Preamble

Out of all currently known physical quantities, perhaps only kinematic ones, namely, spatial dimensions (length or distance), duration in time, as well as their combinations (area, volume, speed of movement in space, etc.), are understandable not from the point of view of a theorist, but from the position of a researcher and practitioner, i.e. sensed and meaningful within a person’s ability to perceive the surrounding world through their senses. Accordingly, such factors as the size and shape of physical bodies and objects, the duration of the observed action in time or the frequency of periodic processes seem real to a person.

Other physical quantities, for instance, dynamic and electromagnetic ones, such as mass, force, energy or electric charge, are essentially «shapeless». The electric charge and body mass are generally accepted to be the key in the family of electromagnetic and dynamic quantities, since they are used as mandatory components of such quantities as force, energy, pulse, current strength, etc.

With regard to the electric charge, it is only clear that this value is somehow related to the property, let`s say, of two electrified bodies, to create a force field in the surrounding space, the elasticity of which can be felt, for example, when manipulating a pair of electrified objects or a pair of permanent magnets.

The essence of such a parameter as body mass is totally unclear. The value was introduced as a measure of inertia, as a characteristic physical property of a body that determines the relationship between the force acting upon the body and the acceleration it imparts to the body [See 1, p.95]. Whereby, the forces are defined as interactions of bodies that cause accelerations [See ibid, p.81].

To some extent, the idea of dynamic and electromagnetic quantities is clear, the formulas of which additionally contain kinematic components that contribute to the clarity. For example, the density of a substance, which is the mass of a substance in a volume unit, is understood only when referred to as specific (herein mass). The situation is similar, for example, with the concept «power», which means the amount of work per time.

Thus, we see that the «dimensions» of these quantities can hardly be called «visual» or «tangible» in contrast to the extent in space, duration in time or speed of movement. While we see and feel the distance in space or the size of an object, we understand what this means in visible reality and, accordingly, we can measure it using a standard that we understand, for example, a scale ruler. We can also really feel the duration in time and can measure it using some natural periodic process as a reference, for example, the rotation of the Earth around its axis. But how could the effect of bodies on each other, creating acceleration and called force, be expressed? What is the cause, as well as the measure of such an action?

Body mass, as mentioned above, was called a characteristic physical property of a body, which determines the relation between the force acting on the body and the acceleration communicated to the body. From this definition— to determine the specified ratio — only the function of the mass is clear, while the physical «meaning» of the mass itself remains vague.

As for the electric charge, its direct definition is generally absent in textbooks on physics. It is only indicated that there are electric charges in electrified bodies, whereas the essence of this physical phenomenon remains an open question.

The supporters of the kinematic (L,T) system of physical quantities seem to have been guided by considerations of «visibility» and «tangibility» of kinematic quantities, while it is known that the creator of the famous (L,T) table R.O. Bartini developed his theory as well as the kinematic system to solve applied problems in physics and mechanics. His theory implies introducing the the notion of a «volume of time», which together with the spatial extent forms a six-dimensional manifold, where the L and T dimensions are defined by him as «elements of space-like and time-like extensions of subspaces» [2].

The critics of (L,T) system point at the lack of a basic quantity, such as mass, responsible for materiality. But aren’t space and time given to us in sensation? Matter is known as a philosophical category designating objective reality, while space and time are universal objective forms of existence of matter. But what is the ground for the preference of «mass» priority over spatial and temporal characteristics in terms of materiality? The substance is indeed material and we feel can it. But «mass» is not a substance, it`s the measure of inertia of a material body. So what is the ground for this parameter not to have a dimension, for example, a combination of units of length and time?

Let`s talk about force and acceleration

Before we start, I would like to say that we do not aim to criticize the conventional physics, there is plenty of such criticism in information space today. Nor is there any intention to impose one’s point of view, much less to claim the truth of knowledge. The truth is owned by the One Who created our world, leaving us users to reason, assume and believe.

