We tend to make decisions using the information before us, ignoring irrelevant of distracting information. That habit of focus means we tend to neglect the importance, or even existence, of information that is absent. A tool known as a possibility grid can help us notice when we’re being misled by the information we aren’t considering.

At exactly fifteen minutes past eight in the morning, on August 6, 1945, Japanese time, at the moment when the atomic bomb flashed above Hiroshima, Miss Toshiko Sasaki, a clerk in the personnel department of the East Asia Tin Works, had just sat down at her place in the plant office and was turning her head to speak to the girl at the next desk. At that same moment, Dr. Masakazu Fujii was settling down cross-legged to read the Osaka Asahi on the porch of his private hospital, overhanging one of the seven deltaic rivers which divide Hiroshima; Mrs. Hatsuyo Nakamura, a tailor’s widow, stood by the window of her kitchen, watching a neighbor tearing down his house because it lay in the path of an air-raid-defense fire lane; Father Wilhelm Kleinsorge, a German priest of the Society of Jesus, reclined in his underwear on a cot on the top floor of his order’s three-story mission house, reading a Jesuit magazine, Stimmen der Zeit; Dr. Terufumi Sasaki, a young member of the surgical staff of the city’s large, modern Red Cross Hospital, walked along one of the hospital corridors with a blood specimen for a Wassermann test in his hand; and the Reverend Mr. Kiyoshi Tanimoto, pastor of the Hiroshima Methodist Church, paused at the door of a rich man’s house in Koi, the city’s western suburb, and prepared to unload a handcart full of things he had evacuated from town in fear of the massive B-29 raid which everyone expected Hiroshima to suffer. A hundred thousand people were killed by the atomic bomb, and these six were among the survivors. They still wonder why they lived when so many others died. Each of them counts many small items of chance or volition—a step taken in time, a decision to go indoors, catching one streetcar instead of the next—that spared him. And now each knows that in the act of survival he lived a dozen lives and saw more death than he ever thought he would see. At the time, none of them knew anything.

 
 
 
 
 
 
 
 
 
 
 
 
 
すごい物理学講義 (Time doesn’t exist)
by Carlo Rovelli

書評「めぐりあう書物たち」 (Book review ”Book come across”)
by 尾関章 (Akira Ozeki)
 

In this column, we often cover one book over two weeks. At first, I advocated reading one book a week, but I started to think it was ridiculous to earn that many books that way. Sometimes one book every two weeks is enough. Well, sometimes it’s okay to read one book every three weeks or one book every four weeks.

So this week, I will continue with “Amazing Physics Lectures” (written by Carlo Rovelli, translated by Kaoru Takeuchi, translated by Toshihide Kurihara, published by Kawade Bunko, 2019). The reason why I linger so long on one book is because I want to get to the bottom of the loop quantum gravity theory that the author talks about, and see how the world looks.

Roughly speaking, the story of the week before last went like this. The physical world has the character of “particles”. There is a minimum unit of size, and it cannot be divided into smaller units. The microscopic world is geometric, and the way it curves can be calculated probabilistically using equations.

Last week, we looked into the nature of “particles” in the physical world. The image is like a ball packed into a box, with links between adjacent particles. It can be said to be a network-like world image. When you go around the link from particle to particle, you can see the curvature of space.

There is another feature of the space of loop quantum gravity theory that should be kept in mind. This means that it should not be seen as “an amorphous container that contains things.” The quantum of space “exists among the quanta that are adjacent to itself.” Space should be viewed as a “fabric of relationships with neighbors.”

If you review it like this, you will notice something. I wonder if this book is getting too caught up in discussing space and neglecting time. In fact, the author seems to have been concerned about this as well. In the middle of the book, at the beginning of Chapter 7, “Time Doesn’t Exist,” he frankly admits that he had not tried to discuss time until the previous chapter. However, since modern physics views time and space together as “space-time,” he declares that “it’s time to bring time back into the blueprint.”

There is also such an honest confession. Quantum gravity researchers “worked exclusively on spatial problems” until they “gathered the courage to face time.” The understanding of time has been progressing for about 15 years at the time of writing this book. Is this something that researchers have only become interested in in recent years?

