Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

by Max Tegmark

because eternal inflation enables everything that can happen to actually happen:

In other words, inflation is a process converting potentiality into reality.

gravity makes things clumpy and interesting on smaller scales, and inflation makes things diverse and interesting on larger scales.

there’s been a striking shift in the scientific community during the past decade, where multiverses have gone from having lunatic-fringe status to being discussed openly at physics conferences and in peer-reviewed papers.

This would also give many numbers we’ve measured in physics a new meaning: they’re not telling us something fundamental about physical reality, but merely something about our location in it, forming part of our cosmic postal code.

illustrates how these three—protons, neutrons and electrons—are arranged much like a miniature solar system with electrons orbiting the compact ball of protons and neutrons that we call the atomic nucleus.

Whereas the Earth is kept in its orbit around the Sun by the attractive gravitational force between them, the electrons are kept in the atoms by the electrical force that attracts them to the protons (electrons have negative charge, protons have positive charge, and opposite charges attract).

An atom is simply named according to the number of protons it contains (1 = hydrogen, 79 = gold, etc.),

The laws of economics tell us that atoms are expensive if they’re rare, and the laws of physics tell us that they’re rare if they require unusually high temperatures to make. Putting this together tells us that if atoms could talk, the priciest ones would tell the best stories.

Gold, on the other hand, is produced when a star dies in a supernova explosion so violent and rare that it, during a fraction of a second, releases about as much energy as all the other stars in our observable Universe combined. No wonder making gold eluded the alchemists.

collide these smallest known building blocks together really hard and check if they break apart. This procedure has been tried with ever-larger particle colliders, but electrons still show no sign of being made of anything smaller despite having been smashed at 99.999999999% of the speed of light

Colliding protons, on the other hand, has revealed that both they and neutrons are made of smaller particles known as up quarks and down quarks.

since quarks are building blocks a full three levels down in the Lego hierarchy (Figure 7.1), you don’t need to be Sherlock Holmes to start wondering whether there are even more levels that we’re failing to discover simply because we don’t have enough energy in our particle accelerators.

If he’d play atom Lego by setting them on fire, immersing them in acid, or using some alternative method to rearrange their atoms, he’d be doing chemistry. If he’d play nucleon Legos by rearranging their neutrons and protons into different kinds of atoms, he’d be doing nuclear physics. If he’d smash his pieces together near the speed of light to rearrange the energy, momentum, charge, etc., of their neutrons, protons and electrons into new particles, he’d be doing particle physics.

Electrons orbiting around a nucleus of protons and neutrons; the number of protons in an atom determines its name (1 = hydrogen, 2 = helium, etc.)

(by increasing frequency, we call them radio waves, microwaves, infrared, red, orange, yellow, green, blue, violet, ultraviolet, x-rays, gamma rays), but they’re all forms of light and they’re all made of photons. The more photons an object emits each second, the brighter it looks.

the Sun can radiate light energy only one photon at a time, and the typical energy kT available for making a photon falls far short of the amount of energy hf required to make even a single gamma ray.

This means that the electron orbit isn’t a circle, but a death spiral (Figure 7.5): after about 100,000 orbits, the electron has crashed into the proton and the hydrogen atom has collapsed, at the ripe old age of about 0.02 nanoseconds.1

microscopic particles violate the laws of classical physics.

So are microscopic particles above the law? No, they obey a different law: Schrödinger’s.

That was the good news, for which Bohr won a Nobel Prize (as did most of the others I mention in this chapter). The bad news was that Bohr’s model didn’t work for any atoms other than hydrogen, except if all but one of their electrons were removed.

This means that, just as a flute, the Sun vibrates only with certain special frequencies.1 In his 1924 Ph.D. thesis, de Broglie applied this reasoning to waves going around the hydrogen atom instead of the Sun, and obtained the exact same frequencies and energies as the Bohr model had predicted.

This is the essence of the Heisenberg uncertainty principle: Werner Heisenberg showed that if you confine something to a small region of space, then it will have lots of random momentum, which tends to make it spread out and become less confined.

This means that if a hydrogen atom tries to collapse as in Figure 7.5 (left) by sucking the electron into the proton, then the increasingly confined electron will get enough momentum and speed to come flying back out to a higher orbit again.

In contrast, quantum mechanics predicts that each particle will act like a wave and pass through both slits in a quantum superposition, interfere with itself, and form an interference pattern

Eventually this quantum physics gave us the laser, the transistor, the integrated circuit, computers and smartphones.

