Just a hundred years ago, scientists discovered that our Universe is rapidly increasing in size.
In 1870, the English mathematician William Clifford came to the very deep idea that space can be curved, and not the same at different points, and that its curvature can change over time. He even admitted that such changes are somehow connected with the movement of matter. Both of these ideas many years later formed the basis of the general theory of relativity. Clifford himself did not live to see this - he died of tuberculosis at the age of 34, 11 days before the birth of Albert Einstein.
Redshift
The first information about the expansion of the Universe was provided by astrospectrography. In 1886, the English astronomer William Huggins noticed that the wavelengths of starlight were slightly shifted compared to the terrestrial spectra of the same elements. Based on the formula for the optical version of the Doppler effect, derived in 1848 by the French physicist Armand Fizeau, it is possible to calculate the magnitude of the star's radial velocity. Such observations make it possible to track the movement of a space object.
A hundred years ago, the concept of the Universe was based on Newtonian mechanics and Euclidean geometry. Even a few scientists, such as Lobachevsky and Gauss, who admitted (only as a hypothesis!) The physical reality of non-Euclidean geometry, considered outer space to be eternal and unchanging. The expansion of the universe makes it difficult to judge the distance to distant galaxies. The light that reached 13 billion years later from the galaxy A1689-zD1 3.35 billion light years away (A), “reddens” and weakens as it traverses the expanding space, and the galaxy itself recedes (B). It will carry information about the distance in redshift (13 billion light years), in angular size (3.5 billion light years), in intensity (263 billion light years), while the real distance is 30 billion light years. years.
A quarter century later, this opportunity was re-exploited by Vesto Slipher, an observatory in Flagstaff, Arizona, who had been studying the spectra of spiral nebulae since 1912 with a 24-inch telescope with a good spectrograph. To get a high-quality image, the same photographic plate was exposed for several nights, so the project moved slowly. From September to December 1913, Slipher studied the Andromeda nebula and, using the Doppler-Fizeau formula, came to the conclusion that it approaches the Earth by 300 km every second.
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In 1917, he published data on the radial velocities of 25 nebulae, which showed significant asymmetries in their directions. Only four nebulae approached the Sun, the rest escaped (and some very quickly).
Slipher did not strive for fame or publicize his results. Therefore, they became known in astronomical circles only when the famous British astrophysicist Arthur Eddington drew attention to them.
In 1924, he published a monograph on the theory of relativity, which included a list of 41 nebulae found by Slipher. The same four blue-shifted nebulae were present there, while the remaining 37 spectral lines were red-shifted. Their radial velocities varied in the range of 150 - 1800 km / s and, on average, 25 times higher than the velocities of the Milky Way stars known by that time. This suggested that the nebulae are involved in other movements than the "classical" luminaries.
Space islands
In the early 1920s, most astronomers believed that spiral nebulae were located at the periphery of the Milky Way, and beyond it there was nothing but empty dark space. True, even in the 18th century, some scientists saw giant star clusters in nebulae (Immanuel Kant called them island universes). However, this hypothesis was not popular, since it was not possible to reliably determine the distances to nebulae.
This problem was solved by Edwin Hubble, who worked on a 100-inch reflector telescope at the Mount Wilson Observatory in California. In 1923-1924, he discovered that the Andromeda nebula is composed of many luminous objects, among which are variable stars of the Cepheid family. It was already known then that the period of change in their apparent brightness is associated with the absolute luminosity, and therefore the Cepheids are suitable for calibrating cosmic distances. With their help, Hubble estimated the distance to Andromeda at 285,000 parsecs (according to modern data, it is 800,000 parsecs). The diameter of the Milky Way was then assumed to be approximately 100,000 parsecs (in fact, it is three times less). From this it followed that Andromeda and the Milky Way must be considered independent star clusters. Hubble soon identified two more independent galaxies,which finally confirmed the hypothesis of "island universes".
In fairness, it should be noted that two years before Hubble, the distance to Andromeda was calculated by the Estonian astronomer Ernst Opik, whose result - 450,000 parsecs - was closer to the correct one. However, he used a number of theoretical considerations that were not as convincing as Hubble's direct observations.
