meatbag
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I wanted to start a thread about this topic. The following is an excerpt from the book "Matter and Man"
-
First of all, the concept of the recycling evolution of matter is utterly insolvent. According to this theory, stars form out of nebulae of gas and dust, the they cool, then dissipated energy condenses in some unknown way, stars collide, explode and turn back into gas and dust, and it all starts over again. Today we can say that if such a recycling of matter does occur – and on a certain scale it does – it is not dominant or determinative in the evolution of matter on the universal scale.
There is also the “non-recycling” theory of the “heat-death of the universe”. Imagine two cylinders of gas, one hot and one cold. If we mix the two gases the mixture will be neither hot nor cold. It will be warm, the temperature being the average of the two extremes. This is obvious, just as it is obvious that one cannot separate the gases into the cooler and hotter ones again and that it is impossible for one side of a room to be cooler than the other without external interference. In natural processes temperature eventually tends to level off. Formulation of this principle gave rise to a question of interest to physicists and philosophers alike.
If all temperatures tend to level off, why do high-temperature stars exist alongside cold cosmic bodies? Why are the temperature extremes of the universe so great? Is this proof of a primeval impulse which brought huge sources of concentrated energy into being, and of the fact that now a leveling off is taking place? The first attempt to answer this question was the famous physicist Ludwig Boltzmann. Boltzmann studied the kinetic theory of gases and matter and formulated the basic principles of gas dynamics and kinetics. He established that the molecules comprising a gas have different velocities. Most of them move with more or less the same speed, which determines the temperature of the gas, but at each instant there are always present some relatively slow- and fast-moving molecules.
Imagine a gas consisting of only ten molecules, five moving faster than the mean, and five slower. With so few molecules it is quit possible that at some moment all the fast molecules will gather on one side of the room and all the slow ones on the other. The probability, though not very great, is not altogether impossible. This means that motion in the gas can take place not only in the direction of a leveling off of the temperature but also in the direction of creating a temperature drop. Natural processes opposed to the leveling off of temperature, process in which temperature differences develop, are due to statistical fluctuation phenomena. Undoubtedly, small fluctuations occur continually in gases and one could always find small regions and groups of molecules where the temperature is above the average.
Boltzmann suggested that the observable universe represents a gigantic fluctuation within the greater universe , which faces the prospect of heat-death, that the observable universe is a “group of molecules” with a momentarily “higher-than-average” temperature. Boltzmann's conception was of a progressive nature, but it did not win many adherents. It was debated heatedly, but the arguing sides overlooked one important consideration: the investigations of experts in gas kinetics deal with the microcosm of gas molecules. But the universe is not all made up of hydrogen molecules – it contains many different molecules and atoms. Can a conclusion drawn from the study of gases be extended to the whole of the universe? Of course not, and for that reason Boltzmann’s ideas and the conclusions of the exponents of his theory were erroneous.
Only Einstein (Albert) was right when he wrote, without it laying claim to the comprehensiveness of his investigations, that it was hardly reasonable to extend the laws of finite matter to the infinite universe. Investigations of the finite universe yielding general ideas about matter and the laws of motion can be applied to develop very general and approximate premises concerning processes involving the infinite universe.
Is the pessimistic conclusion concerning the inevitable “heat-death” of the universe at all valid? There is a branch of mathematics, known as set theory, developed by the 19th-century German mathematician George Cantor. It studies sets of infinite numbers of particle, integers, letters, or other elements. Being a theory which attempts to penetrate the laws of infinity, it draws some interesting conclusions which, if applied to physical laws, might be able to answer the question as to why the universe appears to be eternally unbalanced. These conclusions are very complicated and can therefore be considered only in the most simplified form.
We have noted on several occasions that the greater universe is non-homogeneous in composition and contains an infinite number of infinitely diverse particles. It contains interstellar gas consisting of ionized atoms of hydrogen with admixtures of atoms of other elements, comparatively small-sized lumps of solid matter like meteoroids and asteroids, large lumps of planets, giant spheres of plasma- stars, stellar systems, galaxies, and vast domains like the observable universe which are described by Einstein's formulas. Each such formation contains a virtually infinite set of “lower” elements: asteroids are made of molecules, the universe of galaxies, etc. For the energy of the infinite elements comprising the universe to level off, all of them, from the last ionized atom of interstellar gas to the greatest galaxy, must interact with an exchange of energy.
