6 Choosing Our Universe




ACCORDING TO THE BOSHONGO PEOPLE of central Africa, in the beginning there was only darkness, water, and the great god Bumba. One day Bumba, in pain from a stomachache, vomited up the sun. In time the sun dried up some of the water, leaving land. But Bumba was still in pain, and vomited some more. Up came the moon, the stars, and then some animals: the leopard, the crocodile, the turtle, and finally man. The Mayans of Mexico and Central America tell of a similar time before creation when all that existed were the sea, the sky, and the Maker. In the Mayan legend the Maker, unhappy because there was no one to praise him, created the earth, mountains, trees, and most animals. But the animals could not speak, and so he decided to create humans. First he made them of mud and earth, but they only spoke nonsense. He let them dissolve away and tried again, this time fashioning people from wood. Those people were dull. He decided to destroy them, but they escaped into the forest, sustaining damage along the way that altered them slightly, creating what we today know as monkeys. After that fiasco, the Maker finally came upon a formula that worked, and constructed the first humans from white and yellow corn. Today we make ethanol from corn, but so far haven’t matched the Maker’s feat of constructing the people who drink it.

Creation myths like these all attempt to answer the questions we address in this book: Why is there a universe, and why is the universe the way it is? Our ability to address such questions has grown steadily in the centuries since the ancient Greeks, most profoundly over the past century. Armed with the background of the previous chapters, we are now ready to offer a possible answer to these questions.

One thing that may have been apparent even in early times was that either the universe was a very recent creation or else human beings have existed for only a small fraction of cosmic history. That’s because the human race has been improving so rapidly in knowledge and technology that if people had been around for millions of years, the human race would be much further along in its mastery.

According to the Old Testament, God created Adam and Eve only six days into creation. Bishop Ussher, primate of all Ireland from 1625 to 1656, placed the origin of the world even more precisely, at nine in the morning on October 27, 4004 BC. We take a different view: that humans are a recent creation but that the universe itself began much earlier, about 13.7 billion years ago.

The first actual scientific evidence that the universe had a beginning came in the 1920s. As we said in Chapter 3, that was a time when most scientists believed in a static universe that had always existed. The evidence to the contrary was indirect, based upon the observations Edwin Hubble made with the 100-inch telescope on Mount Wilson, in the hills above Pasadena, California. By analyzing the spectrum of light they emit, Hubble determined that nearly all galaxies are moving away from us, and the farther away they are, the faster they are moving. In 1929 he published a law relating their rate of recession to their distance from us, and concluded that the universe is expanding. If that is true, then the universe must have been smaller in the past. In fact, if we extrapolate to the distant past, all the matter and energy in the universe would have been concentrated in a very tiny region of unimaginable density and temperature, and if we go back far enough, there would be a time when it all began-the event we now call the big bang.

The idea that the universe is expanding involves a bit of subtlety. For example, we don’t mean the universe is expanding in the manner that, say, one might expand one’s house, by knocking out a wall and positioning a new bathroom where once there stood a majestic oak. Rather than space extending itself, it is the distance between any two points within the universe that is growing. That idea emerged in the 1930s amid much controversy, but one of the best ways to visualize it is still a metaphor enunciated in 1931 by Cambridge University astronomer Arthur Eddington. Eddington visualized the universe as the surface of an expanding balloon, and all the galaxies as points on that surface. This picture clearly illustrates why far galaxies recede more quickly than nearby ones. For example, if the radius of the balloon doubled each hour, then the distance between any two galaxies on the balloon would double each hour. If at some time two galaxies were 1 inch apart, an hour later they would be 2 inches apart, and they would appear to be moving relative to each other at a rate of 1 inch per hour. But if they started 2 inches apart, an hour later they would be separated by 4 inches and would appear to be moving away from each other at a rate of 2 inches per hour. That is just what Hubble found: the farther away a galaxy, the faster it was moving away from us.

It is important to realize that the expansion of space does not affect the size of material objects such as galaxies, stars, apples, atoms, or other objects held together by some sort of force. For example, if we circled a cluster of galaxies on the balloon, that circle would not expand as the balloon expanded. Rather, because the galaxies are bound by gravitational forces, the circle and the galaxies within it would keep their size and configuration as the balloon enlarged. This is important because we can detect expansion only if our measuring instruments have fixed sizes. If everything were free to expand, then we, our yardsticks, our laboratories, and so on would all expand proportionately and we would not notice any difference.


