Lecture
A field in physics is a physical object that is classically described by mathematical scalar, vector, tensor, spinor field (or some combination of such mathematical fields), obeying dynamic equations (equations of motion, called in this case field equations or field equations, are usually partial differential equations in partial derivatives). In other words, a physical field is represented by a certain dynamic physical quantity [1] (called a field variable [2] ) defined at all [3] points of space (and accepting generally different values at different points in space, also changing with time [4 ] ). [ source not specified 293 days ]
In quantum field theory, a field variable can be considered formally, just as the spatial coordinate is considered in ordinary quantum mechanics, and the quantum operator [5] of the corresponding name is associated with a field variable.
The field paradigm , which represents the whole physical reality at the fundamental level, reduced to a small number of interacting (quantized) fields, is not only one of the most important in modern physics, but, perhaps, undoubtedly dominant [6] .
The physical field, therefore, can be characterized as a distributed dynamic system having an infinite number of degrees of freedom.
The role of a field variable for fundamental fields is often played by potential (scalar, vector, tensor), sometimes a quantity called field strength. (For quantized fields, in a certain sense, the corresponding operator is also a generalization of the classical concept of a field variable).
Also, a field in physics refers to a physical quantity, considered as a place-dependent: as a complete set, generally speaking, of different values of this quantity for all points of some extended continuous body - a continuous medium, describing in its entirety the state or movement of this extended body [10] . Examples of such fields can be:
The dynamics of such fields are also described by partial differential equations, and historically the first, starting from the XVIII century, in physics were considered precisely such fields.
The modern concept of the physical field grew out of the idea of an electromagnetic field, first realized in a physically specific and relatively close to the modern form by Faraday, mathematically consistently implemented by Maxwell - initially using a mechanical model of a hypothetical continuous medium - ether, but then going beyond the use of a mechanical model.
Among the fields in physics emit the so-called fundamental. These are fields that, according to the field paradigm of modern physics, form the basis of the physical picture of the world, all other fields and interactions are derived from them. They include two main classes of fields interacting with each other:
There are theories (for example, string theory, various other theories of unification) in which several other, even more fundamental from the point of view of these theories, fields or objects play the role of fundamental fields (and the current fundamental fields appear or should appear in these theories to some extent as a “phenomenological” consequence). However, while such theories are not sufficiently confirmed or generally accepted.
Historically, among the fundamental fields, fields were first discovered (namely, as physical fields [11] ) that are responsible for electromagnetic (electric magnetic fields, then combined into an electromagnetic field), and gravitational interaction. These fields were discovered and studied in sufficient detail in classical physics. At first, these fields (in the framework of the Newtonian theory of incidence, electrostatics, and magnetostatics) looked to most physicists rather as formal mathematical objects, introduced for formal convenience, and not as a full-fledged physical reality, despite attempts at a deeper physical understanding, which remained however rather vague or not bearing too substantial fruits [12] . But starting with Faraday and Maxwell, the approach to the field (in this case, to the electromagnetic field) as a completely substantial physical reality began to be applied systematically and very fruitfully, including a significant breakthrough in the mathematical formulation of these ideas.
Fields corresponding to weak interactions and strong interactions (playing an important role in nuclear nuclear physics and particle physics; the latter — among other things, in explaining nuclear forces) are discovered much later, since practically they manifest themselves only in nuclear and particle physics and at such energies and distances, which in principle belong to the field of quantum theories.
Nevertheless, in principle (despite the fact that it is not easy to detect directly for all of them), all four mentioned fields manifest themselves as intermediaries in the interaction of charged (various types of charges) bodies (particles), transferring this interaction with a finite velocity (the speed of light), while the intensity (force) of the interaction is determined, in addition to the position and movement of bodies, their charges: mass (gravitational charge) for the gravitational field, electric charge for electromagnetic, etc.
Experimental confirmation of Maxwell’s theory in 1887 by Heinrich Hertz, who obtained direct experimental evidence of the existence of electromagnetic waves predicted by Maxwell (which, among other things, allowed us to finally connect optics, which had previously been an independent field of physics, to electromagnetic theory, and this was a very significant advance in the direction of increasing the internal connectivity of physics).
