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by
Max Tegmark
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September 27 - November 26, 2018
One could indeed argue that space is a mathematical object, in the sense that its only intrinsic properties are mathematical properties—properties such as dimensionality, curvature and topology.
our Solar System was found to be reminiscent of a clockwork, with its parts moving in precise orbits over and over again, seemingly forever.
The most common isotope of uranium atoms spontaneously decays into thorium and other lighter atoms at such a rate that half of the atoms have fallen apart after 4.47 billion years. Such radioactive decays generate enough heat to keep Earth’s core nice and toasty for billions of years, explaining why Earth is so warm even if it’s way older than 20 million years.
have been found to be over 4.404 billion years old. The record age for meteorites is 4.56 billion years, suggesting that both our planet and the rest of our Solar System formed in the ballpark of 4.5 billion years ago—in good agreement with those much cruder estimates from tides.
Friedmann discovered that the most natural state of affairs was to find yourself in a universe that’s either expanding or contracting.
Red light has the lowest frequency of all the colors in the rainbow, so if a galaxy is moving away from us, the colors of all its spectral lines will be redshifted, shifted toward redder colors, and the higher its speed, the greater its redshift. If the galaxy is moving toward us, its colors will instead be blueshifted toward higher frequencies.
When we do this today, using Friedmann’s equations and modern measurements, we find that the required correction is quite small, at the percent level: after its Big Bang, our Universe spent about the first half of its time decelerating, then the rest of the time accelerating, so the corrections roughly cancel out.
so doesn’t this violate Einstein’s claim that nothing can go faster than light? The answer is yes and no: it violates Einstein’s special relativity theory from 1905 but not his general relativity theory from 1915, and the latter is Einstein’s final word on the subject, so we’re okay.
If we think of space as expanding, then we can rephrase this by saying that nothing is allowed to move faster than light through space, but space itself is free to stretch however fast it wants to. Speaking of distant galaxies, I’ve
Here the answer is that we’re not seeing these distant galaxies where they are now, but where they were when they emitted the light that reaches us now.
you suddenly realize that there’s energy coming from beyond that empty last row: the rear wall of the auditorium isn’t completely dark, but gives off a faint glow of microwaves!
This means that when we gaze ever farther into space as in Figure 3.3, we should encounter old galaxies nearby, then young galaxies beyond them, then transparent hydrogen gas, then a wall of glowing hydrogen plasma. We can’t see beyond this wall, because it’s opaque and therefore obstructs what came before it like a cosmic censor.
When you measure the helium fraction of distant intergalactic gas by studying its spectrum with a telescope, you find … 25%! To me, this finding is just as impressive as discovering a fossilized Tyrannosaurus rex femur: direct evidence that crazy things happened in the past, in this case everything being crazy hot like the center of the Sun.
As Fred Hoyle was the first to realize, this coincidence enabled stars in the late stages of their lives to turn helium into carbon, oxygen and most of the other atoms that you and I are made of. Moreover, it became clear that stars end their lives by blowing apart, recycling many of the atoms that they’ve made into gas clouds that can later form new stars, planets and ultimately you and me. In other words, we’re more connected to the heavens than our ancestors realized: we’re made of star stuff.
Over the billions of years that followed, gravity transformed our Universe from uniform and boring to clumpy and interesting, amplifying the tiny density fluctuations that we see in the cosmic microwave background into planets, stars, galaxies and the cosmic large-scale structure that we see around us today.
However, we now understand a great deal about what’s happened during the 14 billion years since then: expansion and clustering. These two basic processes, both controlled by gravity, have transformed hot, smooth quark soup into today’s star-studded cosmos.
In the cosmic example, the farther our Universe gets from perfect uniformity, the more forcefully gravity amplifies its clumpiness. If a region of space is slightly denser than its surroundings, then its gravity will pull in neighboring material and make it even denser.
Indeed, dark matter from space that strikes Earth appears to typically pass unaffected through our entire planet, emerging unscathed on the other side.
Specifically, Einstein’s equations show that the more matter space contains, the more curved space gets. This curvature of space causes things to move not in straight lines, but in a motion that curves toward massive objects—thus explaining gravity as a manifestation of geometry.
But all this matter makes up only 30% of the total budget, which means that the remaining 70% must be some form of matter that doesn’t cluster—so-called dark energy.
1998, they announced a startling discovery that earned them the 2011 Nobel Prize in physics: after spending its first 7 billion years slowing down, the cosmic expansion started speeding up again and has accelerated ever since!
In this sense, we can think of the cosmic microwave–background fluctuations as the cosmic DNA, the blueprints for what our Universe will grow to become.
The fraction of our observable Universe (left) that has been mapped (center) is tiny, covering less than 0.1% of the volume. Just as for Australia in 1838 (right), we’ve mapped a thin strip around the perimeter while most of the interior remains unexplored.
Einstein’s gravity theory arguably broke the record as the most mathematically beautiful theory, explaining gravity as a manifestation of geometry. It shows that the more mass space contains, the more curved space gets. This curvature of space causes things to move not in straight lines, but in a motion that curves toward massive objects.
