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"What is mind - No matter. What is matter? - Never mind" -Thomas Hewitt Key
Contents
The author wishes to address the thinker who is not satisfied with past explanation and theories about the structure of the Universe. The article is primarily intended for generally educated readers, both atheist and believer. In the article, we will calculate and compare the numerical results, or magnitude, of some general properties of matter such as:
Also we should recall that some force (F) must act upon a material object before any change in motion occurs. The units of measurement of the International System (SI) will be used in this manuscript:
The unit of force will be measured in Newton’s (N), one Newton of force imparts an acceleration of one meter per second squared to a mass of one kilogram. Thus the dimensions of force equal: (kilogram) x (meter) x (second) -2 or (kilogram) x (meter) / (second) 2, which means the same as Newton (N). Scientific Notation We shall have to deal with numbers that are extremely big, such as: 1,000,000,000,000,000,000,000, which is believed to be approximately the radius of our galaxy in meters, and we can express that number as 10 21 meters. Also, we shall deal with numbers that are tiny, such as: 0.0000000001 of meter (or 100 trillionth of meter), which is approximately the radius of the atom, and we can express that number as 10 -10 meters. The method of expressing numbers as powers of 10, or exponents of 10, or as an order of magnitude is as simple as it is economical. When we have to multiply two such powers of 10, we simply add their exponents. Thus one million times one billion is: (10 6) x (10 12) = 10 18, and (10 -12) / (10 18) = 10 6 Similarly, if we encounter some fraction of ten, and we need to divide two such numbers, we simply subtract their exponents. Therefore, four trillion divided by two million is: (4 x 10 12) / (2 x 10 6) = 2 x 10 6, or 2,000,000 while (10 -15) / (10 -5) = 10 -10 , and (10 -12) / (10 5) = 10 -17.
Let us divide the material world into three groups:
As a matter of fact, we ourselves and surrounding as thinks exists between the world of Microstructures and the world of Macrostructures. the other hand , we ourselves and all Macrosubstances simultaneously consist of Microsubstances and are counterparts of the Astrowold. Scientists believe that the Macroworld and the Astroworld are interconnected and held together by gravitational attraction. The Microworld, however, interconnected and held together due to:
Since the gravitational forces appear to be from 10 35 to 10 44 times weaker than electromagnetic and nuclear (strong) forces of interaction, scientists assume that gravity plays practically no direct role in the Microworld. Another obvious distinctions between gravitational and electromagnetic forces is that gravity only attracts, while electrical forces can either attract or repel. Also, gravity cannot by shielded as electricity and magnetism can At the same time our conceptions about electromagnetic and gravitational interactions are somewhat similar. Thus, as charged objects accelerate, they produce a magnetic field. Conversely, electrically charged objects are altered in motion when a magnetic field, moves through. Similarly, scientists believe that the acceleration of both Macrobodies and Astrobodies exerts gravitational field, or gravitational radiation [1], and that gravitational fields cause both Macrobodies and Astrobodies to change their state of motion. Therefore, scientists constantly hope to discover a unified essence of force that governs all interactions and some similar mechanisms that will explain rising fields at any scale, from sub-microscopic to the infinite. Although some of the world’s greatest scientists continue to study this problem, no one has yet successfully proven that interaction on both atomic and galactic level are really two different manifestations of the same phenomenon. This manuscript will not attempt to discover any new unified force or field of interactions, but, rather, to show that the known interactions in the Micrworld, Macroworld and Astroword appear to us incompatible primarily because of the subjectivity and relativity of our perceptions, measurement and analysis. This work will attempt to convince the thinker that a qualitative similarity in both the underlying structure and the forces of interactions might exist between basic subatomic and galactic formations.
The relativity of our perceptions Whether viewed from the standpoint of the most recent scientific theories or the supposition of ancient thinkers and mystics, the material world represents various forms, or manifestation of matter-energy. Basically our knowledge of the world depends on our ability to interpret the vibrations or radiation that we receive through our senses of sight, touch, hearing and smell. Consciousness is the state of the human mind that reflects and interprets the vibrations of matter-energy received through our senses. The range of perception of our five senses is far too limited to register the full range of radiation that permeate the Universe. Because man perceives time, space, mass, and energy through such limited faculties, he is confinedto a limited, and not always reliable, comprehension of the material world. Albert Einstein was the first scientist to apply the relativistic approach to our analysis of what we call "reality". Since Einstein presented his Special Theory of Relativity, many scientists believe that the mass, space, and time are not absolute, unchanging entities, but are elastic, and can be stretched or contracted by motion. For example, if we could place a clock in space vehicle as it approached the speed of light, then, according to Einstein, it would run far more slowly than the same clock sitting on a shelf in your home. This leads to the familiar "twins effect". If one twin were to travel in space at a speed that approached the speed of the light while the other twin remained on Earth, the astronaut, upon returning to Earth, would find his twin brother much older than himself. During the time that the astronaut traveled at a speed approaching the speed of light, every year of his life corresponded to several years in the life of a person moving at terrestrial speed. In this paper we will not consider whether or not this is true. We will, however, assume that, under Einstein’s theory, the twin brothers would have had different coordinates or scales of space - time. Their conclusion about reality would be different. My twin brother’s perceptions If, during his flight, our astronaut could have observed the speed and force of various processes on the Earth, he would have seen all terrestrial activities, such as the movement of cars and the growth of trees, taking place on a much more intensive level than people on the Earth would perceive them. Because of the speed at which astronaut was traveling, his biological, physical and mental activities would have been different from ours, as would his notion of "strong", "fast" and "large". Now, if we agree with Einstein that, as a speed or gravity changes, the mass, linear dimensions and time coordinate of an object also change, then it logically follows that objects that have different mass and different spatial dimensions, each possess their own, individual natural speed and characteristic time to complete one cycle of a natural process in their motions. Therefore, all internal and external forces will effect them differently. The observer may also be such an object. Such concepts as fast and slow, long and short, large and small, strong and weak are meaningless without a frame of reference. Such a frame of reference does, in fact, rest on our own physical capabilities, our human speed, our bodily dimensions, and the density of our tissues. We involuntary compare the properties of surrounding material objects with our own properties and our own rate of physical activity. All properties of material objects (weight, density, solidity, etc.) - as well as the magnitude of the forces of interaction between objects - are relative conceptions and depend on the such quality as the spatial dimensions and mass of the observer. If, for example, we had been born into the Microworld, what would our consciousness reflect about the properties of compound?
