Judging by the astronomical discoveries of the last two decades, we live in a similar universe.

In Einstein’s model, time is separated from space, like Newton’s, and therefore the coefficient in front of dt2 is equal to one (remember, if we assume that c = 1). In the de Sitter model, it clearly depends both on the parameter R and, more importantly, on the radial component r (through the coefficient cos2χ, or, which is the same, cos2 (r / R)). It follows from this that in the de Sitter model, at different distances from the origin, time flows at different speeds! This speed is maximum at r = 0, when cos2χ = 1, and drops to zero when r takes on its maximum value πR / 2, which corresponds to χ = π / 2. Therefore, in de Sitter’s model “there is no universal time, just as there is no fundamental difference between“ time ”and three other coordinates, none of which has real physical meaning. In system A, on the contrary, time is essentially different from spatial coordinates. “

De Sitter traced a number of paradoxical (in his words) consequences of the “mixing” of time and space in his model. For example, free particles in it do not move at a constant speed along straight lines. Beams of straight trajectories diverge exclusively from the origin of coordinates (that is, the point where r = 0), however, as the radius of the speed of such particles increases, it changes. At the “border” of space (at r = πR / 2), both the velocity and the kinetic energy of any of these particles vanish. As de Sitter writes, on this hypersurface “four-dimensional space-time is reduced to three-dimensional space: there is no time, and therefore there is no movement” (author’s italics). For the same reason, a ray of light emitted from the origin (not to mention material particles) will never reach the border in a finite period of time.

Another important consequence of the presence of the factor cos2χ in front of dt2 de Sitter formulated in the end, at the very end of the article. Thanks to this factor, “the frequency of light vibrations decreases with distance from the origin. Therefore, the spectral lines of light from very distant stars and nebulae should shift due to the systematic redshift, creating the illusion of positive [that is, directed from the Earth – AL] radial velocity. ” Thus, de Sitter, on the basis of his model, predicted the redshift of the spectra of very distant space objects, but explained it not by the expansion of the Universe, but by the slowing down of time at its boundaries.

As an astronomer, de Sitter went further. He considered it necessary to note that there is already information about the scattering of several spiral nebulae, “although these observations are still very unreliable.” He highlighted three nebulae (the Andromeda galaxy, NGC 1068 and NGC 4594), whose spectra allow an estimate of radial velocities of about 600 km / s. In the last paragraph, de Sitter did not fail to note that “if subsequent observations confirm the presence of positive radial velocities, this will undoubtedly prove to be an argument in favor of adopting hypothesis B instead of hypothesis A.” If the systematic redshifts of the spectra of distant objects were not detected, this fact would have to be interpreted either as evidence in favor of hypothesis A, or as an indication that the radius of the Universe R is much larger than it was believed at that time.

It is with this prediction that de Sitter’s remarkable work ends, which, following Einstein’s article, marked the emergence of modern cosmology. Later, theorists made considerable efforts in attempts to interpret it in its entirety and, in particular, to understand the nature of the redshift arising in this model, which was called the de Sitter effect. Reviewing these studies would take us too far, so I will focus only on key points.

First, de Sitter did not predict the effect of the recession of distant galaxies described by Hubble’s law. Let me remind you that, according to this law, the radial velocity of a galaxy is proportional to its distance from the Sun: v = Hr (where H is the Hubble parameter). On the other hand, this speed is proportional to the relative displacement of the spectral lines, which, therefore, should linearly depend on the distance r. De Sitter’s model makes it possible to calculate this dependence, although he himself did not. Such calculations were made by Eddington seven years later. He showed that the relative shift of spectral lines in the de Sitter model is proportional to (r / R) 2 if r is much less than R, and otherwise is expressed by a more complex formula. So Hubble’s law does not follow from de Sitter’s model. This law was first theoretically derived by Georges Lemaitre (two years before the empirical discovery of Hubble) and immediately interpreted it as a manifestation of the expansion of outer space (G. Lemaître, 1927. Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques).

Secondly, the static nature of de Sitter’s model turned out to be only an appearance. Let me remind you that de Sitter noted (albeit in passing) that free particles, not subject to the action of external forces, move with variable speed in his universe. This property looks completely mysterious, since there are no force fields in this Universe, the gradients of which can cause such accelerations. But it’s not only that. If the addition of negligible amounts of matter to the de Sitter space triggers dynamic processes in it, then its static nature turns out to be as unstable as the static nature of Einstein’s model.

