There are even smaller times for which, unfortunately, no prefixes have been invented.

There are even smaller times for which, unfortunately, no prefixes have been invented.

Well, here is a typical picture, also, in my opinion, quite beautiful, which is obtained in the collision of ultrarelativistic atomic nuclei. Here it is shown schematically. This means that this is all the cutting edge of elementary particle physics. This article here is even unpublished, which appeared in December last year. This means that it shows the successive stages of the collision of ultrarelativistic nuclei. That is, well, you imagine that ultrarelativistic nuclei, when they accelerate to high speed, they flatten out due to the Lorentz contraction, and when they collide head-on-head, this does not mean at all that at this moment you suddenly have “Bang”. In your case, everything happens within the framework of relativistic mechanics. That is, in the first yoctoseconds after this collision, you have two nuclei of these now passing through each other, that is, those quark distributions that were in each nucleus, they pass through each other and still do not touch each other. However, a gluon force field is stretched between them. And this state, which was realized only recently, is called “glazma”, and it exists literally in a few yoctoseconds.

Then, on a scale of about 10, there, 20 yoctoseconds, this gluon field begins to decay into hadrons, these hadrons begin to decay into other particles, and in about 30, 50, this quark-gluon plasma decays into a gas of individual hadrons, particles. And these particles are already scattering away from you and are detected in the detectors.

But this is all, you see, of course, very indirect methods of observation. That is, in reality, of course, no one can consistently check these steps in time. Here. But they can be verified indirectly, for example, by calculating, within the framework of the assumption, say, that there is glazma, the angular distribution of the particles produced, and comparing them with experimental data. Well, this is of course an indirect method, but nevertheless better than nothing at all.

Here. There are even smaller times for which, unfortunately, no prefixes have been invented. That is, yoctoseconds are the most recent prefixes that are fixed in the SI system of units. But some of the processes that we already know with certainty are even faster. For example, the heaviest elementary particle, the top quark, decays in about 0.4 yoctoseconds. Here.

Physicists are now looking for the Higgs boson. Depending on how much mass it will have, it will have a different level of instability. And it will decay from tens of yoctoseconds, maybe up to even hundredths of a yoctosecond. And, of course, now physicists want to study what happens next, and, unfortunately, it is not yet known for certain, that is, the experiment does not yet say anything. There are many theories about what happens on even smaller time scales, but all of them will have to be tested by experiment. And here, in fact, one of the questions why we are making large colliders, in particular the LHC, the Large Hadron Collider, is to study what is happening with our world, with matter, with energy and, perhaps, with space-time on times even less than 10-24 seconds.

Here. This is where I end. Thanks for attention.

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Any point z of the complex plane has its own character of behavior (remains finite, tends to infinity, takes fixed values) during iterations of the function f (z), and the entire plane is divided into parts. In this case, the points lying on the boundaries of these parts have the following property: for an arbitrarily small displacement, the nature of their behavior changes dramatically (such points are called bifurcation points). Moreover, sets of points with one specific type of behavior, as well as sets of bifurcation points, often have fractal properties. These are the Julia sets for the function f (z).

See also: How to draw it

Next: Halley’s Fractal

Possible side view of our Milky Way galaxy. The current position of the Sun and its trajectory around the galactic center are also shown. Image from

The nearest stars are far beyond the solar system; the typical distance between them in our corner of the galaxy is several light years. This means that the light flies to them for several years. But the stars themselves move relative to each other much slower than the speed of light (their typical speeds are on the order of ten km / s), which means that the time it takes for them to noticeably move relative to their neighbors is longer:

T ~   several St. years   ~ One hundred thousand years.
c / 30,000

This simple calculation gives the time during which the familiar outlines of the constellations will be greatly distorted.

Stars add up to galaxies. Our Milky Way galaxy contains under a hundred billion stars, which means that its size is several orders of magnitude larger than the typical distance between the stars themselves. The sun is located in a fairly ordinary place in the Milky Way at a distance of about 26 thousand light years from its center and orbits around the galactic center at a speed of 220 km / s. These numbers allow us to calculate the “galactic year” for the Sun:

T =   2 π · 26,000 sv. years   ~ 230 million years.
c / 1400

So, hundreds of millions of years is one beat of the life of a typical galaxy.