Natural speed, size and time scale No a single process or object exists separately and independently. Each interacts with other bodies in space and time by means of various fields. At the same time, any object represents a structure or system of interconnected elements, and every one of those elements is, itself, a structure. Furthermore, no object is totally at rest. Even a rock on the surface of the Earth is in constant motion, together with the Earth, as the Earth spins on its axis and rotates around the Sun, which moves through our solar system, as it moves around the nucleus of our galaxy, and so forth. We can only guess at the absolute distance that any object travels in a given time period; however, we can measure the distance that it moves with respect (i.e., relative) to some particular observer. Basic movement From the time of Aristotle, men have believed that natural motion was inherent in the nature of bodies. The natural speed of elements that make up a body and the natural speed of the body, itself, are functions of the internal and external natural forces of interactions currently acting on that body. Waves, oscillation and rotation around the center of a mass are the three basic types of natural motion in the Universe. The speed (v) of a material body during circular motion around some given center can be expressed by the equation: v = lf = 2pr / t (meters) / (seconds) Formula (1) where: (l) is the wavelength or circumference, (t) is the period or time required for the passage of one wave through a given point in space, or the time required for a full rotation around some point, (f) is the frequency of oscillation or rotation: f = 1/ t (second) -1, (r) the radius, and (p) is the ratio of the circumference of any circle to its radius (approximation is equal to 3.14).
The acceleration (a) may then be determined using the Newton-Huygens formula: a = 4p 2r / t 2 (meters) / (seconds) 2 Formula (2) For an example of such motion of some matarial substance around some center on the Astronomical scale, let us look at our solar system. According to astrophysics, the radius (r) of our galaxy is on the order of 10 21 meters. The period (t) required for one rotation of our solar system in its circular orbit around the center of our galaxy is believed to be on the order of 10 16 seconds. The frequency (f) of this process and the number of rotation per our unit of time (one second) will be 10 -16. For an example of such motion of some material substance around some center in the Microworld, let us look at an electron. The radius (r) of the orbit of the rotation of an electron around the nucleus in hydrogen atom, for example, is on the order of 10 -10 of a meter.The period (t) required for one rotation of an electron around the nucleus is on the order of 10 -15 of a second. So the frequency (f) of the process and number of rotation per our unit of a time (one second) will be on the order of 10 15 or 10 to the 15th. power. How swift we are? During uniform motion we ordinarily define the speed as the distance traveled during a giving time period. If we assume that the linear dimension (d) of any object is the distance traveled, then the speed (written in the same form as the wave formula, above, except that the wavelength will be the length of the object and the period will represent the time required for the length of the body to pass a given point) will be: v = d / t (meters) / (seconds), Formula (3) and the acceleration will be: a = d / t 2 (meters) / (seconds) 2 Formula (4) For simplicity, let us consider the average human trunk to be one meter in linear size. The trunk is the main mass of the human body. Since, the word trunk sounds to anatomical let as call it jast a human body. Walking at a leisurely pace, a person of this dimension develops a speed of approximately one meter per second. This is because our natural walking speed basically depends upon: a) our size and mass b) the acceleration of a free-falling body (g), which, on the Earth’s surface, is equal to: g = 9.8 (meters) / (seconds) 2. Under these circumstances, a man can travel a distance equal to the length of his body during one second. We can say that our natural human waking speed is: v = d / t = 1 meter / 1 second = 1(meter) / (second) It happens that the linear dimension of our body (d) and the period of time (t) required for passage of this linear dimension through a given point are on the same order of magnitude as the unit of length in (SI) (one meter) and of time (one second). Let us call this period (t) 1 second - our human time-scale. People or animals with smaller bodies and, accordingly, shorter legs, walk with a quicker stride than big ones. In the flight of a bird, the frequency of its wing beats decreases as the size of the bird increases. The heartbeat of a human baby is twice as fast as that of adult. Everywhere in nature, we observe the interrelation - expressed mathematically in our wave formula Formula (1), between: a) natural speed of movement or rotationb) linear size or radius, and c) the period required to complete one cycle of a process - which we will call the time-scale of any phenomenon.The relativity of our time – scale We see that, during that same one second (our human time-scale), we register an enormous number of rotation of electrons around the nucleus of an atoms in the Microworld and only a tiny fraction of any process in the Astroworld. Therefore, we may assume that any species of observers which differs from us in mass, linear dimensions, and time-scale will interact with the Universe on a different level than we do and would have physical, biological, and mental activities correspondingly different from our own. What we consider quick and strong might be slow and weak from their point of reference. Similarly, their perceptions about the properties of the material world will be different from ours.