One of the conclusion of set theory states that, even given an infinite period of time, all of these infinite interactions can never take place. (The conclusions arising from an analysis of this problem were published in 1949 by one when “someone” dredged the sea to heap up the mountain of energy. This “someone” must occasionally wind the clock of the universe to keep it ticking.
A hundred years after Newton, the French scientist Laplace outlines to Napoleon the gist of his materialistic hypothesis of the origin of the solar system – a hypothesis that explained the “initial impulse” which Newton could not explain.
“and Where does God fit in?” Napoleon asked.
“Sire,” Laplace replied, “I had no need for that hypothesis.”
It took less than a hundred years to refute the exponents of the “heat-death” theory.
After the enunciation of the general theory of relativity, the theory of the so-called pulsating universe came into vogue. According to this theory the universe periodically compresses and expands. In the course of each pulse the galaxies, stars and planets develop. The energy released at the beginning of each expansion is gradually dissipated in overcoming the common gravitational field of all the masses filling the universe. When it is expended complete contraction beings.
Every year spring comes with sunshine and flowers to replace the winter frosts. Then comes summer, the sodden mists of autumn, and again the white blanket of winter covers the land. This is the seasonal cycle, which repeats itself over and over again just as the earth circles the sun in its orbit again and again. Yet no cycle is an exact repetition of the previous one. Each new spring is in some way different from the one before. The seedling in a young grove have grown taller,. A might old tree has decayed and topples over. Erosion has undermined an overhanging cliff, and sandbars in a river mouth have grown bigger. These are doubtlessly trifling events in the great cycles of nature, but the accumulation of such trifles yields evolution. Mountain slides do not change the mountain landscape very much, but geologists know that whole mountain ranges have been worn down by wind and water, which leave hardly a trace of their work from day to day.
The circles of seasonal changes is actually broke: it is rather a spiral, with repetitions always occurring on a higher and higher level. Even the earth;s orbit around the sun is a closed ellipse only when we do not take into account the sun’s motion. The sun itself participates in the rotation of the milky way and in the milky ways flight through the universe. The resultant motion of the earth is complex indeed. It stands to reason, then, that even in a pulsating universe. The resultant motion of the earth is complex indeed. It stands to reason, then, that even in a pulsating universe no two pulses can be absolutely identical. It is impossible for all processes to be reversible. In the long run changes in quantity must lead to to changes in kind and a transition to a new state. Can we at least attempt to imagine what such transitions could lead to?
Before answering this question let us return from the boundless expanses of the universe to the microcosm of elementary particles. The atom was once considered the smallest, indivisible particle of matter ( the word “atom” means “indivisible” in Greek). Then it was found that the atom consists of a nucleus with electrons revolving around it, and these were declared indivisible. Today, in the age of nuclear energy, a schoolchild knows that the atomic nucleus is a complex structure which can be split and transformed. An electron colliding with a positron (anti-electron) turns into radiation whose energy and mass, in accordance with Einstein’s principle of equivalence, must correspond to the energy and mass of the colliding particles. In any case, the electron is no longer regarded as a tiny solid ball incapable of further division. As Lenin wrote, the electron is inexhaustible.
Like protons, neutrons and other “elementary” particles, the electron undoubtedly has a complex structure. What we call “elementary” particles are probably some highly compressed substance which can never remain at rest and pulsates incessantly. At least, this conception does not contradict any of the known facts. In such pulsations an elementary particles interacts with the surrounding field. Each expansion “pushes” the field aside, and this causes an expenditure of the energy which is responsible for the field. Does the energy flow back to the particle when it compresses? Probably not always, and the pulsating particles gradually dissipates energy. This means that it loses mass, that is to say, the mass of an elementary particles is not necessarily constant.
Today, at the present stage in the evolution of matter, an electron’s mass equals 9x10-28 gram, and a proton weighs” 1,7x10-24 gram. Ten thousand million years ago they were heavier, and ten thousand million years hence all the elementary particles in the inverse may “weigh” less than today. The change in mass could affect other properties of elementary particles. This microcosmic process would suggest the non-repetitive evolution of matter in the universe.