At one time, the formula of the force acting on the body was accepted (Huygens was involved, should the history of physics be trusted), expressing, as per the textbook, Newton’s second law, and having the form of F = m · a (1), where m is the mass of the body, and a is the acceleration imparted to the body by force. At the same time, according to Newton’s third law, for two interacting bodies, the force formula has the form of F = m₁·a₁ = m₂·a₂ (2). Forces are referred to as the actions of bodies on each other that create accelerations. `It`s just that simple`, one might resume. It appears, though, the formula that in order to find out the magnitude of the force, it is necessary, apparently, to measure the mass and acceleration while to get accelerated motion of the body, a constant force must be applied to it for a certain period of time. Let’s see how in reality we can use this formula of force acting at direct contact of bodies, and meditate on the acceleration imparted to the body by force. Note that the acceleration reported to the body is understood as acceleration while force is in effect, but not after the termination of the action.

When the acceleration of the body is mentioned, it is implied that the body is continuously accelerating as a whole, with all its segments. To prevent friction, environmental resistance and gravity, imagine the acceleration of a space satellite in its orbit by a spacecraft with an engine. If a ship with the engine turned off simply collides with a satellite (it is clear that the collision will be elastic enough) and does not push it further, then after the collision the satellite will continue to move by inertia at a new constant speed. Such an interaction means that the force acts during the elastic contact of the apparatuses and according to Newton’s third law, the apparatuses must accelerate in opposite directions during contact, since only one force acts on the apparatus (from the other apparatus) and for every action there is an equal reaction [1,p.101-102].

A similar picture can be observed on a billiard table if we hit the center of the ball at rest with a cue ball. Since the balls have the same mass and size, the cue ball will stop, and the ball that used to be at rest, having acquired during the contact the pre-collision speed of the cue ball, will roll in the same direction without acceleration. Similar to the phenomenon of «quantum teleportation», during the collision the balls will exchange their states («properties»).

To illustrate the fulfillment of Newton’s third law a popular physics textbook also mentions the collision of two billiard balls when they change their speed, i.e. both balls get accelerations [1, p. 101]. Indeed, they do change their speed, but once the speed changes, the balls do not accelerate. The change in velocity, i.e. the transition from one frame of reference to another, occurs by a leap, meaning not instantly, but through the stage of elastic deformation of the balls, during which the balls, as if «stuck together» and forming a whole body, compress and decompress, then after the equilibrium of the system they immediately fly apart at a terminal velocity without any acceleration. During the contact in the case of a frontal collision viewed above, we can talk about the acceleration of individual parts of the body, but not about the movement (especially accelerated) of the ball as a whole, i.e. the force formula does not work here. Of course, it may be objected that the center of the ball moves during elastic vibrations, indicating the movement of the ball entirely along a certain trajectory, yet this contradicts the definition of translational motion of the body, in which all points of the body must move in the same way[1,p.24]. It is obvious that during the contact, i.e. under the force action, there is no translational movement of the balls (nor do we say that a piece of meat moves entirely on the cutting board when it is beaten off) and, accordingly, there is no acceleration of the balls.

Let us consider another situation when a space satellite accelerates if the ship «sticks» to it from behind and accelerates it by means of engine running. If the satellite and the ship alone are taken into account in this force interaction, what kind of accelerations of these devices is applicable in the force formula then? Is it he acceleration with which they both move in the orbit? If so, there is a discrepancy with Newton’s third law — when the apparatuses react, their accelerations are supposed to have opposite directions, and if their masses are different, then all the more the action is not equal to the reaction, since the accelerations of the apparatuses remain the same in magnitude. The above refers to the reference frame coordinated with the initial position of the satellite before the collision with the ship (i.e. satellite-before-the-collision coordinated system). Yet, if we switch to a reference system coordinated with «stuck» devices, we find there is no movement relative to each other in such interaction and, accordingly, there are no accelerations in this reference system. Probably, it would be more correct to consider both accelerating vehicles as one moving body with a total mass, which is accelerated by the engine, however, the engine also accelerates in the same direction and the same questions arise on the application of the formula [2].

At a static power load, the body is put under pressure, we observe a static picture – nothing moves or accelerates, while the force acts. We understand that the pressure produced is the result of some processes taking place somewhere and something is moving somewhere, forcing us to maintain the pressure. In the textbook we find an explanation that when two forces balancing each other act on a body, the latter does not receive acceleration, and these forces, each acting on the body individually, would inform it of equal accelerations directed oppositely, yet this is not our case where the resultant force is zero[1,p.82]. However, this explanation cannot be considered satisfactory, since at first the forces are defined as the actions of bodies upon each other, producing accelerations [p.81], and then, under certain conditions, it may turn out that the body will not receive acceleration under the action of forces [p.82], which, of course, cannot be an excuse, dare we say, for violating Newton’s universally recognized second law [1]. Note that the term «balancing» is borrowed from the weighing of bodies on scales, when at equilibrium we observe a static picture without any movements, let alone accelerations, yet at the same time we are clearly aware of the real effect of the weight force.

