Current page: 7 (book has 24 pages total) [available reading passage: 16 pages]
Why can’t each of these stars have the same magnificent retinue as our Sun - a retinue of planets served by moons?
And nothing bad happened to him - at least the church didn’t do anything to him.
Copernicus was one of the first to realize the great truth: our place in the universe is unremarkable. This lesson must be learned by humanity time after time. Our mediocrity extends far beyond the solar system. Galileo noted that there are countless stars in the universe, and all have an equal right to claim the title of the center of the universe.
A system of globular clusters in projection onto the galactic plane. Galactic longitude is marked every thirty degrees. The “Local System” lies entirely within the smallest circle, enclosed by a solid line, having a radius of a thousand parsecs. The larger circles outlined by a solid line are also heliocentric, but their radii increase at intervals of 10,000 parsecs. The dotted line marks the supposed major axis of the system, the dotted circles are concentric with respect to its center. The dots are about four times larger than the actual diameters of the clusters at this scale. Nine clusters are more than 15,000 parsecs from the galactic plane and are not included in this diagram.
In 1918, astronomer Harlow Shapley mapped 69 globular clusters in the Milky Way. These are very close groups of one hundred thousand stars, or even more, and it was reasonable to assume that globular clusters are distributed symmetrically relative to the center of the galaxy. Shapley discovered that our place cannot be considered privileged even within our own galaxy. We are just one of about 10 billion star systems in the outback.
Douglas Adams writes about the same thing:
Somewhere in the back streets of one unfashionable area of the western spiral branch of the Galaxy, which is not even on the map, there is a small, inconspicuous yellow sun. About ninety-two away 44
Adams is not an astronomer or, for that matter, an Englishman, so we will forgive him for the mistake in translating metric measures. In reality, this value is closer to 93 million miles.A completely nondescript green-blue planet revolves around it for millions of miles, whose inhabitants, descended from apes, are so primitive that they still consider electronic watches something outstanding.
(Translated by Yu. Arinovich)
But this is far from over. In the 1920s, Edwin Hubble showed that our galaxy is just one of a colossal number of island universes floating through space. As we have already seen, the SDSS survey has mapped over one hundred million galaxies, but conservative estimates put the total number in the observable universe at several trillion. On average, these trillions of galaxies appear to be distributed in space with remarkable uniformity. In the language of symmetry, this means that the universe homogeneous. Likewise, the northern hemisphere of the universe appears to be more or less the same as the southern hemisphere. Again, scientifically speaking, the universe appears to be isotropic.
These observations formed the basis of the so-called cosmological principle. In essence, it says that the universe is more or less the same everywhere and in all directions. Observations confirm this, but in fact the cosmological principle is an axiom. Much like the assumption that the immutability of physical laws allows us to interpret the past and predict the future, the cosmological principle allows us to reasonably interpret data obtained from other parts of the universe.
We owe the first glimpses of understanding what the universe outside our galaxy is like to Edwin Hubble. As we have already seen, it not only showed us the scale of the universe, but also revealed that almost all the galaxies in the universe seem to be moving away from us.
The idea that the universe is expanding has probably given you the erroneous idea that the universe has a center. No, the universe has no center. To understand why, we need to talk a little about relativity. We have already made sure that special The theory of relativity assumes a close relationship between time and space. And genius general The theory of relativity is that, according to it, gravity is capable of bending both space and time, as well as both at the same time.
The expanding universe is like a sheet of rubber
If you don’t have an intuitive sense of what space curvature is, don’t worry. It is very easy to get confused in equations and formulas. Fortunately, however, the International Guild of Cosmology Promoters has come up with an excellent analogy, and if you give me your word not to take it too literally, I will follow the example of my colleagues.
Glue a handful of small plastic galaxies onto a huge sheet of rubber.
Find a group of strong men and together with them grab the sheet from all sides.
Pull properly.
An ant living in one of the galaxies will consider himself the navel of the universe, since all other galaxies from his point of view will be moving away. Moreover, the greater the distance between two galaxies, the faster - from the ant's point of view - they will move away from each other: this is precisely the effect that Hubble observed.
I can throw you into any galaxy, and if you have enough egocentrism, you will consider yourself the center of the universe. However - and this is the most important thing - any observer in any galaxy will see the same thing.
Turn the clock of the universe back, and the distances between all galaxies will shrink to zero. Where did the Big Bang happen? And everywhere!
However, taking this analogy too literally is dangerous. A particularly stubborn ant, just like that, will build a lovely starship and go, for example, to look for the edge of a rubber sheet. But in our (non-rubber) universe, it is basically impossible to reach the edge, there is nothing to even dream about. The universe has no center and no edges either. So we are left with only two options.
The first one, to be honest, is chilling. It may turn out that the universe really is infinite. That is, not just very, very large, but truly infinite. Think about it - endless!
Toroidal universe
We'll get back to the practical differences between a giant universe and an infinite universe, but personally I'm much more comforted by option number two: perhaps the universe is closed in on itself. It's like Pac-Man disappearing on one side of the screen and then appearing on the opposite side. From Pac-Man's point of view, he goes on and on and cannot reach the end.
Don't worry - the Earth behaves exactly the same. If you ignore the demarcation lines arbitrarily set by our fellow humans, like the International Date Line, you can walk endlessly eastward and never reach the edge or the center. You will constantly go through the same places - that’s all.
From a practical point of view, there is not much difference between an infinite and a repeating universe. The expansion of the universe and the limited speed of light conspired to prevent us from even flying around the universe and returning to our starting point. But this does not prevent us from asking the following question: how big is the universe?
Space is big. Very.
But we can’t say exactly what size it is, to be honest. We are not able to look at the entire universe, since it has existed for only 14 billion years, and the speed of light is what it is. On Earth we call the line beyond which we cannot see the horizon, and this also applies to the universe as a whole.
In principle, we can fit trillions of galaxies into this horizon, but nowhere does it say that this will all end. There is a very real possibility that the universe beyond the horizon, where we cannot see it, is completely different from what is nearby. Not only are we unable to see what is happening hundreds of billions of light years away, because everything in general moves either at the speed of light or slower: everything that is beyond the horizon is in no way affected by what is happening here on Earth.
But this is not enough: as the universe expands at an accelerating rate, it turns out that over time, more and more galaxies will disappear from our field of view. The galaxies within our horizon are only 60 billion light years away from us. And everything that happens next will forever remain a mystery.
