Read the book “Eternity” online. In search of the final theory of time

White holes: black holes in reverse

If you think about it, there is something very intriguing in this whole black hole story - a pronounced asymmetry of time. In the previous discussion, we kept playfully turning in expressions that suggested the directionality of time: we said “once you go beyond the event horizon, you can’t come back” - but not “once you go beyond the event horizon, you can’t come back.” And this is not a manifestation of our linguistic carelessness - the very nature of a black hole implies an asymmetry in time. The Singularity is always in your future, not in your past, and there can be no two opinions about this.

This is not a manifestation of any fundamental physical laws. General relativity is perfectly symmetrical in time: for each space-time solution to Einstein's equation, there is another solution that is identical to the previous one, but has the reverse course of time. A black hole is one of the solutions to Einstein’s equation, therefore there are equivalent solutions “living in the other direction” - white holes.

To get the definition of a white hole, you just need to take the description of a black hole and replace all the words related to time with terms with the opposite meaning. In this case, the singularity will be in the past, from which the light cones appear. The event horizon will lie in the future relative to the singularity, and even further away will be the outside world. The horizon represents a place beyond which you can never return to the area of the white hole.

However, why do we constantly hear about black holes in the Universe, but almost no one talks about white ones? Let's start with the fact that it is impossible to “create” a white hole. Since we are in the outside world, the singularity and event horizon of the white hole are necessarily left in our minds. past. So we shouldn't worry about how to construct a white hole at all. If we ever discover such an object, it will mean that it has existed in the Universe from the very beginning.

If we approach the issue with all seriousness, then the word “create” should alert us. Why, in a world governed by the reversible laws of physics, do we think in terms of “creating” things that continue to exist in the future, but not things that can go into the past and take their rightful place there? For the same reason we believe in free will: a low-entropy condition in the past places strict limits on what could happen before, and the absence of such boundary conditions in the future leaves a virtually infinite number of possibilities. further development events.

Rice. 5.6. The space-time of a white hole is a time-reflected version of a black hole.

Consequently, the answer to the question “Why does the process of formation of a black hole seem quite clear, and if we find white holes in the Universe, then they are already in a ready-made state?” should be obvious: because the entropy of a black hole is greater than the entropy of the things from which it could be made. In fact, calculating the value of entropy is quite difficult; Hawking radiation must be taken into account (we'll talk about this in Chapter 12). Key moment for us - that the entropy of a black hole is extremely high. It is black holes that can shed light on the connection between gravity and entropy - two critical ingredients in the final explanation of the arrow of time.

Don't worry about tomorrow
for tomorrow will take care of its own things:
Enough for every day of your care.
(Matt 6:34)

Good afternoon, dear readers and moviegoers!

Quite recently, a film was released that is of particular interest not so much because storyline, acting, special effects or atmosphere, as much as due to the non-triviality of the underlying idea.

In the distant future, and most likely in an imaginary universe, humanity was able to come close to immortality. Any person is capable of living for centuries while remaining forever young. Once people reach the age of 25, they stop aging. There is only one “but” left: their biological clock, symbolically represented as a timer on the left hand (yes, very similar to the “inscription” from), from this moment begins to count down. A person is given only one year of life for nothing, the rest of the time he literally has to earn.

“Time” (In Time, 2011).

Time is the universal currency of this world. It is the single measure of everything. With your own time a person pays for housing, food, clothing, entertainment... It can be given as a gift, won, stolen.

Placed in harsh conditions of survival - to survive from one day of life to the next - people do not even have time to think about the evils of the system: the unfair distribution of time. Social inequality here is elevated to the absolute: the poor are given days and hours, the rich are given millennia. The picture is completed by the division of the entire territory into temporary zones, cut off from each other by almost insurmountable barriers.

For Will Salas (Justin Timberlake), simple guy from the outskirts, the world remained like this until the day when he decided to protect a strange rich man who dreams of only one thing - death.

The director, producer and screenwriter of the film is Andrew Niccol. It was he who wrote the script for the films “The Truman Show” (The Truman Show, 1998), “The Terminal” (2004), and also acted as both a screenwriter and director of such films as “Gattaca” (1997), “Simone "(S1m0ne, 2002), "Baron of Arms" (Lord of War, 2005).