That the universe is expanding was news to Einstein. But the possibility that the galaxies are moving away from each other had been proposed a few years before Hubble’s papers on theoretical grounds arising from Einstein’s own equations. In 1922, Russian physicist and mathematician Alexander Friedmann investigated what would happen in a model universe based upon two assumptions that greatly simplified the mathematics: that the universe looks identical in every direction, and that it looks that way from every observation point. We know that Friedmann’s first assumption is not exactly true-the universe fortunately is not uniform everywhere! If we gaze upward in one direction, we might see the sun; in another, the moon or a colony of migrating vampire bats. But the universe does appear to be roughly the same in every direction when viewed on a scale that is far larger-larger even than the distance between galaxies. It is something like looking down at a forest. If you are close enough, you can make out individual leaves, or at least trees, and the spaces between them. But if you are so high up that if you hold out your thumb it covers a square mile of trees, the forest will appear to be a uniform shade of green. We would say that, on that scale, the forest is uniform.

Based on his assumptions Friedmann was able to discover a solution to Einstein’s equations in which the universe expanded in the manner that Hubble would soon discover to be true. In particular, Friedmann’s model universe begins with zero size and expands until gravitational attraction slows it down, and eventually causes it to collapse in upon itself. (There are, it turns out, two other types of solutions to Einstein’s equations that also satisfy the assumptions of Friedmann’s model, one corresponding to a universe in which the expansion continues forever, though it does slow a bit, and another to a universe in which the rate of expansion slows toward zero, but never quite reaches it.) Friedmann died a few years after producing this work, and his ideas remained largely unknown until after Hubble’s discovery. But in 1927 a professor of physics and Roman Catholic priest named Georges Lema?tre proposed a similar idea: If you trace the history of the universe backward into the past, it gets tinier and tinier until you come upon a creation event-what we now call the big bang.

Not everyone liked the big bang picture. In fact, the term “big bang” was coined in 1949 by Cambridge astrophysicist Fred Hoyle, who believed in a universe that expanded forever, and meant the term as a derisive description. The first direct observations supporting the idea didn’t come until 1965, with the discovery that there is a faint background of microwaves throughout space. This cosmic microwave background radiation, or CMBR, is the same as that in your microwave oven, but much less powerful. You can observe the CMBR yourself by tuning your television to an unused channel-a few percent of the snow you see on the screen will be caused by it. The radiation was discovered by accident by two Bell Labs scientists trying to eliminate such static from their microwave antenna. At first they thought the static might be coming from the droppings of pigeons roosting in their apparatus, but it turned out their problem had a more interesting origin-the CMBR is radiation left over from the very hot and dense early universe that would have existed shortly after the big bang. As the universe expanded, it cooled until the radiation became just the faint remnant we now observe. At present these microwaves could heat your food to only about ?270 degrees Centigrade-3 degrees above absolute zero, and not very useful for popping corn.

Astronomers have also found other fingerprints supporting the big bang picture of a hot, tiny early universe. For example, during the first minute or so, the universe would have been hotter than the center of a typical star. During that period the entire universe would have acted as a nuclear fusion reactor. The reactions would have ceased when the universe expanded and cooled sufficiently, but the theory predicts that this should have left a universe composed mainly of hydrogen, but also about 23 percent helium, with traces of lithium (all heavier elements were made later, inside stars). The calculation is in good accordance with the amounts of helium, hydrogen, and lithium we observe.

Measurements of helium abundance and the CMBR provided convincing evidence in favor of the big bang picture of the very early universe, but although one can think of the big bang picture as a valid description of early times, it is wrong to take the big bang literally, that is, to think of Einstein’s theory as providing a true picture of the origin of the universe. That is because general relativity predicts there to be a point in time at which the temperature, density, and curvature of the universe are all infinite, a situation mathematicians call a singularity. To a physicist this means that Einstein’s theory breaks down at that point and therefore cannot be used to predict how the universe began, only how it evolved afterward. So although we can employ the equations of general relativity and our observations of the heavens to learn about the universe at a very young age, it is not correct to carry the big bang picture all the way back to the beginning.