Does the concept of pulsating elementary particles agree with the hydrodynamic theory of gravitation mentioned before? An answer may be found in a theoretical experiment described by Nikolai Zhukovsky, the “father of Russian aviation”. Imagine two spheres immersed in an incomprehensible fluid. If the spheres are made to pulsate synchronously, so that the maximum volume of one corresponds to the maximum volume of the other, they will gravitate towards each other. Moreover, the law of attraction will be expressed by a formula identical to Newton’s formula of universal gravitation: the force will be proportional to the energies “radiated” by the spheres and inversely proportional to the square of the distance between them. If the pulsation is not “in step” and the maximum volume of one corresponds to the minimum volume of the other, they will repel each other with a force given by the same formula.
Obviously, the analogy between pulsating elementary particles in a gravitational field and pulsating spheres in a fluid is remote. But it does offer an idea of the hydrodynamic theory of gravitation. Possibly in the course of this pulsation the elementary particles eject elementary packets of energy in the form of gravitons.
Although the mass of elementary particles appears to decrease, the latest findings of theory indicate that the total mass and energy in our region of the universe in constant. Along with the creation of gravitons there takes place a continuous creation of new elementary particles out of “old” gravitons at an estimated rate of 10-45 gram per cubic centimeter per second. This is accompanied by a change in the so-called world of constants: the gravitational “constant” increases, the elementary charge and Planck’s “constant” decrease. Only the speed of light does not change.
Slowly but surely matter changes from one form into another. A steady accumulation of quantitative changes is taking place which must inevitably develop into a qualitative leap. What kind? With out present knowledge we are unable to say. In any case it will mean an end of out three-dimensional closed universe. It may may represent merely the completion of one turn of the evolutionary spiral on an incredibly great scale. Be that as it may, but it will also represent a new stage in the evolution of matter, eternal and indestructible.
-
This is a discussion of the Set theory from the same section of the book:
In so far as in investigating the general state of matter in the universe one must deal with an infinite variety of particles, a knowledge of some of the most general properties of certain infinite sets is essential.
The simplest infinite set is the set of positive integers 0,1,2,3,4,5..n where n tends to infinity. This is a so called countable set; 1,10,100,1000,10000,100000 is also countable and that the numbers of the first and second set can be put into one to one correspondence for the numbers of the second set can be written down in the form 100, 101, 102, 103, 104 105, etc. This is one of the paradoxes of infinity. A countable infinity is the weakest of infinities.
For example, an infinite set of positive integers cannot be used to count all of the points on a straight line segment. A set of points on any section of a straight line segment, or on an infinite straight line, or in the whole of space, is non-countable, it constitutes a continuum which cannot be exhausted by any counting operations. This is known as “the power of the continuum” or cardinality.
In particular, it is easy to show that in fact to every point of a line segment there corresponds one and only one point on an infinite straight line. Consider a semi-circle the length of which is equal to the length of a given line segment. From the center of the semicircle project all of its points on an infinite straight line passing below it. You will readily perceive the truth of the foregoing statement made above. We can make use of the concepts of countable sets and cardinality to investigate the most general laws of behavior of the infinite set of particles of matter in the infinite universe.
Divide the infinite universe into a countable set of finite domains. Evidently each finite domain contains a finite number of material particles. To take into account the interaction of matter with the field for which it’s responsible, (electromagnetic and gravitational) assume, proceeding from the quantum theory of matter, that a finite domain of the universe contains a finite number of quanta. For the purpose of our reasoning we can also assume that some elementary quanta can be as small as we wish-not in the sense that quantum is regarded as “point-energy” but in the sense that a countable set of such quanta occupies a finite volume and carries a finite energy.
Thus, in our finite volume of space there may even be, not a finite, but a countable set of elementary particles. Hence, in all space there will be a countable set of elementary particles.
Evidently, a set of interactions between the particles within each finite column of space in a finite time interval will be countable, if the particles make up a countable set, and finite, if the particles make up a finite set. In the whole of infinite space there will occur in a finite time interval (for both assumptions) a countable set of interactions (by interaction we understand any process involving two particles which result in a change of their masses or energies).
In so far as any infinite time interval can be divided into a countable set of finite intervals, a countable set of finite intervals, a countable set of interactions will occur in the course of an infinite time interval in the whole of the universe.
A set of all possible interactions for a countable set of particles represents a set of all the subsets of the given countable set, that is, this set of all possible interactions will possess cardinality.
The continuum of possible interactions (states) cannot be exhausted by a countable set of real interactions in any infinite time interval.