Everywhere in the nature, we see that objects of different size and mass are different in shape and exhibit different behavior. They also need a different duration of time to accomplish some similar action. A change in quantity leads to a change in quality. As the simpliest example of similar objects, we can examen and compare the behaviour of two pendulums of different lengths. The square of period (the time necessary for one swing, to and fro, of the pendulum) will be: t 2 = 4p 2d / g (seconds) 2 Formula (5) Where: (t) - the time for one full swing, to and fro. (d) -the length of pendulum. (g) - the acceleration of a freely falling body on the Earth’s surface. The ratio of the square of the periods of two pendulums of different length will be: t 2 / t’ 2 = d / d’ Formula (6) Since circular velocity v = 2pd / t, we can write: v 2 = 4p 2d 2 / t 2 and v’ 2 = 4p 2d’ 2 / t’ 2 therefore v 2 / v’ 2 = d 2 x t’ 2 / d’ 2 x t 2 substituting the ratio t’ 2 / t 2 for the ratio d’ / d, according to formula (6), we will get: v 2 / v’ 2 = d 2 x d’ / d’ 2 x d = d / d’ , and thus: v 2 / v’ 2 = t 2 / t’ 2 = f’ 2 / f 2 = d / d’ Formula (7) In our everyday experience, we do not see the geometric similarity [2] between plants or between animals that are have same density, but vary significantly in size - that would seem contrary to nature. However, some plants or animals that are relatively close in size we might consider geometrically similar. Also, within a reasonable difference in size, we can build some structure or mechanisms that are geometrically similar. How the effects of gravity, acceleration and the ability to withstand a load (including the load of that object’s own weight), will wary for structures that are different in size and mass but geometrical similar is reflected in "model laws" and "similarity mechanics" that engineers and architects use in modeling analyses of structures. Laws of "similarity mechanics "describe the relationships between performance of experimental models and "real-life" objects. 4 times bigger is not necessary 4 times quicker For example, we can predict the performance of the prototype of a car, aircraft, or ship by testing a small model, because we can compute the relationship between their speed, the time to accomplish similar actions, and the frequency of rotation of engine of the model with a full-sized, geometrically similar prototype of that model by using Formula (7). In animate nature we also observe the same relationship between the size, the time to accomplish similar action and walking or running speed. Consider two representatives of the animal kingdom - the cat and the tiger. They are nearly geometrically- similar creatures that differ only in their linear dimensions and, accordingly, in their masses. Therefore, their natural speeds and times to accomplish similar motions will differ just like to those two pendulums of different length.
Let us assume that a cat 0.4 meters in length can run at a speed of 20 kilometers per hour (or, 5.5 meters per second). What speed, then, can the tiger reach, when the linear dimensions of the tiger are bigger than the cat by, let us suppose, a factor of 4 (which translates to 1.6 meter in length)? According to Formula (7): v 2 (tiger) / v 2 (cat) = d (tiger) / d (cat) v 2 (tiger) = d (tiger) x v 2 (cat) / d (cat) = 1.6 x 5.5 2 / 0.4 = 121 So, v (tiger) = square root of 121, what is 11 meters per second or about 40 kilometers per hour. Their period or time-scale will differ as: t 2 (tiger) / t 2 (cat) = d (tiger) / d (cat) = 1.6 / 0.4 = 4 t (tiger) / t (cat) = square root of 4 = 2 Thus, according to model lows or lows or lows of similarity mechanics, our cat moves through life at an intensity of two times greater than that of the tiger. A cat’s physical activity (such as its heartbeat or a jump), for example, will be twice as quick as a tiger’s. Further, let us see why geometric similarity is impossible when the difference in size and mass between objects is much greater than the difference between our cat and our tiger.
Viewing Reality from different scale Now, let us suppose, there exists a species called Lilliputians, the inhabitants of an imaginary island in Swift’s Gulliver’s Travels. Further, let us assume that the linear dimensions of such Lilliputians are smaller by a factor of 100 than our own dimensions. For the sake of simplicity, we shall assume again that the length of our body (trunk) is equivalent to one meter , that our natural walking speed is one meter per second, and our mass is in the order of 10 2 kilogram.