We will get to the issue of the origin of the universe shortly, but first a few words about the first phase of the expansion. Physicists call it inflation. Unless you’ve lived in Zimbabwe, where currency inflation recently exceeded 200,000,000 percent, the term may not sound very explosive. But according to even conservative estimates, during this cosmological inflation, the universe expanded by a factor of 1,000,000,000,000,000,000,000,000,000,000 in.00000000000000000000000000000000001 second. It was as if a coin 1 centimeter in diameter suddenly blew up to ten million times the width of the Milky Way. That may seem to violate relativity, which dictates that nothing can move faster than light, but that speed limit does not apply to the expansion of space itself.

The idea that such an episode of inflation might have occurred was first proposed in 1980, based on considerations that go beyond Einstein’s theory of general relativity and take into account aspects of quantum theory. Since we don’t have a complete quantum theory of gravity, the details are still being worked out, and physicists aren’t sure exactly how inflation happened. But according to the theory, the expansion caused by inflation would not be completely uniform, as predicted by the traditional big bang picture. These irregularities would produce minuscule variations in the temperature of the CMBR in different directions. The variations are too small to have been observed in the 1960s, but they were first discovered in 1992 by NASA’s COBE satellite, and later measured by its successor, the WMAP satellite, launched in 2001. As a result, we are now confident that inflation really did happen.

Ironically, though tiny variations in the CMBR are evidence for inflation, one reason inflation is an important concept is the nearly perfect uniformity of the temperature of the CMBR. If you make one part of an object hotter than its surroundings and then wait, the hot spot will grow cooler and its surroundings warmer until the temperature of the object is uniform. Similarly, one would expect the universe to eventually have a uniform temperature. But this process takes time, and if inflation hadn’t occurred, there wouldn’t have been enough time in the history of the universe for heat at widely separated regions to equalize, assuming that the speed of such heat transfer is limited by the speed of light. A period of very rapid expansion (much faster than light speed) remedies that because there would have been enough time for the equalization to happen in the extremely tiny preinflationary early universe.

Inflation explains the bang in the big bang, at least in the sense that the expansion it represents was far more extreme than the expansion predicted by the traditional big bang theory of general relativity during the time interval in which inflation occurred. The problem is, for our theoretical models of inflation to work, the initial state of the universe had to be set up in a very special and highly improbable way. Thus traditional inflation theory resolves one set of issues but creates another-the need for a very special initial state. That time-zero issue is eliminated in the theory of the creation of the universe we are about to describe.

Since we cannot describe creation employing Einstein’s theory of general relativity, if we want to describe the origin of the universe, general relativity has to be replaced by a more complete theory. One would expect to need a more complete theory even if general relativity did not break down, because general relativity does not take into account the small-scale structure of matter, which is governed by quantum theory. We mentioned in Chapter 4 that for most practical purposes quantum theory does not hold much relevance for the study of the large-scale structure of the universe because quantum theory applies to the description of nature on microscopic scales. But if you go far enough back in time, the universe was as small as the Planck size, a billion-trillion-trillionth of a centimeter, which is the scale at which quantum theory does have to be taken into account. So though we don’t yet have a complete quantum theory of gravity, we do know that the origin of the universe was a quantum event. As a result, just as we combined quantum theory and general relativity-at least provisionally-to derive the theory of inflation, if we want to go back even further and understand the origin of the universe, we must combine what we know about general relativity with quantum theory.

To see how this works, we need to understand the principle that gravity warps space and time. Warpage of space is easier to visualize than warpage of time. Imagine that the universe is the surface of a flat billiard table. The table’s surface is a flat space, at least in two dimensions. If you roll a ball on the table it will travel in a straight line. But if the table becomes warped or dented in places, as in the illustration below, then the ball will curve.