Assume (thought it is not so) that the whole of the universe is filled with particles of one class, molecules, for instance. Then the set of all possible states possess cardinality. But, the set of independent (un-repetitive) states would be countable, hence in the infinite life-span of the universe it would already have achieved equilibrium, or we must assume that we live in a vast unbalanced domain of the universe which formed as a result of a highly improbable process of fluctuation. This is the process in which one could expect all the fast molecules in a region of space to gather at one side, and all the slow molecules at the other. For a small number of molecules this may occur fairly frequently, but for a great number the probability of such a process is vanishingly small.
To be sure, we could also assume that the universe was “created” a finite time ago, but this is even less likely. The universe, of course, does not consist of one class of molecules, and we must therefore conclude that there is always present in the universe a countable set of classes of different “particles” (elements) such that every “particle” of one class may include “particles” of lower classes. By “particle” we can understand any autonomous formation: a photon, molecule, star, stellar system, etc. We can assume that the infinite diversity of classes of different “particles” is a consequence of the interaction of matter with the fields for which its responsible. Every “particle” may exist in the universe in any (apparently infinite) number.
A set of all possible interactions of the whole diversity of “particles” without any repetition of state processes cardinality. Hence, the totality of interactions of different formations in the universe cannot be exhausted by any counting operations, which leads to the non-cyclic development of matter and this makes possible its infinite development.
–------------------------------------------------------------------------------------------------------------------------------
The following are excerpts from the scientist NA Kozyrev on the issue:
In the universe, however, there are no signs of the degradation which is described in the second law of thermodynamics. Stars die and are born again. The universe sparkles with inexhaustible variety. In it no one finds traces of an upcoming thermal and radiation death. Apparently here is where the basic contradiction lies – A deep contradiction which may not be explained away through a reference to non-applicability of the second law of thermodynamics to the infinity of the universe. The fact is that not only separate stellar bodies but whole systems are isolated from each other to a degree that they may be regarded as closed systems, for all practical purposes. (Usually the second law is applied only to closed systems) For them the thermal death could visibly draw nearer before any aid could come from outside. Such sytems, in a state of degradation, should prevail in the universe, and yet they're almost non-existent.
Time doesn’t propagate (for example like EM-waves) but appears at once all over the Universe. That is why the connection through time must be an instantaneous one. So it’s possible to observe some phenomena of very far astronomical bodies in real time, without delay. This perspective does not contradict the special theory of relativity because when we have instantaneous connection through time, there are not movements of material objects.
-Kozeryv
-
First of all, the concept of the recycling evolution of matter is utterly insolvent. According to this theory, stars form out of nebulae of gas and dust, the they cool, then dissipated energy condenses in some unknown way, stars collide, explode and turn back into gas and dust, and it all starts over again. Today we can say that if such a recycling of matter does occur – and on a certain scale it does – it is not dominant or determinative in the evolution of matter on the universal scale.
There is also the “non-recycling” theory of the “heat-death of the universe”. Imagine two cylinders of gas, one hot and one cold. If we mix the two gases the mixture will be neither hot nor cold. It will be warm, the temperature being the average of the two extremes. This is obvious, just as it is obvious that one cannot separate the gases into the cooler and hotter ones again and that it is impossible for one side of a room to be cooler than the other without external interference. In natural processes temperature eventually tends to level off. Formulation of this principle gave rise to a question of interest to physicists and philosophers alike.
If all temperatures tend to level off, why do high-temperature stars exist alongside cold cosmic bodies? Why are the temperature extremes of the universe so great? Is this proof of a primeval impulse which brought huge sources of concentrated energy into being, and of the fact that now a leveling off is taking place? The first attempt to answer this question was the famous physicist Ludwig Boltzmann. Boltzmann studied the kinetic theory of gases and matter and formulated the basic principles of gas dynamics and kinetics. He established that the molecules comprising a gas have different velocities. Most of them move with more or less the same speed, which determines the temperature of the gas, but at each instant there are always present some relatively slow- and fast-moving molecules.
Imagine a gas consisting of only ten molecules, five moving faster than the mean, and five slower. With so few molecules it is quit possible that at some moment all the fast molecules will gather on one side of the room and all the slow ones on the other. The probability, though not very great, is not altogether impossible. This means that motion in the gas can take place not only in the direction of a leveling off of the temperature but also in the direction of creating a temperature drop. Natural processes opposed to the leveling off of temperature, process in which temperature differences develop, are due to statistical fluctuation phenomena. Undoubtedly, small fluctuations occur continually in gases and one could always find small regions and groups of molecules where the temperature is above the average.
