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November 29 - December 27, 2022
The ancients were right: beneath the surface complexity of nature lies a hidden subtext, written in a subtle mathematical code. This cosmic code4 contains the secret rules on which the universe runs.
science has uncovered the existence of this concealed mathematical domain. We human beings have been made privy to the deepest workings of the universe. Other animals observe the same natural phenomena as we do, but alone among the creatures on this planet, Homo sapiens can also explain them. How has this come about? Somehow the universe has engineered, not just its own awareness, but also its own comprehension. Mindless, blundering atoms have conspired to make not just life, not just mind, but understanding.
For all we know, this is the first and only time anywhere in the universe that minds have glimpsed the cosmic code.
the distance the ball travels increases as the square of the time. The ball will fall four times as far in two seconds as in one, nine times as far in three seconds, and so on.
the way magnets lose their grip on each other with separation. Line them up side by side and measure the force as the distance between them increases. You will find that the force diminishes with the cube of the distance,
“The universe appears to have been designed by a pure mathematician.”
Even today, millions of people base their worldview on a religious interpretation of nature.
When it comes to actual physical phenomena, science wins hands down against gods and miracles.
Key Points Many big questions of existence are now on the scientific agenda. A really big question is why the universe is fit for life; it looks “fixed up.” The universe obeys mathematical laws; they are like a hidden subtext in nature. To appreciate this book you have to be comfortable with that idea.
The mathematical laws of physics underlie everything. Many physicists think they are real and that they inhabit a transcendent Platonic realm. Science reveals that there is a coherent scheme of things, but scientists do not necessarily interpret that as evidence for meaning or purpose in the universe. Most, but by no means all, scientists are atheists or agnostics. Somehow I am supposed to explain all this.
we can put quite a precise date on the big bang. The best current estimate is 13.7 billion years ago. For comparison, the Earth is 4.56 billion years old.
The radiation is evenly distributed across the sky at a temperature1 of 2.725 K, or about minus 270°C—so don’t expect the sky to be glowing dull red. Radiation at this temperature lies mainly in the microwave region of the electromagnetic spectrum, so the heat from the big bang is known as the “cosmic microwave background,” usually abbreviated as CMB.
There Is a Horizon in Space Beyond Which We Cannot See
Distant galaxies, for example, can be effectively retreating from us at faster than light speed. This does not contradict the rule as applied within special relativity, which refers to a local situation and not to the global motion of the universe.
The Observable Universe
The simplest assumption is that the region of space within our horizon is typical of the entirety: this is the principle of mediocrity again.
The Entire Universe
This includes all of (possibly infinite) space, within and beyond our horizon, plus all of its contents, on the said assumption that t...
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whole. Later we shall see that this simple view of the universe, based on an uncritical application of the principle of m...
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The Pocket U...
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This is the region of space out as far as it resembles the observable universe we see today (which may extend a very long way indeed—far beyond our horizon). But if we inhabit a pocket universe10 there would be a boundary somewhere, far, far away, beyond which things would look very different. There would, however, be other pocket universes...
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The Multiverse
Roughly speaking, this is the collection of all pocket universes (probably infinite in number) plus the gaps in between.
The most extreme bending of light—or warping of space—occurs around a black hole. In this case the spacewarp is so strong that it actually traps light completely, preventing it from escaping.
The volume of a region of space can be assessed by counting the number of galaxies it contains.
Einstein’s famous equation E = mc2, which tells us that mass is energy, and energy has mass.
gravity is a form of energy. But now we notice a curious fact. Imagine trying to pluck the Earth out of its orbit around the sun. You would have to do work—that is, expend energy—to draw it away against the sun’s gravitational pull. So the gravitational energy binding the Earth to the sun is negative (it requires work to sever the bond). If the gravitational field has negative energy, it must also have negative mass and must be subtracted from the positive mass-energy of the sun and planets.
To within the 2 percent accuracy of the measurement, the satellite found space to be flat, which translates into the conclusion that the universe contains no net mass at all! And that, as we shall see later, is yet another one of those “coincidences” that is needed for a life-permitting universe.
Key Points The universe began with a hot big bang 13.7 billion years ago and is still expanding. The expansion is best envisaged as the stretching of space between the galaxies. Space is filled with heat radiation that is a remnant, or afterglow, of the hot early phase of the universe. The cosmic microwave back ground (CMB) radiation has been intensively studied, most notably by the WMAP satellite, because it contains lots of important data about the history and structure of the universe. Fluctuations in the CMB reveal the seeds of the large-scale structure of the universe (clusters of
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canceled by the negative mass-energy of the gravitational field of all the matter in the universe. There may be additional dimensions of space over and above the three we perceive. Some theories of physics require this. Extra dimensions can be concealed from view, for example, by rolling them up to a tiny size.
nuclear fusion, a process that is very well understood. Protons and neutrons could begin combining together to make composite nuclei only once the temperature had fallen enough so that the newly minted nuclei would not immediately be fragmented again by the intense heat.
the universe is made almost entirely of hydrogen and helium in a roughly three-to-one ratio. Helium, then, is a relic of the first few minutes of the universe.1
The story of the early universe is one of seesawing fortunes in this respect. Sometimes the cosmic material keeps up with the expansion; sometimes it gets frozen in a state determined at an earlier moment. We shall see in later chapters how such “freeze-out” events were crucial in establishing a universe fit for life.
Figure 12: Gravity slows the expanding universe. The size of the universe should increase with time, according to the general theory of relativity. It starts out expanding explosively fast at the big bang origin, but progressively slows as the attractive force of gravitation acts like a brake.
how inflation neatly solves the problem of cosmic uniformity. Any initial irregularities would be “stretched to death,” in the same way that an inflating balloon loses its crinkles. In effect, inflation obliterates all records of previous complexity and generates a naturally smooth universe. And there is a bonus. Just as inflating a balloon reduces the curvature of its surface, so inflating space makes it less and less curved. Inflate it enough (and a factor of 1025 is enough) and it will be indistinguishable from flat. So inflation explains both the uniformity and the flat geometry of the
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The gravitational effect of field energy depends on the nature of the field: some fields (for example, electric) would make the universe shrink; others would create antigravity and make it expand. The latter include so-called scalar fields,
hypothetical entity the inflaton field.
Negative pressure isn’t especially exotic: it is no more than what we normally call tension—a stretched elastic band provides a familiar example. In three dimensions, a block of rubber pulled in all directions would have negative pressure.
grand unified theories, or GUTs—attempts
The cosmic microwave background pervading the universe today—the afterglow of creation—represents the remnants of the inflaton field energy.
The next step is to turn heat into matter.
At the end of inflation, the intense energy released would have heated the universe to around a thousand trillion trillion degrees—more than sufficient to create all 1050 tons of matter in the observable universe.
eternal inflation,
when heat radiation is emitted by a hot body, it comes out only in discrete little packets, or quanta,
a central tenet of quantum mechanics called Heisenberg’s uncertainty principle, This forbids a quantum object from possessing a full set of familiar physical attributes at any given time.
Quantum randomness, by contrast, is irreducible, which is to say that quantum processes are in some sense genuinely spontaneous—without any specific cause.
All measurable quantities are subject to quantum fluctuations, to an extent prescribed by Heisenberg’s uncertainty principle.
Mathematicians call the infinite curvature limit of spacetime a singularity.
The best way to think about singularities is as boundaries or edges of spacetime.
The theory of relativity links space and time together to form a unified spacetime.