Now then, what is the time image of loop quantum gravity theory? As this column has repeatedly written, the Wheeler-de Witt equation, which is the basis of loop quantum gravity theory, does not have a time variable “t”. As you read this book, you will understand what that means.

Firstly, there is a story that Galileo Galilei noticed the isochronism of the pendulum while looking at the candlesticks in the ceiling of the cathedral in Pisa. Although it seems doubtful whether this is a true story, “tradition” says that Galileo measured the period of the flickering of the candlestick by his own pulse. As a result, he realized that the period of a pendulum does not change regardless of its amplitude. The author raises the issue here. On what basis did Galileo become convinced that the pulse beats at a constant time?

There is a flip side to this. After Galileo’s discovery, doctors began using pendulums as clocks to measure patients’ pulses. He uses the pulse to check that the oscillations of the pendulum are regular, and uses the pendulum to check that the pulse is regular – that’s what we do.

The author says. Whether observing a pendulum or measuring one’s pulse, one is not measuring “time itself.” It simply measures multiple physical quantities and compares one variable with another. However, until now physics has “assumed” the existence of a time variable “t”. Quantum gravity theory breaks this custom. If we have physical quantities A, B, and C, we can define them not as functions A(t), B(t), and C(t) of “t” but as mutual functions of variables A(B), B(C), Try to think like C(A).

From this perspective, changes in the world come from changes in the relationships between things, and the world does not “change over time.” This idea is similar to viewing space not as a “container,” but as a “fabric of relationships with one’s neighbors.” It seems that time is not a “container” either.

Now, from here on it’s difficult to understand. In this column, I have no choice but to rely on the images presented in this book to proceed with the discussion. The author explains physical phenomena using “boxes.” Let’s take the example of two billiard balls colliding and rolling in two directions, and use a box to represent the time and space in which this happens. In the diagram included in this book, the box is a rectangular parallelepiped, and one side of the box appears to be a time axis, but as you read the text, you will see that this is not simply the case. This is because “the box itself “contains” space and time.”

There is another expression on the box, which makes more sense. They say it resembles a small piece of “mollusc” and is “shaped like sushi.” As an aside, there is a reason why the author brought up the term “mollusk”. This is because Albert Einstein compared the gravitational field, which is the curvature of space-time, to a “mollusk”. What made the metaphor jump to “sushi” is probably a service aimed at Japanese readers. I’m sure he himself loves Japanese food.

The question is, what is something like “sushi”? In loop quantum gravity theory, when considering the physical process of a collision between billiard balls, one must take into account not only the balls themselves, but also “everything surrounding the balls,” such as space and time. “Sushi” includes all of these.

According to this book, what we should focus on here is the end of “sushi.” One of the two ends corresponds to the beginning of the physical process, and the other corresponds to the end. The equations of loop quantum gravity theory calculate the probabilities of all possible states at the beginning and end of a process. Returning to billiards, this allows us to know probabilistically how a colliding ball enters the “sushi” and how it leaves the “sushi”. .

So, what about the space between the ends? This is where the world picture of quantum mechanics comes in handy. One is Werner Heisenberg’s matrix mechanics. “Quantum mechanics does not tell us what happens during a process,” he says. The other is Richard Feynman’s “path summation.” View the movement of particles as a bundle of paths. Based on this idea, there exists a “cloud” between the two ends that contains all possible paths that particles can take, and includes all possible space-times.

Loop quantum information theory views space as a “net.” It is said that it appears at the end of “sushi” in time and space. Now imagine the act of “holding a net in your hand and moving it”. As a result, the points of the “nodes” that are the knots of the “net” become lines, and the lines of the connections (“links”) between “nodes” become planes. The author calls this the “history of the net” and the “progress of the net,” and likens the resulting structure to a “foam.” It seems that the “clouds” in space and time can be seen as the overlapping of “all possible bubbles.”

According to this book, physicists use these “bubbles” to calculate the probability of a particular physical process. What is needed here is to add up all the “bubbles” that share the same end and find the “sum”. The equations of loop quantum theory of gravity make this calculation possible.

The time depicted in this book can be summarized as follows. There is no time or space in the world to serve as a “container” prior to an event. Space is a “net” of relationships made up of “nodes” and “links,” and “space-time” is created when the state of the “net” changes.

