that, at the end of an advanced course in classical mechanics, when reading about the Poisson brackets.
However, is important to notice that not all phys. syst. are stationary and not always the identity df /d t = 0 follows, i.e., the distribution function - f is not always time-independent, i.e., f (r, p) is just true for some cases in classical and non-relativistic quantum mechanics, and the time dependence “t” is crucial for the majority of cases in our universe, since is out of equilibrium.
In addition, physical kinetics as a “method to study many-particle systems” involves the knowledge of 4 physics subjects: classical mechanics, electrodynamics, non-relativistic quantum mechanics & statistical mechanics.
The most important fact is that it studies the scattering/collision of particles without linear momentum conservation p, where: the time dependence & the presence of external fields are crucial to study any particular physical phenomena. That means that PK is the natural method to study out of equilibrium processes where the volume of the scattering phase space is not conserved & particles interact/collide with each other.
If the phase scattering space vol is not conserved, then we have the so-called out of equilibrium distribution function which follows the general equation:
df (r, p, t) / d t = W (p,p¨), (1)
where: d/dt = ∂/∂t + r´. ∂/∂r + p´. ∂/∂p, with units of t -1or ω/(2π).
The father of physical kinetics is Prof. Ludwig Eduard Boltzmann (1844 – 1906) [1]. He was able to establish the H theorem which is the basis for the PK subject and also he wrote the main equation (1), i.e., the Boltzmann equation to describe the out of equilibrium dynamics of an ideal gas. r´ & p´ in d/dt are derivatives, p¨ in W is another momentum position
Another physicist who established the first deep understanding and condensed the subject into a book was Prof. Lev Emmanuilovich Gurevich (1904 - 1990). He was the first to point out that the kinetic effects in solids, i.e., metals and semiconductors are determined by the "phonon wind", i.e., the phonon system is in an unbalanced state [2]
Physical kinetics has 3 main approaches:
- The qualitative approach involves the evaluation of several physical magnitudes taking into account the order of magnitude for each of them.
- The second approach is the theoretical approach which involves complicated theoretical solutions of the kinetic equation using different approximations for the scattering integral such as the t approximation. For graduate courses, I follow [8], an excellent textbook by Prof. Frederick Reif. For undergraduate teaching, I followed the brief introduction at the end of Vol V of Berkeley Phys C.
- The numerical approach since most problems involving PK requires extensive numerical and complicated self-consistent calculations.
The fields where PK is useful are many:
- The physics of normal metals and semiconductors out of equilibrium.
- The hydrodynamics of reacting gases & liquids, quantum liquids, and quantum gases at very low temperatures.
- The physics of superconductors, phase transitions, and plasma physics among others.
There is a quantum analog to the classical Boltzmann equation, we ought to mention three cases: the density matrix equation for random fields, the density matrix equation for quantum particles, and the Wigner distribution function. Main graph 1 is adapted from [4] to the English language, LB picture from [7], and LG picture from [3].
Any contributions to this thread are welcome, thank you all.
References:
1. https://www.wikiwand.com/en/Ludwig_Boltzmann
2. Fundamentals of physical kinetics by L. Gurevich. State publishing house of technical and theoretical literature, 1940. pp 242
3. Lev Emmanuilovich Gurevich. Memories of friends, colleagues, and students. Selected Works, by Moisey I. Kaganov et. at (1997) pp 318. ISBN:5-86763-117-6. Publishing house Petersburg Institute of Nuclear Physics. RAS
4. Белиничер В.В. Физическая кинетика. Изд-во НГУ.Новосибирск.1996.
5. Lifshitz E., Pitaevskii L. 1981. Physical Kinetics. Vol. 10, (Pergamon Press).
6. Thorne, K. S. & Blandford, R. D., Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, & Statistical Physics (2017) (Princeton University Press).