If, in addition to sharing a geometric similarity with us, such a Lilliputian had the same density of physiological tissue that we do, then the length of his body will be equal to 0.01 meters, and his mass will be one milion times less than ours, giving him a weight of about 0.1 grams. We can determine his walking speed by using Formula (7): v 2 (lil.) = v 2 (man) x d (lil.) / d 2 (man) = 1 x 0.01 / 1 = 0.01 v (lil.) = square root of 0.01 = 0.1 meters per second. On the basis of Formula (3), the period or time-scale of the Lilliputian will be: t = d / v = 0.01 / 0.1 = 0.1 (seconds). So the frequency or the number of lengths of his body that pass a given point in one second will be: f = 1 / t = 1 / 0.1 = 10 (seconds) -1 Such a Lilliputian would exist 10 times more intensely than we do, and would be 10 times as agile. Accordingly, he would require less time than we do to accomplish corresponding biological and physiological actions. We would perceived all his actions as moving ten times faster than our corresponding actions. However, based on his scale of space-time, he would consider that passing through a distance of 10 times the length of his body during a time period of one second as just normal as we consider normal to pass through a distance of just one length of our body during the same second. He would also perceive all of our human actions as being slowed down by a factor of 10, just as we perceive the motion of creatures mach larger than ourselves to be proceeding at a slower rate. Even if our Lilliputian should choose the same units of measurement that we use, so that the numerical values of speed, acceleration, force and so forth in his calculations would be the same as in ours, all existing forces would affect him in a different degree. Journey in to another scale If we set out to learn how an object or creature of a different scale would experience speed, acceleration, force, and so forth , we could analyze one single rotation, cycle, or phase of the phenomenon that we want to examine. We would: a) Calculate the frequency or the number of rotation, or the cycles of the process per second, or the number of lengths of the body that pass a given point in one second; b) Write down the formula of dimensions of quality to be determined. For example, as we have mentioned above, the formula of dimensions of such quality as a force will be: Newton or ( kilogram) x (meter) / ( second) 2. c) Determine where in this formula our measure of time (the second) occurs - (in the numerator or in the denominator) and to what power it is raised; d) The result of calculation of some quality (velocity, force, power, energy, or whatever) should be either
or
For example,we already know the frequency of such action as walking speed of our Liliputian (or the number of lengths of the body of our Lilliputian that pass a given point in one second) is: f (lil.) = 10 (seconds) -1 How such Liliputians will perceive gravitational attraction on the Earth ? We know that the formula of dimensions of an acceleration is: (meter) / (second) 2 The measure of time is the second, - (it is squared and is located in the denominator). The gravitational acceleration (g) on the surface of the Earth which is equal to 9.8 meters / (second) 2, should be divided by the frequency squared, so gravitational attraction will affect a Lilliputian 100 times less that it will affect us: g (lil.) = g / f 2 (lil.) = 9.8 / 100 = 0.098 (meters) / (time-scale of a Lilliputian)2 In addition, since the linear dimensions of such a Lilliputian is smaller than ours by a factor of 100, and he is sharing geometrical similarity and the same density of tissue with as, the cross-section of his legs would be smaller than ours by a factor of ten thousand, but his weight would be less than ours by a factor of one million. Of course, such Lilliputians, if they were to exist, would have a shape different from ours - their legs would be thinner in relation with their bodies than those of a normal-size human being.
That is why geometric similarity of objects of different size and mass appears contrary to nature. Creatures that are smaller than we are in linear dimensions, let us say, by a factor of 100 like some insects have a different body structure than we have. Why the lizard can climb up on the tree but not a crocodile ? However, like our imaginary Lilliputian, that insect (the ant, for example), can cover a distance of 10 times its body length during one second. As we do, an ant moves through a distance equivalent to its length during its period (an ant’s time-scale), which is about 0.1 of second. Like a Lilliputian, the ant would experience gravitational acceleration on the surface of the Earth approximately 100 times weaker than we do. Therefore, it should not surprise us that the ant can easily move objects much heavier than its body. For the same reason, the casual hop of a flea is the equivalent of a jump over 40-story building for a creature the size of a man. The fact that a fly can freely run upside down on a ceiling loses its mystery when we understand that the force of gravity affects the fly much less than we think. Similarly, that fly can travel so many lengths of its body during one second ( our time-scale), that it appears to us far more agile than we see ourselves. The real difference lies in the scale of our subjective perceptions. So far as the fly is concerned, it is flying at a leisurely pace, as it sniffs the air, looking for a place to alight and for a bite to eat. Poor dinosaurs, they have been too overweight
On the other hand, suppose that somewhere on Earth there a giant whose linear dimensions were greater than ours by a factor of 100. With a body size of 100 meters, a shape geometrically similar to our body structure, and the same density of tissue as our own, the mass (M) of such giant would be greater than ours by a factor of one million – so he would weight about one hundred thousand tons or 10 8 kilograms.
According to Formula (7), the period (t) (or, the time that required to travel a distance equal to the length of his body) will be 10 seconds. Therefore, the frequency (f) (or, the number of lengths of the body of this giant that pass a given point in one second) will be: f (giant) = 1 / t = 1 / 10 (second) = 0.1 (seconds) -1 The numerical magnitude of gravitational acceleration on the surface of the Earth should be divided by (f) squared, which means that the gravitational acceleration perceived by this giant will affect him 100 times stronger than its affects us: g (giant) = g / f 2 = 9.8 / 0.01 = 980 (meters) / (time-scale of giant) 2 Obviously, then, such a giant could not exist on the Earth. If he had a shape and tissue density similar to ours, he would be crushed by his own weight. To feel as comfortable as we do on the surface of the Earth, this giant would have to select a planet with gravitational field about 100 times less than our gravitational field. Experts in modeling analysis of structures know how to determine whether a construction on the drawing board will be capable of withstanding its own weight, when it is built. For that; the small geometrically similar model of a projected structure, if it were made of the same material as the prototype, should be tested with a load exceeding the weight of its parts by as many times as the model is smaller in linear dimensions than the designed structure (prototype). Alternatively, we can achieve the same result (to predict the capability of withstanding their own weight) if the geometrically similar to the model under test projected or designed structure ( prototype) is made of a material that is as many times lower in density than the material of the model as the model is smaller in linear dimensions than the projected structure.
