GRAVITATIONAL SELF-REGULARIZATION OF QUANTUM FIELDS AT PLANCK SCALES
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
Loop diagrams with near-Planck energies create a strong external gravitational field, which slows down local processes for distant observers up to their freezing. Since Planck length is the gravitational radius of the system of quanta, the events of this and smaller scale cannot occur in finite world time t and do not contribute to the S-matrix. Consequently, gravitational time dilation, leading to a strong redshift of local frequencies, provides gravitational self-regularization of the loop diagrams. The loop corrections without gravity effects, cut off at Planck energy, give upper bounds for the corrections with gravity effects and this fact leads to simple rules of gravitational regularization. The corrections with quanta of gauge fields and gravitons are small, and the perturbation theory series converge. At pre-Planck energies, one-loop graviton contributions are sufficient, since the multi-loop ones are damped by high degrees of the relation “energy/Planck energy”. Scalar field with power-law growing corrections should be effective field. Non-linearity of fields enhances gravity and get faster freezing, which suppresses the high energy terms. Nonrenormalizable models are finite, but become consistent only when their loop corrections remain small on Planck scale and this occurs in quantum gravity. Gravitationally regularized Extended Standard Model (ESM), including gravitons and Standard Model with effective scalars, is renormalizable and finite, which simplifies its further generalization.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 2, 015, 12 p., 04.11.2021 https://qgph.org/015.html
DOI: http://doi.org/10.9751/QGPH.2-015.7613
pdf: http://qgph.org/1/QGPH2-015-7613.pdf
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
Loop diagrams with near-Planck energies create a strong external gravitational field, which slows down local processes for distant observers up to their freezing. Since Planck length is the gravitational radius of the system of quanta, the events of this and smaller scale cannot occur in finite world time t and do not contribute to the S-matrix. Consequently, gravitational time dilation, leading to a strong redshift of local frequencies, provides gravitational self-regularization of the loop diagrams. The loop corrections without gravity effects, cut off at Planck energy, give upper bounds for the corrections with gravity effects and this fact leads to simple rules of gravitational regularization. The corrections with quanta of gauge fields and gravitons are small, and the perturbation theory series converge. At pre-Planck energies, one-loop graviton contributions are sufficient, since the multi-loop ones are damped by high degrees of the relation “energy/Planck energy”. Scalar field with power-law growing corrections should be effective field. Non-linearity of fields enhances gravity and get faster freezing, which suppresses the high energy terms. Nonrenormalizable models are finite, but become consistent only when their loop corrections remain small on Planck scale and this occurs in quantum gravity. Gravitationally regularized Extended Standard Model (ESM), including gravitons and Standard Model with effective scalars, is renormalizable and finite, which simplifies its further generalization.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 2, 015, 12 p., 04.11.2021 https://qgph.org/015.html
DOI: http://doi.org/10.9751/QGPH.2-015.7613
pdf: http://qgph.org/1/QGPH2-015-7613.pdf
DIFFUSION TREATMENT OF QUANTUM MECHANICS AND ITS CONSEQUENCES
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 2, 013, 7 p., 01.11.2021 https://qgph.org/013.html
DOI: http://doi.org/10.9751/QGPH.2-013.7610
pdf: http://qgph.org/1/QGPH2-013-7610.pdf
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 2, 013, 7 p., 01.11.2021 https://qgph.org/013.html
DOI: http://doi.org/10.9751/QGPH.2-013.7610
pdf: http://qgph.org/1/QGPH2-013-7610.pdf
DIFFUSION GRAVITY AND ITS CONSEQUENCES
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 2, 014, 4 p., 01.11.2021 https://qgph.org/014.html
DOI: http://doi.org/10.9751/QGPH.2-014.7610
pdf: http://qgph.org/1/QGPH2-014-7610.pdf
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 2, 014, 4 p., 01.11.2021 https://qgph.org/014.html
DOI: http://doi.org/10.9751/QGPH.2-014.7610
pdf: http://qgph.org/1/QGPH2-014-7610.pdf
ON SOLUTIONS OF PROBLEMS OF 20th CENTURY PHYSICS AND FOUNDATIONS OF THEORETICAL PHYSICS OF 21st CENTURY
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
