What is mass, energy and charge? Why are they here together? How do they relate to each other?? And how it manifests itself in physics?

Massa. This word is used extremely widely.. And in everyday life, and in science. The same can be said for words “energy” and “charge“. I will not talk about the everyday uses of these words here.. But even in science, the meaning of these words remains to a certain extent mystical., not completely clear. And this at that time, when the concepts behind them, are at the very core of our knowledge of the nature of things. Therefore, it is highly desirable, so that these words are perfectly clear and understandable terms of physics as a science. And this can be achieved. so, first “weight”. Historically, in physics, three ideas about body weight. One of them considers body weight as a measure of its inertia, magnitude, characterizing the measure of the body's resistance to the force acting on it. You can say, that this representation connects mass with the body, as inherent in him “passive” characteristic. Second idea of body weight as a value, characterizing the force created by this body, attracting other bodies, also having mass, in a sense the opposite. In this case, the mass can be considered “active” body characteristics, themes, what creates strength. In this case, the first representation is, in a certain sense, broader., more general. The thing is, what mass, as a measure of resistance to acceleration by force, the same for any possible forces. And the mass, as a value that creates force, creates only gravity, gravity. Third view of mass as the amount of substance in a given object compatible with any of the first two. It just states, that in both cases the mass, as a characteristic of the body, is an additive quantity, ie. the mass of a full body consists of the masses of its constituent parts. And in terms of its inertia, and from the point of view of the gravitational force created by the body. And therefore can be considered as an indicator of the number of these parts. Last performance, quite fair in the classical approximation, turned out to be incorrect in the quantum approximation. When studying many phenomena of nuclear, and in some cases atomic physics, it turned out, what is the mass of the composite object, for example atomic nucleus, always differs in the smaller direction from the total mass of its parts, taken separately. This property is usually called “mass defect”.

Eenergy. This concept in physics was also initially ambiguous.. One side, the idea of kinetic energy of the body. Energy, characterizing the presence of a body of some speed relative to other bodies. This form of energy is associated with body movement.. On the other hand, there was also an idea of potential energy of the body, energy owing its existence to a certain position of the body relative to other bodies. You can say, that this form of energy is associated with the rest of the body. Energy can change from potential to kinetic, and vice versa. Both of these forms can be called mechanical energy.. At certain stages in the development of physics, other ideas about energy appeared. (thermal, chemical, etc.), but today there is no doubt, that all other types can always be reduced to a mechanical form of energy. In both its forms, the mechanical energy was proportional to the mass, considered as a measure of inertia. But since both forms of mechanical energy are clearly linked to the mutual relative position or motion of bodies, then there was no direct correspondence between the energy and mass of an isolated body at rest. This connection manifested itself only with the advent of the special theory of relativity.. There is a widespread representation, that SRT made it possible to establish the equivalence of energy and mass, and this equivalence is written using the famous formula E=mc². This representation is a very strong simplification., even a distortion of the actual situation. In fact, the real state of affairs is somewhat different..

IN physics, besides mass and energy (mechanical), there is one more important concept, characterizing the movement of bodies. This concept is called pulse, or amount of body movement. This characteristic of the body is also proportional to its mass., but, as opposed to mass and energy itself, has more than one, and the three components. Regarding transformations of three coordinates, chosen to describe the space, momentum behaves like a vector. Mass and energy during such transformations remain unchanged., scalars. Special theory of relativity combined not only space and time into a single entity, dubbed space-time. She also combined into a single entity and two, seemingly, different body characteristics, momentum and energy. This unification was expressed in the understanding that, that the energy and three components of the momentum in any chosen coordinate system (four-dimensional, including three spatial coordinates and time) are the components of the four-dimensional vector, called the energy-momentum vector. With respect to coordinate transformations, affecting both space and time, momentum is not a vector, and energy is not a scalar. These two characteristics of body movement are involved in such transformations together., as components four-dimensional vector. But such transformations combine in one consideration the movements of the body with different speeds., including zero speed, ie. resting state. In some coordinate systems, the four-dimensional energy-momentum vector has zero spatial components. And here is the temporary component for bodies, having mass, zero does not exist. This component in all other coordinate systems is considered as energy. Consequently, it should be considered in the same way in the rest systems of a given body. Rest energy. But this is a previously unknown potential form of mechanical energy.. The four-dimensional energy-momentum vector is associated only with a given body, and exists even then, when there are no other bodies, relative to which position or movement can be determined. Rest system can (must) be defined as private case of body movement relative to itself (there may be other bodies at rest in this system, but their presence is not necessary at all). In this way, energy concept, previously associated only with relative motion or body position, turned out to be tied to each individual body, seemingly regardless of the states of other bodies. Previously, only the mass was such an individual characteristic.. However, there was no increase in the number of individual characteristics of the body., since the concept of rest energy turned out to be identical to the concept of rest mass. Actually, the number of body characteristics has decreased in general to a single body characteristic. This whole set of values ​​of mechanics — weight, energy, pulse — merged into a single object, energy-momentum vector. In this sense, one can say, that energy is mass, and mass is energy (slightly different numerical coefficient,c²).