Alexey Byalko”Nature” # 6, 2020

Fig. 1. Zodiacal light against the background of the Milky Way. The panorama is composed of four separate shots taken on March 10, 2010 in Teide National Park on the island. Tenerife. Photo by Daniel López,

about the author

Alexey Vladimirovich Byalko – Doctor of Physical and Mathematical Sciences, Associate Researcher at the Institute of Theoretical Physics named after V.I. LD Landau RAS, deputy editor-in-chief of the journal “Nature”. Research interests – theoretical physics, earth sciences.

Zodiacal light is a white, glowing cone visible in the west a few hours after sunset or in the east before dawn (Fig. 1). Its brightness is comparable to that of the Milky Way. The zodiacal light extends upward from where the sun has gone under the horizon in the evening or is about to rise in the morning. Its direction coincides with the ecliptic – the path of the Sun and planets through the starry sky, on which the zodiacal constellations are located. The best places to observe the zodiacal light are in subtropical latitudes far from city illumination, the most successful observation time is clear moonless nights around the spring and autumn equinox, when the ecliptic is perpendicular to the horizon.

From the spectrum of the zodiacal light, it is clear that this is reflected radiation from the Sun, although it is not known exactly where the scattering objects are located. This problem could be called half-forgotten, since more than half a century has passed since the review publication of NB Divari [1], although the importance of the author’s research is emphasized by the fact that his book was recently published in English [2]. Subsequent works [3] refined the measurement data, but did not add anything fundamental to the understanding of the nature of this phenomenon. So let’s turn to Divari’s review.

What observations show

Let us quote the beginning of the article: “At present, the generally accepted, although not the only, hypothesis is that the zodiacal light is caused by the scattering of solar radiation on particles of interplanetary dust concentrated in the form of a lenticular cloud, elongated along the ecliptic. The possibility of such an explanation was pointed out as early as 1683 by J. Cassini, who gave the first scientific description of the zodiacal light. “

Further, Divari describes in detail the history of observations of the zodiacal light, then analyzes the dependence of its brightness on elongation – the angular distance along the ecliptic, as well as in the direction perpendicular to it. He gives an analysis of spectral measurements, showing a sufficient closeness of the radiation of the zodiacal spectrum to the solar one, but notes that the deep Fraunhofer lines turned out to be slightly blurred. Polarization measurements have found that it has a maximum of about 0.25 at elongation values ​​of about 60 °. Various researchers noted fluctuations in the brightness of the zodiacal light, but they failed to come to a confident conclusion about the presence of seasonal and interannual fluctuations.

In conclusion, Divari discusses various hypotheses regarding where exactly the scattering dust is in outer space. Summing up his review, he writes: “Observational facts do not exclude the possibility that the zodiacal light is due to the dust cloud surrounding the Earth.”

A significant contribution to understanding the nature of the zodiacal light was made by W. T. Reach of NASA’s Goddard Space Flight Center [4–7]. His analysis of microwave observations at wavelengths of 5–16 µm showed that the particles responsible for the zodiacal light have dimensions exceeding 10 µm and are located within 1 AU. e. from the Earth. The spectra of reflected solar radiation correspond to different silicates, which are similar in composition to carbonaceous chondrites. The temperatures of dust particles correspond to equilibrium radiation temperatures with an albedo not exceeding 8%. As for the volume distribution of dust, then, according to Rich’s assumption, it is an ellipsoidal cloud near the earth’s orbit, possibly with a power-law decrease in the concentration of particles with distance. I will put forward a different hypothesis based on the dynamics of the motion of dust particles.

Three-body solutions

I’ll make a reservation that the explanation of the zodiacal light was not an end in itself. The hypothesis, which will be further stated, did not arise as an independent task, but as a side effect of the study of another problem, it will have to be briefly described.

Recently, together with Academician MI Kuzmin, I posed and solved the problem [8] about the further fate of those fragments of the formation of the Moon, which in the process of the Giant collision of Proto-Earth with Tefia acquire speeds sufficient to escape from the Earth’s gravitational field to infinity. But this infinity is not that far away. These fast debris begin their movement around the Sun in elliptical orbits and, after one or several orbital periods, return to that very narrow region of the Solar System, where the Giant Collision took place. The mathematical approach to the problem was to find a numerical solution to the restricted three-body problem.

A significant proportion of these debris then collide with the Earth, and their volatile constituents form the primary atmosphere and ocean. However, in our article it was also suggested that some of the fragments may be near the so-called triangular Lagrange points (L4 and L5) of the Sun-Earth system.