7. https://es.wikipedia.org/wiki/Ludwig_Boltzmann
8. Fundamentals of Statistical and Thermal Physics: F. Reif Mc Graw-Hill, 1965
I think it would be useful to distinguish the historical from the logical presentation. Equilibrium means that time translation invariance is a global symmetry; out of equilibrium that it’s a local symmetry. This, in turn, implies that out of equilibrium phenomena are naturally described in the framework of a curved spacetime, which indicates that holography might be the natural context.
Dear Prof. Stam Nicolis . I acknowledge the important point noticed in your post.
I invite you please, to help us with the logical presentation of the subject since I studied physical kinetics, 30 years ago in Moscow following mostly applications to anomalous skin effect and then, in Toronto the problems related to low-temperature transport coefficients and data fitting such as ultrasound attenuation and thermal electronic conductivity.
I wish I could have a course on foundations of physical kinetics, I used to teach at the graduate level the magnificent book by Prof. F. Reif [8]. For the undergraduate level, I used the Berkeley V volume of the same author, the last chapter of V Vol. is a very intuitive introduction to physical kinetics that I like very much.
Of course topics, such as the H theorem, the detailed balancing & the symmetry of the kinetic coefficients were briefly taught in the context of the 60s quantum solid-state physics. There were no more discussions in the courses I taught or took, related to the global symmetries involving not equilibrium processes.
Thank you so much in advance.
Physical kinetics is a research tool where the many particles dynamical model is used as follows:
The states of an N-particles dynamical system correspond to points in the corresponding 6N (3 ri , 3 pi) - dimensional phase space with (i,j) taking x, y & z indices values.
The state of an N-particle statistical system is classically characterized by the N-particle distribution function f(r,p) (in QM it corresponds to the density matrix ρ(.) being now & the operators of observables, they are given in the same 6N-dimensional phase space.
Visually the distribution function f(r,p) gives the mathematical function of the state of an N-particles statistical system.
But the N-particles distribution function is only an intermediate link *. In reality, physical kinetics operates with 1-, 2-, & rarely 3-particle distribution functions f(r,p).
Formally, they are defined as statistically averaged, respectively, over N-1, N-2, and N-3 particles of the N-particles distribution function, but in reality, as solutions of the corresponding “equation of motion” that uses only as an analogy, the model of an N-particles dynamical system.
* Taken from the Russian post with some small modifications related to translations and interpretation.
Foundations of statistical physics and kinetics and their connection with classical mechanics by A. Lipkin *
*https://mipt.ru/education/chair/philosophy/publications/works/lipkin/philsci/statphys.php
The first chapter of kinetic physics is dedicated to gases, 4 physical mechanisms are important:
- The thermal conduction
- The bulk viscosity
- The dynamical viscosity
- The electrical conduction
The 4 cases are of importance for ideal gases and also for gases external fields as in the case of astrophysical gases where hydrogen recombination takes place.
The references for the astrophysical case are within the following works, mostly used for recombining stellar gases:
Article Damping of sound waves by bulk viscosity in reacting gases
Article An Eigenvalue Analysis of Damping in Optical Thin Plasmas
Physical kinetics helps to understand the behavior of conduction electrons in disordered metallic alloys when the inverse of the Fermi wavevector kF-1 ~ a (the red lattice parameter).
However, to understand the picture, the disorder is needed since there could be different compelling behaviors.
A qualitative description in physical kinetics starts always with main two parameters:
ℓ - mean free path
τ -mean free time
ℓ ~ (n σ)-1 & τ ~ (n σ)-1 v-1
where n - is the density of particles, σ - is the scattering cross-section, and v - is the thermal velocity.
See for example the last chapter of Statistical Physics: Berkeley Physics Course, Vol. 5 by Prof. F. Reif which has a marvelous introduction.
Four phenomena* are the basis to start learning physical kinetics and non-equilibrium processes:
- Viscosity which relays in momentum p transport
- Thermal conductivity which relays in energy transport
- Diffusion which relays in the transport of particles
- Conductivity which relays in the transport of charges
* Statistical physics Berkeley physics course —volume V - grant from the National Science Foundation to Educational Services Incorporated by F. Reif Professor of Physics - University of California, Berkeley, McGraw Gill 1965.