By 1926, Hubble had carried out a statistical analysis of observations of four hundred "extragalactic nebulae" (he used this term for a long time, avoiding calling them galaxies) and proposed a formula to relate the distance to a nebula with its apparent brightness. Despite the huge errors of this method, new data confirmed that nebulae are distributed more or less evenly in space and are located far beyond the boundaries of the Milky Way. Now there was no longer any doubt that space is not closed on our Galaxy and its nearest neighbors.
Space Modelers
Eddington became interested in Slipher's results even before the final elucidation of the nature of spiral nebulae. By this time, a cosmological model already existed, in a sense predicting the effect revealed by Slipher. Eddington thought about it a lot and, naturally, did not miss the opportunity to give the observations of the Arizona astronomer a cosmological sound.
Modern theoretical cosmology began in 1917 with two revolutionary articles that presented models of the universe based on general relativity. One of them was written by Einstein himself, the other by the Dutch astronomer Willem de Sitter.
Hubble's laws
Edwin Hubble empirically revealed the approximate proportionality of redshifts and galactic distances, which he, using the Doppler-Fizeau formula, turned into a proportionality between speeds and distances. So we are dealing with two different patterns here.
Hubble didn't know how they relate to each other, but what does today's science say about this?
As Lemaitre showed already, the linear correlation between cosmological (caused by the expansion of the Universe) redshifts and distances is by no means absolute. In practice, it is well observed only for displacements less than 0.1. So the empirical Hubble's law is not exact, but approximate, and the Doppler-Fizeau formula is valid only for small shifts of the spectrum.
But the theoretical law linking the radial velocity of distant objects with the distance to them (with the proportionality coefficient in the form of the Hubble parameter V = Hd) is valid for any redshifts. However, the velocity V that appears in it is not the velocity of physical signals or real bodies in physical space. This is the rate of increase in the distances between galaxies and galaxy clusters, which is due to the expansion of the Universe. We would be able to measure it only if we were able to stop the expansion of the Universe, instantly stretch measuring tapes between galaxies, read the distances between them and divide them into time intervals between measurements. Naturally, the laws of physics do not allow this. Therefore, cosmologists prefer to use the Hubble parameter H in another formula,where the scale factor of the Universe appears, which precisely describes the degree of its expansion in different cosmic epochs (since this parameter changes over time, its modern value is designated H0). The universe is now expanding with acceleration, so the value of the Hubble parameter is increasing.
By measuring cosmological redshifts, we get information about the degree of expansion of space. The light of the galaxy, which came to us with the cosmological redshift z, left it when all cosmological distances were 1 + z times smaller than in our epoch. Additional information about this galaxy, such as its current distance or the rate of distance from the Milky Way, can only be obtained using a specific cosmological model. For example, in the Einstein-de Sitter model, a galaxy with z = 5 moves away from us at a speed of 1.1 s (the speed of light). But if you make a common mistake and just equalize V / c and z, then this speed will be five times the speed of light. The discrepancy, as we can see, is serious.
Dependence of the speed of distant objects on the redshift according to SRT, GRT (depends on the model and time, the curve shows the present time and the current model). At small displacements, the dependence is linear.
Einstein, in the spirit of the times, believed that the Universe as a whole is static (he tried to make it infinite in space as well, but could not find the correct boundary conditions for his equations). As a result, he built a model of a closed universe, the space of which has a constant positive curvature (and therefore it has a constant finite radius). Time in this Universe, on the contrary, flows in a Newtonian way, in the same direction and at the same speed. The space-time of this model is curved due to the spatial component, while the time component is not deformed in any way. The static nature of this world provides a special "insert" into the basic equation, preventing gravitational collapse and thereby acting as an ubiquitous anti-gravity field. Its intensity is proportional to a special constant,which Einstein called universal (now it is called the cosmological constant).
Lemaitre's cosmological model of the expansion of the universe was far ahead of its time. Lemaitre's universe begins with the Big Bang, after which the expansion first slows down and then begins to accelerate.