It is easy to see how the billiard table is warped in this example because it is curving into an outside third dimension, which we can see. Since we can’t step outside our own space-time to view its warpage, the space-time warpage in our universe is harder to imagine. But curvature can be detected even if you cannot step out and view it from the perspective of a larger space. It can be detected from within the space itself. Imagine a micro-ant confined to the surface of the table. Even without the ability to leave the table, the ant could detect the warpage by carefully charting distances. For example, the distance around a circle in flat space is always a bit more than three times the distance across its diameter (the actual multiple is ?). But if the ant cut across a circle encompassing the well in the table pictured above, it would find that the distance across is greater than expected, greater than one-third the distance around it. In fact, if the well were deep enough, the ant would find that the distance around the circle is shorter than the distance across it. The same is true of warpage in our universe-it stretches or compresses the distance between points of space, changing its geometry, or shape, in a way that is measurable from within the universe. Warpage of time stretches or compresses time intervals in an analogous manner.


Armed with these ideas, let’s return to the issue of the beginning of the universe. We can speak separately of space and time, as we have in this discussion, in situations involving low speeds and weak gravity. In general, however, time and space can become intertwined, and so their stretching and compressing also involve a certain amount of mixing. This mixing is important in the early universe and the key to understanding the beginning of time.

The issue of the beginning of time is a bit like the issue of the edge of the world. When people thought the world was flat, one might have wondered whether the sea poured over its edge. This has been tested experimentally: One can go around the world and not fall off. The problem of what happens at the edge of the world was solved when people realized that the world was not a flat plate, but a curved surface. Time, however, seemed to be like a model railway track. If it had a beginning, there would have to have been someone (i.e., God) to set the trains going. Although Einstein’s general theory of relativity unified time and space as space-time and involved a certain mixing of space and time, time was still different from space, and either had a beginning and an end or else went on forever. However, once we add the effects of quantum theory to the theory of relativity, in extreme cases warpage can occur to such a great extent that time behaves like another dimension of space.

In the early universe-when the universe was small enough to be governed by both general relativity and quantum theory-there were effectively four dimensions of space and none of time. That means that when we speak of the “beginning” of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist! We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics. If in the early universe all four dimensions behave like space, what happens to the beginning of time?

The realization that time can behave like another direction of space means one can get rid of the problem of time having a beginning, in a similar way in which we got rid of the edge of the world. Suppose the beginning of the universe was like the South Pole of the earth, with degrees of latitude playing the role of time. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. The universe would start as a point at the South Pole, but the South Pole is much like any other point. To ask what happened before the beginning of the universe would become a meaningless question, because there is nothing south of the South Pole. In this picture space-time has no boundary-the same laws of nature hold at the South Pole as in other places. In an analogous manner, when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless. This idea that histories should be closed surfaces without boundary is called the no-boundary condition.

Over the centures many, including Aristotle, believed that the universe must have always existed in order to avoid the issue of how it was set up. Others believed the universe had a beginning, and used it as an argument for the existence of God. The realization that time behaves like space presents a new alternative. It removes the age-old objection to the universe having a beginning, but also means that the beginning of the universe was governed by the laws of science and doesn’t need to be set in motion by some god.

If the origin of the universe was a quantum event, it should be accurately described by the Feynman sum over histories. To apply quantum theory to the entire universe-where the observers are part of the system being observed-is tricky, however. In Chapter 4 we saw how particles of matter fired at a screen with two slits in it could exhibit interference patterns just as water waves do. Feynman showed that this arises because a particle does not have a unique history. That is, as it moves from its starting point A to some endpoint B, it doesn’t take one definite path, but rather simultaneously takes every possible path connecting the two points. From this point of view, interference is no surprise because, for instance, the particle can travel through both slits at the same time and interfere with itself. Applied to the motion of a particle, Feynman’s method tells us that to calculate the probability of any particular endpoint we need to consider all the possible histories that the particle might follow from its starting point to that endpoint. One can also use Feynman’s methods to calculate the quantum probabilities for observations of the universe. If they are applied to the universe as a whole, there is no point A, so we add up all the histories that satisfy the no-boundary condition and end at the universe we observe today.

In this view, the universe appeared spontaneously, starting off in every possible way. Most of these correspond to other universes. While some of those universes are similar to ours, most are very different. They aren’t just different in details, such as whether Elvis really did die young or whether turnips are a dessert food, but rather they differ even in their apparent laws of nature. In fact, many universes exist with many different sets of physical laws. Some people make a great mystery of this idea, sometimes called the multiverse concept, but these are just different expressions of the Feynman sum over histories.