Everything that is outside our horizon is, from any practical point of view, a different, independent universe, and therefore, whether we like it or not, we live in multiverse- in a certain sense. If you are a science fiction buff 45
Of course, an expert, how could it be otherwise?
You are at least superficially familiar with the idea of a multiple universe, but everyone understands the phrase “multiple universe” in their own way. Luckily for us, MIT physicist Max Tegmark has developed a detailed hierarchical classification of multiple universes. Hand on heart, everything in this classification, except for the first level, which we already have no doubt about, is extremely speculative - and the further it goes, the more speculative it becomes. So let's agree that for now we're just laying everything out on the shelves.
From a practical point of view, it is quite possible to consider any part of the universe 100 billion light years in size as an island. However, if the islands are not connected to each other, a reasonable question arises as to why this happened and why each individual section must be similar to all the others.
Imagine, this question is quite possible to get an answer. However, first we state a fact confirmed by observations: we are surrounded by radiation left over from the beginning of the universe, and this radiation is uniform with an accuracy of approximately one hundred thousandth. This fact becomes even stranger when we remember that the light that hits us “from above” and “from below” - from the north and south poles - comes from incredibly distant points in the universe. Two photons from these streams have most likely never been in regions that have ever been in thermal contact with each other.
This is one of the deepest and most painful questions in cosmology. Initially, the universe was very small, but this did not last long. It appears that areas of the sky that are more than a degree apart have had no opportunity to mix with each other—and yet the universe as a whole appears surprisingly homogeneous. Let me remind you that this is one of the assumptions of the cosmological principle.
In the 1980s, Alan Guth, then at the SLAC National Accelerator Laboratory, proposed the inflation hypothesis to circumvent the horizon problem. And although it is difficult to grasp, I warn you in advance that at the moment the inflationary model has become dogma for most cosmologists. It allows us to explain a huge number of phenomena in the universe as we observe it.
In the first moments of the existence of the multiverse, there was a lot of activity here, especially in the first 10–35 seconds. During this brief moment, the universe underwent a colossal exponential expansion, and individual sections of space - individual bubbles - grew 10 60 times or more.
If the inflation hypothesis is true, and I repeat, we are practically convinced that it is, then there is still a lot of space beyond visible space. Each bubble is a universe in itself, and it is easy to imagine that if there were enough of them, many of them could be similar to ours, probably even exactly like ours. According to most models of inflation, bubbles beget other bubbles, and so on ad infinitum, resulting in the infinite universe that scared us so much at first.
What size must the first-level multiple universe reach in order for every person on Earth to have an exact double? Simply monstrous. According to Tegmark's estimates, from here to the identical universe is approximately 10 to the power of 10 29 meters - on the pages of this book there will be no numbers larger than this, except for infinity itself. This means that every atom in the duplicate universe is in exactly the same place and moves at the same speed, up to quantum uncertainty, as in our own universe. This means that even if your double's biography is different from yours, the double's brain is designed so that he thinks that he has exactly such a biography.
Do you see? We're back to the topic of scoundrel twins!
If the universe is infinite, there will be room in it not just for your double, but for countless numbers of your doubles!
It's humiliating and a little scary. It’s as if you have an endless number of spies sneaking a peek at you.
If the universe is not infinite, you can calmly rest on the laurels of your own uniqueness. According to conservative theoretical estimates, the minimum size of our multiple universe is about 10 80 meters, which seems like a lot until you remember that this is only a tiny fraction of the space required for the appearance of doubles.
Our part of the universe grew out of a tiny piece of the just emerging multiple universe, however, as we already understood, our bubble is not the only one. Moreover, it is possible that in some of these bubbles, and perhaps in all, the laws of physics are somewhat different from ours. Either the electricity in them is a little stronger or weaker, or the strong interaction (which holds neutrons and protons together) is not quite the same as ours, or there are more than three dimensions.
Let me clarify some circumstances of the existence of second-level multiple universes.
1. It is not obvious that this model is correct. It is possible that fundamental forces are actually the very basis of all existence and that all universes are built on the same physical laws.
2. If there really are second-level multiple universes, they are not necessarily like ours. Perhaps many of them have no stars or galaxies, some are almost completely empty, some have collapsed under the influence of their own gravity. To create, for example, stars or heavy elements, physics must be very, very finely tuned, and so are we, and most universes simply do not pass the selection.
3. The universe still has no edge. Universes are not fenced off from each other by a brick wall. All universes within a second-level multiple universe are potential first-level multiple universes.
However, the story does not end at the second level. Tegmark suggests the existence of both third and fourth level multiple universes, which are even more speculative and have nothing to do with the question of symmetries and whether the laws of physics are the same everywhere. But we’ll talk about them anyway, it’s very interesting.
I've already talked a little about how quantum mechanics works, and most physicists simply take it for granted that there must be some randomness in the world (maybe the lion's share) and the possibility of strange, ingenious connections between widely separated events.
However, not everyone is so sure about this. In 1957, Hugo Everett, working as a scientific consultant at the Pentagon, came up with the "many-worlds interpretation" of quantum mechanics. It's not as if Everett created an entirely new set of physical laws. Essentially what he wanted to say was, “You know all those experiments that show quantum behavior? So, you can look at them from a different point of view.”
According to the many-worlds interpretation, every time a quantum event can be measured, a new set of universes is created. In one universe, the electron's spin can be estimated to be upward. In the other - as if directed downwards. Interestingly, according to the many-worlds interpretation, these universes can interact with each other, causing strange behavior - quantum interference.
As I said, mathematically, the many-worlds interpretation expects the same things from quantum experiments as the standard - Copenhagen - interpretation, which most physicists, including myself, adhere to. But it also provides us with a whole new perspective on the multiverse—and, frankly, a perspective that offers fantastic promise if writing science fiction is your life's work. Still, I have to warn you: if you subscribe to the many-worlds interpretation, be very clear that neither Everett nor anyone else has proposed a physical mechanism for travel between universes. Fantasize to your heart's content, but you won't get anywhere from here.
On the fourth level, things get even weirder. Levels one through three assume that the laws of physics at least vaguely resemble those in our universe. In a fourth-level multiple universe, Tegmark believes, “All structures that exist mathematically also exist physically,” although it is not entirely clear how many universes there are that can be described mathematically.