What kind of vector is this? Why is it so important to describe the chosen physical body? We assign to any physical body in each coordinate system, describing the area of ​​space-time, in which this body exists, some trajectory. Of course, we associate the only trajectory with the body only then, when we consider it to be point, ie. neglect size body versus our selected units. Consider for now the case of a point body, as the easiest to understand. The trajectory of such a body in space-time can be described in two ways. Using the system of equations, and in the form of coordinates on the trajectory, depending on scalar (which does not change when other coordinate systems are selected) parameter. These forms are equivalent. As a matter of fact, the second form is the most convenient way to write down the solution of a system of equations with the understanding that, that the solution of this system is some one-dimensional subspace in four-dimensional space-time, line. This form of notation allows you to see it explicitly.. Besides, it also allows us to understand the meaning of this scalar parameter. The scalar parameter is nothing more than internal to the trajectory (lines) coordinate. Recognition of the fact, what trajectory is this exactly one-dimensional subspace. If the solution to the system of equations were the two-dimensional subspace, then two parameters would be required, two internal coordinates. Internal in the sense, that they are chosen on the subspace of the body, on the trajectory regardless of the choice of the coordinate system in the ambient four-dimensional world. And when changing the enclosing coordinate system, they do not have to transform, remain unchanged. It does not mean, that such a parameter on the trajectory is the only one. Not at all. You can also parameterize a line in an infinite number of ways., if only every new parameter is a smooth function of the old. But it's important to understand, what is this parameter conversion, one or another of his choices, does not affect the choice of the enclosing coordinate system in any way. As well as vice versa. It is not by chance that I pay so much attention to this moment.. It is one of the most important for understanding the meaning of such a concept as an energy-momentum vector. so, what quantities can we describe the existence of a point body in space-time? Body position relative to the selected coordinate system (in four-dimensional space-time — history of its existence) we write it as a set of its four coordinates: xⁱ(s). We wrote them as functions of the scalar parameter s (unique internal coordinate on the subspace of existence). Index i can take values {1,2,3} for spatial coordinates and 4 for time. Besides, together with the position, we also have the scalar parameter s, which can also be viewed as a function of the coordinates s(xⁱ). Of course, it may not be the smoothest of all functions, but we have the right to consider the scalar parameter as a general function. Together with these two characteristics, two four-dimensional vectors immediately appear in our description of a point body: pⁱ=dxⁱ(s)/ds и p_i=ds/dxⁱ.

Since scalar parameter is not the only one, it is defined up to a transformation smooth on the entire trajectory, then a pair of these vectors is also not the only one. There are the same number of these pairs, how many scalar parameters themselves. If used the same scalar parameter, then these vectors are not independent, since their work (at the same point) equal to one. Ie. in a certain sense they are mutually inverse. These vectors are obtained using differentiation operations. First, which is called the vector tangent to the trajectory, is a complex of derivatives of coordinates on a trajectory when the scalar parameter changes along it. Second, which, under certain restrictions, can be considered the gradient of some scalar function, is a complex of derivatives of the scalar parameter with respect to coordinates. Yet again, in the strictest sense, it exists only along the trajectory. The restrictions on the possibility of considering this vector as the gradient of a function are associated with the concept of charge, but we'll talk about this later. There are no other natural vectors for describing the trajectory of a point body.. Therefore, the desire immediately arises to identify one of these natural vectors, better both at once, with the energy-momentum vector. And it can be done easily. But for this you need to take another close look at the scalar parameter on the trajectory, now into some of the specific shades of his physical meaning.

The scalar parameter is the internal coordinate of the trajectory, considered as a unique one-dimensional space, point object line of existence. The existence of a point object outside its connections with other objects allows us to speak only about the time of its existence, own time this object. It is this meaning that every internal coordinate has physical point object. The unit of time in this case can be , basically, any, including even changing along with the point of the trajectory, if we assume the existence of an object to be continuous. Of course, this change can only be noticed from the outside, looking at a trajectory from full space-time. From an internal point of view, the units of measure will be the same for all points of the trajectory for any choice. If all points of existence (being) are absolutely equal, are no different, then there is no way to select any special set of time units and the corresponding internal coordinate. The situation is different, if among the points being there are some special, events. Highlighting special moments in existence, events, a fairly common thing for our everyday language. Moreover, this is one of the main features of the description of existence. The very existence of something we always think of as a sequence of events. And tend to discern moments of existence, when nothing happens, from those moments of existence, when something happens. Moreover, we associate the time in everyday life with any chosen sequence of events.. for instance, sometimes we hear the chiming of the clock and mark it as special events, separated by an hour gap. Scalar parameter, which will turn out when describing our existence as a point object under the condition, that all successive moments, when we heard the clock strike, correspond to the sequence of its values 1, 2,3, 4,….. (o'clock), will be special for us, associated with this particular watch. Other watches — in general, another parameter, but each one will be in some way special, related to specific hours.