To confirm Newton’s third law, the textbook provides an experiment with stretched dynamometers hooked to each other, in which the readings of both dynamometers coincide at any stretching, while it is concluded that the force with which the first dynamometer acts on the second one is equal to the force with which the second dynamometer acts on the first one[1, p.101-102]. However, in the experiment, dynamometers are stretched in opposite directions with hands holding them by the free ends, i.e. two forces are applied to each dynamometer from different sides, not one, so it is incorrect (to put it mildly) to mention only the action of one dynamometer on the other. Accordingly, nor is applicable here the formula (2) from Newton’s third law describing the effect on a body from another body of a single force. What we have here is the above-mentioned case with balancing forces when two forces act on a body with an obvious absence of accelerations. Again , the question arises whether it is appropriate to introduce acceleration into the force formula and whether such a formula is practically applicable when measuring force in the case of its action in direct contact of bodies.

In practice, force is measured with instruments that are calibrated in accordance with the standard of force (the simplest such means is, for example, a dynamometer), recognized as the weight of a platinum calibration weight, while the equation of the force acting on an object has the form of F = m · g (3), where g is the acceleration of gravity at the Earth`s surface. Since g is a constant for all objects close to the Earth’s surface, the mass of an object is always calculated through the force of the weight of the object, and is not measured by itself, in fact, there is no tool for direct measurement of mass. Thus, mass is essentially a conditionally chosen quantity, which is obviously not suitable for the role of a basic physical quantity, unlike the force of weight. We see that the measurement of force does not need to use its constituent quantities m and a, which are calculated quantities, one of them is calculated from the body weight formula, and the other — from the force formula (1) if needed.

Another force formula was suggested by Hooke for the case of elastic deformation of a thin rod, namely F = S·E·Δl/l (4), where S is the cross-sectional area of the rod, E is Young’s modulus, Δl/l is the relative deformation of the rod. The peculiar thing is that mass and acceleration are not involved here, which, in our opinion, makes this formula more practical, although in reality the exact measurement of relative deformation seems to be quite a difficult task. Studies of elastic interaction of bodies, during collision, for example, convincingly demonstrate that force is always directly related to the deformation of bodies during their contact and is the product of the interaction of at least two bodies. This is also true for non-contact (field) interaction, when a deformation of the field around the body occurs, leading to the motion of the body relative to another body.

The introduction of acceleration into the force formula might have been influenced by centuries-old observations of accelerated free fall of bodies from a height. As per another version, observations and experience show that bodies receive acceleration relative to the Earth, i.e. they change their velocity relative to the Earth in magnitude or direction, only when other bodies act on them [1, p. 76]. Note that the change in speed is identified with the occurrence of acceleration. However, we do not see confirmation of this in the examples of elastic (as well as non-elastic) collision of bodies, when upon a short-term stop (in the reference frame of the contacting surfaces of bodies), the bodies immediately fly apart at acquired speeds, and their further braking is already conditioned by other factors (friction, resistance of the medium, etc.).

The connection between force and acceleration has become so axiomatic in people’s minds that even the authors of modern theories and hypotheses alternative to conventional physics do not challenge this connection. Accordingly, nor is the belief that the dimension of the gravitational field strength in the law of universal gravitation is to coincide with the dimension of acceleration, respectively, questioned by many authors.

For forces acting at a distance, the force formula takes the form of Newton’s laws of universal gravitation and the interaction of Coulomb’s electric charges, which, for example, in the SI system, are written as F = G·M·m/r² (5) and F= q₁·q₂/4πε₀r² (6) respectively. As is known, the expression a₁·r²= m₂·G (7) (when writing the law of gravitation in the form of F = m₁·a₁=G·m₁·m₂/r²) has the dimension of L³/T², i.e. with constant masses of interacting bodies, the acceleration of the body is inversely proportional to the square of the distance between the bodies. What can this mean in a physical sense?