The list is very interesting. Special attention, in my opinion, deserves "Gattaca". In it, as in “Time,” the world of the genetic future is outlined, in which perfection prevails: people have learned to program their offspring even before birth, rejecting “low-quality material” and adding to their taste any properties necessary for success - beauty, health, intelligence ...

But if “Gattaca” was about an attempt to deceive a blind system that destroys destinies and dreams, then “Time” is more straightforward - it’s just about exploding the system from the inside.

In general, the simplicity and schematic nature of “Time” is perhaps the main advantage of this film. The characters' characters are only outlined, the conflict is obvious, and the actions are predictable.

“Time” is made up of simple diagram cubes, and it is in the gap between them that you can find space for your own thoughts. This is, perhaps, what characterizes popular cinema: the ability to play with this construction set in your own way.

From this point of view, "Time" is a very good modern parable oh, served with the sauce of chases, shooting, noble robbery and the fight for justice.

Will Salas, an everyman turned hero, literally holds the key to change in his hands. His is to become the liberator of humanity.

The deliberate naivety and pathos of his mission gives us a chance to ask ourselves burning questions about the meaning of life and the meaning of death.

Despite the sketchiness of the picture, it turned out to be surprisingly fresh: they had never talked about time, eternity and immortality like that before, we had never been asked such questions.

After all, if you look closely, we already pay for everything in our lives with our time, it’s just that the calculation scheme is more complicated. It includes such an element as money. If you have worked at your job, you will receive a salary.

However, how often do we analyze our lives, how often do we try to understand its meaning? What would you do if you had all eternity? But just one day?

The key scene of the film, and this is worth noting, plays out long before the ending, in the dialogue between Will and Henry Hamilton, a rich man tired of the meaninglessness of an endless life.

“Don’t waste my time,” with these words he says goodbye to Will, giving him his remaining years.

“Live in the present moment, as if you were to die tomorrow,” is the meaning put into the film by its creator Andrew Niccol.

Our right is to endow these lines with gospel meaning.

Sean Carroll

Eternity. Looking for final theory time

Jenny all time

Does anyone actually know what time it is?

Chicago, Does Anyone Really Know What Time It Is?

This book is about the nature of time, the origins of the Universe, and the fundamental structure of physical reality. We do not think here in some small, insignificant categories. We are looking at age-old, fundamental problems. Where did time and space come from? Is everything really limited to the Universe that we see, or are there other “Universes” beyond what we can see? How is the future different from the past?

According to the authors of the Oxford Dictionary, time– the most commonly used noun in English language. Throughout our lives, we move through time, obsessively follow it and try to surpass it every day - and yet, surprisingly, there are few people who can in simple words explain, what is time?

We live in the Internet era, so it would be logical to turn to the free encyclopedia Wikipedia for help. At the time of this writing, the article Time begins with the following words:

Time is a component of a measurement system used to determine the order of events, to compare the duration of events and the intervals between them, and to quantitatively describe the movement of objects. Time is a major topic of religious, philosophical, and scientific inquiry, but even the greatest scientists fail to define time in a consistent manner that applies to all areas of study.

Let's go. By the end of the book we will be able to formulate very precise definition time, which will be applicable to all areas. Unfortunately, it is much less obvious Why time has the properties that it does - although we will still explore a few intriguing ideas.

Cosmology, the study of the entire Universe, has advanced greatly over the past hundred years. Fourteen billion years ago, our Universe (or at least the part of it that we can observe) was in an incredibly hot, dense state that we call the Big Bang. Since then, the Universe has been expanding and cooling, and it looks like it will continue to do so for the foreseeable future, and perhaps for eternity.

A hundred years ago, none of this was known to us - scientists had virtually no idea about the structure of the Universe outside the galaxy Milky Way. Today, when we have been able to take measurements of the observable Universe, we are able to describe in detail not only its size and shape, but also its components and the approximate course of history. However, we cannot yet answer many important questions, in particular those related to the first moments of the Big Bang. As we learn, these questions play critically important role in our understanding of time - not only in the vast expanses of space, but also in our laboratories on Earth and even in our Everyday life.

