The natural world is a difficult place. Harmonies allow people and scientists to discern the order in it. Physicists have long understood that the principle of symmetry is closely related to conservation laws. The three most famous rules are: conservation of energy, momentum and its momentum. Preservation of pressure is a consequence of the fact that the attitudes of nature do not change at any intervals. For example, in Newton’s law of gravity, one can imagine that GN, the gravitational constant, depends on time.
In this case, the energy will not be saved. From experimental searches for energy-saving violations, strict limits can be set for any such change in time. This principle of symmetry is quite wide and is applied in quantum, as well as in classical mechanics. Physicists sometimes call this parameter the homogeneity of time. Similarly, momentum conservation is a consequence of the fact that there is no special place. Even if you describe the world using Cartesian coordinates, the laws of nature will not care about what is considered a source.
This symmetry is called "translational invariance" or the homogeneity of space. Finally, the conservation of angular momentum is associated with the familiar principle of harmony in everyday life. The laws of nature are invariant with respect to rotations. For example, not only does it not matter how a person chooses the origin, but it doesn’t matter how he chooses the orientation of the axes.
Discrete class
The principle of space-time symmetry, shift, and rotation are called continuous harmonies, because you can move the coordinate axes by any arbitrary value and rotate by an arbitrary angle. Another class is called discrete. An example of harmony is both reflection in the mirror and parity. Newton's laws also have this principle of bilateral symmetry. One has only to observe the movement of an object falling in a gravitational field, and then study the same move in the mirror.
While the trajectory is different, it obeys Newton's laws. This is familiar to anyone who has ever stood in front of a clean, well-polished mirror and is confused about where the object was and where the mirror reflection was. Another way to describe this principle of symmetry is the similarity between the left and the opposite. For example, three-dimensional Cartesian coordinates are usually written in accordance with the "rule of the right hand." That is, the positive flow along the z axis lies in the direction in which the thumb points, if a person turns his right hand around z, starting with x Oy and moving to x.
An unconventional coordinate system 2 is the opposite. On it, the Z axis indicates the direction in which the left hand will be. The statement that Newton’s laws are invariant means that a person can use any coordinate system, and the rules of nature look the same. And it is also worth noting that the symmetry of parity is usually denoted by the letter P. Now we turn to the next question.
Operations and types of symmetry, principles of symmetry
Parity is not the only discrete proportionality of interest to science. Another is called time change. In Newtonian mechanics, you can imagine a video of an object falling under the influence of gravity. After that, you need to consider starting the video in the opposite direction. Both the “forward in time” and “backward” moves will obey Newton’s laws (reverse movement may describe a situation that is not very plausible, but it will not violate the laws). The time reversal is usually indicated by the letter T.
Charge conjugation
For every known particle (electron, proton, etc.), there is an antiparticle. It has exactly the same mass, but the opposite electric charge. The antiparticle of an electron is called a positron. A proton is an antiproton. Recently, antihydrogen has been produced and studied. Charge conjugation is the symmetry between particles and their antiparticles. Obviously, this is not the same thing. But the principle of symmetry means that, for example, the behavior of an electron in an electric field is identical to the actions of a positron in the opposite background. The charge pair is indicated by the letter C.
These symmetries, however, are not exact proportions of the laws of nature. In 1956, experiments unexpectedly showed that in a type of radioactivity called beta decay, there is an asymmetry between left and right. It was first studied in the decays of atomic nuclei, but it is most easily described in the decomposition of a negatively charged π - meson, another strongly interacting particle.
It, in turn, can be decomposed either into a muon or into an electron and their antineutrin. But decays on this charge are very rare. This is due (using an argument that uses special relativity) to the fact that a concept always arises with its rotation parallel to its direction of movement. If nature were symmetrical between left and right, it would be possible to find the neutrino half of the time with its spin parallel and part with its antiparallel.
This is due to the fact that in the mirror the direction of motion is not modified, but by rotation. A positively charged π + meson and antiparticle π - are associated with this. It decays into an electron neutrino with a parallel spin to its momentum. This is the difference between his behavior. Its antiparticles are an example of violation of charge conjugation invariance.
After these discoveries, the question was raised whether the invariance of time reversal T was violated. According to the general principles of quantum mechanics and relativity, the violation of T is related to C × P, the product of conjugation of charges and parity. SR, if this is a good principle of symmetry, it means that the decay π + → e + + ν should go at the same speed as π - → e - +. In 1964, an example of a process that violates superlattices was discovered, involving another set of strongly interacting particles called Kmesons. It turns out that these particles have special properties that allow you to measure a slight violation of CP. Only in 2001, the collapse of SR was convincingly measured in the decays of another set, B mesons.
These results clearly show that the absence of symmetry is often as interesting as its presence. Indeed, shortly after the discovery of violation of SR, Andrei Sakharov noted that it is in the laws of nature a necessary component for understanding the predominance of matter over antimatter in the universe.
Principles
It is still believed that the combination of CPT, conjugation of charges, parity, temporary circulation, are preserved. This follows from the fairly general principles of relativity and quantum mechanics, and today is confirmed by experimental studies. If any violation of this symmetry is detected, this will have profound consequences.
The proportions discussed so far are important in that they lead to conservation laws or relations between reaction rates between particles. There is another class of symmetries that actually defines many forces between particles. These proportions are known as local or gauge proportions.