Note that the force or acceleration in these laws does not depend on the distance between the bodies (otherwise the force would be inversely proportional to the distance r), but on the square of the distance r², which in itself does not carry a semantic charge, since it is a mathematical sign, not a physical quantity. In this case, only the surface area having the dimension of the square of the distance can have a physical meaning. Yet, a square surface with an area of r², for example, logically does not fit into the picture of the interaction in the central field of forces. This seems to suggest, in these laws, a spherical surface with an area of 4πr² which, for example, in the case of the law of gravity, is to be equidistant,  from the center of the lead ball in the Cavendish torsion balance (4πr², actually, appears in the Coulomb formula (6) in the SI system). That logic suggests that the force is to be inversely proportional to the area of the sphere in the center of which the body is located. Besides, it is necessary to emphasize that physical laws expressed by a mathematical formula should reflect the relations between physical quantities rather that their dependence on mathematical signs or symbols. Therefore, in the denominator of the right-hand side of the formulas under consideration, a physical quantity should be found, behind which there is a real physical factor. It could be argued, of course, that in the case of electric charges, the right-hand side of the formula can be interpreted as the product of two potentials, then out of r² one r refer to each potential, while the F force would only depend on the potentials. However, It should be noted that the electric potential is a contrived quantity introduced to solve practical problems in electrical engineering, and compared to an electric charge, the electric potential is not a primary physical value, nor is energy, for example.

If this is the case, then the expression (7) is to be corrected to take the form of a₁·4πr² = m₂·4πG = m₂·G* (7^), where G* = 4πG. Now, as we can see, the expression a₁·4πr² essentially characterizes the acceleration field in the central field of forces.

Another challenge is to justify again the acceleration of the body the force formula — now for field interaction,- which is also inversely proportional to the squared distance between the bodies. Was the presence of acceleration of the body really experimentally proved in the experiments at the Cavendish apparatus? Or maybe even in experiments with electric charges, in which charged bodies were clearly attracted or repelled, as opposed to dubious attractions (if you believe the history of these experiments) when measuring gravitational force? It is only known that the gravitational force of the interaction was fixed after rotating the lever into the equilibrium position with the elastic force of the fiber.

The textbook on physics says that Newton was aware of the inverse proportionality of the accelerations of the planets of the solar system to the squared distance of the planet from the Sun, which lay the foundation for the law of universal gravitation [1, с. 241-243]. This conclusion is based on substituting the centripetal acceleration formula into Kepler’s third law equation [1, с. 241]. But again we are faced with a situation in physics when it comes to theoretically assumed and actually virtual acceleration, which is not observed in practice. When describing the motion of the planets, it is confidently stated, along with the statement of the uniform circular motion of the planet, that there is a complex acceleration of the planet directed towards the Sun [1, с. 241]. The use of the rule of similar triangles in deriving the centripetal acceleration formula, with the volitional transfer of the velocity vector along the circle from the end point to the initial one, thereby creating a velocity increment vector that does not exist in real uniform circular motion, having a scalar increment value at [1, с. 69-70] that does not exist in real motion, to put it mildly, is a highly dubious technique. As a result of using the «imaginary» scalar of the velocity increment, we obtained the well-known formula of centripetal acceleration in the form a = v²/R (8), which was also a reason why a statement occurred about the actual existence of normal or centripetal acceleration for planets, which is inversely proportional to the squared distance of the planet from the Sun. As a result, we have the law of universal gravitation in its existing form.

Apparently, the main reason for the above-mentioned misunderstandings with accelerations under the action of forces was the initially incorrect definition of accelerated motion. Initially, it is stated that if the instantaneous velocity of a moving body increases, then the motion is called accelerated, acceleration, in its turn, is the ratio of the speed increment to the time interval during which this increment occurred [1, pp. 50-51]. Note that so far we are talking about scalar quantities, since the speed of uniform motion has already been defined before as the ratio of the path traversed by the body to the time interval in which this path is traversed [1, p. 36] (by the way, the 1975 edition of this textbook speaks about the ratio of the path length). But then there emerged a need to take into account the direction of movement, since movement in space is the movement of a body along some trajectory. And then a strong-willed decision is made that, in the same way, the velocities and accelerations of bodies should be characterized not only as numerical values, but also as the direction. The concept of a vector quantity, or vector, is introduced and such quantities as motion, velocity and acceleration are called vectors, emphasizing that they are not scalar quantities [1, pp. 61-62]. In other words, these quantities that used to be scalar quantities (you can’t call a path length a vector) turned into vectors with all the consequential effects of vector calculus.