So why do we feel that time is flowing uniformly? This book suggests that “space and time are approximate entities that only appear on a large scale.” The “large scale” seems to have a mechanism that makes you feel the passage of time. This is explained in detail by the author in another work, and has already been introduced in this column. There is a chapter at the end of the book that will give you some hints, but for the time being I will conclude this series with three parts. Let’s take a chance and try again.

All I can say now is to stop seeing time as absolute. Time lies in the relative change of events. When I think about it, I feel like each day has become a little longer.

 
 
 
 
 
 
 
 
 
 
 
 
 
すごい物理学講義 (Time doesn’t exist)
by Carlo Rovelli

書評「めぐりあう書物たち」 (Book review ”Book come across”)
by 尾関章 (Akira Ozeki)
 

If you continue reporting on science for a long time, you can kind of see the changes in scientists’ interests. One of the reasons is that in recent decades, more emphasis has been placed on things than things.

The reason behind this is that the elemental reductionism that colored 20th century science has reached its climax. In physics, this is the case with the rush to discover elementary particles. In the life sciences, genome decoding corresponds to this. We are approaching the limit of our ability to explore the origins of matter and life.

What emerged in its place was the science of complex systems. I’m not really interested in dividing things into smaller parts. What interests me is the relationship between things. It can also be called a network. Network theory is discussed across disciplines, from physics to biology, and from basic science to applied technology.

The trend of emphasizing networks may be related to the fact that humans themselves have become components of networks. With the spread of computers and the advancement of information technology (IT) in the latter half of the 20th century, everyone became able to connect with people around the world through the Internet. Nowadays, human society cannot exist without networks. Our thinking is connected to networks on a daily basis. Naturally, science will change as a result.

The reason why I mentioned this topic to Pillow is because I associate networks with the theory of quantum gravity in “Amazing Physics Lectures” (authored by Carlo Rovelli, supervised translation by Kaoru Takeuchi, translated by Toshihide Kurihara, published by Kawade Bunko, 2019), which I have been discussing since last week. This is because there are stories that will make you do it. Since the author considers infinitesimal space, at first glance it may seem like elemental reductionism. However, as I read further, it seems that this is not the case. Although we are assuming elements, we are looking at something network-like.

Now, let’s return to the contents of this book. Last week, this book led me to the entrance to the theory of quantum gravity, which aims to integrate quantum mechanics and general theory of relativity. It can be summarized in two points. The first point is that space is not infinitely divisible, but has a “granular” quality in extremely small areas. Another is that there is a basic equation called the Wheeler-de-Witt equation in this area, and this equation allows us to imagine space as a “cloud made up of different geometric figures overlapping each other.”

However, even if you say that, it doesn’t make sense. The fact that space is “particles” and the fact that it is “cloud-like” are not connected. I want to read this book further this week and get rid of this feeling of confusion.

Let’s start by asking whether the Wheeler-de Witt equation can be solved. According to the book, the equations were improved around the end of the 1980s, and a “strange solution” was discovered. The solution was obtained when “closed lines” (rings, loops) in space were “objected to calculation.” Another way of saying this is that a “closed line” “appears in the solution.” Apparently, loops have a special meaning. This is where the name “loop quantum gravity theory” comes from.

This doesn’t get the point across, so let’s get some help from visual materials. The book contains images of ring-like loops intertwining in all directions. If you read the text, you will see that the solution to the Wheeler-de Witt equation seems to represent the state of each loop.

The author also calls the loop the “Faraday field line of the gravitational field.” Michael Faraday (1791-1867) expressed the force of electric and magnetic fields using Faraday field lines, but this is a gravitational version of Faraday’s field lines. Since we are visualizing the state of the gravitational field, it must also be related to the curvature of space.

The points where loops touch each other are “nodes.” According to the book, these are “quantum grains of space,” or “quanta of space.” What must not be overlooked is the statement that the “volume of space” is “inside the nodes.” According to our common sense, “volume” is a continuous quantity that spreads out in space, but in quantum gravity theory it is different. “Nodes” have the character of “discrete small boxes that form a volume.” As a result, the “volume” takes on the value of Tobitobiki, and is counted as one or two.

This book also emphasizes that the “quanta of space” called “nodes” “have no place.” Since the “knots” themselves “shape the space,” they cannot locate their “place” within the space. This is very different from photons (particles of light), which are quanta of electromagnetic fields.