The qualitative approach in physical kinetics can also be used to infer the limits where quantum physics plays a role for free neutral particles instead of the classical approach.
I have prepared a slide concerning this issue which is attached to this post:
I have explained in a slide for the young generations the qualitative approach of sound absorption in physical kinetics:
Let us explain self-diffusion in a fashion qualitative way:
We start from the diffusion coefficient in a binary mixture & let us denote the “intrinsic” diffusion coefficient of the 1st ideal gas on a stationary background of the 2nd ideal gas as 𝐷′1
If 𝑗1 = 𝑛1𝑢1 = − 𝑛1𝑢 ′ 1/( 1 + 𝑛1/ 𝑛2) = − 𝑛2 / 𝑛 𝐷′ 1 ∂𝑛1 / ∂𝑥,
Then we have if m1 = m2 that leads to
𝐷′ 1 ~ 𝐷𝑠 ~ √2/3 𝑣av/𝑛𝜎
where self-diffusion is called diffusion in a mixture of identical molecules, note that if all molecules in the system are completely identical (as in an ideal gas), their diffusion at the macroscopic level cannot be observed.
The effect of the pressure in self-diffusion leads to a directed gas flow according to the laws of hydrodynamics:
If we divide an ideal simple gas into two subsystems with concentrations 𝑛1 and 𝑛2, then the condition of mechanical equilibrium in the absence of external forces: 𝑃 = (𝑛1 + 𝑛2) 𝑘B𝑇 = const will mean that ∂𝑛1 / ∂𝑥 = − ∂𝑛2 / ∂𝑥, i.e. the total flux is zero: 𝑗 = 𝑗1 + 𝑗2 = 0.
If a gradient of the total concentration arises in a pure gas, this will not lead to the emergence of a diffusion flow 𝑗 = −𝐷𝑠 ∂𝑛/ ∂𝑥 in some inside partial environment but to the violation of the condition of mechanical equilibrium and the appearance of a pressure gradient ∂𝑃/ ∂𝑥 = 𝑘B𝑇 ∂𝑛/∂𝑥, which causes a directed gas flow according to the laws of hydrodynamics, in a faster way than diffusion itself.
Summary from: Diffusion chapter in a course General physics by P. Popov, Moscow MFTI, 2016
Best Regards.
The qualitative physical kinetics of normal metals is very amazing.
By writing this thread I have learned many things that were taught to me by my former diploma supervisor at the beginning of the 90s, but since I am a refugee and displaced person, I do not have my student notes with me.
For normal metals is always valid that they are quantum objects, so a simple question arises: what makes them be quantum objects?
There is a simple answer, the linear momentum module p ~ ℏ/a with a - the lattice constant.
The kinetic energy E of the electrons in normal metals then is given by the expression:
E ~ p2/me ~ ℏ2/ (m a2) ~ 5 eV >> T (any T such as room temperatures)
but following Dulong Petit law: E ~ T
In this new post, E = ε is the Fermi energy of 1 electron and we will derive the Wiedemann-Franz universal law between the electronic flux heat and the charged current flux, follow the attached file:
Adapted from: Krajnov V.P. 1989, Kachestvennye metody v fizicheskoj kinetike i gidrogazodinamike.
Normal state metals qualitative physical kinetics attached screenshot
CC Eugeniy Beliayev
,Dianela Osorio
In the following slide, I explain the relationship between the Prof. Wigner distribution probability function for one particle in physical kinetics & the one-particle QM density matrix:
Qualitative theory of "thermal conductivity in gases":
Weak inhomogeneity of gases is associated with the presence of a small temperature gradient dT/dx in a gas of identical molecules.
This gradient takes the gas out of the thermodynamic state. It is called the Fourier law and phenomenologically is given by:
q = _ λ d T/ d x (1)
Out of dynamical equilibrium generates a flow of energy q, λ is called thermal conductivity coefficient.
