Greetings to all readers and subscribers, and special greetings to the paid subscribers!

Here’s a very early draft of Chapter 9 of my new book “*Irrational mechanics: Narrative sketch of a futurist science & a new religion*” (2024).

Note that this and the others draft chapters are very concise. At this point I only want to put down the things I want to say, one after another. Later on, when the full draft for early readers is complete, I’ll worry about style and all that.

## 9 - Zooming in and out (I)

Zooming in an image reveals more detail, but at times you need to filter detail out to see things clearly. That is, you need to zoom out. You must have seen those images with hidden text that you can read only when you move away from the image or squint your eyes to blur the image. So you have to zoom in to see certain things, but you have to zoom out to see other things.

When you study physical reality, it’s more or less the same thing: you need to zoom in and out. When scientists talk about the renormalization group [Chapter 11], they mean zooming out.

But let’s zoom in first and take a look at the microphysics of 2024, both mainstream and respectably speculative (as opposed to wildly, lunatically speculative like my irrational mechanics).

Matter is made of atoms. Some materials like water are made of molecules (groups of atoms bound together). A molecule of water consists of two hydrogen atoms and one oxygen atom bound together and acting as a whole. Other materials can be described directly in terms of atoms and subatomic elementary particles.

Zooming down beyond molecular and atomic scales we find subatomic elementary particles of matter like quarks and electrons. The protons and the neutrons that we find in atomic nuclei are made of quarks bound together.

These little things don’t behave according to our intuition of how things should behave. Quantum mechanics [Herbert 1985, Susskind 2014], our best mathematical description of matter at small scales, doesn’t lend itself to intuitive visualization. This is not surprising, since we evolved to stay alive and reproduce in a human-sized world where quantum effects are not immediately apparent. Simply put, we evolved to escape hungry predators, not angry quarks.

But don’t think that quantum mechanics doesn’t apply to our human-sized world. It does. Quantum mechanics seems to be fundamental and applicable to everything. According to Scott Aaronson, “quantum mechanics is the operating system that other physical theories run on as application software” [Aaronson 2013]. Quantum effects are often washed out at human-sized scales, but the behavior of quantum matter like superconductors and superfluids (and arguably brains) depends strongly on quantum effects.

Now I should explain quantum mechanics to you, but I can’t do so because I don’t understand it. Who does? “Nobody does,” said Richard Feynman [Feynman 2006]. But he suggested ways to understand it better.

Quantum mechanics is not deterministic but probabilistic, and the behavior of quantum probabilities seems weird to us. The probability for something to happen is the square of the length of a complex number called probability amplitude. Being a complex number, an amplitude has a phase besides a length.

If something can happen in alternative ways and it is possible to find out which way it happened, then the probability is the sum of the probabilities. For example if a particle can reach a point following two alternative paths with certain probabilities, and it is possible to find out which path has been followed, then the probability for the particle to reach the point is the sum of the probabilities, just like our intuition expects.

But if it is not possible to find out which way is followed, then it is the amplitude that is the sum of the amplitudes. The phases interfere with each other, and the probability is not the sum of the probabilities.

Note that in this description I didn’t use human observers. It doesn’t matter if we are looking. What matters is if information on which path has been followed is recorded in some or some other physical system. If there is no information then the paths are indistinguishable and the amplitudes sum, but if there is information then the paths are distinguishable and the probabilities sum.

Seems weird? Yes, it does. This thing with probabilities and amplitudes is “the central conceptual point” of quantum mechanics [Aaronson 2013]. It is often called a mystery, but why should the universe compute probabilities like our intuition expects?

In Feynman’s “path integral” formulation of quantum mechanics [Feynman 2010], the amplitude for a physical process is calculated by summing up (integrating) the amplitudes for all ways the process can happen. For example, the amplitude for a particle to move from here to there in a certain time is found by integrating over all paths that the particle could take. It turns out that most paths cancel each other by interference, and only certain paths contribute significantly to the path integral. These paths are close to the classical path that is followed when quantum effects can be ignored.

The formulations of quantum mechanics given in most textbooks, with the Schrödinger equation, operators in Hilbert space and all that, can be derived from the path integral approach. The properties of quantum particles are often quantized (can assume only discrete values). This is the case of spin.

Light (or more precisely electromagnetic radiation) is made of particles called photons. The electromagnetic force (aka interaction) between charged particles (e.g. electrons) can be pictured as an exchange of photons that are emitted and absorbed by the particles. Think of two persons (electrons) exchanging a ball (a photon). Other photon-like particles are associated with other forces. For example, gluons are associated with the strong force between quarks.

So, besides elementary particles of matter, there are elementary particles of force. The elementary particles of matter and force are called, respectively, fermions and bosons. In certain units, fermions have half integer spin and bosons have integer spin.

The best mathematical descriptions of interacting elementary particles that we have found so far are built on top of quantum mechanics and called quantum field theories. A quantum field theory called quantum electrodynamics [Feynman 2006, Close 2011, Kane 2017] describes the interactions of charged particles and photons. Quantum electrodynamics is part of a more general quantum field theory of electroweak interactions. Similarly, quantum chromodynamics [Kane 2017] describes the interactions of quarks and gluons.

Calculations in quantum field theories are done with the help of Feynman diagrams that represent possible ways for certain input particles to interact and produce certain output particles. We can calculate an amplitude for each diagram, then sum up all the amplitudes to calculate the amplitude and the probability of the output. A problem is that there’s an infinite number of Feynman diagrams for given input/output. For example a particle can emit and reabsorb another particle, which in turn can emit and reabsorb another one and so forth. But it is often the case that only the simplest diagrams give a significant contribution.

What I have (very) roughly sketched is called the standard model. It is mathematically complicated, often inelegant and messy, and at times inconsistent, but it gets the job done and is rightly considered one of the triumphs of 20th century physics. Scientists are striving to devise a unified treatment of particles and fields that would include gravitation [Weinberg 1994].

The concepts of scale and energy are related: we need higher and higher energies to probe smaller and smaller scales. For example, visible light photons carry more energy than microwave photons, and therefore can resolve smaller scales. This is why elementary particle physics is often called high energy physics.

Experimenting with higher and higher energies, scientists hope to devise quantum field theories that cover all scales all the way down to the Planck scale, beyond which quantum field theories break down.