So, is there an alternative to the “quantum of space”? According to this book, yes. That is information about what is next to each other. Next to one “quantum of space” there is another “quantum of space”. The landscape of a space changes depending on who is next to whom.

This is the highlight of this book. “Who is next to whom?” means focusing on relationships. An image of a network comes to mind. The author’s theory of quantum gravity traces space down to the smallest particles and seems to see a web within it.

According to the author, the structure of space is made up of “nodes” that “touch each other”. At this time, a line called a “link” is assumed to connect the “nodes”. “Only through links, only in the relationships between one link and another, can individual spatial quanta be located.” The relationship between “links” also affects the “quantum of space.” I would like to note here that the author himself uses the word relationship.

By the way, from the perspective of the Wheeler-de Witt equation, a “link” can be said to be part of a loop. It can be thought of as a manifestation of the gravitational field. The gravitational field also follows quantum theory, so just as electromagnetic fields appear in the form of quanta called photons (particles of light), “links” also have quantum aspects. According to this book, this quantum is quantified by the width of the boundary surface when two nodes touch each other. Therefore, “area” also takes a value of Tobitobiki, similar to quantum theory.

The author points out that the “volume” of “nodes” and the “area” of “links” “characterize the quantum network of space.” As I read this book, I kind of realized that when we talk about what the space of the microscopic world is like, we should not imagine this space that we are currently in. There is no common sense space there. There are only “nodes”, which are particles of space, and “links” that connect them. Together with quantities such as “volume” and “area,” they form a gravitational field.

This book also includes schematic diagrams of “sections” and “links.” At first glance, they look like the vertices and edges of a polyhedron. It also resembles a diagram simulating a network such as a communication network. From this diagram, we are convinced that the latest physics, known as loop quantum gravity theory, sees networks at the root of the world.

Anyway, what exactly is a loop? This book also has some hints. The author argues that by walking the links from node to node and back, you can measure the curvature of space in one turn. This is similar to how humans measure the curvature of the Earth. For example, if you travel in a loop from the North Pole, go south, move east-west around the equator, go north, and go to the North Pole, you can detect how the Earth’s surface is curved. The loop seems to be related to spatial distortion.

Let’s summarize the story so far. In loop quantum gravity theory, the microscopic world has a granular nature. The grains of space are called “nodes.” A “node” is itself a space, so it is not in space. The location of a “section” is determined by information such as “who is next to whom.” A network of nodes and links connecting them forms the structure of the space. If you follow the “link” once, it becomes a loop, and from there you can see the curve of the space.

I see, the structure of space is like that. However, the topic of time does not come up easily. The author says that we don’t need time, but he doesn’t seem to be completely denying the flow of time. What happens to time in a microscopic world where space becomes particles? I will continue reading this book next time.

 
 
 
 
 
 
 
 
 
 
 
 
 
すごい物理学講義 (Time doesn’t exist)
by Carlo Rovelli

書評「めぐりあう書物たち」 (Book review ”Book come across”)
by 尾関章 (Akira Ozeki)
 

Recently, this column has been confronting the mystery of time. The reason is probably because I’m older. Every day is so precious. To put it more simply, I love every moment. However, you cannot capture that moment and save it somewhere. There is no cryopreservation in time.

In May of this year, I read “Time Doesn’t Exist” by theoretical physicist Carlo Rovelli (translated by Sei Tominaga, published by NHK Publishing, 2019). The emphasis was on the fact that physics can work without time. Physical phenomena can be described without the time variable “t”. If you use mathematical formulas to relate the way one quantity changes to the way another quantity changes, you can accomplish the mission of physics – it’s surprising when you think back to science class, but it was a point that made sense once you heard it. .

However, this cannot explain how we experience time every day. What makes “Time Does Not Exist” admirable as a book for the general public is that it does not ignore its drawbacks. The author, Rovelli, used thermodynamic considerations to reveal the true nature of time as we humans perceive it.

However, since I was a science reporter, I would like to take a step closer to Rovelli’s physics, which says that there is no need for time. What kind of philosophy did he draw from? How is he trying to change his worldview? There are many things I want to dig into. So this time I will be looking at another book by the same author. Coincidentally, this column, including its predecessor column, has now reached its 700th anniversary. I once had a sign saying “Bunri Yuyu” in the name of my column, so I think it’s a fitting choice for this milestone.