Einstein's model made it possible to calculate the size of the universe, the total amount of matter, and even the value of the cosmological constant. This requires only the average density of cosmic matter, which, in principle, can be determined from observations. It is no coincidence that Eddington admired this model and used Hubble in practice. However, it is ruined by instability, which Einstein simply did not notice: at the slightest deviation of the radius from the equilibrium value, the Einstein world either expands or undergoes a gravitational collapse. Therefore, this model has nothing to do with the real Universe.
Empty world
De Sitter also built, as he himself believed, a static world of constant curvature, but not positive, but negative. It contains Einstein's cosmological constant, but there is no matter at all. When introducing test particles of arbitrarily small mass, they scatter and go to infinity. In addition, time flows more slowly at the periphery of de Sitter's universe than at its center. Because of this, light waves come from large distances with a redshift, even if their source is stationary relative to the observer. So in the 1920s, Eddington and other astronomers wondered if de Sitter's model had anything to do with the reality reflected in Slipher's observations?
These suspicions were confirmed, albeit in a different way. The static nature of de Sitter's universe turned out to be imaginary, since it was associated with an unfortunate choice of the coordinate system. After correcting this error, the de Sitter space turned out to be flat, Euclidean, but non-static. Due to the anti-gravitational cosmological constant, it expands, while maintaining zero curvature. Because of this expansion, the wavelengths of the photons increase, which entails the shift of the spectral lines predicted by de Sitter. It is worth noting that this is how the cosmological redshift of distant galaxies is explained today.
From statistics to dynamics
The history of openly non-static cosmological theories begins with two papers by the Soviet physicist Alexander Friedman, published in the German journal Zeitschrift fur Physik in 1922 and 1924. Friedman calculated models of universes with time-variable positive and negative curvatures, which became the golden fund of theoretical cosmology. However, his contemporaries hardly noticed these works (Einstein at first even considered Friedman's first article mathematically erroneous). Friedman himself believed that astronomy did not yet have an arsenal of observations that would allow deciding which of the cosmological models is more consistent with reality, and therefore limited himself to pure mathematics. Perhaps he would have acted differently if he had familiarized himself with the results of Slipher, but this did not happen.
The greatest cosmologist of the first half of the 20th century, Georges Lemaitre, thought differently. At home, in Belgium, he defended his dissertation in mathematics, and then in the mid-1920s studied astronomy - at Cambridge under Eddington and at the Harvard Observatory at Harlow Shapley (during his stay in the United States, where he prepared his second dissertation at MIT, he met Slipher and Hubble). Back in 1925, Lemaitre was the first to show that the static nature of de Sitter's model was imaginary. Upon his return to his homeland as a professor at the University of Louvain, Lemaitre built the first model of an expanding universe with a clear astronomical basis. Without exaggeration, this work was a revolutionary breakthrough in space science.
Ecumenical revolution
In his model, Lemaitre retained a cosmological constant with an Einstein numerical value. Therefore, its universe begins in a static state, but over time, due to fluctuations, it enters the path of constant expansion with an increasing speed. At this stage, it retains a positive curvature, which decreases as the radius grows. Lemaitre included in the composition of his universe not only matter, but also electromagnetic radiation. Neither Einstein, nor de Sitter, whose works were known to Lemaitre, nor Friedman, about whom he knew nothing at the time, did this.
Associated coordinates
In cosmological computations, it is convenient to use accompanying coordinate systems that expand in unison with the expansion of the universe. In the idealized model, where galaxies and galactic clusters do not participate in any proper motions, their accompanying coordinates do not change. But the distance between two objects at a given moment in time is equal to their constant distance in the accompanying coordinates, multiplied by the magnitude of the scale factor for that moment. This situation can be easily illustrated on an inflatable globe: the latitude and longitude of each point do not change, and the distance between any pair of points increases with increasing radius.