For all we know, it is possible that there is some universe where only one or none of our fundamental interactions are present. Since we still don't fully understand physics in our part of the multiple universe, even if there is a fourth-level multiple universe, we cannot say what its constituent universes are, even with a modicum of certainty.
The problem we've been facing throughout this chapter is partly that we don't know whether the parameters that describe our universe are really necessary, whether a consistent universe can exist without them, or whether they are completely arbitrary. The fourth level multiple universe according to Tegmark’s classification may well assume the existence of both an infinite number of universes and just one.
If you're already dizzy with the diversity of multiple universes, thinking about possible sets of parameters isn't going to help you much.
However, in fact, we will be talking about multiple universes of the first and second levels. After all, in case you forgot, the main purpose of our conversation is to understand the question of whether the laws of physics are the same throughout the universe.
I've already warned you, but a little extra caution is in order: while symmetries allow us to better understand the mysteries of nature and the form of the laws of physics, they do not tell us anything about the specific meaning of the constants included in these laws. We are not going to “infer” the mass of the electron (at least we haven’t been able to do that so far). Perhaps there is something fundamental in the universe that will allow us to derive all the physical constants, but for now we are groping in the dark. This means that we do not know whether physical constants were inherent in the laws from the very beginning or whether they turned out to be so relatively by chance - just as the temperature outside the window is random on a given day. Symmetry tells us how to write the equations, but it is silent about the numerical values of the variables.
There are quite a few parameters, such as the charge of an electron, that are taken more or less out of thin air. Perhaps these parameters vary from end to end of the gigantic universe, and certain areas - for example, our observable universe - are simply lucky that they are suitable for the emergence of complex life.
There is nothing mysterious about the fact that we, by pure chance, live in a region where the laws of physics are ideal for human existence. It couldn't be any other way! Otherwise, you and I wouldn’t exist and there would be no one to talk about it. That is, most physicists really do not like the anthropic argument. Most of us cherish the hope that someday we will be able to develop a Theory of Everything based solely on first principles.
And if they are not embedded in the very fabric of the universe, how much fine-tuning does the laws of physics need for us to exist? What are our chances?
Let me anticipate the typical question about the fine tuning of the universe. Why does light travel at 299,792,458 meters per second? As we have already seen, the short answer is that it makes much more sense to simply say that light travels at the speed of one light-second per second and leave aside the question of the definition of the meter as a historical curiosity.
In other words, parameter values expressed in some units are almost never relevant, since they obviously depend on what units you choose. I bring this up because there are several ways to combine physical constants so that all units cancel. Here, for example, is the so-called fine structure constant (in short - PTS), which is simply a number without any units.
What kind of letters are these? In this equation e– electron charge, With– of course, the speed of light, and ћ
– Dirac’s constant, also known as reduced Planck’s constant 46
If you casually mention her at the next cocktail party, don't miss the opportunity! – call it “ash-crossed out”. Professionals will understand immediately.
It comes out wherever quantum mechanics is involved.
The fine structure constant is approximately 1⁄137.035 999 08, and is among the most accurately calculated constants in the history of physics. And with all this precision, we have no idea where it came from. This does not happen with numbers in pure mathematics. For example, the number p can be deduced from first principles, even if you have never seen a circle in your life. Here's how Richard Feynman puts it:
We know very well what dances must be performed in experiments in order to measure this number with very high accuracy, but we do not understand what dances must be performed on the computer in order to get this number - unless we secretly enter it there!
PTS is a measure of the strength of the electromagnetic interaction and, as you may have noticed, it is much less than one. From an objective point of view, the electromagnetic force is very weak. On the other hand, compared to other interactions, electromagnetism is incredibly strong. Just think about the fact that the electrostatic repulsion between our sneakers and the floor easily overcomes the gravitational attraction of the entire Earth!
Our standard models of cosmology and particle physics contain at least 25 different dimensionless and apparently independent parameters. Suppose we take and change only the PTS. What will happen?
If the PTS were, for example, greater than 0.1 (about 14 times the measured value), then carbon—and therefore all elements heavier than carbon—could not be produced in stars. This would be a disaster for carbon-based life forms.
Or let's take another parameter - the strength of the strong nuclear interaction, the same one thanks to which the nuclei of atoms do not crumble. If the strong force constant were increased by just four percent, the protons would quickly bond with each other and form helium-2, an isotope that has no neutrons at all. The stars would quickly burn out and produce only inert helium - and nothing interesting would arise.
This seems to be the case with most fundamental constants. We live in a universe where the ratio of parameters is such that it ensures our existence. This allows us to draw only three possible conclusions - and all of them are not very tempting.
1. The universe was created specifically for people or for complex life in general.
2. The parameters of the universe naturally follow from some yet undiscovered law of physics, and we are just damn lucky that this law allows our existence.
3. Parameters in the multiverse vary, and by necessity we live in one of the regions (possibly very rare) that is capable of providing conditions for life (because otherwise we would not exist).
The first option simply has nothing to do with physics, which is why I don't like it. The second option seems to be true, but physicists have yet to discover the Theory of Everything. In the meantime, very little can be said about this, and therefore the second option leaves me with a feeling of deep dissatisfaction. What can be said about the third option?
Instead of asking what would happen if the PTS (or any other parameter) changed, one can ask the question that will be answered by observations - the question of whether it changes at all - and for this one will have to look into the abyss of space.
If we want to look at how the universe changes at cosmological distances from us, we will have to start by observing objects that are billions of light years away from us. Fortunately, nature has provided us with ideal beacons - quasars. In essence, quasars are giant black holes that absorb huge amounts of matter. As matter falls into them at near-light speed, it heats up and produces enough radiation to be visible to the far reaches of the Universe.
The space between us and quasars is filled with clouds of gas, and this gas partly absorbs the radiation on its way to us. Clouds absorb light only in a certain range of wavelengths, and these wavelengths are determined by the PTS value. If you change the PTS, this range will also change.
Since 1999, John Webb of the University of New South Wales and his collaborators have been testing whether the PTS changes with time and distance by observing photons absorbed by a variety of iron and magnesium ions in very distant clouds. By studying the relative wavelengths of absorbed photons, scientists are able to compare the PTS at cosmological distances with what is obtained from laboratory measurements here on Earth.
The results were extremely unexpected. Data from observations of distant galaxies in one area of the sky show that the PTS there is approximately one hundred thousandth more than on Earth, and in another area - by one hundred thousandth less.