“Amazing Physics Lecture” (written by Carlo Rovelli, translated by Kaoru Takeuchi, translated by Toshihide Kurihara, Kawade Bunko, published in 2019). This is a paperback version of the Japanese translation published by Kawade Shobo Shinsha in 2017. The original book was published in Italy in 2014, three years earlier than the original publication of “Time Doesn’t Exist.”

The author is from Italy. He is searching for a theory that integrates quantum mechanics and general relativity, and advocates the “loop quantum gravity theory” as a trump card. This theory is tied to cosmology and is deeply concerned with what happened at the beginning of the universe. This is one of the reasons why I am trying to read this author’s book again. If time does not exist in physics, as “time does not exist” says, then what was the origin of the universe? I would like to get that hint as well.

Let’s get into the contents of this book. Chapter 1, “Grains: The Great Discovery of Ancient Greece” states, “The universe is granular and does not continue smoothly.” Its origin seems to be the atomic theory of the ancient Greek philosopher Democritus. The idea is that the work of cutting the universe into pieces cannot continue indefinitely, and this has the advantage of resolving Zeno’s paradox that the hero Achilles cannot catch up with the tortoise. As you read this book, you will find that the author also takes the position of Democritus.

This is where the word “granularity” comes from. The author says that “at the root of all things” is “the nature of particles.” Quantum theory considers that electromagnetic waves are also swarms of photons (particles of light), but quantum gravity theory seems to believe that space and time also have “granularity.”

This book cites former Soviet physicist Matvey Bronstein (1906-1938) as a pioneer in this research. He viewed space as a “continuum that can be infinitely divided” and published a paper in the 1930s that showed that quantum mechanics and general relativity were incompatible. He theoretically proved that if quantum mechanics and general relativity are both correct, space has a “granular” quality. This man was sentenced to death for criticizing the Stalinist regime in the former Soviet Union, and was executed at a young age.

This is how the proof works. If you try to place a particle in a very small region of space, that particle will follow Heisenberg’s uncertainty principle and try to escape from that region at extremely high speed. The energy of the particles becomes enormous. According to general relativity, the result is that space bends so much that its interior becomes unobservable. In modern terms, this creates a black hole. It can be said that “areas below a certain scale” are “inaccessible” and therefore nothing exists there.

Bronstein calculated that “certain scale”. This can be obtained by multiplying Planck’s constant h by Newton’s gravitational constant G, dividing it by the cube of the speed of light c, and taking the square root of the result. It will be done. h is a fundamental constant related to the discrete values of energy in quantum theory. c is a constant essential to relativity theory. A calculation formula that includes both is suitable for attempting to reconcile quantum mechanics and general relativity. The value thus obtained was the “minimum length” that exists in the world.

This length is 1 trillionth of 1 trillionth of 1 cm (10 to the minus 33rd power cm). The physics community has named this the “Planck length,” but the author says, “I would like to call it the “Bronstein length.” This is probably a tribute to the pioneers of quantum gravity theory.

John Wheeler (1911-2008), a prominent American physicist, made a major contribution to the development of quantum gravity theory. It is said that it was because of this person’s intention that a celestial body that collapses due to gravity came to be called a black hole. According to the book, Wheeler was able to visualize quantum space in a single image after carefully reading Bronstein’s paper. It was “a cloud-like thing made of different geometric figures overlapping each other.”

Speaking of “cloud”, the electron cloud of quantum mechanics comes to mind. When we consider the electrons around the atomic nucleus using Schrödinger’s equation, they do not exist at a single point unless they are observed, but instead exist in a series of overlapping states at various positions. It is a “cloud of probability.” According to the theory of quantum gravity, does this mean that space is similar? However, it is not the positions of the electrons that overlap, but the shapes of the geometric figures. I feel like I understand something, but this alone doesn’t make sense.

The author compares this to the sea level. If you look at the ocean from above, it looks like a flat, blue plate, but if you get closer, you’ll see bubbles floating here and there. When viewed macroscopically, space is “flat and smooth” and follows Euclidean geometry, but this is not the case with microscopic scenery.