Gradually it turned out that the field possesses almost all the attributes of a full-fledged physical reality, including the ability to transfer energy and momentum, and even under certain conditions to have an effective mass [13] .
On the other hand, as quantum mechanics developed, it became increasingly clear that matter (particles) possesses properties that are theoretically inherent in fields.
After the creation of quantum mechanics and the sufficiently deep development of quantum concepts, it became obvious that all matter, including matter, is described by quantized fields: individual fundamental fields (like an electron) or their collective excitations (like a proton composed of three quarks of an igluon field). Single quantum excitations of fundamental fields and are elementary particles. Photons, vector bosons, gluons, gravitons (not yet fixed as separate particles), leptons and quarks belong to such quantum excitations of fundamental fields of different types [14] . The field equations for free fields, their quantization, the interaction of various fields were discovered and studied in detail [15] .
Thus, it turned out that the physical picture of the world can be reduced in its foundation to quantized fields and their interaction.
To some extent, mainly within the framework of the formalism of integration along trajectories and Feynman diagrams, the opposite movement took place: the fields became possible to a large extent represented as almost classical particles (more precisely, as a superposition of an infinite number of almost classical particles moving according to imaginable trajectories) , and the interaction of fields with each other - as the birth and absorption of each other by particles (also with a superposition of all conceivable variants of such). And although this approach is very beautiful, convenient and allows you in many ways to psychologically return to the notion of a particle as a good old classic particle with a well-defined trajectory, it, nevertheless, cannot cancel the field view of things and is not even a completely symmetrical alternative. (and therefore, nevertheless, closer to a beautiful, psychologically and practically convenient, but still just a formal reception, than to a completely independent concept). The point here is in two key points:
Thus, it can be concluded that the path integration approach is, although very psychologically convenient (after all, a point particle with three degrees of freedom, for example, is much simpler than an infinite-dimensional field that describes it) and has proven practical productivity, but it’s just some reformulation albeit a rather radical, field concept, and not its alternative.
And although in words in this language everything looks very “corpuscular” (for example: “the interaction of charged particles is explained by the exchange of another particle — the carrier of interaction” or “the mutual repulsion of two electrons is due to the exchange between them by a virtual photon”), but behind this are typically typical field reality, like the propagation of waves, albeit fairly well hidden for the sake of creating an efficient computation scheme, and in many ways providing additional opportunities for qualitative understanding.
Currently (2012), the fundamental boson (gauge) fields are considered to be several fields associated with electroweak, strong game gravitational interactions. The spinor fields of several “generations” of leptons and quarks belong to the fundamental fermion fields.
In the framework of the Standard Model, the following fields appear as fundamental
Each fundamental fermion (each type of quarks and each type of leptons) in the Standard Model has its own field, mathematically represented by a spinor field.
These fields in the framework of the standard model are calibration fields. Their types are known:
Any theoretical objects (for example, fields) that are described by theories that do not contain internal contradictions can be considered hypothetical in a broad sense, which clearly do not contradict the observations and can at the same time give observable consequences that allow making a choice in favor of these theories compared to those which are accepted now. In practice (in order to cut off a vast amount of potentially possible, but useless theories), the principle of falsifiability is also applied. Below, we will speak (and this generally corresponds to the usual understanding of the term) mainly about hypotheticality in this narrower and more strict sense, implying the validity and falsification of the hypothesis that we call a hypothesis.
In theoretical physics, many different hypothetical fields are considered, each of which belongs to a very specific definite theory (in their type and mathematical properties, these fields may be quite or almost the same as known non-hypothetical fields, and may differ more or less strongly; in that and in another case, their hypothetical meaning is that they have not yet been observed in reality, have not been detected experimentally, and in relation to some of the hypothetical fields there may be a question Oguta whether they occur in principle, and even if they exist at all - for example, if the theory in which they are present, suddenly appears self-contradictory).