Of course the definition of similarity is a tricky one because , as we mentioned above, we do not see in our earthly surrounding, geometrically similar objects that differ greatly in size. Plants and animals that differ in size must have a different shape and body structure. Full similarity However, we can recognize that some of the phenomenon that we observe in Nature have geometric similaritryof. We can say, for instance, that waves of different frequency in some homogeneous medium are similar in shape if they have similar pattern and amplitude. Since the speed of their propagation (v) is the same and equal to the speed of light, than, according to formula (1), the ratio of their wavelength (l} will be equal to the ratio of their periods (t). v = l / t and v’ = l’ / t’ since v = v’ l / t = l’ / t’ and l / l’ = t / t’ We can also see this type of similarity in a gear, where the ratio of radii (r) of different (in size), interconnected cogwheels will be equal to the ratio of their periods of rotations around their axles. (t). Let us call it Cogwheels Similarity. From our previous examples, we see that, on the surface of the Earth, where (g) is a constant, if a model is smaller (in linear dimensions) than its prototype by a factor of 100, then the period (t) (or, the time required to complete one similar cycle), according to Formula (6), will be different not 100 times less, but only by a factor of 10.
Heavenly turf Just as we do not see Cogwheels Similarity in the motion of formations that differ significantly in size here, on our own surrounding, neither do we see Cogwheel Similarity in the motion of formations that differ significantly in size on the Macro- and Astroscale. According to Kepler’s law, the squares of the rotational periods of the planets around the Sun will be proportional to the cubes of their orbital radii and inversely proportional to GM: t 2 = k d 3 / G M where (k) is the coefficient that depends on the shape of the planet’s orbit, (G) is the gravitational constant and (M) the mass of the Sun. Therefore, the ratio of the square of the rotational periods of any two planets will equal: t’ 2 / t 2 = r’ 3 / r 3 However, when we compare objects on the subatomic scale (the Microworld) with the objects on the galactic scale (the Astroworld) the picture changes. For example, the circular orbital velocity of an electron during its rotation around a proton, according to Formula (1) is: v (micro) = 2pr / t r - is the radius of the orbit of an electron (it is believed equal to 10 -10 meters). t - is the period required for a full rotation of the electron around the nucleus of the hydrogen atom, (most physicist believe that it is on the order of 10 -15 seconds). Therefore, v (micro) = 2 x 3.14 x 10 -10 / 10 = 6.3 x 10 5 (meters) / (seconds) Using this same formula, the circular orbital velocity of our solar system, for example, during its rotation around the nucleus of the galaxy, is: v (astro) = 2pr / t (r) - is the radius of the orbit of our solar system around the nucleus of the galaxy, (which astrophysicists believe to be equal to 10 21 meters). (t) - is the period required for a full rotation of the solar system around the center of our galaxy, (which astrophysicists believe is on the order of 1016 seconds). Therefore, v (astro) = 2 x 3.14 x 10 21 / 10 16 = 6.3 x 10 5 (meters) / (seconds) Although the orbital velocity is the same, the diameter of the proton is as many times smaller than the diameter of the galaxy as many times the period of rotation of an electron around the nucleus of the atom is shorter than the period of rotation of some stellar formation around the nucleus of the galaxy. Thus, the periods and radii of these formations will be related like cogwheels and will satisfy our definition of Cogwheel Similarity: t (micro- structure) / t (astro-structure) = r (micro- structure) / r (astro-structure) Divine Architect As we mentioned previously, to handle a relatively similar assignment, the bigger prototype should be as many time lower in density than the material of the model as the model is smaller in linear dimensions than the prototype. Theoretically, if we set out to build a structure that is geometrically similar to the nucleus of, say, a hydrogen atom (the radius of the proton is on the order of 10 -14 meters), but bigger in linear dimensions by a factor of 10 35 (representing the difference in the radius between our galaxy and the nucleus of the atom), we should foresee that the density of this projected structure will be lower then the density of the nucleus of the hydrogen atom by the same order of magnitude (10 35). If this were not so, then there would be gravitational collapse. Apparently, then, the Creator of the Universe has made the Microcosm a miniature version of the Astrocosm If the radius of the proton is on the order of 10-14 meters and its mass is about 10 -27 kilograms, then the density (r) of the atomic particle would be equal to: Density = mass / volume, the volume of some spherical structure is equal approximately to its r 3, so: r (atom.part.) = 10 -27 / (10 -14) 3 = 10 -27 / 10 -42 = 10 15 (kilograms) / (meters) 3 Similarly, if the radius of our galaxy, as we believe, equal to 10 21 meters and its mass is on the order of 10 43 kilograms, then the density (r) of our galaxy would be: r (galaxy) = 10 43 / (10 21 ) 3 = 10 43 / 10 63 = 10 –20 (kilograms / (meters) 3 Therefore, the ratio will be: r (atom.part.) / r (galaxy) = 10 15 / 10 -20 = 1 0 35 (kilograms) / (meters) 3 We see that the galaxy was created of material 10 35 times lower in density than the material of the proton. The radius of a galaxy is in 10 35 times bigger that the radius of the proton. The period to accomplish some similar action, like the rotation of some material substance around the nucleus, on a micro and astro-scale might be also differ by a factor of 10 35. Let us call that condition the Universal similarity. r (Subatomic - structure ) / r (Astro –structure) ~ ~ t (Subatomic - structure ) / t (Astro –structure) ~ ~ r (Subatomicstructure ) / r (Astro –structure) Formula (8) Of course all such comparisons are both simplified and speculative. The diameters of the atoms and galaxies, the size of their respective nuclei, and their speeds of rotation can vary by many orders of magnitude. We are not attempting in this manuscript to propose some particular figure to define that variation, but rather to persuade serious thinkers about the possibilities