For example, suppose we look into a world where the scale of a ruler is as small as Planck’s length. Space is there “chopped and bubbling.” The book explains that this “bubbling of space” is “a wave of probability made up of different geometric figures.”

What was brave about Wheeler was that he attempted to describe the “bubbling of space” using a mathematical formula. He was collaborating with a young researcher, Brice de Wit. In the 1960s, the two discovered the “Wheeler-de Witt equation.” It was estimated that the probability of observing a particular curved space could be determined from this formula. If successful, it will be a quantum gravity theory version of Schrödinger’s equation that gives the probability that a particular particle state will be observed.

So, did you solve the Wheeler-de Witt equation as expected? I’d like to go into that, but I’ve run out of lines this week. I’ll be taking up this book again next week and talking about it.

This time, I would like to add one more thing about the Wheeler-de Witt equation. In “Time Doesn’t Exist,” the author described this formula as “pointing out possible relationships between varying quantities without involving the time variable.” This book says the same thing.

According to modern cosmology, the universe began in an ultra-microscopic world. According to quantum gravity theory, the author’s position seems to be that it can be drawn without the time variable “t”. The world became what it is today due to rapid expansion (inflation) or a big explosion (big bang).

What I would like to mention here is Stephen W. Hawking’s theory. It is said that there was an imaginary amount of time at the beginning of the universe. At this time, “Time and space may come together to form a curved surface of finite size but without any boundaries or edges.” (“Hawking talks about the universe: From the Big Bang to black holes.” “Until” (written by Stephen W. Hawking, translated by Kazu Hayashi, Hayakawa Bunko NF). Is it impossible to distinguish between time and space?

Whether you accept the Wheeler-de Witt equation or support Hawking’s cosmology, it seems that when thinking about the beginning of the universe, you should put time aside and focus on space for now. The question is, what is the space like? That’s what we’ll focus on next week.

 
 
 
 
 
 
 
 
 
 
 
 
 
時間は存在しない (Time doesn’t exist)
by Carlo Rovelli

書評「めぐりあう書物たち」 (Book review ”Book come across”)
by 尾関章 (Akira Ozeki)
 

Last week, I talked about how physics doesn’t require time. The book he read was “Time Doesn’t Exist” (written by Carlo Rovelli, translated by Sei Tominaga, published by NHK Publishing in 2019). Since it was written by a theoretical physicist, it cannot be dismissed as some sort of nonsense. At least I was satisfied.

The heart was something like this. When things change, we describe the change as a function of the time variable t. “T” is like the hands of a clock. In other words, in our daily lives, we relate changes in things to changes in the clock.

However, the author argues that the person to be associated does not have to be a watch. It does not have to be a guideline for a day, month, or year like the rotation of the Earth, the revolution of the Moon, or the revolution of the Earth. If you relate one change to another change, you can create a physical equation.

I see. In that case, it may be safe to say that “time does not exist.” But there’s a trick here. It is hidden in the word “change”. When we say things change, we think of time. Getting rid of “t” does not mean getting rid of time.

Let us recall philosopher John Ellis McTaggart’s theory of time, which we discussed in this column the other day. This also referred to the “unreality of time.” However, in the process of proving this, he also taught me that there is an aspect of time that cannot be expressed with the letter “t”.

According to McTaggart, time can be divided into three series: A, B, and C. Both series A and B are important; series A focuses on the “distinction between past, present, and future,” and series B focuses on “the distinction between earlier and later.” Neither of these two points of view can fit within the “t” frame.

As for the A series, in this world a change is occurring in which future events turn into present events, and then eventually become past events. This change cannot be explained only by the time axis representing “t”. On the other hand, the B series is a bit more complicated. “Before and after” are easy to fit into the image of a time axis. However, why do we view the negative direction as “before” and the positive direction as “later”? There is something about time that cannot be measured by the number of “t”s.

What we can say from the above is that although the world exists without the time variable “t”, we still recognize that there is time in the world. This is another theme of this book, “Time Doesn’t Exist,” and is explained in detail later in the book. This week, let’s focus on that.

The keyword here is “blur”. “The existence of time is deeply connected to blurring,” the author declares, “blurring occurs because we are unaware of the microscopic details of this world.” He says that time is nothing but a manifestation of human ignorance.