Fourier 1D law contains only the first derivative with respect to x, it is a
a consequence of the weak inhomogeneity of the gas, when the gradient terms
are small in the parameter ℓ/L, where ℓ is the mean free path, and L is a characteristic dimension over which temperature T changes.
Positive thermal energy flow q+ is associated with the flow of n - particles of the gas according to
q+= E(T) i = E(T) n v (2)
where E(T) is the thermal energy of one molecule, i is the heat flow & v is the molecular speed. Next, we compare, the flow (i) balance of the thermal energy when molecules move from left to right and from right to left through a unit area perpendicular to the gradient of T
q ~ n v ℓ d E / d T ~ C v ℓ d T / d x (3)
where C = n d E/d T is the heat capacity per unit volume.
Finally, from (1) and (3) we obtain the qualitative estimate for the heat transfer
thermal conductivity coefficient:
λ ~ C v ℓ ~ n v ℓ ~ 1/σ √ T/M (4)
when obtaining (4) it is used the expression ℓ ~ 1/ n σ that is given at the beginning of the thread for the mean free path ℓ and it is taken into account that the thermal heat capacity C ~ 1.
Adapted from: Krajnov V.P. 1989, Kachestvennye metody v fizicheskoj kinetike i gidrogazodinamike.
Congratulations, and best wishes with your working outs to be supported.
My best regards
Fatema Miah
Thank you so much, Prof. Fatema Miah, I apologize for the late reply, best regards.
P. Contreras,
No need for apology, you are welcome.
Though, your working out is beyond my understandability, in spite, my best wishes with you.
Regards,
Fatema Miah.
Thank you so much, Prof. Fatema Miah
Indeed physical kinetics is considered the hardest topic in physics since it takes into account the evolution in time and in phase space of the distribution function of different sets of particles such as fermions or bosons.
It involves the calculation of the scattering cross-section in non-relativistic quantum mechanics, check the attached slide, please.
Best Regards.
If the Fermi Surface presents peculiarities in 2D or 3D, there can be a singular behavior in some of the kinetic coefficients or in the same mean free path ℓ and scattering lifetime τ.
This can be seen in different cases in the solid-state physics field.
There is a very interesting theory that I guess is a part of physical kinetics, the so-called "Theory of active collisions".
The theory of active collisions (TAC) is one of the first directions in the development of the theory of elementary reactions but it seems to be part of physical kinetics.
Physical conditions that TAC should meet:
1. Molecules have balls shape.
2. In order for an interaction to occur, a collision of molecules is needed.
3. The process occurs only if the collision energy is greater than or equal to a certain value of energy, which is called the activation energy.
This theory is based on two subjects:
The molecular-kinetic theory & the Boltzmann theory.
CC Dianela Osorio
&Eugeniy Beliayev
Prof. Oumar Ndiaye
Thank you very much for following this humble RG adventure.
You are right, physical kinetics is an adventure today in physics, it is a subject where there is no quantization that is not explained by experiments and is a window to the classical world, full of exciting surprises.
Thank you very much on behalf of the old physics teacher school, they were never wrong.
God Bless the Old School of the beginning of the XX century.
My respect to you, for pointing it out.
Physical kinetics is among the topics with more physical intuition.
Unique phenomena observed for particular conditions are of interestest for wide subfields of physics.
Molecular physics and their main two parameters play a fundamental role in the most diverse topics of solid state physics for example.
Soon a new pedagogical paper will appear in this section.
CC Shikhgasan Ramazanov
Yes, Prof. Zachary Knutson
, you are right. Perturbation theory works sometimes, but we must agree that there is not a unique approach to solving the kinetic equation.I apologize for the late reply.
The reason why perturbation does not work always is that there are many physical phenomena that involve processes out of equilibrium with chaoticity and randomness, in addition to.
- Nonlinearity.