To picture this, let’s alter Eddington’s balloon analogy and instead think of the expanding universe as the surface of a bubble. Our picture of the spontaneous quantum creation of the universe is then a bit like the formation of bubbles of steam in boiling water. Many tiny bubbles appear, and then disappear again. These represent mini-universes that expand but collapse again while still of microscopic size. They represent possible alternative universes, but they are not of much interest since they do not last long enough to develop galaxies and stars, let alone intelligent life. A few of the little bubbles, however, will grow large enough so that they will be safe from recollapse. They will continue to expand at an ever-increasing rate and will form the bubbles of steam we are able to see. These correspond to universes that start off expanding at an ever-increasing rate-in other words, universes in a state of inflation.


As we said, the expansion caused by inflation would not be completely uniform. In the sum over histories, there is only one completely uniform and regular history, and it will have the greatest probability, but many other histories that are very slightly irregular will have probabilities that are almost as high. That is why inflation predicts that the early universe is likely to be slightly nonuniform, corresponding to the small variations in the temperature that were observed in the CMBR. The irregularities in the early universe are lucky for us. Why? Homogeneity is good if you don’t want cream separating out from your milk, but a uniform universe is a boring universe. The irregularities in the early universe are important because if some regions had a slightly higher density than others, the gravitational attraction of the extra density would slow the expansion of that region compared with its surroundings. As the force of gravity slowly draws matter together, it can eventually cause it to collapse to form galaxies and stars, which can lead to planets and, on at least one occasion, people. So look carefully at the map of the microwave sky. It is the blueprint for all the structure in the universe. We are the product of quantum fluctuations in the very early universe. If one were religious, one could say that God really does play dice.


This idea leads to a view of the universe that is profoundly different from the traditional concept, requiring us to adjust the way that we think about the history of the universe. In order to make predictions in cosmology, we need to calculate the probabilities of different states of the entire universe at the present time. In physics one normally assumes some initial state for a system and evolves it forward in time employing the relevant mathematical equations. Given the state of a system at one time, one tries to calculate the probability that the system will be in some different state at a later time. The usual assumption in cosmology is that the universe has a single definite history. One can use the laws of physics to calculate how this history develops with time. We call this the “bottom-up” approach to cosmology. But since we must take into account the quantum nature of the universe as expressed by the Feynman sum over histories, the probability amplitude that the universe is now in a particular state is arrived at by adding up the contributions from all the histories that satisfy the no-boundary condition and end in the state in question. In cosmology, in other words, one shouldn’t follow the history of the universe from the bottom up because that assumes there’s a single history, with a well-defined starting point and evolution. Instead, one should trace the histories from the top down, backward from the present time. Some histories will be more probable than others, and the sum will normally be dominated by a single history that starts with the creation of the universe and culminates in the state under consideration. But there will be different histories for different possible states of the universe at the present time. This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us.

The idea that the universe does not have a unique observer-independent history might seem to conflict with certain facts we know. There might be one history in which the moon is made of Roquefort cheese. But we have observed that the moon is not made of cheese, which is bad news for mice. Hence histories in which the moon is made of cheese do not contribute to the present state of our universe, though they might contribute to others. That might sound like science fiction, but it isn’t.

An important implication of the top-down approach is that the apparent laws of nature depend on the history of the universe. Many scientists believe there exists a single theory that explains those laws as well as nature’s physical constants, such as the mass of the electron or the dimensionality of space-time. But top-down cosmology dictates that the apparent laws of nature are different for different histories.

Consider the apparent dimension of the universe. According to M-theory, space-time has ten space dimensions and one time dimension. The idea is that seven of the space dimensions are curled up so small that we don’t notice them, leaving us with the illusion that all that exist are the three remaining large dimensions we are familiar with. One of the central open questions in M-theory is: Why, in our universe, aren’t there more large dimensions, and why are any dimensions curled up?