Time after the Big Bang

It is obvious that the Universe evolves over time: the early Universe was hot and dense, the modern Universe is cold and rarefied. But I'm going to outline much deeper connections. The most mysterious characteristic of time is its directionality: the past is different from the future. This arrow of time. Unlike directions in space, which are equal to each other, the Universe undoubtedly has a preferred orientation in time. The main theme of this book is that the arrow of time exists because the universe evolves in a certain way.

The reason time has a direction is because the universe is full of irreversible processes—events that happen in one direction of time but never in another. You can turn an egg into an omelet, like in classic example, but it is impossible to make a whole egg out of an omelet. Milk is mixed with coffee; fuel burns and turns into exhaust gases; people are born, grow up and die. In Nature we find everywhere sequences of events in which one type of event always precedes another, and another always follows. Together they define the arrow of time.

It is noteworthy that at the heart of our entire understanding of irreversible processes lies a single concept - what is called entropy and measures the “disorder” of an object or collection of objects. Over time, entropy stubbornly increases or at least remains constant - this is the famous second law of thermodynamics. And the reason why entropy tends to increase is deceptively simple: there are many more ways to create disorder than to create order; therefore (other things being equal), ordered configurations will naturally flow into increasingly disordered ones. It is not at all difficult to mix the molecules of an egg in order to get an omelette, but we cannot carefully assemble them back to form a whole egg.

On this traditional history, which physicists usually tell about themselves, ends. But there is another ingredient of incredible importance that has not yet received the attention it deserves: if everything in the universe is evolving towards increasing disorder, then it must have started out with an incredibly ordered configuration. All this logical chain, which explains why it is impossible to turn an omelet into an egg, is obviously based on a fundamental assumption about the early Universe: it was in a state of very low entropy and very high order.

The Arrow of Time connects the early Universe to what we literally experience at every moment of our lives. It's not just about breaking eggs and other irreversible processes like adding milk to coffee or cluttering a room that no one cleans. The arrow of time is the reason why time seems to pass us by, or (if you prefer) why we float through time. This is the reason why we remember the past but not the future. Why we grow and change, why we metabolize and why we eventually die. Why we believe in cause and effect. This is a fundamental component of our idea of free will.

And all this thanks to the Big Bang.

We don't see everything

The mystery of the arrow of time essentially boils down to this: why conditions in the early Universe were the way they were; Why was there a low entropy configuration that allowed all these interesting and irreversible processes to occur? Dedicated to research on this issue this book. Unfortunately, no one yet knows the correct answer to this. But in development modern science we have reached the stage where we already have necessary tools in order to take this mystery seriously.

Both scientists and ancient thinkers have always tried to understand time. IN Ancient Greece philosophers of pre-Socratic times, Heraclitus and Parmenides, occupied different positions on the question of the nature of time: Heraclitus emphasized the primacy of change, while Parmenides denied the reality of change in general. The nineteenth century was the heroic era of statistical mechanics: people learned to infer the behavior of macroscopic objects from their microscopic constituents—when figures such as Ludwig Boltzmann, James Clerk Maxwell, and Josiah Willard Gibbs were able to define entropy and describe its role in irreversible processes. However, they knew nothing about Einstein's general theory of relativity or quantum mechanics, and certainly not about modern cosmology. For the first time in the history of science, we at least have a chance of putting together a sound theory of time and the evolution of the universe.

I'm going to propose the following version: Big Bang was not the beginning of the Universe. Cosmologists sometimes say that the Big Bang represents the true boundary of space and time, before which nothing existed - in fact, even time itself did not exist, so the concept of "before", strictly speaking, cannot be applied in this case. However, we know too little about the ultimate laws of physics to make such statements with confidence. Scientists are increasingly beginning to appeal to the possibility that the Big Bang was not really the beginning of everything - it was just a phase through which the Universe, or at least our part of the Universe, passed. If this is true, then the question about our low-entropy beginning takes on a different form: not “Why did the Universe begin in such a low-entropy state?” but “Why did our part of the Universe go through a period of such low entropy?”