During three quarters of 20th century, due to successes of experimental physics, significant progress occurred in the foundations of theoretical physics, and the result of this joint development is the modern physical picture of the world. But in the last quarter of this century, all progress has been reduced to speculative mathematical models without any experimental basis and hope for confirmation. Moreover, the formation of the basic theories of physics, general relativity, quantum mechanics and quantum field theory, still remained incomplete due to ambiguities and a number of fundamental problems in their foundations and important applications. In the previous review article (Zakir, 2020), the main part of these problems was considered and solutions for them, proposed by the author in 2006-2020, were summarized. This review is its revised version, supplemented with several new problems and their solutions found by the author in 2021-2022. Unlike other attempts proceeded from speculative hypotheses, the proposed formulations of basic theories and their applications are based on physical principles following from experimental facts. As a result, the basic theories, which remained successful mathematical models only, finally became consistent physical theories. Problems of a «technical» nature, which have arisen due to deviation from the basic principles, are removed by strict following to these principles. Other problems have been solved by introducing new principles or changing old ones, but also on the basis of facts. Therefore, these solutions, in one form or another, will enter the new physics that is initiated by them. The contours and prospects of the theoretical physics of 21st century are considered. The causes of the crisis in the foundations of theoretical physics of the 20th century and ways to overcome it are discussed. It is shown that the main cause of the crisis was the departure of the scientific community from the methodology and ethics of the natural sciences, and the theoretical physics of 21st century is now being formed as a result of a return to them.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 3, 020, 62 p., 17.04.2022 https://qgph.org/020.html
DOI: http://doi.org/10.9751/QGPH.3-020.7777
pdf: http://qgph.org/1/QGPH3-020-7777.pdf
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
During three quarters of 20th century, due to successes of experimental physics, significant progress occurred in the foundations of theoretical physics, and the result of this joint development is the modern physical picture of the world. But in the last quarter of this century, all progress has been reduced to speculative mathematical models without any experimental basis and hope for confirmation. Moreover, the formation of the basic theories of physics, general relativity, quantum mechanics and quantum field theory, still remained incomplete due to ambiguities and a number of fundamental problems in their foundations and important applications. In the previous review article (Zakir, 2020), the main part of these problems was considered and solutions for them, proposed by the author in 2006-2020, were summarized. This review is its revised version, supplemented with several new problems and their solutions found by the author in 2021-2022. Unlike other attempts proceeded from speculative hypotheses, the proposed formulations of basic theories and their applications are based on physical principles following from experimental facts. As a result, the basic theories, which remained successful mathematical models only, finally became consistent physical theories. Problems of a «technical» nature, which have arisen due to deviation from the basic principles, are removed by strict following to these principles. Other problems have been solved by introducing new principles or changing old ones, but also on the basis of facts. Therefore, these solutions, in one form or another, will enter the new physics that is initiated by them. The contours and prospects of the theoretical physics of 21st century are considered. The causes of the crisis in the foundations of theoretical physics of the 20th century and ways to overcome it are discussed. It is shown that the main cause of the crisis was the departure of the scientific community from the methodology and ethics of the natural sciences, and the theoretical physics of 21st century is now being formed as a result of a return to them.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 3, 020, 62 p., 17.04.2022 https://qgph.org/020.html
DOI: http://doi.org/10.9751/QGPH.3-020.7777
pdf: http://qgph.org/1/QGPH3-020-7777.pdf
METRIC TIME, METRIC ANGLE AND METRIC CALENDAR: DESCRIPTION, ADVANTAGES AND STAGES OF TRANSITION
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
The current systems of units for time and angle, as well as the calendar, are archaic and have many weaknesses, in particular, they are not based on the decimal system, not rational and are unpractical. The article substantiates the need for their gradual replacement with metric time (MT), metric angle (MA) and metric calendar (MC). The basic versions of MT, MA and MC are described, which can be further developed. In them, base units, their multiples and submultiples are introduced as in the metric system, making the values of time and angles decimal numbers, which simplifies data recording and speeds up calculations. The base unit of MT, a decimal second (desecond), is 0.864 times shorter than the SI second and in a day, instead of 86400 seconds, there are 100000 deseconds. 