When I hear this story, people like me, who studied physics in my student days, feel like I understand that he is talking about entropy. Entropy is a numerical value that appears in thermodynamics and statistical mechanics. I remember that in the lecture, it was explained as “the total amount of information that has been lost.”

Let’s take a glass of water as an example. What we are looking at is the “macroscopic state” of liquid water in a transparent container. There are countless water molecules in water, each in a variety of positions that are difficult to distinguish. This blurring is entropy. The author explains that the value of entropy is determined by the number of configurations that are indistinguishable to us, based on the theory of Austrian physicist Ludwig Boltzmann.

In physics, there is a “law of increasing entropy” (the second law of thermodynamics), which states that entropy only increases. It refers to a situation where the documents stacked neatly on a desk suddenly turn into a pile of disorganized paper. There, an “orderly arrangement” changes to a “chaotic arrangement.” This is not just about paper documents. The author sees the state of the universe as “a gradual process of disorder, like a deck of cards being shuffled out of order.”

What is interesting is that this book uses entropy to explain the difference between the past and the future. According to the author, the past “leaves its traces in the present.” Craters on the moon, fossils of ancient creatures, and memories in the brain are nothing but such “traces.” So, why are there traces of the past but no traces of the future? According to the authors, this is due to “low entropy in the past.” He says he cannot find anything else that “creates the difference between the past and the future.”

I wonder if it’s true. This seems to be related to the law of conservation of energy. Traces are created when something stops moving and kinetic energy turns into thermal energy, like when a meteorite hits the moon and creates a crater. Since the change to heat is disordered, it progresses over time. In this way, the traces can be seen after the fact. Future events will also leave traces, but they cannot be confirmed in advance at the present moment.

According to the author, the reason we feel that the past is “fixed” is because there are many traces. As a result, the brain develops an “extensive map of past events,” and is bound to that past. In contrast, in the future, there are no visible traces, so there are many options.

Now that we’ve come this far, let’s review last week’s story again. According to this book, the world is made up of a network of events. Therefore, it can be described by the relationships between many variables. In fact, this week’s story is not unrelated to this world image.

According to this book, we “belong” to “parts” of the world. What it means to be a part is that the variables that interact with us are not all variables. It is a position that believes that humans are not concerned with the world as a whole, but only with a part of it.

This affects entropy. Entropy reflects the degree of “blurring,” but the degree of blurring depends on “which variables we interact with.” “Which variables interact with” differs from part to part, so the degree of “blurring” also depends on the part to which you belong. So where are we humans? The authors explain that the images are placed in areas where “entropy when the world began” “appears to have been extremely low.”

The author understands the state of low entropy in the early universe as follows. “The universe is not arranged in a special way.” “We belong to a special physical system, and the state of the universe related to that physical system is special.” – Here, “physical system” refers to It’s about the parts.

I think this view is closely related to the anthropic principle of cosmology. The anthropic principle holds that the universe is the way it is because otherwise humans could not exist. The author’s view of time is similar to this, and seems to be saying that the reason why time flows in this way in the universe is because humans would not be able to sense time otherwise. You could say that we happen to be in a part of the universe where time flows like this.

There is one more thing I would like to add about “parts”. The author connects the meaning of “perspective” to “interacting with a small portion of the countless variables in the universe.” Since we see the universe “from within,” we cannot describe the world without a “perspective.” What cannot be ignored are words such as “now,” “here,” and “me,” which change their designation depending on the situation…This thesis reminded me of McTaggart’s theory of time.

The translator’s “Appendix” to “The Unreality of Time” (written by John Ellis McTaggart, translated by Hitoshi Nagai, commentary and commentary, Kodansha Academic Library) is associated with “the simple present” and “the simple self” It was done. Whether you’re a philosopher or a physicist, is it essential to have an inside perspective when talking about time?

After reading this book, “Time Doesn’t Exist,” I realized that the image of time in the sciences and humanities has gotten much closer in recent years. However, there is still a wall between the two that must be overcome. For example, how does “trace” relate to the “distinction between past, present, and future” in McTaggart’s theory of time? Or, how does the “change” in which the future becomes the present and eventually reaches the past relate to an increase in entropy? There are so many questions I want to ask. I want to continue to think more slowly about time.