The missing mass is ghostly, being both invisible and able to pass through us undetected. Its gravitational effects suggest that it consists of two separate substances of opposite character, dubbed dark matter and dark energy: Dark matter clusters, dark energy doesn’t. Dark matter dilutes as it expands, dark energy doesn’t. Dark matter attracts, dark energy repels. Dark matter helps galaxies form, dark energy sabotages.
Surely, Alan Guth argued, there must be some mechanism that caused our Universe to have exactly the right density required for extreme flatness early on.
Similarly, when inflation dramatically expands our own 3-D space, the space within any given cubic centimeter becomes almost perfectly flat.
A rubber band has negative pressure because you need to work to expand it. For a substance with positive pressure, like air, it’s the other way around: you need to do work to compress it.
Again Einstein comes to the rescue with a loophole, this time from his general relativity theory, which says that gravity is caused not only by mass, but also by pressure.
In summary, an inflating substance produces an antigravity force that blows it apart, and the energy that this antigravity force expends to expand the substance creates enough new mass for the substance to retain constant density.
Doesn’t creation of the matter around us from almost nothing by inflation violate energy conservation? We’ve seen that the answer is no: all the required energy was borrowed from the gravitational field.
just can’t shake the uneasy feeling that I’m living in a Ponzi scheme of cosmic proportions.
Well, one of the beauties of inflation is that it connects the smallest and largest scales: during the early stages of inflation, the region of space that now contains our Milky Way Galaxy was much smaller than an atom, so quantum effects could have been important.
But inflation predicts that these properties hardly change over time for a very simple reason: the local physical conditions that generate the quantum fluctuations hardly change over time either, since the inflating substance isn’t noticeably changing its density or other properties.
Figure 5.7: Schematic illustration of eternal inflation. For each volume of inflating substance (symbolized by a cube) that decays into a non-inflating Big Bang universe like ours, two other inflating volumes don’t decay, instead tripling their volume. The result is a never-ending process where the number of Big Bang universes increases as 1, 2, 4, etc., doubling at each step. So what we call our Big Bang (one of the flashes) isn’t the beginning of everything, but the end of inflation in our part of space.
for inflation to work in the first place, the inflating substance needs to expand faster than it decays, and this automatically makes the total amount of inflating stuff grow without limit.
We see that even our Big Bang is just a small part of something much grander, a treelike structure that’s still growing. In other words, what we’ve called our Big Bang wasn’t the ultimate beginning, but rather the end—of inflation in our part of space.
Indeed, inflation can do something even better, which I think is its most amazing trick of all: it can create an infinite volume inside a finite volume! Specifically, it can start with something smaller than an atom and create an infinite space inside of it, containing infinitely many galaxies, without affecting the exterior space.
Once inflation ends in a given region, the traditional Big Bang story from the last two chapters starts unfolding there, with a hot cosmic fusion reactor eventually cooling to form atoms, galaxies, and perhaps observers like us.
This idea can lead to one of Einstein’s core insights, immortalized by the slogan “It’s all relative”: that different observers can perceive space and time in different ways. In particular, simultaneity can be relative.
But can we really be sure that A happened before B, given that the two events are too far apart for light to have time to reach one from the other? Einstein’s answer is no.
The fact that space expands inside doesn’t necessarily increase the amount of room it all takes as seen from outside: remember that Einstein allows space to stretch and produce more volume from nothing, without taking it from someplace else.
Q: What caused our Big Bang? A: The repeated doubling in size of an explosive subatomic speck of inflating material. Q: Did our Big Bang happen at a single point? A: Almost: it began in a region of space much smaller than an atom. Q: Where in space did our Big Bang explosion happen? A: In that tiny region—but inflation stretched it out to about the size of a grapefruit growing so fast that the subsequent expansion made it larger than all the space that we see today. Q: How could our Big Bang create an infinite space in a finite time? A: Inflation produces an infinite number of galaxies by
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It explains the origins of these 0.002% fluctuations as quantum fluctuations stretched by inflation from microscopic to macroscopic scales, then amplified by gravity into today’s galaxies and cosmic large-scale structure.
Inflation theory says that our Universe grew much like a human baby: an accelerating growth phase, in which the size doubled at regular intervals, was followed by a more leisurely decelerating growth phase.
Yet the epistemological borderline between physics and metaphysics is defined by whether a theory is experimentally testable, not by whether it’s weird or involves unobservable entities.
Moreover, universes can overlap just as fog spheres can: just as someone 30 meters away on the field can see both you and regions that you can’t see, the universe of someone in a galaxy 5 billion light-years from us would contain both Earth and regions of space that lie outside of our Universe.
In the same way, detailed study of the smallest building blocks of nature suggests to us that, with enough energy, they could be rearranged in a way such that our Universe would operate differently—
our cosmic history has been a gravitational tug-of-war between dark matter trying to pull things together and dark energy trying to push them apart.
Supposedly, all nine dimensions started out curled up, and then in our patch of space, inflation stretched three of them out to astronomical size while leaving six of them tiny and invisible.