of qualitative similarity between micro and astrocosm. Resemblance of incompatible Theoretically, material formations at a subatomic and galactic scale might even be similar in shape and architecture in spite of (rather because of) the staggering difference in their size, characteristic time to complete alike actions, and density. Again, the tremendous density of subatomic particles is a relative concept. If an observer could shrink his linear dimensions by 10 35 times, her time scale would be reduced by an equal amount. All properties of our material world, including her perception of the density of her surrounding Universe, would be different from ours. We should also mention here that the similarity between Microstructures and Astrostructures , what we try to propose out of this paper, by no means implies identity. Each group of material substances (such as, elementary particles, atoms, molecules, stars, galaxies and so on), in fact, each element of every material substance, includes a different quantity of matter and is, therefore, unique. However, the recurrence of some basic qualitative properties is possible between basic groups of material structures of the Microworld and basic groups of material structures of the Astroworld. Philosophically, this recurrence can represent a sort of spiral of the evolution of matter from an infinitely small to an infinitely large manifestation. Indeed, even within molecular scale, the properties of the known elements that make up our compounds reoccur with sufficient regularity for us to order those elements in a "Periodic Table" in which elements with similar "valences" (i.e., the same number of electrons in their outermost orbits) share similar properties.
On all scales - the Microcosm, Macrocosm and the Astrocosm - we observe that, although material substances differ in mass and size, they can be arranged in a hierarchy of structure that represents some finite number of basic qualitative groups of matter. Let us look first at the Astro-Universe. This is a world of stellar formations. In all regions of space accessible to our observation, we see galaxies. Despite their various sizes, masses and shapes, they represent a particular qualitative group of material substances. The building material or elements of those various stellar formations, clusters, islands, and different types of galaxies are the stars. In turn, although each stars might have its own distinctive size, mass and brightness, together they represent their own particular qualitative group of material substances - the stars. In spite of tremendous distances between them (the distance between stars in our galaxy averages on the order of 1017 meters) [3], any star can participate in some gravitational interrelation with other stars to form a stellar constellations.
In turn, each stellar constellation can interact with other constellations to form galaxies that, in turn, interact with the others galaxies in a vast sea of space (rotating, moving, evolving or decaying in space and time).
If stars are the basic material - the "elements" - that compose the more complex Astro-phormations, it would be logical to imagine the existence in nature of tiny material bodies, let us name them Microstarss. Such hypothetical Microstars , similar to their big sisters in our Astrocosm, could also participate in , let us say, Microgravitational relationships to form elementary particles like quarks and electrons. It is no secret for many thinkers that elementary particles are not elementary, at all. Yet Aristotle believed that all material substances could be divided into ever- smaller parts, without any limit. Matter is mostly empty space The summary volume of space that might be occupied by the Microstars that make up such an elementary particle is negligible compared to the volume that is occupied by that complete particle, itself, as a structure – just as the summary volume that is occupied by the stars that make up some stellar cluster is tiny in comparison to the volume that is occupied by this solar clusters, itself, as a structure. The fact is that matter is distributed in space, by natural forces of interaction, in such a way that everywhere the sizes of the material substances that make up more complex structures are many times smaller than the distances between those substances. For example, if we imagine that a proton and a neutron in the atom are each one meter in diameter, than the smaller particles inside an atom (like quarks and electrons) would be less than one millimeter in size, while the entire atom would be about one hundred kilometers across. In other words, any atom is mostly empty space. Its nucleus and surrounding electrons occupy only a tiny fraction of the volume of an atom. Let us suppose, that average radii of our hypothetical Microstars are smaller than the average radii of our known stars by the same order of magnitude than the radius of the nucleus particle (such as, proton) of an atom is smaller than the radius of our galaxy; r (prot.) / r (gal.) = 10 -14 / 10 21 = 10 -35 , and so: r(microstar) / r(star) = 10 -35, and r (microstar) = 10-35 x r (star) Within the known Universe, both our sun and our entire galaxy are of average size. Since the radius of the sun about 10 10 meters, the radius of our hypothetical Microstar could be in the order of: r (microstar) = 10 -35 x 10 10 = 10 -25 meters What are Black Holes made of? The distance between the stars in our galaxy averages on the order of 1017 meters. If we again use for comparison the difference between the radius of a galaxy and the radius of the nucleus of the atom, then the distance between Microstars that form Micrododies might be as much as 35 orders of magnitude smaller than the distance between the stars - or about 10-18 meters. If the density (r) of the galaxy is 10 35 times lower than the density of the proton, we can assume that the density of average star, like our sun, for example (the density of the sun is on the order of 10 3) is also 10 35 times lower than the density of any such hipothetical Microstars . Therefore: r (microstar) / r (star) = 10 35 r (microstar) = 10 35 x r (star) = 10 35 x 10 3 = 10 38 (kilograms / meters) 3 Such a tremendous density might be the density of what science calls a black hole, in which the complete gravitational collapse of some macro- or astro-body might reduce its size and, therefore, increase its density to that of packed Microstars. Invisible Matter