The question of what should be considered a criterion that allows you to transfer some specific field from the hypothetical category to the real one is rather subtle, since the confirmations of a particular theory and reality of certain objects contained in it are often more or less indirect. In this case, it usually boils down to some kind of rational agreement of the scientific community (whose members are more or less detailed in what degree of evidence they are actually talking about).
Even in theories that are considered to be fairly well confirmed, there is a place for hypothetical fields (here we are talking about the fact that different parts of the theory have been tested with varying degrees of thoroughness, and some fields that play an important role in them have not yet clearly appeared in the experiment that is, it looks like a hypothesis, invented for various theoretical purposes, while other fields that appear in the same theory have already been studied well enough to speak of them as reality).
An example of such a hypothetical field is the Higgs field, which is important in the Standard Model, the remaining fields of which are by no means hypothetical, and the model itself, albeit with unavoidable reservations, is considered to describe reality (at least to the extent that reality is known).
There are many theories containing fields that have (so far) never been observed, and sometimes these theories themselves give such estimates that their hypothetical fields seem to be (due to the weakness of their manifestation, following from the theory itself) and cannot be detected in the foreseeable future (for example, a torsion field). Such theories (if they do not contain, besides practically unverifiable, also a sufficient number of easier verifiable consequences) are not considered of practical interest, unless some nontrivial new way of their verification emerges, allowing to circumvent the obvious limitations. Sometimes (as, for example, in many alternative theories of gravity — for example, the Dicke field), such hypothetical fields are introduced, about the force of manifestation of which the theory itself cannot say anything at all (for example, the coupling constant of this field with others is unknown and can be quite large , and arbitrarily small); с проверкой таких теорий обычно также не торопятся (поскольку таких теорий много, а своей полезности каждая из них ничем не доказала, и даже формальнонефальсифицируема), за исключением случаев, когда какая-то из них не начинает по каким-то причинам казаться перспективной для разрешения каких-то текущих затруднений (впрочем, от отсеивания теорий на основании нефальсифицируемости — особенно из-за неопределенных констант — тут иногда отказываются, т.к. серьезная добротная теория иногда может быть проверена в надежде, что ее эффект обнаружит ся, хотя гарантий этого и нет; особенно это верно, когда теорий-кандидатов вообще немного или некоторые из них выглядят особенно фундаментально интересными; также — в случаях, когда можно проверять теории широкого класса все сразу по известным параметрам, не тратя специальных усилий на проверку каждой в отдельности).
Следует также заметить, что принято называть гипотетическими лишь такие поля, которые совсем не имеют наблюдаемых проявлений (или имеют их недостаточно, как в случае с полем Хиггса). Если же существование физического поля твердо установлено по его наблюдаемым проявлениям, и речь идет лишь об улучшении его теоретического описания (например, о замене ньютоновского гравитационного поля на поле метрического тензора в ОТО), то говорить о том или другом как о гипотетических обычно не принято (хотя для ранней ситуации в ОТО можно было говорить о гипотетическом характере тензорной природы гравитационного поля).
В заключение упомянем о таких полях, сам тип которых достаточно необычен, т.е. теоретически вполне мыслим, но никакие поля подобных типов никогда не наблюдался на практике (а в некоторых случаях на ранних этапах развития их теории могли возникали и сомнения в ее непротиворечивости). К таким, прежде всего, следует отнеститахионные поля. Собственно, тахионные поля можно назвать скорее лишь потенциально гипотетическими (то есть не достигающими статуса обоснованного предположения ), т.к. известные конкретные теории, в которых они играют более или менее существенную роль, например, теория струн,
Еще более экзотические (например, лоренц-неинвариантные — нарушающие принцип относительности) поля (при том, что абстрактно-теоретически вполне мыслимы) в современной физике можно отнести к стоящим уже достаточно далеко за рамками аргументированного предположения, то есть, строго говоря, их не рассматривают даже в качестве гипотетических [16] .
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Introduction to Physics, Fundamentals
Terms: Introduction to Physics, Fundamentals