Although this question may not seem simpler, it is a different question, and it opens up a new range of possible answers. It is possible that the Universe we see is just part of a much larger Multiverse, which does not originate in a low-entropy configuration. I will argue that the most reasonable model of the Multiverse is one where entropy increases simply because entropy is capable of increasing Always: There is no state of maximum entropy. As additional bonus The multiverse can be absolutely symmetrical in time: starting from some point in the middle, when entropy is high, it evolves towards the past and future into states in which entropy is even higher. The Universe we see is just a tiny outgrowth of an incredibly massive ensemble, and our particular journey from the dense Big Bang to the eternal void is part of a larger desire of the entire Multiverse to increase its own entropy.

In any case, this is just one possibility. Consider this an example of one of the scenarios that cosmologists should consider if they decide to seriously tackle the problems posed by the arrow of time. And whether or not this particular idea takes us in the right direction, the problems themselves are already incredibly exciting and real. Throughout this book we will study the problems of time from the very beginning. different points view: time travel, information, quantum mechanics, the nature of eternity. When you are not yet sure what the final answer should sound like, you should try to ask the question in every way possible.

There will always be skeptics

Not everyone agrees that cosmology should play a significant role in our understanding of the arrow of time. I once had the opportunity to conduct a seminar on this topic in large audience at the physics department of one large educational institution. One of the older professors of this department did not consider my speech convincing enough and made efforts to ensure that everyone present knew about his displeasure. The next day, he sent an email to other faculty members and was kind enough to include me in the mailing list:

Finally, the entropy of the Universe as a function of time is interesting problem for cosmology, but to assume that the laws of physics depend on it is complete nonsense. Carroll's claim that the second law of thermodynamics owes its existence to cosmology is one of the stupidest claims I have ever heard in a physics seminar, with the exception of [name redacted]'s claim about consciousness in quantum mechanics. I am surprised that the physicists present were willing to listen to such nonsense. I later had dinner with several graduate students who readily supported my objections, but Carroll remained unmoved.

I hope he reads this book. There are a lot of big claims here, but I will be careful to classify them into three types: 1) remarkable results of modern physics, which sound surprising but are nevertheless generally accepted facts; 2) large-scale statements with which not all working physicists agree, but which nevertheless must be accepted, since their truth does not raise any questions; 3) speculative ideas outside the comfort zone current situation affairs in science. We will certainly not shy away from abstract and speculative reasoning, but it will always be clearly identified as such. Ultimately you will be armed with everything necessary knowledge in order to independently decide which parts of the story make sense and which do not.

Time theme includes great amount ideas - from everyday to shocking. We will look into thermodynamics, quantum mechanics, special and general theory relativity, information theory, cosmology, particle physics and quantum gravity. The first part of the book can be considered as sightseeing tour, which talks about entropy and the arrow of time, the evolution of the Universe and various concepts of the very idea of \u200b\u200b"time". After this, we will try to approach the issue in a more systematic way: in the second part we will think deeply about space-time and relativity, including the possibility of traveling back in time. In Part 3, we'll take a serious look at the concept of entropy, exploring its role in a variety of contexts, from the evolution of life to the mysteries of quantum mechanics.

In Part 4, we'll bring it all together to face up to the puzzles that entropy poses for modern cosmologists: what should the Universe look like, and how similar is it to what the Universe actually looks like? I will demonstrate that the Universe does not look at all like it “should” (by explaining, of course, what I mean by using this word) - at least that is the case for the Universe that we see around us. If our Universe began in the Big Bang, then its existence is burdened by a finely tuned boundary condition for which we cannot find a worthy explanation. However, if the observable Universe is part of a larger ensemble - the Multiverse, then perhaps we have a chance to explain why, in a tiny part of this ensemble, the entropy at one end of time is so strikingly different from the entropy at the other.

All this, of course, is unforgivable theorizing, but these fabrications should be taken seriously. The stakes are high—time, space, the Universe—so the mistakes we are bound to make along the way will no doubt also be large. Sometimes it's good to let our imaginations run free, even if our ultimate goal is to return to Earth and explain what's going on in the kitchen.

Part I. Time, experience and the Universe

Chapter 1. The past is the memories of the present

What is time? If no one asks me about it, I know; if I wanted to explain to the one who asks, no, I don’t know.

St. Augustine. Confession

The next time you need to pass a couple of hours in a bar, on a plane, or in line for a certificate at the local traffic police station, spend your time usefully: try asking strangers what they think it is. time. By the way, this was part of my research while preparing to write the book you are holding in your hands. I think you will hear many interesting answers: “Time is what moves us forward in life,” “Time separates the past from the future,” “Time is part of the Universe,” and other variations on the same theme. I liked this definition most of all: “Time is what makes us know that something is happening.”