Boltzmann suggested that the observable universe represents a gigantic fluctuation within the greater universe , which faces the prospect of heat-death, that the observable universe is a “group of molecules” with a momentarily “higher-than-average” temperature. Boltzmann's conception was of a progressive nature, but it did not win many adherents. It was debated heatedly, but the arguing sides overlooked one important consideration: the investigations of experts in gas kinetics deal with the microcosm of gas molecules. But the universe is not all made up of hydrogen molecules – it contains many different molecules and atoms. Can a conclusion drawn from the study of gases be extended to the whole of the universe? Of course not, and for that reason Boltzmann’s ideas and the conclusions of the exponents of his theory were erroneous.
Only Einstein (Albert) was right when he wrote, without it laying claim to the comprehensiveness of his investigations, that it was hardly reasonable to extend the laws of finite matter to the infinite universe. Investigations of the finite universe yielding general ideas about matter and the laws of motion can be applied to develop very general and approximate premises concerning processes involving the infinite universe.
Is the pessimistic conclusion concerning the inevitable “heat-death” of the universe at all valid? There is a branch of mathematics, known as set theory, developed by the 19th-century German mathematician George Cantor. It studies sets of infinite numbers of particle, integers, letters, or other elements. Being a theory which attempts to penetrate the laws of infinity, it draws some interesting conclusions which, if applied to physical laws, might be able to answer the question as to why the universe appears to be eternally unbalanced. These conclusions are very complicated and can therefore be considered only in the most simplified form.
We have noted on several occasions that the greater universe is non-homogeneous in composition and contains an infinite number of infinitely diverse particles. It contains interstellar gas consisting of ionized atoms of hydrogen with admixtures of atoms of other elements, comparatively small-sized lumps of solid matter like meteoroids and asteroids, large lumps of planets, giant spheres of plasma- stars, stellar systems, galaxies, and vast domains like the observable universe which are described by Einstein's formulas. Each such formation contains a virtually infinite set of “lower” elements: asteroids are made of molecules, the universe of galaxies, etc. For the energy of the infinite elements comprising the universe to level off, all of them, from the last ionized atom of interstellar gas to the greatest galaxy, must interact with an exchange of energy.
One of the conclusion of set theory states that, even given an infinite period of time, all of these infinite interactions can never take place. (The conclusions arising from an analysis of this problem were published in 1949 by one when “someone” dredged the sea to heap up the mountain of energy. This “someone” must occasionally wind the clock of the universe to keep it ticking.
A hundred years after Newton, the French scientist Laplace outlines to Napoleon the gist of his materialistic hypothesis of the origin of the solar system – a hypothesis that explained the “initial impulse” which Newton could not explain.
“and Where does God fit in?” Napoleon asked.
“Sire,” Laplace replied, “I had no need for that hypothesis.”
It took less than a hundred years to refute the exponents of the “heat-death” theory.
After the enunciation of the general theory of relativity, the theory of the so-called pulsating universe came into vogue. According to this theory the universe periodically compresses and expands. In the course of each pulse the galaxies, stars and planets develop. The energy released at the beginning of each expansion is gradually dissipated in overcoming the common gravitational field of all the masses filling the universe. When it is expended complete contraction beings.
Every year spring comes with sunshine and flowers to replace the winter frosts. Then comes summer, the sodden mists of autumn, and again the white blanket of winter covers the land. This is the seasonal cycle, which repeats itself over and over again just as the earth circles the sun in its orbit again and again. Yet no cycle is an exact repetition of the previous one. Each new spring is in some way different from the one before. The seedling in a young grove have grown taller,. A might old tree has decayed and topples over. Erosion has undermined an overhanging cliff, and sandbars in a river mouth have grown bigger. These are doubtlessly trifling events in the great cycles of nature, but the accumulation of such trifles yields evolution. Mountain slides do not change the mountain landscape very much, but geologists know that whole mountain ranges have been worn down by wind and water, which leave hardly a trace of their work from day to day.
The circles of seasonal changes is actually broke: it is rather a spiral, with repetitions always occurring on a higher and higher level. Even the earth;s orbit around the sun is a closed ellipse only when we do not take into account the sun’s motion. The sun itself participates in the rotation of the milky way and in the milky ways flight through the universe. The resultant motion of the earth is complex indeed. It stands to reason, then, that even in a pulsating universe. The resultant motion of the earth is complex indeed. It stands to reason, then, that even in a pulsating universe no two pulses can be absolutely identical. It is impossible for all processes to be reversible. In the long run changes in quantity must lead to to changes in kind and a transition to a new state. Can we at least attempt to imagine what such transitions could lead to?