- Self consistency.
- Many bodies.
- Scattering involving those many bodies
So sometimes if the problem can be linearized, then perturbation can be used, but sometimes.
Let us see, for example, superconductivity by only considering the T different from the 0 K case (Matsubara frequencies is usually and correctly named) and only taking into account the first term in the zero temperature energy gap (that takes into account self-consistency, or another example is the Vlasov equation in the case of linearization for plasmas is a wonderful example of linearization where perturbation theory applies as you stated.
Best Regards.
Damping of Fermi QP with the reservoir and the kinetic equation, simple derivation, see the attached slide.
Yes, Prof. Zachary Knutson
What is interesting here is that the temporal aspect of weight is also present in the distribution function f(r,p,t)
Thank you for your post. Best Regards.
I want you to discover the applications of this work about physics kinetics. It is an article of a new mechanics method in order to avoid time dilation problems. Here is the link to my work on researchgate:
https://www.researchgate.net/publication/347239549_A_thesis_about_Newtonian_mechanics_rotations_and_about_differential_operators
Thank You, Prof. Akram Louiz for your post and the publication. I will read it.
Best Regards.
The kinetic Physic has arisen in several stages, spanning the 17th century period to the early 20th century. For that raison, taking a deep look to its history is a fundamental way to ensure a more complete view of the whole picture and to perceive the right meaning of each equation involved in this vast field. In fact the historical aspect is so important to distinguish between kinetic physic and the other fields of mechanics and dynamics. All these fields are inter-connected and difference between some of them may be subtle but still exist. In this connection, the velocities distribution function f is a principle feature of the statistical mechanics and not of the kinetic physic, although it is the main quantity in the Boltzmann equation. The real defining ‘mission’ of kinetic theory is not to study how particles are ‘statistically’ distributed in the phase space and over time but rather to calculate the flux of transport (which is function of f) of any physical property, such as mass, momentum, energy, pressure, electrons, bosons, etc. and their rates. The ‘dynamics’ of physical quantities is the keystone and the strength point of the kinetic physics.
Because he had established the fundamental mathematical equation we can admit that the father of physical kinetic is Prof. Ludwig Eduard Boltzmann, but that does not neglect the efforts of others who had provided the elementary and basic kinetic concepts, the first sparks of its appearance. For that, let me say that Prof John Herapath is the grandfather of physical kinetics.
best regards
Thank you so much for your detailed answer, Dr. Donia Salem
Any reference to Prof. John Herapath that you consider important will be appreciated.
So all readers of the thread can follow and read it.
Best Regards.
Physical kinetics means the solution of nonlinear integrodifferential equations.
There are a few methods that allow us to try to solve the main equations, see for example:
Statistical Physics. by Y Klimontovich. Taylor & Francis, 1986, pp. 734.
- First, sorry for not replying sooner.
- Second, participate in this thread gives me great pleasure, especially because it concerns a subject of great interest to me.
- Third, because I am working on this, if you find it useful I can speak about the resolution of the Boltzmann equation by using the Chapman-Enskog method.
- Concerning the references, just google it and you will find several documents that talk about Prof. Herapath. Kindly, it is not fair to suggest one or two specific references because all are good. But in return, allow me to give a brief synopsis;
The story began when scientists of that era (18th century) tried to find a plausible definition of heat. At that time, the most widely accepted theory in that field was the caloric theory, which is now obsolete, according to which heat is considered as a fluid composed of particles that repel each other but are attracted to the particles of ordinary matter. Due to the fact that it had provided valuable physical insight into some aspects of heat, the caloric theory was strongly supported and any idea adduced against it were in general rejected.