If such Microstars exist, they could be found in any region of space, but we would not be capable of detecting them with either our unaided senses nor our current instruments. Perhaps even such incredibly complicated Microgravitational formation of Microstars that we may call Microgalaxies would be undetectable. We are physically capable of recognizing only a limited range of manifestation of matter. Even our best current instruments can only register such material things as these hypothetical Microgalaxies when they join in, let us say, a Microgravitational relationship to form subatomic particles particles, like quarks [4] and electrons. It is not a new idea that space may contain some invisible and currently undetectable particles. Current candidates include neutrinos [5] with zero rest mass, or gravitons [6]. We can interpret Dirac’s theory to define a vacuum as an energy level crowded with fermions, from which particle-antiparticle pairs virtually arise and disappear. However, in this article we will propose that a vacuum is crowded with our hypothetical Microgalaxies. In accordance with the law of the conservation of mass and energy, during the complete decay or annihilation of material substances, the energy of radiation will be equal to the product of the mass times the speed of light squared, according to Einstein’s well known formula: E = MC 2 Formula (9) This energy of radiation is released Microgravitational energy, which held together the atoms of a Macrobody before decay. After the annihilation or disintegration of any formations of our hypothetical Microgalaxies, thoseMicrogalaxies will dissipate into the cosmos and becomet the undetectable, for us, part of that free cosmic mater-energy field, that we perceive as a vacuum. Thus we can say that, in Astroworld, Macroworld and Microworld, energy is not the only thing that cannot be destroyed. It is also possible that mass, as a basic attribute of matter, cannot be destroyed, although it can be disintegrated and synthesized into different manifestation of material formations (even if we are not capable of weighing or registering it, with our limited tools and perceptions). In fact, the structural similarity of material formations on both the subatomic and galactic scale can only exist in the Universe in combination with the similarity of its corresponding forces of interactions.
As we have mentioned previously, physics recognizes four basic forces that act in the Universe: A moving electric charge gives rise to a magnetic field, and variation of that magnetic field in turn produces an electric field, cousing a charged body to be attracted to, or repelled by, other charged bodies. The strength of any electromagnetic force also depends on the "medium" between the charges. Usualy, a non-conducting material media placed between the charges produces a shielding effect and decreases the force. 1) The strong (or nuclear) force holds quarks together to form protons and neutrons. In general, this force binds inter-atomic elementary particles into a nuclear structure. This force has a very short range (about 10 -15 meters) and so it acts only within the nucleus. 2) The weak force is responsible for a variety of nuclear radioactivity decay processes - such as Beta decay, when a neutron decays into a proton and an electron.. It is a very short range of interaction (about 10 -18 meters) and, like the strong force, only affects objects within the nucleus of atoms. Its strength is a billion times weaker than that of the strong force. 3) The electromagnetic force holds electrons in orbit around an atom’s nucleus. This force is responsible for repulsion of like and attraction of unlike electric charges. It also governs the behavior of light and other forms of electromagnetic radiation. It is a long-range force, involving the electric and magnetic properties of elementary particles. 4) The gravitational force holds matter together, but it is so weak that its effect is only noticeable when large masses are involved. Therefore, it seems, gravity plays no practical role in the Microworld; it interconnects (and binds into the structures) only material objects on the Macroscale and Astroscale. On the other hand,the gravitational force apparently acts across an infinite range in space and cannot, as far as we know, be shielded by any practical means. Also, gravity is the only one of the four forces that can only attract; the strong, weak and electrical forces may either attract or repel. The unifying differences We that see these four fundamental forces have different character, behavior, manifestation and range. They also vary greatly in strength. If we assign the strong force a "relative strength" of 1, then the relative strength of electromagnetism will be 10 -3, the weak force will be 10 -16 and the gravitational force a mere 10 -41. Scientists since Albert Einstein have searched for a way to describe all four forces as manifistations of a single, unified force. To date, they have explained the link between the electromagnetic and weak forces, but they haven’t yet found any theory that unifies any of the other forces. Also, neither one has found why gravitational and electromagnetyic forces have such incredible difference in the magnitude. From our human scale of space-time (which sits between the world of Microstructures and world of Astrostructure), we are not capable of registering the consistent evolution of processes on a subatomic level. This world is too small, from our perspective, and we cannot bring its whirling interaction to a stop in order to take a picture. However we can register different patterns and spectrums of space radiation caused by a change in the state of the motion, decay, synthesis of Microbodies or the collision between such Microsubstances. On the opposite side, we cannot observe any consistent evolutionary processes on the Astronomical level either, - they occur too slow for us to see the difference. From our scale of space-time, it is difficult to measure, let us say, Astro-radiation or to register Astro-electromagnetism caused by decay, synthesis of Astrostructures or collisions between stellar formations. Still, we can take a picture of Astronomical interactions (which we cannot do on the subatomic level), and we can read some valuable information from that snapshot. For example, because most visible galaxies have a spiral shape, we can assume that most galaxies are spinning structures.
