About the name Unified Field Theory

Why such a name?

First Theory.

Concept “theory” seems comparatively simple. There is practically no need to explain this word. It, apparently, everyone understands. But anyway, for, to highlight some important points, worth defining. Especially, that today there are examples in physics, when constructions so far from this concept are called theories, what takes you (“theory” superstring, eg).

Theory in physics (not in math) – this, desirable, completely self-consistent belief system, explaining a certain set of facts and / or phenomena of the real world. The theory is usually based on a number of definitions and conventions., desirable, explicitly. Ideally, they should not all contradict each other.. Besides, methods and terminology should be outlined, used by theory. In science, it is, of necessity, methods of logic and mathematics. In fact, many successful theories in their field do not fully follow this definition. But moments like this are their weak points. and, in the end, the presence of such deviations leads to the need for their modification or even replacement with other theories. Nonetheless, the presence of all three components — definition systems, rules for working with concepts defined in theory and, what extremely essential for physics, the correspondence of these concepts to a certain range of facts and phenomena of the real world, is decisive for, so that we can talk about some, albeit mathematical, building how about physical theory.

Later Field.

This concept is much less clear.. In physics, there can be “just a field”. It's always a field of something. Word “field” in physics always implies the distribution of something in something. Ie, first of all, carrier must be present, eg, space-time, whose element is usually called a point. If something else, some another quantity is associated with points of the carrier, exists in them (not necessarily in all), then they talk about the field of this quantity over space-time. Respectively, field theory by default implies the theory of distributed quantities. There are many fields of different sizes in physics.. But when they talk about field theory, still imply a field of a very specific value – field strength. More precisely, since forces in physics are of a different nature, different fields of these forces.

AND, finally, United.

Word “united” implies some integrity. What can it mean when applied to field theory?? Most often today, they put in this term, what all fields (different forces, or, using another term, interactions) should be described by theory from the same positions, with the same methods. Reducing the number of fields in theory down to a single desirable, but not necessarily. Initially, they tried to build a theory of a single field, such, that all known are only special cases of it under certain conditions. Often, so, the name was different – Unified Field Theory.

Well, the words separately seemed to clarify. And now – what do they mean together. And it's already harder. because, that different people put a rather different meaning in this phrase.

Historical excursion.

Physicists strive for the unity of the description of the world, and not without some success, for a very long time. Throughout the nineteenth century, previously virtually unrelated branches of physics, such as the theory of heat, theory of electricity, theory of magnetism, optics all became just sections of a unified theory. With the understanding of that fact, that all the phenomena of heat-gas-hydrodynamics are just manifestations of the mutual mechanical motion of the particles constituting the body, mechanics increasingly claimed the role of the general foundation of physics. The theory of electromagnetism, absorbing optics, remained a separate piece of the mosaic for now, which could not be integrated into the general mechanistic picture of the world. The theory of gravity was in the same position.. The theory of space and time stood apart. Both Newton a special position of an indifferent arena was assigned, where all physics games are played. Need to say, that from the very beginning there were doubts about such a special position of space and time. But we won't go into details. I need this historical excursion here only for that, to illustrate the fact, that the title theory has always been the goal of physics as a science.

At the turn of the 19th and 20th centuries, the first synthesis of space and time into a single structure took place. (initiated, surprisingly, realities of the theory of electromagnetism), and then the theory of gravity was also integrated into it. The resulting structure also absorbed the mechanics of the point., as such. Through the work of many scientists, first of all, Boltzmann, the building of the theory of continuous media in all its manifestations on the basis of mechanics and statistical physics was first laid and then practically in general outline was built, which is a way of thinking, method and in no way competes with the actual mechanics, as the basis, the foundation of these branches of physics. Although there still remains one value of the most important value (entropy), the meaning of which is not clear in everything, despite significant progress in this direction. So after all, in the very mechanics of the most basic concepts, such, as weight and act, eg, kept too (and while they keep) a touch of mysticism. In this way, it seemed, it remains to unite only the theory of gravity (this is what is now commonly called the unified theory of space-time with gravity and mechanics) and the theory of electromagnetism. Both theories at that time were well-formed field theories.. In one case, the theory of the gravitational field, in a different – electromagnetic. It is to this time that they ascend, for real, terms “Unified field theory” and “Unified field theory“. It was about the unification of gravity and electromagnetism. About the desire to describe both of these fields as manifestations of one single. Widely known, what A. Einstein spent most of his life on this task with no apparent success. And not only he did it, of course.