The paper of John Herapath, entitled ‘A mathematical inquiry into the causes, laws and principal phenomena of heat, gases, gravitation, etc.’, constitute a serious objection to the caloric theory. This work was rejected by the Royal Society (natural resistance to unfamiliar ideas). Even though this paper was published later in the Annals of Philosophy, this rejection reflected badly on the Herapath’s theory (No recognition from the scientific community). After a good period of time, the ideas of Herapath were finally admitted by scientists and considered as coherent concepts to construct plausible theories and formalisms. This happened only when these ideas were revived and adopted firstly by Joule and then by Clausius, which is one of the four pioneering figures of the Modern Kinetic Physics (Clausius, Maxwell, Van Der Walls and Boltzmann)
All the concepts published by Herr. Herapath are interesting, see attached picture below, especially the following two fundamental notions;
1. Heat is the consequence of particles motion (not a material substance)
2. Molecules moves in gases freely (not vibrating around fixed positions).
- Finally, I kindly invite the participants of this thread, interested ones, to take a look at the history of the kinetic physics; the progress of its theories, even the rejected ones, and all its contributors even those who did not draw profound traces.
Kind Regards, :)
Thank you so much for your interesting contribution to this thread, Prof. Donia Salem
I apologize for all days I has been absent from the platform. Health issues do not allow me to be around as it was before. We will continue the discussion as soon as God allow me to retake my duties.
Best Regards.
A new preprint concerning this thread on unconventional superconductors and its relation to two field of physics:
-Statistical Mechanics and -Nonrelativistic Quantum Mechanics is available in the following link and in RG platform:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4322259
Kind Regards.
Actually, the relativity of Einstein was the lie of the twentieth century that has not been yet defeated despite the two World wars in Europe. Hence, I published a Physics letter about this matter and I explained many facts about this problem of light. I hope that you will read objectively this letter in order to be convinced that the developed countries dare lie to the peoples of the World who are cultivated enough to know. I added in this letter also a remark about the permeability and permittivity of Maxwell equations with a little suggestion. Here is the link :
https://www.researchgate.net/publication/369143082_Physics_letter_Cosmical_observations_and_experiments_against_the_relativistic_explanations_of_the_Doppler_effect_and_the_Gravitational_effect_of_the_light
Dear Doctor
A review of the kinetics and mechanisms of formation of supported-nanoparticle heterogeneous catalysts
Joseph E. Mondloch, Ercan Bayram, Richard G. Finke
Journal of Molecular Catalysis A: Chemical
Volume 355, March 2012, Pages 1-38
"Introduction
Heterogeneous catalysts are used in many important and industrially relevant catalytic reactions such as hydrogenations, catalytic cracking, or naptha reforming; heterogeneous catalysts are also employed in the water–gas shift reaction, the synthesis of ammonia and for ethylene oxidation, to name a few additional reactions [1], [2], [3], [4]. Often these heterogeneous catalysts take the form of nanoparticles supported on high-surface-area materials [3], [5]. Key properties inherent to these supported-nanoparticle catalysts are known to affect greatly the resultant catalytic performance [6], [7]. For example, the size [8], [9], [10], structure [11], [12], [13] and the lesser investigated, but crucial, surface composition [14], [15], [16], [17] of the supported-nanoparticles can influence the catalytic selectivity [6], [13], [18], [19], activity [8], [20] and lifetime [21]. Hence, in order to exploit these key catalytic properties for catalysis, uniform catalysts of the appropriate size, structure and composition are needed [22], [23].Unfortunately, as Schlögl has recently noted [7], “catalysts are currently prepared rather than synthesized” so that rationally guided syntheses of the desired size, structure and compositionally controlled supported-nanoparticle catalysts are generally lacking. One main reason for this gap is the relatively poor understanding of the mechanism(s) that govern the formation of these supported-nanoparticle heterogeneous catalysts. In particular, kinetic studies are often lacking, kinetics being one of the general tools crucial in elucidating reliable reaction mechanisms [24], [25], [26], [27], [28].