Units of measurement conversions Different branches of science and technology are engaged in research on various manifestations of matter and energy. Not surprisingly, these different disciplines focus on different concepts and so employ different units of measurement. In dealing with a mechanical or gravitational interaction, we are usually operating with such concepts as a mass, length , time, force, work, energy, power and so on. When we deal with electricity, we apply such additional concepts as charge, current, voltage, inductance, capacitance, and resistance. However, all units of measurement are based on a unified, essential framework - the quantity of matter that takes part in that process we want to measure, the region of space involved, and the time that it takes to accomplish some change in the state of motion or status of that object or the process. In many reference books of Units and Dimensions the mass, length and time are called primary or fundamental dimensions The System International des Unites (SI) has expanded the list of primary dimensions as well as the list of primary units also defines primary units of Amper, for the dimension of electrical current (I). The flow of an electric charge that transports energy from one place to another is electrial current. One ampere is a flow of 6.25 x 10 18 electrons or protons per second or one coulomb per second. At the same time, if one ampere of current is flowing, a force equal to 2 x 10 -7 Newtons will be exerted between two parallel conductors that are set one meter apart, along one meter of their length. Thus we see how electromagnetic properties of matter are inseparably linked with fundamental units of dimensions and with the concepts of quantity of matter (mass), length and time. It would be easier to visualize the qualitatively similar processes that might take place on the Microscale, Macroscale and Astroscale if we recall that the electrical units of the International System (SI) of measurement can be converted into the fundamental units (meter - kilogram - second) or the (MKS) System (also known as LMT Sistem). We can make such conversions from the electrical units of measurement of the International System into the (MKS) System using eguivalents ("conversion factors"), found in (dimensional analysis) reference books for physical science. Thus, the electrical unit of charge (Q), using the dimensions of (SI) System, is – coulomb. The equivalent dimention of the coulomb in the (MKS) System is: charge of one colomb or (Q) = (kilogram )1/2 x (meter)3/2 x (second) -1. Accordingly, the equivalent dimensions of charge squared in the (MKS) System will be: (charges)2 or (Q)2 = (kilograms) x (meters) 3 x (seconds) -2 Dimensions of potential squared (V2) (or voltage squared) in (MKS) System coincide with the dimensions of force (F): (volts) 2 or V 2 = (kilograms) x (meters) x (seconds) -2 or (Newtons) In fact, sometimes we artificially differentiate similar types of forces on the Astroscale, Macroscale and Microscale only by giving them different names and measuring them with different units of value. No self-respected experimental physicist would use the term (or concept of) mass, for instance, to calculate certain interactions on the subatomic scale. Rather, he will talk in terms of electron-volts [7] . We, however, are not self-respecting experimental physisists. In this work, with a bit simplification, we will try to calculate the force of any interaction at any scale (Micro, Macro or Astro) using the same well known formulas and the same fundamental units of measurements (meter, kilogram,second). Most basic equation of force In perhaps the physicist’s most basic, well-known equation, the force(F) is ordinarily defined as a product of mass (m) and acceleration (a): F = m a (kilogram) x (meter) / (second) 2 or (Newtons) Formula (10) Also, for any system in the Astroworld, the Macroworld and the Microworld in which some smaller masses are orbiting other, larger masses, their acceleration according to the Newton- Huygens formula (2), will be equal: a = 4p2r / t2 (meters) / (seconds) 2, so we can write that as: F = m x (4p2r / t 2) Newton’s Formula (11) Therefore, knowing a body’s (of our Earth, for example): the radius (r) - [the orbital radius of the Earth is on the order of 1.5 x 10 11 meters] and the period (t) - [one period of rotation of the Earth around the Sun is equal to one year or 3 x 10 7 seconds], we can calculate the magnitude of the acceleration of the Earth during its rotation around the Sun: a (Earth) = (4 x 3.14 2) x (1.5 x 10 11) / (3 x 10 7) 2 = = 6 x 10 12 / 9 x 10 14 = 6.7 x 10 -3 (meters) / (seconds) 2 If, in addition, we know the mass of the Earth (m) [which is equal to 6 x 10 24 kilograms], we can calculate the magnitude of the force (F) of interaction between the Earth and the Sun: F (Earth-Sun) = m x a = (6 x 10 24 ) x (6.7 x 10 -3) = 4 x 10 22 (Newton’s) Also, we can apply this equation (11) to calculate the magnitude of the forces of interactions between Microsubstances. For example, we have enough information to determine the force of interaction between a proton and an electron in the hydrogen atom. Imagine that we do not know whether the force it causes is gravitational, strong or electrostatic. The radius of an orbit of the electron (r) is on the order of 10 -10 meters. The mass of the electron (me) is believed to be on the order of 10 -30 kilograms. The period of one rotation (t) of an electron around the nucleus of the atom is on the order of 10-15 of seconds. So the acceleration will be: a (elec.) = 4p2r / t 2 = (2 x 3.14) 2 x 10 -10 / (10 -15 ) 2 = 4 x 10 21 (meters) / (seconds) 2 and force of interaction between a proton and an electron: F (elec.–prot.) = m x a = m x (4p2r< |