However, it is also explicitly stated there that distance and time are scalars, from which it follows that the ratio of the path length to the time interval defines speed as a scalar quantity, which is clearly contradicted by the volitional definition of speed as a vector quantity. Moreover, the need to characterize the speed or acceleration of a moving body as a direction in space does not stand up to criticism, since the direction can be applied to the movement of a body in space, but not to the parameters of this movement, which are speed and acceleration. When moving in space, the body moves (directs) and changes direction, not its speed or acceleration. 

The fascination with vector algebra when predicting real movements can lead to predictable incidents in practice, when, it is necessary, for example, to move from point A to point C through point B, which is far away from the direct trajectory of the AC, the navigator, referring to the vector addition of the movements of AB and BC, suddenly convinces us, for understandable reasons, to fill the tank with just enough fuel to move along the AC vector, since, according to the rule of the triangle, the vector movements of ABC and AC are equal to each other. Thus, as a result of the willful substitution of real movement in space by vectors on paper, the engine may stall somewhere between points B and C.

Unfortunately, when deriving the centripetal acceleration formula, there was also a substitution of real values with vectors on paper. First, it was agreed that there is always a change in velocity in curved motion, i.e. this movement occurs with acceleration (i.e., even when the numerical value of velocity does not change), and to determine acceleration (in magnitude and direction), it is necessary to find the change in velocity as a vector [1, p. 68]. Further, since the velocity vectors in curvilinear motion have a different direction, then you need to take their vector difference and the velocity increment will be expressed by the vector Δv. Then the acceleration will look like a = Δv/t and will coincide in direction with the vector Δv. At this point of the narrative, it is tempting to ask an innocent question to the authors of the textbook,`Why not present a specific example of calculating acceleration according to the proposed formula? The questions that arise are what is hidden under the Δv sign and what value the authors would substitute into the formula as Δv in the case when the velocity modulus does not change. Is it the difference of directions expressed in angles? And then again, how to explain the compatibility of two velocity vectors and the mentioned difference in directions as the sides of one triangle?

Well, then, when considering uniform motion along a circle after manipulations on paper with invented vectors and triangles that are not comparable in «quality» of the sides, the velocity increment (vector velocity difference) is again expressed in a volitional way in the form of at and the necessary theoretical formula for centripetal acceleration, namely, a = v²/R (8) is easily derived. This disparity means that in one triangle all sides have the dimension of distance, and in the other triangle two sides have the dimension of velocity, while the third side is dimensionless, i.e. the triangles are compared, the sides of which are quantities of different quality. 

Yet most likely, supporters of the existence of real accelerations directed towards the Sun, as always, will fight back, reassuring that the planet is moving in orbit at a constant speed, and the balance of centrifugal and centripetal forces is to blame for the inability to register centripetal acceleration, as well as centrifugal. These forces, acting on the planet individually, of course, would give it equal accelerations directed in the opposite direction, yet in the current situation we do not see these accelerations, although they undoubtedly exist. It’s a shame, though, that experimentally it will never be possible to confirm the undoubted existence of these accelerations, and in particular, to check whether the specified acceleration a = 2πv/T really exists.

Of course, it is possible to point out an increase in the speed of movement in one orbit relative to the speed of movement in an orbit with a large radius, but such virtual acceleration has nothing to do with the real process of circular motion of a planet in its orbit at a constant speed.

Against all odds, with the theoretical formula of centripetal acceleration derived in the above way at hand and using Kepler’s third law, the inversely proportional dependence of the acceleration assigned to the planets of the Solar System on the square of the orbit radius has been accepted.

Velocity field

Returning to the laws of field interaction, namely to the above-mentioned acceleration field a·4πr² in the central field of forces, we dare to note that acceleration cannot be called a successful parameter in this case for other reasons that follow.