Fig. 2. Scheme of the Lagrange points of the Sun – Earth system. Stability regions are shown near triangular points L4 and L5. They are somewhat speculative; in fact, a body that has fallen into these areas or found itself at these points with a velocity other than zero does not remain in them, but drifts along the Earth’s orbit along the ecliptic. Image by NASA (NASA / WMAP)

These points are located at an angle of 60 ° with respect to the Earth (Fig. 2). Lagrange proved their stability. A body that finds itself with zero speed at one of these points does not leave it further. However, in our case, even small velocities of the fragments are quite real. Therefore, it was necessary to investigate the further movement of a small body, which happened to be near one of the triangular points. This was done without much difficulty, since a method for the numerical solution of the three-body problem had already been developed.

The result was somewhat unexpected. In physics, if some area is stable, then, as a rule, small perturbations of coordinates or velocities lead to oscillations around the equilibrium point. Therefore, a natural illustration of Lagrange points in many publications is Fig. 2, which shows the region of stable vibrations near the triangular points. However, this drawing is not accurate.

The two-dimensional motion of a small body in the field of two massive bodies orbiting in a circular orbit of radius 1 (in our case, this is an astronomical unit, a.u.), is determined by the centrifugal potential

U (x, y) = r2 / 2 + (1 – μ) / r + μ / [(x – 1) 2 + y2] 1/2.

Here r (t) = {x (t), y (t)}; r2 = x2 + y2.

Fig. 3. Potential U (x, y) at μ = 0.01. L1 and L2 are saddle points, when the bodies approach them at a low speed, they are reflected, the trajectory returns to the horseshoe-shaped valley. Dimensions are in astronomical units.

Its surface is shown in Fig. 3 for the case when the ratio of the masses of large bodies μ = 0.01. For the Sun – Earth pair μ = 3.06 · 10−6, which is why the image of the surface U (x, y) for our problem is not so clear, but the characteristic features of the potential are retained even at small mass ratios. In particular, the presence of saddle points L1 and L2 is important: it is the increase in potential when approaching them that ensures the repulsion of the third body when it approaches the Earth. In fact, the entire horseshoe-shaped valley between the points L5, L3, and L4 serves as the region of stability up to the growth of the potential when approaching L1 and L2. Note, however, that the centrifugal potential cannot be perceived in the same way as the usual potential of mechanics, in particular, the law of conservation of energy E = mv2 / 2 + U is not fulfilled.

There is a mathematical proof of the stability of the Lagrange points L4 and L5 [9] for μ < 0,135. Этому условию удовлетворяют не только система Солнце — Земля, но также и пары Солнце — Юпитер и Земля — Луна. Доказательство справедливо в том смысле, что тело, стартовав при начальных условиях с небольшим удалением от этих точек Лагранжа и с небольшой скоростью, через год действительно окажется рядом с исходной позицией. Однако более точный анализ показывает, что оно окажется не точно там, откуда начало свое движение. Появится небольшой дрейф. Математически он не существен. Но посмотрим на фактические расчеты.

The motion of a small body with coordinates r (t) and velocities v (t) = {vx (t), vy (t)} was found by numerically solving the differential equations of the restricted three-body problem:

\ (\ frac {∂ ^ 2x} {∂t ^ 2} – \ frac {∂y} {∂t} = \ frac {∂U} {∂x}; \ frac {∂ ^ 2y} {∂t ^ 2 } + \ frac {∂x} {∂t} = \ frac {∂U} {∂y}. \)

Their accuracy was controlled by the constancy of the Jacobi invariant [9]

CJ (x, y) = 2U (x, y) – v2,

the relative variations of which along all the calculated trajectories did not exceed 10−7. Since the coordinates of our problem are close to unity in magnitude, the same number characterizes the accuracy of the solution itself.

Numerical solutions with different initial conditions show a high similarity of trajectories under the condition of small initial deviations from the Earth’s orbit and low velocities. In fig. 4 shows the motion of a body from the Lagrange point L5 with an initial velocity of 0.006 (0.18 km / s in physical units), calculated by numerically solving a system of differential equations. This trajectory consists of a number of loops, the movement along each of them lasts 1 year. After 892 years, the body returns to its starting point at almost the same speed, following a horseshoe-shaped path. Changes in the velocity modulus v and deviation h from the earth’s orbit, corresponding to the solution in Fig. 4 are shown in Fig. 5. As you can see, the speed of a small body throughout the entire trajectory does not exceed 0.035 (ie, 1 km / s). Of course, this is a very small value compared to most bodies in the solar system, but in this case it represents the speed relative to the Earth, which itself moves around the Sun at a speed of about 30 km / s.