Before answering this question let us return from the boundless expanses of the universe to the microcosm of elementary particles. The atom was once considered the smallest, indivisible particle of matter ( the word “atom” means “indivisible” in Greek). Then it was found that the atom consists of a nucleus with electrons revolving around it, and these were declared indivisible. Today, in the age of nuclear energy, a schoolchild knows that the atomic nucleus is a complex structure which can be split and transformed. An electron colliding with a positron (anti-electron) turns into radiation whose energy and mass, in accordance with Einstein’s principle of equivalence, must correspond to the energy and mass of the colliding particles. In any case, the electron is no longer regarded as a tiny solid ball incapable of further division. As Lenin wrote, the electron is inexhaustible.
Like protons, neutrons and other “elementary” particles, the electron undoubtedly has a complex structure. What we call “elementary” particles are probably some highly compressed substance which can never remain at rest and pulsates incessantly. At least, this conception does not contradict any of the known facts. In such pulsations an elementary particles interacts with the surrounding field. Each expansion “pushes” the field aside, and this causes an expenditure of the energy which is responsible for the field. Does the energy flow back to the particle when it compresses? Probably not always, and the pulsating particles gradually dissipates energy. This means that it loses mass, that is to say, the mass of an elementary particles is not necessarily constant.
Today, at the present stage in the evolution of matter, an electron’s mass equals 9x10-28 gram, and a proton weighs” 1,7x10-24 gram. Ten thousand million years ago they were heavier, and ten thousand million years hence all the elementary particles in the inverse may “weigh” less than today. The change in mass could affect other properties of elementary particles. This microcosmic process would suggest the non-repetitive evolution of matter in the universe.
Does the concept of pulsating elementary particles agree with the hydrodynamic theory of gravitation mentioned before? An answer may be found in a theoretical experiment described by Nikolai Zhukovsky, the “father of Russian aviation”. Imagine two spheres immersed in an incomprehensible fluid. If the spheres are made to pulsate synchronously, so that the maximum volume of one corresponds to the maximum volume of the other, they will gravitate towards each other. Moreover, the law of attraction will be expressed by a formula identical to Newton’s formula of universal gravitation: the force will be proportional to the energies “radiated” by the spheres and inversely proportional to the square of the distance between them. If the pulsation is not “in step” and the maximum volume of one corresponds to the minimum volume of the other, they will repel each other with a force given by the same formula.
Obviously, the analogy between pulsating elementary particles in a gravitational field and pulsating spheres in a fluid is remote. But it does offer an idea of the hydrodynamic theory of gravitation. Possibly in the course of this pulsation the elementary particles eject elementary packets of energy in the form of gravitons.
Although the mass of elementary particles appears to decrease, the latest findings of theory indicate that the total mass and energy in our region of the universe in constant. Along with the creation of gravitons there takes place a continuous creation of new elementary particles out of “old” gravitons at an estimated rate of 10-45 gram per cubic centimeter per second. This is accompanied by a change in the so-called world of constants: the gravitational “constant” increases, the elementary charge and Planck’s “constant” decrease. Only the speed of light does not change.
Slowly but surely matter changes from one form into another. A steady accumulation of quantitative changes is taking place which must inevitably develop into a qualitative leap. What kind? With out present knowledge we are unable to say. In any case it will mean an end of out three-dimensional closed universe. It may may represent merely the completion of one turn of the evolutionary spiral on an incredibly great scale. Be that as it may, but it will also represent a new stage in the evolution of matter, eternal and indestructible.
-
This is a discussion of the Set theory from the same section of the book:
In so far as in investigating the general state of matter in the universe one must deal with an infinite variety of particles, a knowledge of some of the most general properties of certain infinite sets is essential.
The simplest infinite set is the set of positive integers 0,1,2,3,4,5..n where n tends to infinity. This is a so called countable set; 1,10,100,1000,10000,100000 is also countable and that the numbers of the first and second set can be put into one to one correspondence for the numbers of the second set can be written down in the form 100, 101, 102, 103, 104 105, etc. This is one of the paradoxes of infinity. A countable infinity is the weakest of infinities.