De Sitter not only recognized and stressed the paradoxical nature of his model, but admitted that, perhaps, it is associated with an unsuccessful choice of the coordinate system. A few years later, this idea was taken up by other scientists. For example, in 1922, the Hungarian mathematician Cornelius Lanczos, who worked in Germany, reformulated de Sitter’s solution in other coordinates. In the metric he found, the variable factor in front of dt2 disappears, and the radius of curvature of space exponentially increases with time. In fact, Lanczos received a model of the expanding Universe, but refrained from such an interpretation. Lemaitre arrived at a similar result in 1925, again based on the choice of a different coordinate system. Later, it was finally proved that the de Sitter model corresponds, so to speak, to a superdynamic spherically symmetric Universe, the radius of which increases with time as quickly as possible – exponentially (this, in particular, elementary follows from the Friedmann equations with a positive cosmological constant and equal to zero pressure and density of matter). The metric of this model in different coordinate systems is extremely diverse (see, for example, Antony Zee, 2013. Einstein Gravity in a Nutshell, p. 643). In an astronomically meaningful (so-called, accompanying) frame of reference using Cartesian coordinates, it is expressed very simply:

\ [\ mathrm {d} s ^ 2 = L ^ 2 \ left (- \ mathrm {d} t ^ 2 + e ^ {2t} \ left (\ mathrm {d} x ^ 2 + \ mathrm {d} y ^ 2 + \ mathrm {d} z ^ 2 \ right) \ right). \]

It is the metric of the modified spacetime of special relativity (Minkowski space), representing the universe expanding with time. At each time slice, its space turns out to be Euclidean (in contrast to space-time, which is naturally curved). Judging by the astronomical discoveries of the last two decades, we live in a similar universe.

What is the conclusion? The first cosmological models a century ago were claimed to be static, but were not. Subsequently, the progress of cosmology was associated with the creation and comprehension of dynamic models of the Universe, which by the mid-1930s received almost complete recognition of astronomers and physicists. But that’s a completely different story.

Alexey Levin

Representatives of the Gorechavkov family. (Illustration from Wikipedia https://en.wikipedia.org/wiki/Gentids)

The aim of this study was to test the hypothesis that alpine species of the Gentianaceae family with green leaves may be partially mycoheterotrophic. The presence of mixotrophy in plants was revealed by modern methods of isotope analysis. The results showed that the enrichment in heavy isotopes characteristic of heterotrophs is observed only in nitrogen, but not in carbon.

Not all plants are equally foraging. The habitual image of a photosynthetic (autotrophic) green plant is actually not so unambiguous. The entire spectrum from completely photoautotrophic to chlorophyll-free heterotrophs can be observed among plants. Carnivorous plants grasping insects immediately come to mind: sundews or the wonderful Venus flytrap (Fig. 1). But in reality, mixotrophy – the ability to obtain nutrients not only through photosynthesis, but also from other organisms – is quite widespread among plants and is not always so “deadly” for the organisms used. Such an opportunity, for example, is provided by the interaction of a plant with fungal hyphae – mycoheterotrophy. Mycoheterotrophy can occur with different types of mycorrhiza and can be partial or complete. According to some scientists, the presence of complete mycoheterotrophy in certain plant species indicates the prevalence among related species of a partial ability to receive nutrients from symbiotic fungi. The aim of this study was to identify the presence (or absence) of mycoheterotrophy in alpine relatives in the Gentianaceae family (Gentian) (Title illustration). Since some plants of this family are capable of complete mycoheterotrophy, the study can confirm (refute) the viability of the hypothesis “about relatives” presented. In addition, it is interesting to check how widespread mixotrophic nutrition is among alpine grasses growing in a short growing season.

Fig. 1 1984 george orwell book review. Carnivorous sundew with its victims. (Photo from the site klubrasteniy.ru)