All these concepts are only partly true. And although it is not so easy to put the concept of time into words, in everyday life we, like St. Augustine, cope with it quite successfully. Most people know how to tell time using a watch, can estimate how long it will take to get from home to work or make a cup of coffee, and are able to show up for dinner with friends at the appointed hour. Even if we cannot clearly define what “time” is, we intuitively understand what it is and how it works.

Like the Supreme Court justice confronted with a blatant display of shamelessness, we are well aware of what is happening before us, and in most cases that is enough. However, certain aspects of time still remain mysterious and incomprehensible. So, do we really know what this word means?

What do we mean by time

The world never gives us abstract concepts on a silver platter so that we can calmly understand them and reconcile them with other concepts. Everything is much more complicated. In our lives we encounter phenomena, observe and describe them. Then, based on the data obtained, we formulate concepts that help us understand how the observed phenomena relate to the rest of our existence. As for elusive concepts such as entropy, everything is more or less clear. These are not some gizmos that you can suddenly stumble upon while walking down the street. We are seeing a variety of natural phenomena and we highlight a certain pattern, a pattern, which is most convenient to think about in terms of a new concept, for example, called entropy. Armed with this useful new concept and noticing various other phenomena, we refine and improve the original definition of entropy.

If we are talking about such a primitive, but at the same time fundamental idea as time, then the fact that the concept of time was also invented, and not received ready-made from the generous Universe, is much less obvious - after all, we literally have no idea life without time. However, one of most important tasks science (and philosophy) is to turn intuitive understandings of basic concepts like time into rigorous scientific concepts. Along the way, it also turns out that we do not unambiguously understand and use the term “time”. He has several different meanings, each of which deserves detailed coverage.

There are three aspects of time, and they are all equally important to us.

1. Time marks moments in the Universe.

Time is a coordinate, it helps us find objects.

2. Time measures the length of periods between events.

Time is what we measure with a watch.

3. Time is the medium through which we move.

Time is the harbinger of change. We move through it or - which is the same thing - time flows through us: from the past through the present to the future.

At first glance it all sounds very similar. Time marks moments, measures duration, and moves from the past to the future - these ideas do not seem to contradict each other. But if you dig deeper, it turns out that they do not necessarily have to be interdependent - rather, they are logically independent concepts that, by some accident, real world closely intertwined. Why is this happening? The answer to this question is extremely important - much more important than was commonly thought in the scientific community.

1. Time marks moments in the Universe

John Archibald Wheeler, the influential American physicist who coined the term “black hole,” was once asked what time is. After thinking a little, he answered: “Time is what prevents everything in nature from happening at the same time.”

In this statement lies important truth, and it is full of deep wisdom. When we think about the world within the framework of familiar everyday concepts - not from the point of view of scientists or philosophers, but as ordinary people living their own lives - we usually identify the “world” as a set of things located in different places. Physicists bring all these different places together into single concept called "space". Depending on the context they use different ways descriptions of what is in space - atoms, elementary particles or quantum fields. However basic idea remains unchanged. You are in a room in which there is furniture, some books, some food, perhaps even other people, and certainly some air molecules. All such things - from those closest to you to those in intergalactic space - form a “world”.

And the world is changing. We see objects in certain combinations with each other, but we also see them in other combinations (it is very difficult to form intelligent sentences describing this idea without reference to the concept of time). But we do not see these different combinations “simultaneously” or “simultaneously”. We see one configuration: here you are sitting on the sofa, and there is a cat on your lap, and then another: the cat jumped onto the floor, offended that you are immersed in a book and are not paying enough attention to its royal person. Thus, the world appears to us in different configurations again and again, and all these configurations are somehow different from each other. Fortunately, we can mark many similar configurations in order not to get confused in all sorts of states of the surrounding world: Murka is leaving “now,” but she was sitting on your lap “before that.” Such marks constitute what we call time.