The use of co-ordinates helps to understand the profound differences between the cosmology of the expanding universe, special relativity, and Newtonian physics. So, in Newtonian mechanics, all motions are relative, and absolute immobility has no physical meaning. On the contrary, in cosmology, immobility in the accompanying coordinates is absolute and, in principle, can be confirmed by observations. The special theory of relativity describes processes in space-time, from which it is possible, using the Lorentz transformations, to isolate the spatial and temporal components in an infinite number of ways. Cosmological space-time, on the contrary, naturally disintegrates into a curved expanding space and a single cosmic time. In this case, the speed of recession of distant galaxies can be many times higher than the speed of light.
Lemaitre, back in the USA, suggested that the redshifts of distant galaxies are due to the expansion of space, which "stretches" light waves. Now he proved it mathematically. He also demonstrated that small (much smaller than unity) redshifts are proportional to the distance to the light source, and the coefficient of proportionality depends only on time and carries information about the current rate of expansion of the Universe. Since it followed from the Doppler-Fizeau formula that the radial velocity of the galaxy is proportional to the redshift, Lemaître concluded that this speed is also proportional to its distance. Having analyzed the speeds and distances of 42 galaxies from the Hubble list and taking into account the intragalactic speed of the Sun, he established the values of the proportionality coefficients.
Unnoticed work
Lemaitre published his work in 1927 in French in the unreadable journal Annals of the Scientific Society of Brussels. It is believed that this was the main reason why she initially went almost unnoticed (even by his teacher Eddington). True, in the fall of the same year, Lemaitre was able to discuss his findings with Einstein and learned from him about Friedmann's results. The creator of general relativity had no technical objections, but he resolutely did not believe in the physical reality of Lemaitre's model (just as he did not accept Friedmann's conclusions earlier).
Hubble plots
Meanwhile, in the late 1920s, Hubble and Humason found a linear correlation between the distances of up to 24 galaxies and their radial velocities, calculated (mostly by Slipher) from redshifts. From this, Hubble concluded that the radial velocity of the galaxy is directly proportional to the distance to it. The coefficient of this proportionality is now denoted H0 and is called the Hubble parameter (according to the latest data, it slightly exceeds 70 (km / s) / megaparsec).
Hubble's paper with a graph of the linear relationship between galactic velocities and distances was published in early 1929. A year earlier, the young American mathematician Howard Robertson, following Lemaitre, deduced this dependence from the model of the expanding Universe, which Hubble may have known about. However, in his famous article, this model was not mentioned either directly or indirectly. Later, Hubble expressed doubts that the speeds appearing in his formula actually describe the movements of galaxies in outer space, but he always refrained from their concrete interpretation. He saw the meaning of his discovery in demonstrating the proportionality of galactic distances and redshifts, leaving the rest to theorists. Therefore, with all due respect to Hubble, there is no reason to consider him the discoverer of the expansion of the Universe.
And yet it is expanding
Nevertheless, Hubble paved the way for the recognition of the expansion of the universe and Lemaitre's model. Already in 1930 she was paid tribute to such masters of cosmology as Eddington and de Sitter; a little later, scientists noticed and appreciated Friedman's work. In 1931, at the suggestion of Eddington, Lemaitre translated into English his article (with small cuts) for the Monthly News of the Royal Astronomical Society. In the same year, Einstein agreed with Lemaitre's conclusions, and a year later, together with de Sitter, built a model of an expanding Universe with flat space and curved time. This model, due to its simplicity, has been very popular among cosmologists for a long time.
In the same 1931, Lemaitre published a short (and without any mathematics) description of yet another model of the Universe, combining cosmology and quantum mechanics. In this model, the initial moment is the explosion of the primary atom (Lemaitre also called it a quantum), which gave rise to both space and time. Since gravity slows down the expansion of the newborn Universe, its speed decreases - it is possible that almost to zero. Later, Lemaitre introduced a cosmological constant into his model, which forced the Universe to move over time into a stable regime of accelerating expansion. So he anticipated both the idea of the Big Bang and modern cosmological models that take into account the presence of dark energy. And in 1933, he identified the cosmological constant with the energy density of the vacuum, which no one had thought of before. It's just amazinghow much this scientist, undoubtedly worthy of the title of the discoverer of the expansion of the Universe, was ahead of his time!
Alexey Levin