The research method is based on the phenomenon of accumulation of heavy isotopes of carbon (13C) and nitrogen (15N) in food chains: the ratio of heavy and light isotopes will increase in the order from autotrophs to heterotrophs. The main difficulty in interpreting the results of analyzing the concentration of isotopes is that these indicators depend not only on the position in the food chain, but also on the microconditions of plant growth. Therefore, the main method is a comparative analysis of isotope ratios with those of reference plants growing under the same conditions, i.e. Next door. For these purposes, the authors collected the leaves of the studied plant (Gentianaceae) and the nearest available plant from the reference species (a representative of a herb with arbuscular mycorrhiza). In total, 9 species of gentian were studied from two regions: in the Northwestern Caucasus (Teberda Nature Reserve, Karachay-Cherkess Republic, Russia; 6 pairs) and in Eastern Tibet (Jiuzhaigou Valley, Sichuan Province, China; 3 pairs). For each species of this. Gentianaceae chose the most common nearby herb with arbuscular mycorrhiza (reference). In each habitat, plants of each species were collected in five replicates. The analysis for stable isotopes was carried out on the Thermo Delta V Plus isotope mass spectrometer and the Thermo Flash 1112 elemental analyzer at the Shared Use Center of the Institute of Ecology and Evolution of A.N. Severtsov RAS, Moscow.

Heavy isotopes of carbon. The concentrations of heavy isotopes of carbon and nitrogen differed both between species and between habitats, which indicates the variability of these parameters. The authors do not undertake to analyze the reasons for the detected variability using this material. Comparative analysis with reference plants growing in the vicinity of the studied plants showed that the latter did not tend to increase the concentration of 13C (Fig. 2). And in some gentian plants, the content of the heavy isotope was even lower than in the reference plant, which usually indicates an autotrophic nature of nutrition.

Fig. 2. Deviation of the concentration of heavy isotope carbon (‰) (left) and nitrogen (‰) (right) for pairs in leaves of Gentianaceae (red bars) and reference plants with arbuscular mycorrhiza (blue bars). The standard error is shown (n = 5). The p-values ​​from LSD post hoc tests are shown below the bars (red numbers: p < 0.05). (По ординате показатель - тысячные доли отклонения содержания изотопа от международного стандарта [(Rпроба – Rстандарт)/Rстандарт] × 1000 (‰), иллюстрация из обсуждаемого исследования)

Heavy nitrogen isotopes. The 15N content in the reference plants was similar to that (known from the data of other authors) in alpine plants with arbuscular mycorrhiza, and these values ​​in the studied gentian plants were significantly higher and similar to alpine legumes and sedges that do not form mycorrhiza (see Fig. 2 ). Thus, the source of nitrogen in gentian plants is apparently different from that in plants with arbuscular mycorrhiza, i.e. partial mycoheterotropy can be assumed.

The discussion of the results. All currently known completely mycoheterotrophic gentians are enriched in heavy isotopes of both carbon and nitrogen. However, in this study, the accumulation of the heavy isotope of carbon was not recorded as an unambiguous trend (shown only for some pairs). In this regard, the authors give examples of mycoheterotrophic species, in which the enrichment in the heavy isotope of carbon is also not observed, in contrast to nitrogen. Such are mycoheterotrophs with arbuscular mycorrhiza: indeed, it is the fungus that uses the organic carbon of the symbiotic plant, and the plant receives its carbon in the usual autotrophic way. On the other hand, there are examples of mycoheterotrophic plants, which under some conditions demonstrate an increased concentration of both heavy isotopes, and in others only the heavy isotope of nitrogen (as in this case). This is, for example, Moneses uniflora from the heather family, which in the USA is enriched in both heavy isotopes, and in Europe it is characterized by an increased content only of nitrogen.

Based on the analysis of the data, the authors suggest the presence of partial mycoheterotrophy in the studied gentian, which may help the species under conditions of a short growing season. These data, according to the authors, support the hypothesis of an increase in the likelihood of partial mixotrophy among the phylogenetic relatives of species with complete mycoheterotrophy, previously expressed by other researchers.

Evgeny Podolsky,Nagoya University (Japan)

Dedicated to my family, Yeoul, Kostya and Stas.

Glaciers on Earth and in the Solar System

About ten percent of the land is covered with glaciers – perennial masses of snow, firn (from German Firn – last year’s packed granular snow) and ice, which have their own motion. These huge rivers of ice, cutting through valleys and grinding mountains, pushing through continents with their weight, store 80% of our planet’s fresh water reserves.

The Pamir is one of the main centers of the modern glaciation of the planet – inaccessible and little explored (Tajikistan; author’s photo, 2009)

The role of glaciers in the evolution of the globe and man is colossal. The last 2 million years of ice ages have become a powerful impetus for the development of primates. Severe weather conditions forced the hominids to struggle for existence in cold conditions, life in caves, the appearance and development of clothing, and the widespread use of fire.