1. The state is described not by positions and velocities of the particles, but by a wavefunction. 2. The change of this state over time is described not by Newton’s or Einstein’s laws, but by the Schrödinger equation.

Specifically, if something is not being observed, then its wavefunction changes according to the Schrödinger equation, but if it is being observed, then its wavefunction collapses so that you find the object only in one place.

Schrödinger’s cat is trapped in a box with a cyanide canister that’s opened if a single radioactive atom decays. After a while, the atom will be in a superposition of decayed and not decayed, which causes the entire cat to be in a superposition of dead and alive. In other words, a seemingly innocent microsuperposition involving a single atom is amplified over time into a macrosuperposition where a cat containing octillions of particles is in two states at once.

At worst, it was inconsistent, since the wavefunction of our whole Universe would never collapse from the viewpoint of someone in a parallel universe who could never observe us.

Where are these parallel universes? Whereas the Level I and Level II kinds are far away in our good old three-dimensional space, the Level III ones can be right here as far as these three dimensions are concerned, but separated from us in what mathematicians call Hilbert space, an abstract space with infinitely many dimensions where the wavefunction lives.3

When I later met Bryce, he told me he’d at first complained to Hugh Everett, saying that he liked his math, but was really bothered by the gut feeling that he just didn’t feel like he was constantly splitting into parallel versions of himself. He told me that Everett had responded with a question: “Do you feel like you’re orbiting the Sun at thirty kilometers per second?” “Touché!” Bryce had exclaimed,

In other words, causal physics will produce the illusion of randomness from your subjective viewpoint in any circumstance where you’re being cloned.

Now I was convinced that consciousness had nothing to do with it, since even a single particle could do the trick: a single photon bouncing off of an object had the same effect as if a person observed

it. I realized that quantum observation isn’t about consciousness, but simply about the transfer of information.

Finally I understood why we never see macroscopic objects in two places at once even if they’re in two places at once: it’s not because they’re b...

As quantum-computing pioneer David Deutsch puts it, “Quantum computers share information with huge numbers of versions of themselves throughout the multiverse,” and can get answers faster here in our Universe by, in a sense, getting help from these other versions.

A quantum computer can be thought of as the ultimate parallel computer, using the Level III multiverse as a computational resource and in a certain limited sense running different parallel calculations in parallel universes.

They suggested that our brains (or at least parts of them) are quantum computers, and that this is a key to understanding consciousness.

Feynman had emphasized that quantum mechanics splits our Universe into two parts: the object under consideration and everything else (referred to as the environment). However, I felt that an important piece of the quantum puzzle was missing here: your mind.

The fact that neurons decohere much faster than they can process information means that if the complex neuron-firing patterns in your brain have anything to do with consciousness, then decoherence in the brain will prevent you from experiencing weird superpositions.

out of all the states that quantum mechanics allows for large objects, these conventional states are the ones that are most robust to decoherence, and therefore the ones that survive. It’s a bit like why deserts tend to have cacti rather than roses: they’re the most robust to the environment.

In summary, here’s how I informally think about this: the entropy of an object decreases while you look at it and increases while you don’t.

The object’s entropy can’t decrease unless it interacts with the subject. 2. The object’s entropy can’t increase unless it interacts with the environment.

In Douglas Adams’s science-fiction spoof The Hitchhiker’s Guide to the Galaxy, there’s an “Infinite Improbability Drive” that makes you experience extremely unlikely events. Although such a device sounds like pure science fiction, it isn’t: the quantum machine-gun effectively acts like one!

Copenhagen interpretation is better thought of as the Copenhagen approximation: even though the wavefunction probably doesn’t collapse, it’s a very useful approximation to do the calculations as if it does collapse when you make an observation.

The color brown doesn’t exist in the external reality, but only in your internal reality: it’s simply what you perceive when seeing dim orange light against a darker background.

the challenge for physics is deriving the consensus reality from the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality.

But if you divide one of these last two numbers by the other, then you get something truly fundamental: the proton is about 1836.15267 more massive than the electron.1 1836.15267 is a pure number, just as π or , in the sense that it’s a quantity that doesn’t involve any human units of measurement such as grams, meters, seconds or volts. Why is it close to 1836? Why not 2013? Why not 42? The short answer is that we don’t know, but that we think we can in principle calculate this number and every other fundamental constant of nature ever measured from just the 32 numbers listed in Table 10.1.

I suspect that most alien civilizations in distant solar systems have also invented a name or symbol for star even if they don’t communicate using sounds.