If these results are correct, their significance is enormous. It turns out that PTS for some reason varies in different areas of the universe - and we must not forget that, first of all, we do not know where the meaning of PTS comes from. This is a slap in the face of the cosmological principle.
Two very important facts. First, even if this result is correct, the deviation is unusually small. What Webb and his colleagues observed does not make either end of the observable universe unsuitable for human life. To do this we would have to climb immeasurably further. Secondly, most physicists are not yet convinced that the result is correct. The signal is relatively weak, and a number of other research groups do not confirm it. Personally, I'm not going to approach my textbooks with a large bottle of line correction just yet. If the laws of physics within the universe change, it is very, very little.
There is, however, a fly in the ointment in this ointment. Even if this deviation really exists, it is so small that we can introduce another symmetry.
Translation symmetry: the laws of physics are exactly the same in all places in the universe.
The large-scale homogeneity—the overall uniformity—of the structure of the universe shows, or at least suggests, that there is translational symmetry inherent in the universe.
Page 1 of 85
© 2013 by Dave Goldberg
© Brodotskaya A. translation into Russian, 2015
© AST Publishing House LLC, 2015
...The Universe in the Rearview Mirror is a great read for anyone seeking to understand why our universe is so complex and so wonderful... Goldberg is a magnificent companion who will lead you to your destination - to admire the beauty of the universe.
...Mathematical symmetries offer answers to many questions, but throughout his witty and light-hearted book, Goldberg lays out milestones for the reader without being overloaded with mathematical calculations. Tip: Don't skip the many footnotes full of highbrow humor!
...Goldberg has a keen sense of humor and the absurd - and he is great at explaining why something we take for granted, such as the equality of gravitational and inertial masses, is actually very strange and not at all obvious... This book is a bit like a rollercoaster ride , built through Tolkien's Moria.
...Wow, how interesting the topic of symmetry turns out to be! Physicist Dave Goldberg takes the reader right into the maelstrom of big physics concepts, but steers the ship so deftly that the reader is not at risk of drowning.
...A meaningful, not overloaded with mathematics, and extremely fascinating book about the concept of symmetry in physics... From start to finish, Goldberg's book is written in an accessible and humorous manner... The author generously peppers his explanations with references to popular culture - from Doctor Who and Lewis Carroll to Angry Birds “- and thanks to the charming manner of presentation, he makes even the most complex topics simple.
...Goldberg talks about the ten most fundamental qualities of the universe with constant humor, but at the same time it is subtle, deep and understandable.
...This book is a fun and engaging exploration of basic physics concepts that includes, among other things, the story of one of the unsung heroines of physics, a giant on whose shoulders many physicists have stood - Emmy Noether!
...Dave Goldberg arranges a real amusement park of fascinating curiosities, puzzling paradoxes and subtle humor... He perfectly explains to the reader what the role of symmetry is in physics, astronomy and mathematics. A wonderful story about a beautiful universe!
...Don't look away! This book is a real gift to any reader who is curious about all the wonders of our wonderful universe. If the fundamental concepts and laws of physics were taught in schools as clearly and fun as Dave Goldberg talks about them in his book, we would be much better able to attract young people to science.
...This book is almost as vast in scope as the physical universe it so wonderfully describes. But the main thing, perhaps, is that Goldberg writes in detail about the underrated merits of Emmy Noether. Her theorem, that for every symmetry there is a conserved quantity, unifies many different areas of physics, and Goldberg explains how and why.
...Dave Goldberg talks about how symmetry shapes the universe with such skill that his book is a pleasure to read. His stories - from the "koan of kaons" and the kingdom of ants to the fuss around the Higgs boson - are impossible to put down, and at the same time they are unusually educational.
Reading this book is like listening to a lecture by the most wonderful physics teacher in the world! Goldberg tells you everything you wanted to know about physics but were embarrassed to ask, such as whether it is possible to build a Tardis, or what would happen if the Earth was sucked into a black hole. A must read for anyone who wants to understand the nature of the universe - and have a laugh at the same time!
Dedicated to Emily, Willa and Lily - you are my life, love and inspiration
It must be remembered that what we observe is not nature as such, but nature subjected to our method of asking questions.
Werner Heisenberg
Why is there something in the world and not nothing? Why is the future not the same as the past? Why does a serious person come up with such questions?
When you talk about popular science, you fall into a kind of daring skepticism of the initiate. You read all these tweets and blogs - and you get the impression that the theory of relativity is nothing more than the idle chatter of some dude at a party, and not one of the most successful physical theories in the history of mankind, which has withstood all experimental and observational tests for a hundred years .
From the point of view of the uninitiated, physics is somehow painfully overloaded with all sorts of laws and formulas. Can't it be simpler? And physicists themselves often revel in the detached complexity of their designs. When Sir Arthur Eddington was asked a hundred years ago whether it was true that only three people in the world understood Einstein's general theory of relativity, he thought for a moment, and then casually remarked: "I'm trying to figure out who the third is." Today, the theory of relativity is included in the standard arsenal of every physicist; it is taught every day to yesterday’s, and even today’s, schoolchildren. So it’s time to abandon the arrogant idea that understanding the secrets of the universe is accessible only to geniuses.
Profound insights into the workings of our world have almost never resulted from the invention of a new formula, whether you were Eddington or Einstein. On the contrary, breakthroughs almost always occur when we realize that we previously thought they were different things, but in fact they are the same thing. To understand how everything works, you need to understand symmetry.
The great physicist of the 20th century, Nobel laureate Richard Feynman likened the world of physics to a game of chess. Chess is a game full of symmetry. Turn the board half a turn and it will look exactly the same as when you started. The figures on one side, with the exception of color, are almost a perfect mirror image of the figures on the other. Even the rules of the game have symmetry. Here's how Feynman puts it:
...According to the rules, the bishop moves on the chessboard only diagonally. We can conclude that no matter how many moves pass, a certain bishop will always remain on the white square... And so it will be, and for quite a long time - but suddenly we discover that the bishop ended up on the black square (in fact, this is what happened: for this time the bishop was eaten, but one of the pawns reached the last row and became a bishop on a black square). Same with physics. We have a law that applies universally for a long, long time, even when we cannot trace all the details, and then there comes a moment when we can open new law.