Imagine now, that every massive object has its own clock like this. That is, a certain set of events in its history is specific to this particular object.. Perhaps not alone. well, for example, if you sit around the clock all day with a fight, then you will completely type in your memory a number of moments, when did you hear this fight. Moving closer to physics, then on the trajectory of an elementary particle, registered vial, there is a sequence of bubbles, which is associated with the events of the interaction of this particle with the medium in the bubble chamber. Obvious enough, that the number of events in such a series will be invariant when changing coordinate systems, describing the region of space-time, in which this trajectory is located. On the other hand, one can also choose such coordinate systems, in which all these events will be located on the coordinate time line, with zero spatial coordinates. And you can still narrow down this group of rest coordinate systems of this particle to such, in which the intervals between successive events will be equal. In this way, we have two entities at the same time, inextricably linked with the existence of a massive body — scalar parameter, counting the number of events in his history, and time coordinate, the unit of which is a multiple of the number of pairs of consecutive events in it. Quite natural, that these two entities are related by the aspect ratio, which is the characteristic of this particular massive body, in a sense, common for all possible coordinate systems. This coefficient is the gradient of the number of events on the trajectory, considered as a scalar parameter, ie. a set of derivatives of the number of events by coordinates. In this way, among the possible scalar parameters, their derivatives with respect to coordinates and associated tangent vectors, for the trajectories of each massive point body, the corresponding subgroups of special parameters are allocated, counting events in the history of a massive point and their corresponding vectors. Let us denote parameters from this subgroup as s₀. In the rest frame of a massive point body, the proportionality between the scalar parameter (number of events) and the time coordinate can be written as s₀= And. The aspect ratio before time simply records that number of events, which appears per unit of time on the trajectory of our body. Its magnitude, of course, depends on the choice of the unit of time, but it is a characteristic of this particular body (and of course those reasons, possibly external to the body, which produce events on its trajectory). In other coordinate systems, related to the rest system by linear transformations, this ratio will be written as s₀=p_ixⁱ. Here s₀ no longer an arbitrary scalar parameter, but only such, which is proportional to the number of events on the trajectory of the body.

We can also give vectors p_i, associated only with such, event-counting parameters, special name. We call such a vector the energy-momentum vector. Really, in the rest frame, this vector has a single component, and exactly the same, as well as the energy-momentum vector. And if we identify it with the energy of rest, ie. with rest mass, taken with a suitable coefficient, then in moving systems we will have exactly the same components of energy and momentum, as in the physical quantity considered above.

I want to note, that such an interpretation of the energy-momentum vector (as the derivative with respect to the coordinates of the scalar parameter, proportional to the number of events along the trajectory) in a completely natural way assumes the positivity of the rest mass of any material point. After all, the number of events in the history of any physical object can only increase over time.. Just because, that the addition of new events to the sequence is the passage of time as such. The connection of this observation with the attractive nature of the gravitational force (ie. it is he, the source of which is body weight) is also quite transparent, but here I do not want to discuss this moment in detail, so as not to stray too far from the stated topic. What to do, peace one and physics, how is his image, should be one. But you have to describe it in pieces, so our description falls to pieces, connections between which protrude from each piece…

Pay special attention to the fact, that here we also have the opportunity to take a fresh look at two more well-known and very important for physics relations. First ratio, associates with each massive point particle some very important physical quantity, own act particles. And this connection in the particle rest system is literally expressed by the very formula, which we wrote above — s₀= And. Action in classical physics is introduced precisely with the help of the formula, as secondary to energy (after establishing the relations of the Special Theory of Relativity, with respect to the energy-momentum vector). but the role of this quantity in physics is by no means secondary. For reasons unknown so far, it turned out, that all the mechanics of a massive point (and not only this branch of physics) can be obtained from the principle of stationarity of action. Although this principle is more often referred to as the principle of minimum action, but the minimum or maximum is reached by the action on real trajectories of particles, not the point. Another thing is important. The trajectories of real massive particles are as follows, so that with variations of their parameters with fixed ends of the trajectory, the action remained stationary, ie. unchanged. Easy to see, that the number of proper events s₀ on some selected segment of the history of any massive particle (fixed ends) quite obviously should remain constant, independent of the choice of method for describing the trajectory itself (ie. with variation of its dependence on coordinates).