Many people would like to believe that there is some mechanism that causes all but three of the space dimensions to curl up spontaneously. Alternatively, maybe all dimensions started small, but for some understandable reason three space dimensions expanded and the rest did not. It seems, however, that there is no dynamical reason for the universe to appear four-dimensional. Instead, top-down cosmology predicts that the number of large space dimensions is not fixed by any principle of physics. There will be a quantum probability amplitude for every number of large space dimensions from zero to ten. The Feynman sum allows for all of these, for every possible history for the universe, but the observation that our universe has three large space dimensions selects out the subclass of histories that have the property that is being observed. In other words, the quantum probability that the universe has more or less than three large space dimensions is irrelevant because we have already determined that we are in a universe with three large space dimensions. So as long as the probability amplitude for three large space dimensions is not exactly zero, it doesn’t matter how small it is compared with the probability amplitude for other numbers of dimensions. It would be like asking for the probability amplitude that the present pope is Chinese. We know that he is German, even though the probability that he is Chinese is higher because there are more Chinese than there are Germans. Similarly, we know our universe exhibits three large space dimensions, and so even though other numbers of large space dimensions may have a greater probability amplitude, we are interested only in histories with three.

What about the curled-up dimensions? Recall that in M-theory the precise shape of the remaining curled-up dimensions, the internal space, determines both the values of physical quantities such as the charge on the electron and the nature of the interactions between elementary particles, that is, the forces of nature. Things would have worked out neatly if M-theory had allowed just one shape for the curled dimensions, or perhaps a few, all but one of which might have been ruled out by some means, leaving us with just one possibility for the apparent laws of nature. Instead, there are probability amplitudes for perhaps as many as 10500 different internal spaces, each leading to different laws and values for the physical constants.

If one builds the history of the universe from the bottom up, there is no reason the universe should end up with the internal space for the particle interactions that we actually observe, the standard model (of elementary particle interactions). But in the top-down approach we accept that universes exist with all possible internal spaces. In some universes electrons have the weight of golf balls and the force of gravity is stronger than that of magnetism. In ours, the standard model, with all its parameters, applies. One can calculate the probability amplitude for the internal space that leads to the standard model on the basis of the no-boundary condition. As with the probability of there being a universe with three large space dimensions, it doesn’t matter how small this amplitude is relative to other possibilities because we already observed that the standard model describes our universe.

The theory we describe in this chapter is testable. In the prior examples we emphasized that the relative probability amplitudes for radically different universes, such as those with a different number of large space dimensions, don’t matter. The relative probability amplitudes for neighboring (i.e., similar) universes, however, are important. The no-boundary condition implies that the probability amplitude is highest for histories in which the universe starts out completely smooth. The amplitude is reduced for universes that are more irregular. This means that the early universe would have been almost smooth, but with small irregularities. As we’ve noted, we can observe these irregularities as small variations in the microwaves coming from different directions in the sky. They have been found to agree exactly with the general demands of inflation theory; however, more precise measurements are needed to fully differentiate the top-down theory from others, and to either support or refute it. These may well be carried out by satellites in the future.

Hundreds of years ago people thought the earth was unique, and situated at the center of the universe. Today we know there are hundreds of billions of stars in our galaxy, a large percentage of them with planetary systems, and hundreds of billions of galaxies. The results described in this chapter indicate that our universe itself is also one of many, and that its apparent laws are not uniquely determined. This must be disappointing for those who hoped that an ultimate theory, a theory of everything, would predict the nature of everyday physics. We cannot predict discrete features such as the number of large space dimensions or the internal space that determines the physical quantities we observe (e.g., the mass and charge of the electron and other elementary particles). Rather, we use those numbers to select which histories contribute to the Feynman sum.

We seem to be at a critical point in the history of science, in which we must alter our conception of goals and of what makes a physical theory acceptable. It appears that the fundamental numbers, and even the form, of the apparent laws of nature are not demanded by logic or physical principle. The parameters are free to take on many values and the laws to take on any form that leads to a self-consistent mathematical theory, and they do take on different values and different forms in different universes. That may not satisfy our human desire to be special or to discover a neat package to contain all the laws of physics, but it does seem to be the way of nature.

There seems to be a vast landscape of possible universes. However, as we’ll see in the next chapter, universes in which life like us can exist are rare. We live in one in which life is possible, but if the universe were only slightly different, beings like us could not exist. What are we to make of this fine-tuning? Is it evidence that the universe, after all, was designed by a benevolent creator? Or does science offer another explanation?



Обращение к пользователям