Dave Goldberg
The universe is in the rearview mirror. Was God right-handed? Or hidden symmetry, antimatter and the Higgs boson
© 2013 by Dave Goldberg
© Brodotskaya A. translation into Russian, 2015
© AST Publishing House LLC, 2015
Book reviews
"The Universe in the Rearview Mirror"
The Universe in the Rearview Mirror is a great read for anyone who seeks to understand why our universe is so complex and so wonderful... Goldberg is a magnificent companion who will take you to your destination - to admire the beauty of the universe.
Nature PhysicsMathematical symmetries offer answers to many questions, but throughout his witty and light-hearted book, Goldberg lays out milestones for the reader without being overloaded with mathematical calculations. Tip: Don't skip the many footnotes full of highbrow humor!
DiscoverGoldberg has a keen sense of humor and the absurd - and he is great at explaining why things we take for granted, such as the equality of gravitational and inertial masses, are actually very strange and not at all obvious... This book is a bit like a rollercoaster ride , built through Tolkien's Moria.
New ScientistWow, how interesting the topic of symmetry turns out to be! Physicist Dave Goldberg takes the reader right into the maelstrom of big physics concepts, but steers the ship so deftly that the reader is not at risk of drowning.
NatureA meaningful, not overloaded with mathematics, and extremely fascinating book about the concept of symmetry in physics... From start to finish, Goldberg's book is written in an accessible and humorous manner... The author generously peppers his explanations with references to popular culture - from Doctor Who and Lewis Carroll to Angry Birds “- and thanks to his charming manner of presentation, he makes even the most complex topics simple.
Publishers WeeklyGoldberg talks about the ten most fundamental qualities of the universe with constant humor, but at the same time it is subtle, deep and understandable.
Kirkus ReviewsThis book is a fun and engaging exploration of basic physics concepts that includes, among other things, the story of one of the unsung heroines of physics, a giant on whose shoulders many physicists have stood—Emmy Noether!
Danica McKellar, actress, author of “Math Doesn’t Suck”Dave Goldberg arranges a real amusement park of fascinating curiosities, puzzling paradoxes and subtle humor... He perfectly explains to the reader what the role of symmetry is in physics, astronomy and mathematics. A wonderful story about a beautiful universe!
Paul Halpern, author of the book "Edge of the Universe"Don't look away! This book is a real gift to any reader who is curious about all the wonders of our wonderful universe. If the fundamental concepts and laws of physics were taught in schools as clearly and fun as Dave Goldberg talks about them in his book, we would be much better able to attract young people to science.
Priyamvada Natarajan, Chair of the Physics and Astronomy Departments of the Women's Faculty Forum at Yale UniversityThis book is almost as vast in scope as the physical universe it so wonderfully describes. But the main thing, perhaps, is that Goldberg writes in detail about the underrated merits of Emmy Noether. Her theorem, that for every symmetry there is a conserved quantity, unifies many different areas of physics, and Goldberg explains how and why.
John Allen Paulos, lecturer in mathematics at Temple University, author of InnumeracyDave Goldberg talks about how symmetry shapes the universe with such skill that his book is a pleasure to read. His stories - from the "koan of kaons" and the kingdom of ants to the fuss around the Higgs boson - are impossible to put down, and at the same time they are unusually educational.
J. Richard Gott, lecturer in astrophysics at Princeton UniversityReading this book is like listening to a lecture from the most wonderful physics teacher in the world! Goldberg tells you everything you wanted to know about physics but were embarrassed to ask, such as whether it is possible to build a Tardis, or what would happen if the Earth was sucked into a black hole. A must read for anyone who wants to understand the nature of the universe - and have a laugh at the same time!
Annalee Newitz, editor and operator of the time distortion field at http://i09.comDedicated to Emily, Willa and Lily - you are my life, love and inspiration
It must be remembered that what we observe is not nature as such, but nature subjected to our method of asking questions.
Werner Heisenberg
Introduction
In which I tell you what and how, so it’s better not to scroll through it
Why is there something in the world and not nothing? Why is the future not the same as the past? Why does a serious person come up with such questions?
When you talk about popular science, you fall into a kind of daring skepticism of the initiate. You read all these tweets and blogs - and you get the impression that the theory of relativity is nothing more than the idle chatter of some dude at a party, and not one of the most successful physical theories in the history of mankind, which has withstood all experimental and observational tests for a hundred years .
From the point of view of the uninitiated, physics is somehow painfully overloaded with all sorts of laws and formulas. Can't it be simpler? And physicists themselves often revel in the detached complexity of their designs. When Sir Arthur Eddington was asked a hundred years ago whether it was true that only three people in the world understood Einstein's general theory of relativity, he thought for a moment, and then casually remarked: "I'm trying to figure out who the third is." Today, the theory of relativity is included in the standard arsenal of every physicist; it is taught every day to yesterday’s, and even today’s, schoolchildren. So it’s time to abandon the arrogant idea that understanding the secrets of the universe is accessible only to geniuses.
Profound insights into the workings of our world have almost never resulted from the invention of a new formula, whether you were Eddington or Einstein. On the contrary, breakthroughs almost always occur when we realize that we previously thought they were different things, but in fact they are the same thing. To understand how everything works, you need to understand symmetry.
The great physicist of the 20th century, Nobel laureate Richard Feynman likened the world of physics to a game of chess. Chess is a game full of symmetry. Turn the board half a turn and it will look exactly the same as when you started. The figures on one side, with the exception of color, are almost a perfect mirror image of the figures on the other. Even the rules of the game have symmetry. Here's how Feynman puts it:
According to the rules, the bishop moves on the chessboard only diagonally. We can conclude that no matter how many moves pass, a certain bishop will always remain on the white square... And so it will be, and for quite a long time - but suddenly we discover that the bishop ended up on the black square (in fact, this is what happened: for this time the bishop was eaten, but one of the pawns reached the last row and became a bishop on a black square). Same with physics. We have a law that applies universally for a long, long time, even when we cannot trace all the details, and then there comes a moment when we can open new law.
Watch the game a few more times and it will suddenly dawn on you that the bishop remains on squares of the same color precisely because it moves only diagonally. The law of conservation of color generally applies, but a deeper law requires a deeper explanation.
Symmetry in nature appears almost everywhere - even if it is unremarkable or even obvious and banal. A butterfly's wings are a perfect reflection of each other. Their functions are identical, but I would really feel sorry for the poor butterfly with two left or two right wings - it would fly helplessly in a circle. Symmetry and asymmetry in nature, as a rule, are forced to compete with each other. Ultimately, symmetry is a tool with which we not only formulate laws, but also understand why they operate.