By identifying the action of physics with the number of proper events on the trajectory of a particle, and the derivative of this number with respect to coordinates with its energy-momentum vector, we immediately obtain the principle of stationarity of the action as a completely natural condition, not requiring any additional justification.

Since the units of energy (masses) and units of time in physics are usually chosen independently of each other, that action, as a physical quantity, will be identified with the number of proper events on the trajectory of the particle indirectly, but as a proportionality ratio, in which the proportionality coefficient will depend on the ratio between the selected units of energy and time (this coefficient is related to Planck's constant). The second relation is no less famous and important in physics., although it is more private. As soon as we take as a special parameter on the trajectory of the particle, the number of its own events, we can take as a unit of time such, which assigns the same value to the time intervals between two adjacent events — period. Then the number of events can also be called the number of periods, associated with the trajectory (with a slight amendment, taking into account, what period — it's not one, a couple or three events). And the energy gets the obvious meaning frequency. Taking into account the above remarks about the choice of units of energy and time, between energy E and frequency ν, as characteristics of a massive particle, the proportionality relation will also take place E=hν. This road leads to quantum mechanics. Now I do not want to go further on it, but I want to refer to the concept charge, to explain the reason, according to which this concept should be considered together with the concepts of mass and energy.

WITHaryad. This word usually means the presence (or lack, if the charge is zero) a material point has properties additional to energy-momentum, expressed in the difference in the trajectory of a material point under certain circumstances (in the presence of electromagnetic forces in the field) from some standard. What is characteristic, all three representations can be applied to the charge, given above for the mass. It is also a measure of interaction with an external force., and measure of strength, created by the material point itself, and additive size, counting the number of charges in a given material point (naturally, in this approximation, when the object is measured as a point). But there is also one significant difference from mass. Charges can be both positive, and negative. In all three senses. And on interaction — can be like attraction between charges, and repulsion, and by the amount — the summation of charges can lead to both an increase, and to a decrease in the final charge.

Let's ask a question, as soon as vector (four-dimensional) energy-momentum is the derivative of the scalar parameter, proportional to the number of events along the trajectory of a material point along the coordinates, and there are events on the trajectories of all material points in a given area of ​​space-time, is this vector gradient of some function, proportional to the number of events not only on separate trajectories, and in the whole considered area? Without going into the intricacies of the question, I will give the answer, famous from mathematics. In general, this is not the case.. Only under certain conditions, with absence “whirlwinds” in the links between events in the area, you can write the following function, proportional to the number of events, for which all derivatives along each chain of related events will be just the implementation of the gradient of this function. In physics this kind of functions are known as potential. Imagine a three-dimensional cubic lattice, each node of which is connected to its neighbors only strictly in one plane. Something like this should be the connection between events. (only already as points in space-time), so that we can talk about the energy-momentum vector as a gradient. Now imagine the presence in some part of the lattice (mandatory only in part!) on some line of bond defect, when at each node along the line there are all connections, but thrown from the usual plane to the diagonal, and then to the next one, etc., with rotation of the corresponding edges when going to the next node to the right or to the left. As such, this lattice by the number of nodes (events) will remain the same. Derivatives with respect to coordinates along the edges of the parameter, proportional to the number of nodes along the edge, will remain the same. But there will be three different cases. First, when no chain of events in the region has this type of connections. Second, when there are chains of events, where the ties are twisted to the right. And the third, when there are chains of events, where the ties are twisted to the left. Quite clear, what are the chains of events, on which connections with the outside world “swirled”, should have trajectories relative to this very surrounding world others, than in the absence of such a swirl. With right and left vortices in our 3D model (lattice) explicitly bind specific vectors (by the gimlet's rule), which will have a direction either along the edge with vortices, either against. Which direction the positive sign is attributed to is not important. There are three meanings of this sign — positive, negative and zero, like the absence of a vortex. It is important to emphasize, what's in the lattice, generated by events in space-time, “ribs”, along which we judge the absence of vortices in the bonds, their presence and sign “vortex” not arbitrary. These are the lines of existence of material points, time lines in their rest system. Respectively, and “vortices” in such a structure there are material points in the rest systems, not destroyed by any coordinate transformation.

In this way, the presence of an electric charge in some material points can be successfully explained by the specifics of the connections of these material points with other material points in the region. No connections “plane-parallel”, but such, “vortex” type. At the same time, the new characteristic is not just some additional label., but has all the necessary properties — in the rest system, this number, accepting positive, zero or negative value. If we consider it from the point of view of all possible frames of reference, then this is a vector, proportional to the tangent to the trajectory vector — current vector.

With this interpretation, it becomes quite obvious how the connection between the concepts of mass and energy-momentum, and the relationship between these concepts and the concept of action. And also the connection between all these concepts and the concept of electromagnetic interaction, with the accompanying concept of charge (current) and its properties.

© Gavryusev V.G.
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