One such symmetry leads to electromagnetic interactions. The other, in Einstein's conclusion, is about gravity. In setting out his principle of the general theory of relativity, the scientist argued that the laws of nature should be available not only so that they are invariant, for example, when the coordinates rotate simultaneously everywhere in space, but with any change.
Mathematics to describe this phenomenon was developed by Friedrich Riemann and others in the nineteenth century. Einstein partially adapted, and re-invented some for his needs. It turns out that to write equations (laws) that obey this principle, it is necessary to introduce a field that is largely similar to an electromagnetic field (except that it has a spin of two). It correctly combines Newton's law of gravity with things that are not too massive, do not move fast or loose. For systems that are such (compared to the speed of light), the general theory of relativity leads to many exotic phenomena, such as black holes and gravitational waves. All this follows from the rather harmless concept of Einstein.
Mathematics and other sciences
The principles of symmetry and conservation laws that lead to electricity and magnetism are another example of local proportionality. To introduce this, you need to turn to mathematics. In quantum mechanics, the properties of an electron are described by the “wave function” ψ (x). For work, it is imperative that ψ be a complex number. It, in turn, can always be written as the product of a real number, ρ, and periods, e iθ. For example, in quantum mechanics, you can multiply the wave function by a constant phase, without effect.
But if the principle of symmetry is based on something stronger, then, that the equations are independent of steps (more precisely, if there are many particles with different charges, as in nature, a specific combination is not important), it is necessary, as in the general theory of relativity, to introduce another set of fields. These zones are electromagnetic. Applying this principle of symmetry requires that the field obeys Maxwell's equations. It is important.
Today, all interactions of the standard model are understood as arising from such principles of local gauge symmetry. The existence of the W and Z zones, as well as their masses, half-lives, and other similar properties were successfully predicted as a consequence of these principles.
Measureless numbers
For a number of reasons, a list of other possible principles of symmetry has been proposed. One such hypothetical model is known as supersymmetry. It was proposed for two reasons. First of all, she can explain a long-standing riddle: "Why there are very few dimensionless numbers in the laws of nature."
For example, when Planck introduced his constant h, he realized that this can be used to record quantities with mass sizes, starting with Newton's constant. This quantity is now known as the Planck value.
The great quantum physicist Paul Dirac (who predicted the existence of antimatter) deduced the "problem of large numbers." It turns out that postulating this nature of supersymmetry can help in solving the problem. Supersymmetry is also an integral part of understanding how the principles of general relativity can be reconciled with quantum mechanics.
What is supersymmetry?
This parameter, if it exists, binds fermions (particles with a half-integer spin that obey the Pauli exclusion principle) with bosons (particles with a whole spin that obey the so-called Bose statistics, which leads to the behavior of lasers and Bose condensates). However, at first glance, it seems foolish to suggest such a symmetry, since if it manifested itself in nature, one would expect that for each fermion there would be a boson with exactly the same mass, and vice versa.
In other words, in addition to the familiar electron, there must be a particle called a selector that has no spin and does not obey the principle of exclusion, but in all other respects it is the same as the electron. Similarly, another particle with a spin of 1/2 (which obeys the principle of exclusion, like an electron) with zero mass and properties, much like photons, should belong to a photon. No such particles were found. It turns out, however, that these facts can be agreed upon, and this leads to one last point on symmetry.
Space
Proportionalities may be proportional to the laws of nature, but do not have to be manifested in the surrounding world. The space around is not uniform. It is filled with all kinds of things that are in certain places. Nevertheless, from the conservation of momentum, man knows that the laws of nature are symmetrical. But in some circumstances, the proportionality is "spontaneously broken." In particle physics, this term is used more narrowly.
Symmetry is called spontaneously broken if the state with the lowest energy is not proportional.
This phenomenon is found in many cases in nature:
- In permanent magnets, where the spin alignment, which causes magnetism in the lowest energy state, violates rotational invariance.
- In the interactions of π-mesons, which blunt the proportionality, called chiral.
The question: “Does supersymmetry exist in such a broken state” is now the subject of intensive experimental research. It occupies the minds of many scientists.
The principles of symmetry and the laws of conservation of physical quantities
In science, this rule states that a particular measurable property of an isolated system does not change, as it evolves over time. Exact conservation laws include energy reserves, linear momentum, its momentum and electric charge. There are also many rules of approximate abandonment, which applies to such quantities as masses, parity, lepton and baryon numbers, strangeness, hyperzarya, etc. These quantities are stored in certain classes of physical processes, but not in all.
Noether's theorem
The local law is usually mathematically expressed as the equation of continuity in partial derivatives, which gives the ratio between the quantity of quantity and its transfer. It says that the number stored in a point or volume can only change by that which enters or leaves the volume.
From the Noether theorem: each conservation law is related to the basic principle of symmetry in physics.
The rules are considered fundamental norms of nature with wide application in this science, as well as in other fields, such as chemistry, biology, geology and engineering.
Most laws are exact or absolute. In the sense that they apply to all possible processes. By Noether’s theorem, the principles of symmetry are partial. In the sense that they are valid for some processes, but not for others. She also claims that there is a one-to-one correspondence between each of them and the differentiable proportionality of nature.
Especially important results are: the principle of symmetry, conservation laws, Noether's theorem.