At the same time it turned out, that methods and views classical mechanics, so successful in macro- and mega-world, fail when describing the phenomena of the microworld. To explain the new range of phenomena, quantum mechanics. One of the by-products of its birth and development was the further integration of the seemingly independent pieces of the mosaic of our knowledge into the general edifice of science.. As a matter of fact, chemistry and with it biology became just branches of physics. Very specific, with its own special terms and methods, but the possibility, basically, come to any concept of these sciences, starting with quantum mechanics, no doubt, although it is a difficult task.

To the middle, but rather, towards the end of the 20th century, the development of the theory of the microworld has come a long way, where new types of interactions were discovered, other than gravity and electromagnetism, and the theory of the latter was naturally integrated into the resulting construction of quantized fields. Many methods of the theory of space-time have found their place in quantum theory., you can say, without them she could not exist at all. But! Gravity theory, ie. general theory of space-time, known as General theory of relativity (OTO) and quantized field theory remain separate buildings in physics. Moreover, seems to, that their foundations are not compatible with each other. And this constitutes a well-recognized problem..

Let's see, which in modern physics seems to be quite complete, and what problems remain.

Physics today offers two main groups of descriptions of the world – classic description (approximation) and quantum description (approximation). Some of the concepts used are common to both approximations., although some of them may acquire in each case certain specific features. The other part of the concepts is completely specific for each approximation and is not applicable in the other.. There are also a number of procedures, connecting both approximations. It cannot be said, that the quantum description is completely independent of the classical, and the second is obtained simply as a certain limiting case of the first. It will be completely wrong. The quantum description itself is impossible without the presence of the classical, because it contains its irreparable components. Namely, frame of reference, which can only be classic. Quantum frames of reference simply do not exist.

In connection with this situation, we start with the classical approximation. We will not go into details.. The physics building is huge and there are many interconnections, as “vertically”, and so “horizontally”. We are only interested in its foundation.

The foundation of the classic (all classic) approximations are the two field theories – electromagnetic and gravitational. Moreover, the gravitational field is inextricably linked with the image of space-time, available in theory, is to a certain extent one of the natural structures of space-time, considered as a 4-dimensional space. Purely geometric structure. The electromagnetic field still seems to be a structure foreign to space-time. This is the first unsolved (obvious) classical theory problem. But in fact, it does not exhaust all the problems of the classical theory., preventing her from counting “good” theory. In what sense is good? In the sense, which we talked about at the very beginning – nor the theory of electromagnetism, nor the theory of gravity are closed self-consistent theories, with an explicit consistent definition of its basic concepts.

Surprisingly, one of such concepts for both theories is the concept masses. You won't find anywhere determination of mass, which would not lean on the concept strength, and determination of strength, which would not lean on the concept masses. When applying the theory of electromagnetism, maximum, which can be determined for an arbitrary particle of matter – this is the ratio of charge to mass. AND for the theory of gravity, OTO, mass is undetectable, external for spatio-temporal structures parameter, which itself determines the structure of space-time. Respectively, and the whole range of concepts related to mass that are most important for physics (energy-momentum, action, etc.) appears to be hanging in the air.

Since space-time, being the subject of one classical theory, also serves as an arena for another theory, then it should be noted, that one of the basic concepts of the theory of space-time, idea of his local pseudo-Euclidean, has the character of a postulate, given. Of course, this is permissible for theory, but is the last word on this issue? Is it possible for this postulate to find sufficiently simple and understandable reasons?

Another problem can be singled out separately.. One of the quantities, secondary to mass (energy), act, is by no means secondary in its position in both classes of theories. On the contrary, in the standard construction of these theories today, act, together with the principle of its stationarity, is the main, maybe the only one, the driving force behind both theories. AND explanations, why this value plays such a huge role is not available. So there is no clear understanding, what this action should be. For theories of quantized fields, it is most common today — choice of action (by choosing Lagrangian density, which is integrated to get the actual action) done by one author or another according to his own taste. And this choice, best case scenario, justified by credibility (varying degrees of agreement with experiment) the results obtained.