When fluid moves in a pipe of constant cross-section under constant pressure, we observe a velocity field when, with uniform motion (for example, laminar flow without friction against the pipe walls) the flow rate in each section is constant. In a tapering flat section of the pipeline, the velocity field is such that the velocity of the liquid is inversely proportional to the width of the section (at constant thickness), and in a tapering cone-shaped section, the velocity is assumed to be inversely proportional to the cross-sectional area of this section. Thus, in the first case we are talking about motion with constant velocity, in the second case — motion with constant acceleration, while in the third case — with a constant parameter having dimension L/T³. At the same time, we observe the dependence v · S = k, where v is the flow velocity, S is the cross-sectional area of the pipeline section, k is the volumetric flow rate, i.e. we have a velocity, not accelerations, field.

It is noteworthy that the velocity of the liquid after exiting the pipeline, regardless of the shape of the end section and the nature of movement along it, will ideally (without taking into account resistance and gravity) be constant, as it should be by inertia. The nature of motion by inertia, i.e. at a constant speed, is essentially basic in conventional physics. This explains why the speed of the flow of time was also agreed to be considered constant. Therefore, unlike uniform motion at a constant speed, accelerated motion has no reason to continue the accelerated outflow after exiting the pipeline.

Thus, despite the possibly rough comparison with hydrodynamics, it would be more logical to see velocity instead of acceleration in the above-mentioned central field of forces, i.e., common sense suggests to introduce the velocity field v·4πr², and not accelerations in the law of field interaction.

I would like to draw your attention to an important point that shows the fundamental difference between the dimensions of the speed of movement L/T and the acceleration of movement L/T² and which is as follows.

In the velocity formula, one-dimensional «elements of space-like and time-like extensions» are compared, using Bartini’s terminology. In this sense, L and T can be called elements of the same quality and the distance travelled can be measured and expressed both as a distance and as a time interval. At the same time, distance and time are measured, actually, on linear scales. To some extent, the speed of movement as a physical quantity performs the function of transition from one frame of reference to another, relative to which it moves at this speed, in other words, it is a kind of «coefficient» or «operator» that allows you to go to measuring the path from length to duration in time and vice versa.

One of the variants of the acceleration formula contains the distance in the numerator, while the square of time is in the denominator, in fact, incomparable quantities are compared, namely the real distance and the virtual square of time, which is not a real physical factor, unlike time in the first degree indicated in the denominator of the velocity formula. Therefore, the correct acceleration formula, of course, is the comparison of speed and time, and not distance and the square of time.

In the case of a velocity field, the expression v·4πr² formally (if we abstract from the field interaction) can mean, for example, the flow rate of some volume l·S/t, where l is the distance travelled by the flow per time t through a spherical cross-section area of S. In another interpretation, v can presumably mean the rate of deformation of the field in some section, i.e. v = Δl/t, if we apply a rough analogy with the elastic collision of thin rods, when the rate of deformation is possibly directly proportional to the total velocity of the colliding rods at the moment of impact. In any case, the velocity field does not cause rejection yet, nor does, for example, constant and habitual time consumption alarm us.

Speaking about the acceleration field in the broadest sense, then in the case of volume consumption, it is formally associated with a constant increase in the consumption of something in any section of the field, which obviously should have led to a universal catastrophe worse than the «Big Bang» long ago so we would not be discussing natural philosophy right now.

And one more remark. Imagine the acceleration of a car during a strength test in a collision with an obstacle. First, the car collides with an obstacle, accelerating to a speed of 20 km/ h, then the obstacle is moved further and the car is accelerated with the same acceleration to a speed of 40 km/h. There is no doubt that the impact force in the second attempt is greater than in the first, since the momentum of the car is greater. But what about acceleration during impact? The acceleration of the car during speed-up, including at the last moment of acceleration, was the same in both cases, as was the mass of the car. That is, the value of m ·a has remained the same and, apparently, it cannot be called the impact force. Let’s say we call it the acceleration force, then how do we measure the force of collision with an obstacle and what formula is to be used?

The mystery of the gravitational constant

Well, now it’s our turn to tell our fairy tale, while showing will and manipulating physical quantities. First we will look at Coulomb’s law in the CGS system, i.e. F = q₁·q₂/r² (9). We will consider this force formula basic, since it lacks the proportionality coefficient, which in Coulomb’s law is known to depend on the choice of units, and also because this formula was used to establish the unit of electric charge — the absolute electrostatic unit of charge [3, p. 36]. Moreover, this formula can be considered basic not only for electric, but also for gravitational force.