Let's say that space and time are not at all as different as they might seem. They are like the right and left wings of a butterfly. The similarity between them formed the basis of the special theory of relativity - and gave rise to the most famous formula in all of physics. Apparently, the laws of physics do not change over time - this symmetry allows us to conclude that energy is conserved. And this is also good: it is thanks to the conservation of energy that our giant battery - the Sun - manages to power all life on Earth.
For many of us (okay, physicists), the laws of symmetry found in the study of the physical universe are as beautiful as the symmetry of a diamond, a snowflake, or the idealized aesthetics of a perfectly symmetrical human face.
The mathematician Marcus du Sautoy writes about this beautifully:
Only the fittest, healthiest plants have a reserve of energy that allows them to maintain balance in creating their form. A symmetrical flower is superior to an asymmetrical one, and this is reflected in the fact that it produces more nectar and this nectar has a higher sugar content. Symmetry tastes sweet.
The challenges that symmetry poses for us are incredibly pleasing to our minds. American crosswords, as a rule, are a pattern of black and white squares that does not change if you turn the entire picture half a turn or look at it in a mirror. Many masterpieces of painting and architecture are built on symmetry - pyramids, the Eiffel Tower, the Taj Mahal.
It’s worth searching the back of your mind and you’ll probably remember the five Platonic solids. There are only five regular polyhedra with identical faces: the tetrahedron (four faces), the cube (six), the octahedron (eight), the dodecahedron (twelve) and the icosahedron (twenty). Some science nerd like me will look back fondly on childhood and realize that this is exactly what the dice looked like in a Dungeons & Dragons set.
Sometimes, in everyday conversation, the word "symmetry" simply refers to the way things "match" or "reflect" each other, but in reality the concept certainly has a precise definition. The formulation we will rely on in the pages of this book belongs to the mathematician Hermann Weyl:
An object is called symmetrical if you can do something to it, and after that it will look the same as before.
Consider an equilateral triangle. You can do whatever you want with this triangle - and it will still remain exactly the same as before. You can turn it a third of a turn and it will look the same. Or you can look at it in the mirror - and the reflection will be exactly the same as the original.
Equilateral triangle
A circle is a perfect symmetrical object. Unlike triangles, which only look the same if you rotate them a certain angle, a circle can be rotated any way you want and it will remain the same. I would not like to explain the obvious, but this is precisely the principle on which the wheel works.
Long before we understood how the planets moved, Aristotle proposed that their orbits should be circular, precisely because of the “perfection” of the circle as a symmetrical shape. Aristotle was mistaken - and no wonder: he was mistaken in almost everything that concerns the physical world.
The temptation is great to wallow in sweet self-satisfaction while ridiculing the ancients, but Aristotle was right about one very important thing. Although the planets actually orbit the Sun in ellipses, the gravitational force pulling them towards the Sun is the same in all directions. Gravity is symmetrical. From this assumption and an ingenious insight into how gravity weakens with distance, Sir Isaac Newton correctly deduced the motion of the planets. This is partly why you are so familiar with this name, although there are many reasons for this. Shapes that don't look nearly as perfect as a circle—the elliptical orbits of planets—are a consequence of much deeper symmetry.
Symmetries point us to the true principles of nature. No one could understand how heredity worked until Rosalind Franklin took X-rays of DNA, which allowed James Watson and Francis Crick to discover the double helical structure. And this structure, consisting of two complementary spiral threads, allowed us to understand the method of copying and inheritance.
DNA double helix
If you move in circles of completely out-of-touch scientific cranks, you've probably heard one of them call this or that theory "natural" or "beautiful." This usually means that the assumption on which the theory is based is so simple that it simply must be true. In other words, starting with a very simple rule, you can describe all sorts of complex systems, such as gravity around black holes or the fundamental laws of nature.
It is only a slight exaggeration to say that physics is the study of symmetry.
Sometimes symmetry is so obvious that it seems completely banal - but leads to incredibly counterintuitive results. When you ride a roller coaster, the body is not able to distinguish whether it is gravity or the acceleration of the trolley that is pressing it into the seat: it feels the same. When Einstein suggested that “feels the same” means “is the same,” he deduced the laws by which gravity operates, which later led to the hypothesis of the existence of black holes.
Or, say, the fact that two particles of the same type can be swapped inevitably leads to an understanding of the fate of our Sun, and to the mysterious Pauli exclusion principle, and ultimately to the functioning of neutron stars and all chemistry in the world.
But the passage of time, on the other hand, seems just as obvious asymmetrical. The past is different from the future, that's for sure. However, oddly enough, the laws of physics know nothing about the time axis - they forgot to tell them about it. At the microscopic level, almost any conceivable experiment goes both ways remarkably well.
It’s easy to succumb to the desire to generalize and assume that everything in the world is symmetrical. I, reader, am unfamiliar with you and therefore am ready to make the most offensive assumptions. In high school or college, have you at least once participated in a mind-bending conversation on the topic “What if, guys, our universe is just an atom in some huge, enormous universe?”
Have you managed to grow up since then? Admit it, you know very well what the movie “Men in Black” is about, and you fondly remember how you read “Horton the Elephant Hears Someone” as a child - but even now you can’t help but wonder if there isn’t a miniature universe out there somewhere that goes far away beyond our perception.
No, my friend, the answer is no - but here we should ask a slightly deeper question: why?
If something can be increased or decreased without changing it, then we have a certain kind of symmetry. Those of you who have read Gulliver will probably remember that as soon as we meet the Lilliputians, Jonathan Swift launches into a long, detailed discussion about everything that follows from the difference in height between Gulliver and the Lilliputians, and then between Gulliver and the giants -brobdingnegs. Here Swift clearly overdid it - he writes the ratio of sizes of everything in the world, from the length of a step to the number of local animals that Gulliver needed to get enough.
However, already in Swift’s time, no one doubted that the existence of such countries and peoples (I’m generally silent about talking horses) contradicted the laws of physics. A century earlier, Galileo Galilei wrote “Two New Sciences,” where he explored the possibility of the existence of giants from a scientific point of view. After much thought, he concluded that the assumption was false - thus depriving future generations of the opportunity to have fun. The trouble is that the bone, having doubled in length, becomes eight times heavier, and its surface increases only four times. So it will break, unable to bear its own weight. Here's how Galileo himself writes about it:
An oak tree two hundred cubits high would not be able to support its own branches if they were distributed in the same way as on a tree of ordinary height; and nature cannot produce a horse twenty times the size of an ordinary horse, or a giant ten times the size of an ordinary man, unless by a miracle, or by greatly altering the proportions of his body, especially the bones, which must be greatly enlarged from the ordinary.