In this way, desirable, so that united classic field theory would suggest a description of both electromagnetic, and the gravitational field from a unified position, showing how their commonality, and a certain independence. It is also desirable, so that it has a stronger foundation, than Maxwell's theory (electromagnetic field) and GR (space-time and gravity) in terms of defining the explicit meaning of the above concepts. And all the others too. Also pretty obvious, that both theories, and Maxwell and Einstein, confirmed by a huge array of our experience, and should be integral parts of a unified theory. But they need a common solid foundation.

If we go to the current state of the quantum description, then one can immediately again point to the problems noted above of the lack of clear definitions of the same fundamental concepts. These problems are common to all approximations.. But the quantum description also has its additional problems., also at the very foundations of this circle of theories. One of the problems appeared from the very beginning, together with the apparatus of the original quantum mechanics. Roughly enough, it can be called the problem of interpreting one of the main tools – wave function, the so-called probability amplitude. What is probability is clear to people well enough. But it is very difficult to find a place for it in any description of the probability. “amplitudes”. Clear, that this is a certain jargon, used when specifying methods for calculating the probabilities of certain quantum-mechanical situations. The real problem to understand is, what, in contrast to the classical approximation, the equations of motion are not applied to the physical quantities themselves, namely, to these very amplitudes of probabilities. And the fields of today's quantum theory are precisely the fields of these very amplitudes.. No more and no less. We already know how to work with them well enough. But their physical meaning is still relatively illusory.. The theory has gone far ahead again, leaving in their rear the most important problem of interpreting their foundations. Problem “collapse of the wave function” as a result of measurements, and other related issues of interpreting the basic concepts of the theory are still on the agenda of physics.

Anyway, but modern quantum theory claims many of the characteristics of a unified field theory. There is a single (although with a fairly large number of free parameters) description of electromagnetic and weak interactions. There is a well-understood path from the quantum description of the electromagnetic field to the classical one.. There is a description of strong interactions similar in methods (although it does not yet have good recipes for how to really make the necessary calculations), which allows us to talk about “great unification” descriptions of electromagnetic, weak and strong interactions. All this is formulated quite clearly within the framework of the so-called standard model of elementary particle interactions (notice, no theory, model!). But it is just not possible to include the gravitational interaction in this scheme.. Huge efforts have been and are being made to create the so-called theory quantum gravity. But without success. About that, how this problem is seen today by other physicists, you can read in article one of the creators “standard” particle models, Nobel laureate Steven Weinberg.

What is expected in this regard (in the quantum approximation) from unified field theory? The general consensus is, what is missing exactly the quantum description of gravity.

All of the above related to clarifying the meaning, behind the words, by which this site is named. Let's move on to the question – why is it so named? Can a belief system, developed by the author of the site, claim the title of unified field theory?

I will say right away. I am not going to give a complete and comprehensive answer to such a question in this short article.. Books and everything in general serve this purpose., what is and will be published on this site.

Here I will only touch on the problems, which highlighted above. And even then only in that sense – are there any solutions offered for them. And to judge that, are these decisions good or bad, you.

Classical approximation. Do gravitational and electromagnetic fields combine into different characteristics of the structure, natural for space-time? The field of which is proposed to be considered a unified field of physics?

In theory, the basis of which is already published in the book “Dimension and Properties of Space-Time” (First part, “Foundations and classical approximation”, in 2004 year; in 2010 year in the second edition supplemented by the second part, “Quantum description”) , space-time is by no means an arena for physics. It's just that, as a mathematical construction, viewed as an image, description of the world (one of the possible). Ie. the world as a whole (The universe) the mathematical construction is matched — space-time. Matching procedures to elements of the world (physical objects) mathematical quantities, shaping space-time as a mathematical concept, are the measurement procedures. Units, being themselves parts of the world, and not external attributes to it, play, hence, decisive role in the resulting properties of the mathematical image of the world. And structure, which describes the behavior of units, field affine connection and becomes a unified field of physics with such a description of the world. AND then, what is usually called “the laws of nature”, in this case turns out to be either the obvious relations, following from the basic definitions, what is what (identities), or by recording the restrictions on those measurement procedures, which are really available to us.