For example, an infinite set of positive integers cannot be used to count all of the points on a straight line segment. A set of points on any section of a straight line segment, or on an infinite straight line, or in the whole of space, is non-countable, it constitutes a continuum which cannot be exhausted by any counting operations. This is known as “the power of the continuum” or cardinality.
In particular, it is easy to show that in fact to every point of a line segment there corresponds one and only one point on an infinite straight line. Consider a semi-circle the length of which is equal to the length of a given line segment. From the center of the semicircle project all of its points on an infinite straight line passing below it. You will readily perceive the truth of the foregoing statement made above. We can make use of the concepts of countable sets and cardinality to investigate the most general laws of behavior of the infinite set of particles of matter in the infinite universe.
Divide the infinite universe into a countable set of finite domains. Evidently each finite domain contains a finite number of material particles. To take into account the interaction of matter with the field for which it’s responsible, (electromagnetic and gravitational) assume, proceeding from the quantum theory of matter, that a finite domain of the universe contains a finite number of quanta. For the purpose of our reasoning we can also assume that some elementary quanta can be as small as we wish-not in the sense that quantum is regarded as “point-energy” but in the sense that a countable set of such quanta occupies a finite volume and carries a finite energy.
Thus, in our finite volume of space there may even be, not a finite, but a countable set of elementary particles. Hence, in all space there will be a countable set of elementary particles.
Evidently, a set of interactions between the particles within each finite column of space in a finite time interval will be countable, if the particles make up a countable set, and finite, if the particles make up a finite set. In the whole of infinite space there will occur in a finite time interval (for both assumptions) a countable set of interactions (by interaction we understand any process involving two particles which result in a change of their masses or energies).
In so far as any infinite time interval can be divided into a countable set of finite intervals, a countable set of finite intervals, a countable set of interactions will occur in the course of an infinite time interval in the whole of the universe.
A set of all possible interactions for a countable set of particles represents a set of all the subsets of the given countable set, that is, this set of all possible interactions will possess cardinality.
The continuum of possible interactions (states) cannot be exhausted by a countable set of real interactions in any infinite time interval.
Assume (thought it is not so) that the whole of the universe is filled with particles of one class, molecules, for instance. Then the set of all possible states possess cardinality. But, the set of independent (un-repetitive) states would be countable, hence in the infinite life-span of the universe it would already have achieved equilibrium, or we must assume that we live in a vast unbalanced domain of the universe which formed as a result of a highly improbable process of fluctuation. This is the process in which one could expect all the fast molecules in a region of space to gather at one side, and all the slow molecules at the other. For a small number of molecules this may occur fairly frequently, but for a great number the probability of such a process is vanishingly small.
To be sure, we could also assume that the universe was “created” a finite time ago, but this is even less likely. The universe, of course, does not consist of one class of molecules, and we must therefore conclude that there is always present in the universe a countable set of classes of different “particles” (elements) such that every “particle” of one class may include “particles” of lower classes. By “particle” we can understand any autonomous formation: a photon, molecule, star, stellar system, etc. We can assume that the infinite diversity of classes of different “particles” is a consequence of the interaction of matter with the fields for which its responsible. Every “particle” may exist in the universe in any (apparently infinite) number.
A set of all possible interactions of the whole diversity of “particles” without any repetition of state processes cardinality. Hence, the totality of interactions of different formations in the universe cannot be exhausted by any counting operations, which leads to the non-cyclic development of matter and this makes possible its infinite development.
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The following are excerpts from the scientist NA Kozyrev on the issue:
In the universe, however, there are no signs of the degradation which is described in the second law of thermodynamics. Stars die and are born again. The universe sparkles with inexhaustible variety. In it no one finds traces of an upcoming thermal and radiation death. Apparently here is where the basic contradiction lies – A deep contradiction which may not be explained away through a reference to non-applicability of the second law of thermodynamics to the infinity of the universe. The fact is that not only separate stellar bodies but whole systems are isolated from each other to a degree that they may be regarded as closed systems, for all practical purposes. (Usually the second law is applied only to closed systems) For them the thermal death could visibly draw nearer before any aid could come from outside. Such sytems, in a state of degradation, should prevail in the universe, and yet they're almost non-existent.
Time doesn’t propagate (for example like EM-waves) but appears at once all over the Universe. That is why the connection through time must be an instantaneous one. So it’s possible to observe some phenomena of very far astronomical bodies in real time, without delay. This perspective does not contradict the special theory of relativity because when we have instantaneous connection through time, there are not movements of material objects.
-Kozeryv