That is why a small dog can sometimes carry two or three dogs of its own size on its back, but I believe that a horse cannot carry even one horse of the same size.
This is why Spider-Man is such a bad idea. He couldn't possibly have the spider's proportionately increased strength. Otherwise, he would have been so massively built that he wouldn’t even have to be pressed. Gravity would do everything itself. As biologist J. B. S. Haldane writes in his essay “The Importance of Being the Right Size” (J. B. S. Haldane, “ On Being the Right Size»):
That is why an insect is not afraid of gravity - it can fall and remain unharmed, it can cling to the ceiling with surprisingly little effort... However, there is a force in the world that an insect fears just as a mammal fears gravity. This is surface tension... An insect that decides to drink is in the same danger as a person hanging from the edge of a bottomless abyss in search of food. Once an insect gets caught in the surface tension of water - that is, simply gets wet - it most likely will not be able to get out and will drown.
In fact, the problem is much deeper than the tensile strength of giant bones and the proportional strength of insects. All objects comparable to the size of a person can seemingly be proportionally reduced and enlarged without much damage - a six-meter killer robot, apparently, with exactly the same device as its three-meter model, will work twice as well - but if you switch to the scale of atoms and molecules, all predictions cease to be justified. The world of atoms is also the world of quantum mechanics, which means that the concreteness of our macroscopic existence is suddenly replaced by uncertainty.
In other words, the act of scaling itself has nothing to do with the symmetry of nature. The map of the cosmic network of galaxies does indeed look a little like a picture of neurons, but this is not some great universal symmetry. That's a coincidence. I could go on describing different cases of symmetry one after another, but I hope I have generally explained what is what. Some changes matter, others don't. In this book, I decided to take this approach: to devote each chapter to a separate question, to which, as it later turns out, there is an answer, albeit indirect, and it is given by the fundamental symmetries of the universe.
On the other hand, even a person’s right hand is different from his left. One of the main mysteries that people ponder is that in some sense the universe is not symmetrical. Your heart is in the left side of your chest, the future is not the same as the past, you are made of matter, not antimatter. So this book is also a book about broken and imperfect symmetry, perhaps even more so than about ideal symmetry. Popular wisdom says that a Persian carpet is perfect in its imperfection and ideal in its imperfection. The patterns on real, traditional rugs are just a little off, and breaking the symmetry gives the whole piece more personality. The same thing happens with the laws of nature - and this is great: a perfectly symmetrical universe would be terribly boring. But our universe cannot be called boring.
The universe we see in the rearview mirror is closer than it seems, and that changes everything. But let's not look back - we are going on a long tour of the universe. And symmetry will be our guide, but when it is broken, we will have something to write home about.
Chapter first. Antimatter
From which we learn why there is something in the world and not nothing
Watching science fiction films in the hope of learning something new about science is generally a pointless idea. Among other things, you will get a very distorted idea, for example, of how explosions roar in space (they are silent), how easy it is to reach superluminal speed (but no way), how many English-speaking and not entirely humanoid, but still devilishly attractive aliens are in space (they are all married). However, all sorts of “Star Wars” and “Star Treks” instilled in us one very correct idea: antimatter is not to be trifled with.
Antimatter contains such amazing power that it is simply impossible to resist the temptation, and if a science fiction writer wants to add “real physics” to his brew, he almost always reaches for a pinch of antimatter: it will add weight in the eyes of the readers. The engine of the space shuttle Enterprise operated on the interaction of matter and antimatter. Isaac Asimov gave his robots a positronic brain—and turned the positron, an antimatter particle, into a sci-fi MacGuffin.
Even in Dan Brown's Angels and Demons, a book that hardly qualifies as true science fiction, antimatter serves as a kind of infernal machine. The villains steal half a gram of antimatter - and this amount is enough to cause an explosion comparable in power to the first nuclear bombs. Not counting the fact that Dan Brown was wrong in his arithmetic calculations by a factor of two, completely misunderstood what was actually happening in a particle accelerator, and missed the mark by about a trillion times when he was estimating how much antimatter could be stored and transported, with his scientific part Everything is fine.
It turns out that we are constantly encountering antimatter - but we completely misunderstand what it is. This substance is by no means the unstoppable killer that you have become accustomed to distrusting for so many years. If antimatter is not disturbed, it behaves quite peacefully. Antimatter is just like the regular matter you know and love—it has the same mass, for example—it's just the opposite: opposite charge and opposite name. It smells fried only if you mix antimatter with ordinary matter.
Not only is antimatter no more exotic than ordinary matter, it also looks and behaves exactly the same in almost all important situations. If all the particles in the universe were suddenly replaced by their anti-version, you wouldn't notice a thing. Simply put, there is also symmetry in the way the laws of physics treat matter and antimatter, and yet they should be a little different: after all, you and everyone you know are not made of antimatter, but of ordinary matter.
We like to think that there are no coincidences, that there is some global reason why you are not currently sitting in a room full of anti-people. To figure out what's going on here, we'll go deeper into the past.
Come on, anti-people, where did I come from?
Explaining where something comes from can be difficult. It is not always possible to accurately attribute everything to the bite of a radioactive spider, the explosion of the home planet, or even the revival of a corpse (for the sake of science, you understand). Our own origin story is a tricky one, but you'll be pleased to know that we (just like the Hulk) are ultimately the result of exposure to gamma radiation. It's a long story.
Physics cannot yet even answer the question of where the universe itself came from, but we can say a lot about what happened after that. At the risk of causing an existential crisis, we can at least try to answer one of philosophy's great questions, a real big shot in its pantheon: "Why is there something in the world and not nothing?"
The question is not as dumb as it might seem. Based on everything we see in the lab, you shouldn't exist. Nothing personal. I shouldn't exist either, and neither should the Sun, the Milky Way galaxy, or the Twilight movie (for a myriad of reasons).
To understand why you shouldn't exist, we need to look into mirror universes, antimatter universes, and our own universe on the smallest scale. It is only at the smallest scale that the difference between matter and antimatter becomes apparent, and even then it is far from obvious.