Abstract
Nanoparticles supported on high surface area materials are commonly used in many industrially relevant catalytic reactions. This review examines the existing literature of the mechanisms of formation of practical, non-ultra high vacuum, supported-nanoparticle heterogeneous catalysts. Specifically, this review includes: (i) a brief overview of the synthesis of supported-nanoparticles, (ii) an overview of the physical methods for following the kinetics of formation of supported-nanoparticles, and then (iii) a summary of the kinetic and mechanistic studies of the formation of supported nanoparticle catalysts, performed under the traditional synthetic conditions of the gas–solid interface. This review then also discusses (iv) the synthesis, (v) physical methods, and (vi) the extant kinetic and mechanistic studies under the less traditional, less examined conditions of a liquid–solid system. A summary of the main insights from each section of the review is also given. Overall, surprisingly little is known about the mechanism(s) of formation of the desired size, shape and compositionally controlled supported-nanoparticle catalysts."
Thank you so much for the contribution to this thread, Dear Prof. Sundus F Hantoosh
Indeed the kinetics of the physical chemistry subject is part of the physical kinetics. Rate equation and son on.
Kind Regards, and I apologize for the delay in replying to your interesting post.
Thank you Dr. Pedro for this thread Physical kinetics, also known as chemical kinetics, is the branch of physical chemistry that deals with the study of the rates of chemical reactions and the factors that influence these rates. It involves the investigation of how reactants transform into products over time, as well as the mechanisms and pathways through which these transformations occur. Physical kinetics is essential in understanding and controlling chemical processes, and it plays a crucial role in various fields, including chemistry, biology, and material science.
Dear Doctor
Go To
Physical Kinetics, Relativism and Nonlocal Physics
Boris V. Alexeev MIREA, Russian State Technological University, Moscow, Russia. DOI: 10.4236/jamp.2022.101007
"Final Remarks and Conclusions
The following results cannot be obtained on the elementary level of consideration. The corresponding strict results can be found in monographs [1] [2] [3] [4]. Nevertheless here I formulate some significant results without additional explanations. What solutions do the equations of Unified Theory (UT, Unified Theory of Transport Processes) lead to?
Let’s formulate conclusions from the solutions at a qualitative level:
1) Nonlocal physics returns 96% of matter and energy to humanity. Therefore, classical local physics of dissipative processes is a deep special case of nonlocal physics. Let us note the fundamentally important stages in the development of nonlocal physics.
In 1926, the brilliant article by Madelung, which I have repeatedly quoted, appeared which turned Schrödinger’s quantum postulate into hydrodynamics. In other words, the evolution of a single bound electron turned out to be possible to interpret as some effective flow.
In 1964, John Stuart Bell [16] established that local statistical theories of dissipative processes are incorrect in principle.
In 2007, B.V. Alexeev established [17] [18] that the Schrödinger equation and its hydrodynamic Madelung form are a consequence of nonlocal kinetic equations as a deep special case of nonlocal equations. This meant that the generalized physical kinetics I had created earlier was extended to quantum physics in the form of quantum hydrodynamics.
2) Nonlocal quantum hydrodynamics leads to non-collapsing solitons and, as a consequence, to the theory of high-temperature superconductivity [19] [20].
3) The developed nonlocal unified statistical theory of dissipative structures has a hydrodynamic shape defined by the genesis of Generalized Hydrodynamic Equations (GHE). GHE are extremely important for astrophysics special cases when density ρ→0�→0 (the initial stage of evolution of the Universe, the Big Bang; transport processes in physical vacuum) and when density ρ→∞�→∞ (evolution of the black hole). Both limiting cases have no physical or mathematical meaning in “classical” hydrodynamics including General Relativity
4) The birth of the Universe is accompanied by an explosion of the primary vacuum (PV)—a medium that does not contain matter, electromagnetic and gravitational fields. A small disturbance is enough for an explosion. From a mathematical point of view, there is Hadamard instability. At the same time, there is a well-known effect in mathematics—the smaller the disturbance, the greater the efficiency of the explosion.