In a nutshell:

Mathematical concept, affine connection coefficient field, which has the physical meaning of the rates of relative changes in scales in the current measurement procedure, identically physical concept Ppotential of a single (the only one) fields. The natural integrity of this structure is evident.
Field tensor curvature corresponds to field single field strengths. The relationship between affine connection and curvature is exactly as follows, as well as between the potential and the strength of physical fields. The latter are specific combinations of partial derivatives of the former.
Curvature has two convolutions, one known as Ricci tensor, and the other, which is an antisymmetric tensor, has a structure exactly corresponding to the tensor of electromagnetic field strengths. Therefore, it is natural to call the second convolution by the Maxwell tensor. These are the integral components of curvature (and independent from each other, and related topics, what are “subsidiary” for the same more complex structure!) and are the intensities of two classical fields – gravitational and electromagnetic.
Maxwell's theory is reproduced in full. Einstein's theory, OTO, also. But for the latest theory, with almost complete repetition of the mathematical apparatus, a slightly different interpretation is given. Besides, the limitations of its field of application become obvious and, together with that, her well-known difficulties become irrelevant (nonlocalizability of gravitational energy, Schwarzschild singularity).
Values such as act, weight (energy-momentum), charge(current), and any others, are depicted by geometrical quantities that are quite well defined in space-time. Wherein act, identified with the number of events on the line of existence of the selected object (scale, or otherwise) is the formative value of the theory, its unconditional invariant, which is formulated as the principle of stationarity of action with variations in the potentials of a single field – space-time connectivity coefficients. The action for an individual particle and for some selected region naturally turns out to be the Lagrangian integral (for the region — Lagrangian density). There is no arbitrariness in the choice of Lagrangians, these are quite definite mathematical constructions, generated by connectivity.
Spacetime is local pseudo-Euclidean (on trajectories of physical objects) because, that such are the measurement procedures available for his description, and not for some unknown reason.
Besides the well-known gravitational and electromagnetic phenomena, in the classical approximation, the phenomena, due to the nonzero torsion field. (Twisting as such is used by us in everyday life very widely. — eg, all kinds of springs, screws, nuts with screws, propellers, turbines, etc., ie. All items, in which the turnover is not closed, a supplemented by a linear offset. Mathematical concept “torsion” is the limit of this concept as the radius of turnover tends to zero, then, when the linear part of the displacement does not vanish at the same time.) Their most likely manifestation in today's experimental data — those phenomena, which inspire speculation about “dark” matter and energy.

Quantum approximation. Is such a description natural and necessary in the proposed system of views? Do phenomenological results and those directions of development of existing quantum theories find their place in the proposed theory?, which by now look the most productive?

Detailed analysis of the image of the world, resulting from measurements, shows, that even in the classical approximation, despite all our desire, the resulting spacetime cannot be uniquely fixed. Image of the world – not the only mathematical space, and some class of spaces. This can be reformulated as a statement, that connectivity as a function of a point in space-time (considered at this level simply as a set of points) is not strictly defined, and belongs to some group of functions. In the classical approximation, this group of functions is determined by the belonging to it of continuous trajectories of physically realizable scales. The quantum approximation arises while the expansion of this group due to the decrease in the limiting conditions — only the belonging of certain points from the trajectories of scales is required, events, but not the whole continuous trajectory.

This is because, that the implementation of any time frame as a sequence of events, and that, that the events available to us, when detailed, are ultimately always discrete, leads to a greater than in the classical case, the uncertainty of the class of mathematical spaces, depicting the world as space-time. Since events are synonymous with action, then quantization (discreteness) it is actions in such a system of views that no longer need justification. Thus, the need for a quantum description arises in the case, when phenomena become the subject of research, containing not too many events. When these events cannot be viewed as a continuous sequence, even approximately. There is no chasm between classical and quantum descriptions, it is an obvious question of choosing the correct approximation.