The Universe on the smallest scale other. Everything we see is made up of molecules, the smallest of which are about a millionth of a millimeter in size. If we compare this to human scale values, then a human hair is approximately one hundred thousand molecules thick. Yes, molecules very small, but no matter how small they are, they are made up of even smaller particles. And this is also good - if we are interested in finding at least some order in the world. According to the Royal Society of Chemistry, we know about 20 million different types of molecules, and new compounds are discovered so frequently that it is not worth even trying to give an exact number. If we didn't understand that molecules are made of something even smaller, we'd get bogged down in listing them.
Fortunately for the universal order, on a smaller and smaller scale, new structures appear. At a scale of less than ten billionths of a meter, we begin to distinguish individual atoms. We know of only 118 chemical elements, and most of them are not found in nature at all or are found only in minute quantities.
© 2013 by Dave Goldberg
© Brodotskaya A. translation into Russian, 2015
© AST Publishing House LLC, 2015
Book reviews
"The Universe in the Rearview Mirror"
The Universe in the Rearview Mirror is a great read for anyone who seeks to understand why our universe is so complex and so wonderful... Goldberg is a magnificent companion who will take you to your destination - to admire the beauty of the universe.
Nature Physics
Mathematical symmetries offer answers to many questions, but throughout his witty and light-hearted book, Goldberg lays out milestones for the reader without being overloaded with mathematical calculations. Tip: Don't skip the many footnotes full of highbrow humor!
Discover
Goldberg has a keen sense of humor and the absurd - and he is great at explaining why things we take for granted, such as the equality of gravitational and inertial masses, are actually very strange and not at all obvious... This book is a bit like a rollercoaster ride , built through Tolkien's Moria.
New Scientist
Wow, how interesting the topic of symmetry turns out to be! Physicist Dave Goldberg takes the reader right into the maelstrom of big physics concepts, but steers the ship so deftly that the reader is not at risk of drowning.
Nature
A meaningful, not overloaded with mathematics, and extremely fascinating book about the concept of symmetry in physics... From start to finish, Goldberg's book is written in an accessible and humorous manner... The author generously peppers his explanations with references to popular culture - from Doctor Who and Lewis Carroll to Angry Birds “- and thanks to his charming manner of presentation, he makes even the most complex topics simple.
Publishers Weekly
Goldberg talks about the ten most fundamental qualities of the universe with constant humor, but at the same time it is subtle, deep and understandable.
Kirkus Reviews
This book is a fun and engaging exploration of basic physics concepts that includes, among other things, the story of one of the unsung heroines of physics, a giant on whose shoulders many physicists have stood—Emmy Noether!
Dave Goldberg arranges a real amusement park of fascinating curiosities, puzzling paradoxes and subtle humor... He perfectly explains to the reader what the role of symmetry is in physics, astronomy and mathematics. A wonderful story about a beautiful universe!
Don't look away! This book is a real gift to any reader who is curious about all the wonders of our wonderful universe. If the fundamental concepts and laws of physics were taught in schools as clearly and fun as Dave Goldberg talks about them in his book, we would be much better able to attract young people to science.
Priyamvada Natarajan, Chair of the Physics and Astronomy Departments of the Women's Faculty Forum at Yale University
This book is almost as vast in scope as the physical universe it so wonderfully describes. But the main thing, perhaps, is that Goldberg writes in detail about the underrated merits of Emmy Noether. Her theorem, that for every symmetry there is a conserved quantity, unifies many different areas of physics, and Goldberg explains how and why.
John Allen Paulos, lecturer in mathematics at Temple University, author of Innumeracy
Dave Goldberg talks about how symmetry shapes the universe with such skill that his book is a pleasure to read. His stories - from the "koan of kaons" and the kingdom of ants to the fuss around the Higgs boson - are impossible to put down, and at the same time they are unusually educational.
J. Richard Gott, lecturer in astrophysics at Princeton University
Reading this book is like listening to a lecture from the most wonderful physics teacher in the world! Goldberg tells you everything you wanted to know about physics but were embarrassed to ask, such as whether it is possible to build a Tardis, or what would happen if the Earth was sucked into a black hole. A must read for anyone who wants to understand the nature of the universe - and have a laugh at the same time!
Dedicated to Emily, Willa and Lily - you are my life, love and inspiration
It must be remembered that what we observe is not nature as such, but nature subjected to our method of asking questions.
Werner Heisenberg
Introduction
In which I tell you what and how, so it’s better not to scroll through it
Why is there something in the world and not nothing? Why is the future not the same as the past? Why does a serious person come up with such questions?
When you talk about popular science, you fall into a kind of daring skepticism of the initiate. You read all these tweets and blogs - and you get the impression that the theory of relativity is nothing more than the idle chatter of some dude at a party, and not one of the most successful physical theories in the history of mankind, which has withstood all experimental and observational tests for a hundred years .
From the point of view of the uninitiated, physics is somehow painfully overloaded with all sorts of laws and formulas. Can't it be simpler? And physicists themselves often revel in the detached complexity of their designs. When Sir Arthur Eddington was asked a hundred years ago whether it was true that only three people in the world understood Einstein's general theory of relativity, he thought for a moment, and then casually remarked: "I'm trying to figure out who the third is." Today, the theory of relativity is included in the standard arsenal of every physicist; it is taught every day to yesterday’s, and even today’s, schoolchildren. So it’s time to abandon the arrogant idea that understanding the secrets of the universe is accessible only to geniuses.
Profound insights into the workings of our world have almost never resulted from the invention of a new formula, whether you were Eddington or Einstein. On the contrary, breakthroughs almost always occur when we realize that we previously thought they were different things, but in fact they are the same thing. To understand how everything works, you need to understand symmetry.
The great physicist of the 20th century, Nobel laureate Richard Feynman likened the world of physics to a game of chess. Chess is a game full of symmetry. Turn the board half a turn and it will look exactly the same as when you started. The figures on one side, with the exception of color, are almost a perfect mirror image of the figures on the other. Even the rules of the game have symmetry. Here's how Feynman puts it:
According to the rules, the bishop moves on the chessboard only diagonally. We can conclude that no matter how many moves pass, a certain bishop will always remain on the white square... And so it will be, and for quite a long time - but suddenly we discover that the bishop ended up on the black square (in fact, this is what happened: for this time the bishop was eaten, but one of the pawns reached the last row and became a bishop on a black square). Same with physics. We have a law that applies universally for a long, long time, even when we cannot trace all the details, and then there comes a moment when we can open new law.
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