5) The primary vacuum is the initial state of the Physical Vacuum (PV). Until now, we could claim that Physical Space (PS) consists of matter and a field. Now we are talking about the existence of the trinity: Matter, Field and Physical Vacuum. All components of the PS can experience mutual transformations.
6) The set of dynamic characteristics of the initial stage of the evolution of the PV contains the speed, the energy of the unit volume of the PV and the force acting on the unit volume of the PV.
7) The explosion “works” in the anti-gravity mode, since there is no substance yet. In the terminology currently in use, PV energy is dark energy.
8) After the birth of matter and gravity, the Hubble expansion mode appears. From the point of view of solving the UT equations, the Hubble expansion is the gravitational self-capture of matter under the conditions of a small influence of central gravitational masses. The Hubble phenomenon is characteristic not only as a dynamic effect characteristic of the entire Universe, but also for individual galactic systems—“Hubble boxes”, in particular, for the Local Group—the system of galaxies to which our Milky Way belongs.
9) The classical Hubble expansion is characterized by a proportional increase in the expansion velocity of the group depending on the distance from the main center of gravity. The proportionality coefficient is the Hubble constant (H0). Naturally, this means that the expansion occurs with acceleration even at a constant coefficient H0. However, recent observations have established (S. Perlmutter, A. Riess (USA) and B. Schmidt (Australia); Nobel Prize 2011) that the expansion of the Universe at this stage of evolution is accompanied by an increase H0.
10) Is this mode unique? There are reasons to give a negative answer. Astronomical observations of the evolution of a Local Group of galaxies can be interpreted as the scattering of Dwarf Galaxies in the mode of the coefficient H0 increasing with distance.
11) There is a feeling that the role of the Creator is reduced to the introduction of the initial disturbance into the PV.
12) But is it possible to avoid the concept of initial perturbation in principle? Generally speaking, it is possible. Solving the UT equations in the Hubble expansion mode allows you to calculate the Hubble coefficient at the same time. It turns out that there really are modes when the Hubble coefficient increases. But there are modes when it decreases and even becomes negative. The latter means that the universe is beginning to “collapse”.
13) The regime of the pulsating Universe no longer requires additional intervention, if we recognize that the primary vacuum has always existed, and explosions are caused by random fluctuations of the PV, which are inherent in any dynamical system. It is possible that there are local volumes of PV, the dynamics of which resembles the dynamics of Hubble boxes.
14) The life of our universe is conditioned by the existence of world constants, among which are the fine structure constant, Planck constant, Boltzmann constant. Other constants represent a completely different evolution of the universe in a specific dynamic scenario of the pulsation cycle. The discovery of voids means that other explosions of the physical vacuum are possible, leading to other world constants and parallel universes.
15) The birth of our universe with a specific set of world constants is the product of a specific fluctuation in the cycle. From this point of view, we can say that we were lucky that we got into the “right fluctuation”.
16) The orbital motion of astronomical objects according to the Vera Rubin model (and not according to Kepler) is a direct consequence (an exact analytical result) of non-local physics. I once again suggest that NASA measure the orbital velocity of motion inside one of Saturn’s rings. The internal orbital velocity of the particles in the ring must be constant (that is, in accordance with Vera Rubin’s model)."
Dear Profs. Manal F Al-Khakani and Sundus F Hantoosh
Thank you so much for your interesting and detailed contributions to this thread.
Prof. Manal F Al-Khakani yes, in Theoretical Chemistry the term is coined as Chemical kinetics and has to be with the interesting fields such as combustion and many others. In combustion for example is well know the stoichiometry methane combustion that has more than 200 reaccions before it produces NO.
Thanks for your contribution, and I apologize for the late reply.
Prof. Sundus F Hantoosh Thank you so much for the detailed answer. Yes, it also has to be with the primary processes such as the Zeldovich mechanism, who studied physical kinetics and also the Theoretical Astrophysic field where chemical reactions play a fundamental role.
Thanks for your contribution, and I apologize for the late reply.
Thanks for your contribution, and I apologize for the late reply.
Kind Regards.
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