Earlier we decided that the force should be inversely proportional to 4πr², then we transform the formula (9) for the case of charges of the same magnitude as follows: F = q·q/4πr² (10). Certainly, when using this formula in practice should, to measure a charge the absolute electrostatic unit of charge divided by the square root of 4π is to be used.

For the purity of our manipulations, we will similarly express the law of universal gravitation in the CGS system and obtain, in the case of identical masses and taking into account the dependence on the spherical surface area, the following formula F = G*·m·m/4πr² (11), where G* = 4πG. Since in the CGS system force is measured in dynas, distance in centimeters, and mass in grams, the numerical value of the gravitational constant G will be three orders of magnitude greater, i.e. 6.67 ·10-8 din·cm²/g², and accordingly G* =8.38· 10-7 din·cm²/r². It is known that Coulomb’s law is similar in form to the law of universal gravitation [3, p. 35]. Then, when comparing formulas (10) and (11), we see that for the same values of force F and distance r, the magnitude of the charge q is equal to m·√G* (12), and the expression (12) can be called a gravitational charge, which has the same dimension as the electric charge.

To a possible question, whether, on the contrary, it is necessary to specify a mass with a constant instead of a charge in Coulomb’s law, we note that the correct mathematical formula describing the dependence of one physical quantity on other physical quantities should not contain any meaningless dimensional constant, like a gravitational one, as a multiplier in the right part due to the functional and, accordingly, practical uselessness of the constant. If the formula of a physical regularity in any generally accepted systems of units of measurement contains a similar constant, then something is wrong in this formula and some component of its physical quantity is determined incorrectly. This happened with the mass, no wonder questions arise around this value when considering the force interaction. Why at all does a formula describing the dependence of one physical quantity on other physical quantities need a constant that does not have any real physical factor behind it and on which the physical quantity on the left side of the formula does not depend by definition?

It seems to us that formula (10) describes correctly the physical regularity in the field interaction of two physical objects, showing a «pure» relationship between the force of interaction, the magnitude of charges and the area of a spherical surface. In the case of gravitational interaction, the charge is represented by the expression (12).

Next, we do the following. Since the acceleration of gravity g and the gravitational constant G were measured at the Earth’s surface, the formula for the force of weight on the Earth’s surface will have the form of F = m·g = G*·M·m/ 4πR² , where M is the mass of the Earth and R is the radius of the Earth. Then g = G*·M/ 4πR² = √G*·√G*·M/4πR² = √G*·Q/ 4πR².

Since we decided to replace the acceleration field with the velocity field, the pure formula of the gravitational charge of the Earth will have the form Q = g·4πR²/√G*, in which the desired velocity at the Earth’s surface v_g is equal to g/√G*. Then the value 1/√G* must have the dimension of time. Calculate the constant √G* and get the number 9.15 · 10^-4, the inverse of which is 1.092 · 10³, i.e. 1 /√G* = t* = 1.092· 10³ seconds.

Multiplying this amount of time by the amount of acceleration of gravity g, we get the velocity at the Earth’s surface v_g = g·t * = 10.7·10³ m/s or 10.7 km/s, the value of which coincides with a very good accuracy with the known calculated value of the second cosmic velocity equal to 11.2 km / s. Accordingly, the force of the body weight at the Earth’s surface will have the form F = m·g = q·v_g.

As you understand, we have got rid of the illogical acceleration in the force formula, replacing it with speed. At the same time, we obtained a «pure» mathematical formula of the law of gravity, in which there is no gravitational constant and there is no place for mass. Instead of acceleration g, which refers to the free fall of a body near the Earth’s surface, we have obtained a sufficiently explicable value of the velocity of a body near the Earth’s surface, necessary to overcome the attraction of the Earth in order to leave the limits of the Earth’s field.

The replacement of mass by charge is also logically justified by the fact that the primary measured force is the field, not the contact interaction, in particular, the force of body weight, while we remind that mass is a parameter calculated precisely from the force of weight at the Earth’s surface.