100 deseconds form a milliday (deminute) and 100 millidays form a deciday (dehours). In MC, the day remains the base unit of the calendar time and contains 10 decidays, or 1000 millidays, or 100,000 deseconds. Multiples and submultiples of the time units are formed as decimal powers of a desecond and a day with metric prefixes. Multiple units of a day are decaday (10 days), centiday (100 days), kilo-, mega-, giga- and teradays. The days of our epoch are counted from January 1, 2001. Epochs of history are entered by 100 kilodays, or 274 years (near, middle and early history), by megadays (2.74 thousand years) and ten megadays (27.4 thousand years). Then May 18, 2022 is 7808th day of our epoch, 107808th day of near history and 1007808th day at shifting to megadays. In geology and astronomy, epochs contain gigadays (2.74 million years) and teradays (2.74 billion years). In MA with decimal angle is introduced as an exact analogue of MT, which simplifies data recording and calculations in engineering, geography and astronomy. A full angle (360 degrees) contains 10 zones, a zone has 100 deminute, and a milliday has 100 deseconds. On the sphere there are 10 zones of longitude (meridians) and 5 zones of latitude (parallels), where the latitude of the north pole is 0 and the south pole is 5. MC is based on MT, but decades are divided into two five day weeks, and 100 days (centidays) are divided into 4 months of 25 days. Centidays and months are only numbered and have no names. The year is a non-system unit for accounting for seasonal and traditional dates. Simplicity, rationality, greater precision and quickness at using MT, MA and MC are decisive in science, technology, economics, education and many other areas of society, and therefore a complete or partial transition to them is inevitable. During the transition period, they can be applied individually and in organizations in cases of obvious advantages and efficiency improvements.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 3, 021, 8 p., 24.05.2022 https://qgph.org/021.html
DOI: http://doi.org/10.9751/QGPH.3-021.7814
pdf: http://qgph.org/1/QGPH3-021-7814.pdf
Zahid Zakir
Center for Theoretical Physics and Astrophysics, Tashkent, Uzbekistan. zzakir@qgph.org, ORCID
Abstract
The current systems of units for time and angle, as well as the calendar, are archaic and have many weaknesses, in particular, they are not based on the decimal system, not rational and are unpractical. The article substantiates the need for their gradual replacement with metric time (MT), metric angle (MA) and metric calendar (MC). The basic versions of MT, MA and MC are described, which can be further developed. In them, base units, their multiples and submultiples are introduced as in the metric system, making the values of time and angles decimal numbers, which simplifies data recording and speeds up calculations. The base unit of MT, a decimal second (desecond), is 0.864 times shorter than the SI second and in a day, instead of 86400 seconds, there are 100000 deseconds. 100 deseconds form a milliday (deminute) and 100 millidays form a deciday (dehours). In MC, the day remains the base unit of the calendar time and contains 10 decidays, or 1000 millidays, or 100,000 deseconds. Multiples and submultiples of the time units are formed as decimal powers of a desecond and a day with metric prefixes. Multiple units of a day are decaday (10 days), centiday (100 days), kilo-, mega-, giga- and teradays. The days of our epoch are counted from January 1, 2001. Epochs of history are entered by 100 kilodays, or 274 years (near, middle and early history), by megadays (2.74 thousand years) and ten megadays (27.4 thousand years). Then May 18, 2022 is 7808th day of our epoch, 107808th day of near history and 1007808th day at shifting to megadays. In geology and astronomy, epochs contain gigadays (2.74 million years) and teradays (2.74 billion years). In MA with decimal angle is introduced as an exact analogue of MT, which simplifies data recording and calculations in engineering, geography and astronomy. A full angle (360 degrees) contains 10 zones, a zone has 100 deminute, and a milliday has 100 deseconds. On the sphere there are 10 zones of longitude (meridians) and 5 zones of latitude (parallels), where the latitude of the north pole is 0 and the south pole is 5. MC is based on MT, but decades are divided into two five day weeks, and 100 days (centidays) are divided into 4 months of 25 days. Centidays and months are only numbered and have no names. The year is a non-system unit for accounting for seasonal and traditional dates. Simplicity, rationality, greater precision and quickness at using MT, MA and MC are decisive in science, technology, economics, education and many other areas of society, and therefore a complete or partial transition to them is inevitable. During the transition period, they can be applied individually and in organizations in cases of obvious advantages and efficiency improvements.
QUANTUM AND GRAVITATIONAL PHYSICS
Vol. 3, 021, 8 p., 24.05.2022 https://qgph.org/021.html
DOI: http://doi.org/10.9751/QGPH.3-021.7814
pdf: http://qgph.org/1/QGPH3-021-7814.pdf
A. F. Ioffe "On Physics and Physicists" 1977 (p. 224-230)
In Zurich, and especially when Einstein took the chair of physics at the University of Prague, his creative work developed widely. Then he moved to a specially created and well-paid position of an academician at the Prussian Academy of Sciences in Berlin ... Here Einstein lectured and actively participated in the colloquium at the university. However, as he once told me, the Berlin situation did not satisfy him. The people with whom he had to discuss questions of physics did not live by science, it was only a side detail of their existence.
And what was the scientific thought for Einstein, shows the case, which I want to remember and tell in all details.