Systematic development of methods for working with a group of space-times, necessary for the image of the world in the quantum approximation was carried out in second part of the book “Dimension and Properties of Space-Time”. It discusses the origins of geometry (actually from the potential dependence on the point of space-time used in the procedures for measuring the scales), structure and the need under these conditions for such a quantum-mechanical concept as a state vector. Shown, how the Feynman formulation of quantum mechanics naturally arises (path integrals). It turns out, why are elementary particles described as representations of various groups of space-time transformations in the state space. And how layered spaces and gauge fields appear in theory by necessity. Similarly considered, how, among all representations in the state space, special unitary groups and, in this way, clarifies the foundations of the current standard model for the classification of fundamental particles.

The most important point of both the classical and quantum approximations in this presentation seems to be the initial understanding, that we are talking about describing the world. I.e, the subject of the theory is the image of the world, which may not be the only one, and is always limited in some way. In some situations, you can make precise statements., in some – only probabilistic and there is no gap between these situations. “Probability amplitude”, and better, “state vector”, which allows you to calculate the probabilities, naturally obeys some equations. AND, since it is an attribute of information, and not a basic physical quantity, does not create any problems with interpretation. for instance, when interpreting such a well-known paradox as “wave function collapse”.

There is no fundamental difference between the quantum and classical approximations., both are descriptions of space-time. Those fields, which in theory we are talking about, in both approximations are natural for space-time structures.

Question about quantum gravity this does not occur at all, since the classical and only classical character of this field becomes completely clear.

Let us briefly list the basic features of the quantum description:

Mathematical concept, state vector, defined as complex-valued 4×4 the matrix, transformation, connecting the value of the vector tangent to the trajectory (initially existing on this trajectory of the time scale) at a given point in the world (space-time) with a value at an arbitrary remote point, where it was known by definition. This concept is identified with the physical concept “state vector” physical object, considered as having no spatial dimension point, in the most fundamental case, we are talking about the state of an elementary particle.
The state vector is calculated (according to the definition) as an exponent of the integral of the connection along the trajectory of the particle between the points under consideration. Different trajectories — different state vectors. Different connectivity — different state vectors. Eventually, at a point, the state vector has an incompletely defined value, a belongs to a certain group of values, to a domain in the space of complex-valued 4×4 matrices. Here lies the bridge to the formulation of quantum mechanics of this R. Feynman.
Areas, to which the state vectors of physical objects belong (in the limit, when a point in space-time is an image of an elementary event, these are elementary particles) arise as representations of the Poincaré group. Just because, that the transformation of the classical coordinate system does not change the essence of the object. However, the state vectors are then transformed according to some representation of this group, staying in a certain region of the matrix state space. It is this region as a whole, and not any specific meaning from it, and is a representation of the object (elementary particle).
Regions in the state space correspond to matrices of a well-defined structure. In particular, columns in matrices of state vectors of particles and rows for antiparticles are transformed as 4x spinors and independently of each other.
The representation of purely spatial transformations of space-time coordinate systems gives a separate meaning to the column in the matrix of the state vector (string for antiparticles), associated with the time coordinate, and column group (term). associated with spatial coordinates. As a matter of fact, state vectors decay into matrices, in which 3 “spatial” column zero, and the fourth, “temporal” — not. These are the state vectors of leptons. And the second group, in which on the contrary, 3 “spatial” columns are present. These are hadrons.
Easy to see, what any hadron always contains exactly 3 “spatial” column. Just because, that all three together, and not each separately, are a representation of a subgroup of purely spatial rotations of classical coordinate systems. There simply cannot be only one. These columns are, what are called quarks in the standard model. Which, naturally, do not fly out one by one.
The same considerations lead to similar classification and interactions between particles, which are described by the connection of the fibered space, providing a connection between matrix state spaces, associated with neighboring points of space-time.

There could be a lot more to add here, but that, who is interested, it's better to turn to book.

As you can see, claims for the correspondence of the proposed theory to the stated goal are quite solid, to get acquainted with all this to spend at least a little of your time.

In this way, the name of this site appears to be appropriate to the material presented.