So the world exists, and moreover, the world is happening again and again. In this sense, the world is analogous to many frames on a film, only the film on this film was shot with a camera capable of capturing the entire Universe in its lens (and also, as far as we know, includes an infinite number of frames, separated by infinitesimal intervals). Of course, film is not just a bunch of individual frames. They must be put in the right order, otherwise the film simply won't make sense. This is the role of time. About some events we can not just say that “this happened,” and “this also happened,” and “that incident also took place.” We can say that the first event happened before the second, and the third - after him. Time is not simply a mark on each of the possible instances of the world; it ensures order by placing each of the instances in its place in the correct sequence.

Of course, the whole Universe is never present in the frame of a real film. Any film is edited: one scene or shooting angle is suddenly replaced by another. Try to imagine a film in which such a transition occurs after each frame, that is, each subsequent frame contains completely new scene. It would be impossible to watch: what is happening on the screen would seem to us a random jumble of images. There seems to be some kind of avant-garde french film, filmed using just such a technique.

The Real Universe is nothing like an avant-garde film. We feel a certain continuity in the movement of time: if a cat is sitting on your lap right now, there is a possibility that it can jump off and leave, but you are unlikely to think about the danger that your beloved Murka will simply dematerialize in a moment. At the microscopic level, continuity is not absolute: particles can appear and disappear, or at least certain conditions transform into particles of a different type. However, reality does not undergo massive changes every moment.

This phenomenon of continuity forces us to look at the “world” from new point vision. Instead of many things scattered here and there in space, constantly changing configuration, we immediately begin to think about the whole stories the world or any of its components. Murka is now for us not a collection of ordered cells and liquids, but a being who has lived his whole life - from the moment of birth to death. The history of an object (cat, planet, electron) over time determines its world line - the trajectory that the object traces in space over time. An object's worldline is just the complete set of positions it has ever occupied in the world, marked by specific points in time.

Rice. 1.1. A world ordered by moments in time. Objects (including people and cats) remain in space from moment to moment, defining world lines that stretch through time

Searching for ourselves

Learning to think about the entire history of the universe at once, as opposed to thinking of the universe as a collection of objects constantly moving back and forth, is the first step to perceiving time as just another space (we will talk about this in detail in future chapters). To keep track of things in the Universe, we use both time and space coordinates. Let's say you want to meet a friend for coffee, or catch a certain movie screening, or arrive at work at the same time as a colleague. To do this, you indicate the time: “Let's meet at the coffee shop at six o'clock in the evening this Thursday.”

However, if you need to meet someone, then, of course, just communicating the time of the meeting is not enough; you must also agree on the location (which coffee shop? we're talking about higher?). Physicists claim that space is “three-dimensional.” This means we need three numbers to uniquely identify any location. If we mean some point located close to the Earth, then the physicist will indicate the values of latitude, longitude and height above the Earth's surface. If we are talking about some distant - in the astronomical sense - location, then it can be denoted by the direction in the sky (these are two numbers similar to latitude and longitude) and distance from the Earth. It does not matter at all in what way these three quantities are indicated; the most important thing is that there are always exactly three of them. These quantities are called coordinates position in space. Just imagine that each point has a small label attached to it, telling you the exact location of that point in space.

Rice. 1.2. Coordinates of any point in space

In everyday life, we have many opportunities to make our lives easier and avoid listing all three spatial coordinates. If you ask a friend to meet “at the coffee shop on the corner of Eighth and Main Streets,” then explicitly tell him two coordinates: “Eighth Street” and “Main Street.” It is unlikely that anyone would assume that the coffee shop is in the air or underground - it is obvious that the building is on the ground. We owe this convenience of marking locations to the fact that in everyday life we most often have to deal with two-dimensional space, that is, with objects located close to the surface of the Earth. However, in order to absolutely accurately indicate the location of a point in space, you still need to provide the values of all three coordinates.

Each point in space occurs once at each moment in time. What can be described by a specific location in space at a specific point in time is called by physicists event(one should not think that this is only said about some exceptionally outstanding events; any random point in empty space at any particular moment in time is called an event if it is designated in a unique way). What we call the “Universe” is just a set of events: every point in space at every moment in time. It turns out that in order to select a unique event, we need four numbers: three spatial coordinates and one time. That is why it is customary to say that the Universe is four-dimensional. This concept is extremely convenient, and we will often use the term "space - time", implying the entire set described above, that is, all possible points in space at any possible time.