During one of my visits to Berlin, Einstein became interested in my research on the mechanical and electrical properties of crystals; he asked me to tell you more about them. I remember that at 3 o'clock in the afternoon I came to him and soon began to present my experiments.
About an hour later his wife came in and asked for Einstein at 5 o'clock. to receive some person who came from Hamburg to get acquainted with the famous scientist. Einstein avoided such meetings and anything that could be in the nature of advertising or emphasize his celebrity. Apparently, he did not find support in his family. So he took me to a nearby park so that we could continue our conversation unhindered. Only when the danger of the meeting had passed did we return to his office.
For about two hours I told everything essential, and then the process of mastering new material for Einstein, exceptional in depth and perseverance, began. This process can be characterized as the organic introduction of new facts into the previously formed unified picture of nature.
Near 8 o'clock. evening, we were called to dinner; but even here the work of thought and the discussion of the topic did not stop, spiritual food continued to be assimilated, and the assimilation of material food took place according to the instructions of the wife - what to take on the fork and when to put it in the mouth. Einstein's attention was far away from the pasta we were treated to. At the end of supper, the work of thought continued; Facts and their interpretation were discussed from new and new sides.
Midnight was approaching, the last train was leaving for Werder, where I lived, near Berlin. I offered to continue the conversation tomorrow or any other day, but I saw that the meaning of my words did not reach Einstein, and did not insist. Finally, at 2 o'clock in the morning, the process ended - everything fell into place, doubts were clarified; one more section was added in the picture of the surrounding world, devoid of internal contradictions, which Einstein created for himself.
Neither I, nor probably the majority of scientists, have ever observed such a prolonged and systematic tension of thought. But for Einstein, this was apparently a common thing. This is how unsolved problems were revealed, how they were resolved or stimulated new ideas.
For many, scientific activity was reduced to the study and solution of those problems or those aspects of them that can be solved. Along with this, perhaps even more fundamental problems remain unexplained, but others will deal with them. For Einstein, there were no particular solutions. The problem is one, and its different sides are only ways to penetrate into what is happening in nature.
In Zurich, and especially when Einstein took the chair of physics at the University of Prague, his creative work developed widely. Then he moved to a specially created and well-paid position of an academician at the Prussian Academy of Sciences in Berlin ... Here Einstein lectured and actively participated in the colloquium at the university. However, as he once told me, the Berlin situation did not satisfy him. The people with whom he had to discuss questions of physics did not live by science, it was only a side detail of their existence.
And what was the scientific thought for Einstein, shows the case, which I want to remember and tell in all details.
During one of my visits to Berlin, Einstein became interested in my research on the mechanical and electrical properties of crystals; he asked me to tell you more about them. I remember that at 3 o'clock in the afternoon I came to him and soon began to present my experiments.
About an hour later his wife came in and asked for Einstein at 5 o'clock. to receive some person who came from Hamburg to get acquainted with the famous scientist. Einstein avoided such meetings and anything that could be in the nature of advertising or emphasize his celebrity. Apparently, he did not find support in his family. So he took me to a nearby park so that we could continue our conversation unhindered. Only when the danger of the meeting had passed did we return to his office.
For about two hours I told everything essential, and then the process of mastering new material for Einstein, exceptional in depth and perseverance, began. This process can be characterized as the organic introduction of new facts into the previously formed unified picture of nature.
Near 8 o'clock. evening, we were called to dinner; but even here the work of thought and the discussion of the topic did not stop, spiritual food continued to be assimilated, and the assimilation of material food took place according to the instructions of the wife - what to take on the fork and when to put it in the mouth. Einstein's attention was far away from the pasta we were treated to. At the end of supper, the work of thought continued; Facts and their interpretation were discussed from new and new sides.
Midnight was approaching, the last train was leaving for Werder, where I lived, near Berlin. I offered to continue the conversation tomorrow or any other day, but I saw that the meaning of my words did not reach Einstein, and did not insist. Finally, at 2 o'clock in the morning, the process ended - everything fell into place, doubts were clarified; one more section was added in the picture of the surrounding world, devoid of internal contradictions, which Einstein created for himself.
Neither I, nor probably the majority of scientists, have ever observed such a prolonged and systematic tension of thought. But for Einstein, this was apparently a common thing. This is how unsolved problems were revealed, how they were resolved or stimulated new ideas.
For many, scientific activity was reduced to the study and solution of those problems or those aspects of them that can be solved. Along with this, perhaps even more fundamental problems remain unexplained, but others will deal with them. For Einstein, there were no particular solutions. The problem is one, and its different sides are only ways to penetrate into what is happening in nature.
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