Conclusions

The main result of our reflections is the transition to the (L,T) system of dimensions for all physical quantities. In the (L,T) system, the key physical quantity, namely the field charge, has dimension L³/T¹ and represents the velocity field in the central field of forces. Actually, the field charge or velocity field, apparently, can be called a physical field, in which the dimension of the field strength has the dimension of the linear motion, in particular, and the dimension of the electric field strength E. Yet, what in reality can move at such a speed and what the physical meaning of the field strength with the dimension of speed is, requires careful study. Most likely, this is due to the elasticity of the field, while the field strength is somehow related to the rate of deformation of the field at a given point of the field.

We see that the quantity we called the gravitational charge formally looks like a certain volume multiplied by a certain frequency, the physical meaning of which is still unclear. If we divide this value by the volume of the body, we get the density of the substance of the body, which has the dimension of frequency.

Further, it is not difficult to deduce the dimension in the system (L,T) of any other existing physical quantity. For example, force has the L⁴/T² dimension, energy — L⁵/T², electric current strength — L³/T², etc.

Thus, the assumption known from the history of physics (including the famous Bartini) is that the dimension of any physical quantity can be expressed through a combination of dimensions of space and time is proven true. Accordingly, it becomes possible to get rid of dimensions that are incomprehensible in the physical sense, such as gram, joule, coulomb, henry, etc., etc.

In the case of the interaction of two charges, the force as a physical quantity is formally the product of the magnitude of one charge by the field strength created by the other charge, i.e. it has dimension L⁴/T². Probably, we can only speak with confidence about the real magnitude of the field strength created by a charge whose charge value is several orders of magnitude greater than the value of another charge, for example, as in the case of the gravitational field of the Sun within the solar system or the Earth’s field in near-Earth space.

Looking at the force formula, we see similarities with the traditional momentum formula. Instead of mass, the magnitude of the gravitational charge appears, which differs from the mass by a multiplier in the form of t*, since m·a = q·v, and the force can be considered a mechanical impulse, or vice versa, the impulse can be considered a force, since in the physical sense in the mass-charge pair the charge is primary, while the mass is its derivative. That means, the charge «works», not the mass, in particular, that is also true for the law of conservation of momentum. So is it the moment of momentum that is hidden behind the mechanical energy (work), or is it the other way round? After all, these values are obtained by multiplying the force or momentum by the distance.

Another consequence of the above analysis throws into question both the existence of the gravitational constant, and the statement that it is a world constant that should be used, in particular, in the entire solar system. Firstly, it was measured on the surface of the Earth and, according to our assumption, its connection with the second cosmic velocity in terrestrial conditions comes out. Secondly, if the coincidence of the velocity vg with the calculated second cosmic velocity in the terrestrial conditions is not accidental, the calculated value of t* on the Sun`s surface, based on the calculated values of acceleration and the second cosmic velocity, should be about twice as large as on Earth, while the value of the gravitational constant should be less.

Obviously, it is worthless either to look for a physical meaning in the value of t*, for example, to consider it the time of any acceleration or deceleration. Firstly, because it should not be present at all in the correct formula of the gravitational attraction of a body, at the Earth’s surface, in particular, as well as the gravitational constant G, and the formula, in our opinion, should have the form F = q·v_g = q·Q/4πR² (13), where Q and R are the charge and radius of the Earth. Secondly, the acceleration of gravity g, which was one of the reasons for the appearance of the gravitational constant, has no direct relation to the gravity itself and the emergence of the body weight force. It is the acceleration of a body initially at rest relative to the Earth, brought out of a state of rest, and has no relation either to the centripetal acceleration approved at the time, calculated by formula (8) during the orbital rotation of bodies or planets. Thus, the gravitational constant appeared at one time due to the incorrect definition of the weight force as F = m·g.

1. Elementary Textbook on Physics, ed. Academician G. S. Landsberg, M., «Science», 2010, vol. 1.

2. Roberto Oros di Bartini. Some relations between physical constants. Reports of the USSR Academy of Sciences, 1965, vol. 163, No. 4, pp. 861-864.

3. Elementary Textbook on Physics, ed. Academician G.S.Landsberg, M., «Science», 1975, vol. 2.

Vladimir A. Denschikov, leading state expert, Federal Institute of Industrial Property, Moscow.

January 13, 2022

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