Physics/Math Jargon Q&A


#1

There’s a lot of physics & math jargon used in this ARG, especially on multiverse-75. I’m not going to claim to be an expert in all things physics, but I am a few years into a PhD in particle physics and can do my best to explain the jargon. It may just add to the experience, or there may be some patterns/info hidden in the jargon.

Leave any questions below, and I’ll do my best to explain concepts (and copy the answers into this main post). If anyone else has a background in physics/math, please help me out by answering questions below too!

Answered questions:

Abelian groups

Abelian groups, same as above. This is so above me.

First off, a group is a mathematical term for a set of elements that combine together under some operation. There are a few requirements for a set to be a group: you need to have an identity (something that doesn’t change another element in the set), you need to have inverses (every element has an inverse that combine together to form the identity), and the group must be closed (when you combine any two elements in the group, the result is also an element in the group). It also needs something called associativity but that isn’t as important for you to know - basically, it has to do with the order of operations and parantheses, saying that (1+2)+3 = 1+(2+3).

An example of this would be the integers {…, -2, -1, 0, 1, 2, …} with the operation of “addition”. For some integer a, a+0 = a. The inverse is -a, since a + (-a) = 0. And if you add any two integers together, you get another integer, so a + b = c, where a and b are any integers, and then c must also be an integer.

Now, an abelian group is one with a particular extra property: commutativity. Meaning, in our example, a + b = b + a. This is true of most groups that most people would be familiar with. One of the simplest examples of a non-abelian group is the group of 2x2 matrices (under matrix multiplication). For a matrix A and a matrix B, AB is not the same as BA in general.

Computationalism

Question: What even is ‘computationalism’?
Answer by @Orioncrush here.
Followup by @Dolnor here.
Wiki: Computational theory of mind

Manifolds

Manifolds? what are those?

Official answer from @bcatrek here

Partial answer by @TooSoonForNow here.

More from @solarparty here

Multiverse (highly recommended read!)

Amazing writeup from @bcatrek here

Particle accelerator

What does a particle accelerator do? And why is that useful?

A particle accelerator is used to, well, accelerate particles! It is used to probe interactions between charged particles (electrons & protons, mainly). Linear particle accelerators speed up particles in a straight line and typically direct them to strike some target, while circular particle accelerators (e.g. the LHC at CERN) speed up particles in a circular path before colliding them with another beam sped up in the opposite direction. In general, to probe the properties of fundamental particles, you need very energetic collisions to see the desired signatures, which is why we need these special particle accelerators in the first place to speed these particles up to very near the speed of light.

Because we speed up the particles to such high energies, the resulting collisions produce an incredible amount of reactions and particles, so lots of different types of detectors are set up around the collision sites to collect data on the types and properties of the products of the collision. Using some extremely fancy physics/math and computation, these results are analyzed to try to measure the properties of, for example, intermediate particles that we cannot detect directly. These intermediate particles usually decay in very particular ways that lead to certain “signatures” in the resulting particles that we can look for. This is exactly how we found the Higgs boson at the LHC a few years ago!

Quantum Electrodynamics

Quantum Electrodynamics-- WHAT? Can we start with the basics, what even are electrodynamics? And then how does the ‘quantum’ prefix tie in?

See another answer from @bcatrek here

Electrodynamics is the classical theory that describes how charged particles interact. It goes through all the fun stuff like charged particles interacting with electric and magnetic fields, and how electric and magnetic fields interact with each other. It also explains how electromagnetic waves propagate through the vacuum of space! It’s a very robust theory, and you can even work special relativity into it very easily.

Quantum field theory is basically the theory behind the Standard Model, saying that there are certain particles in nature that cannot be split into constituent parts. It models these fundamental particles as being excitations of some underlying field - something that permeates the entire universe. So an electron is a particular excitation of the electron field. A common visualization is the field is some flat surface, and an electron is a little spike jutting up from that surface.

Quantum Electrodynamics (QED) takes the ideas of electrodynamics and unifies them with quantum field theory and special relativity. It is the underpinning of all interactions involving electrically charged particles and photons. It is one of the most successful physical theories ever, leading to the most precise agreement between theory and experiment in physics history.

There is a similar but, in many aspects, more complicated theory regarding the interactions of quarks called Quantum Chromodynamics (QCD).

Solar wind / cosmic rays

Follow-up to the radiation belts section.

Solar wind refers to a stream of charged particles - primarily protons, electrons, and alpha particles (a.k.a. helium nuclei, 2 protons + 2 neutrons) - that is steadily discharged from the Sun. It is a form of heat given off by the intense temperatures in the Sun’s corona. The heat gives these particles, which exist freely (i.e. outside of atoms) in the plasma of the Sun, enough energy to overcome the Sun’s escape velocity and fly off into space. However, they are still continually slowed by the Sun’s gravity as they travel outward, so the solar wind is faster on average the closer you are to the Sun. At Earth, the average speed of the solar wind particles is 468 km/s (a little over 1 million mph).

Cosmic rays are a form of high energy radiation, mainly in the form of protons and alpha particles, that originate outside the Solar System. The sources of these particles are, unsurprisingly, some of the most energetically intense phenomena in the universe, including supernovae and active galactic nuclei. It wouldn’t really be right to talk about an “average” speed since they cover a much wider range than solar wind, but suffice to say these particles can get extremely, absurdly fast.

We have all of these particles constantly bombarding us, so you might wonder how we’re all alive in the first place. And the answer is, primarily, Earth’s trusty magnetic field. It does wonders to protect us from these dangerous particles by simply deflecting them (or trapping them in the Van Allen belts). However, many particles still get through, and they generally hit our atmosphere and then react with the air molecules before ever reaching us. Even that doesn’t fully protect us though, so we are constantly exposed to the remaining radiation that makes it through all of Earth’s defenses. Luckily, the amount that ends up reaching us is small enough to not really matter.

Van Allen radiation belt

Question: What’s the ‘Van Allen radiation belt’? and why are the conditions of it something you’d want to recreate? and I guess I’m curious as to how they could possibly recreate one of the van allen radiation belts in their laboratory.

See a followup comment to my explanation from @jojo here

The Van Allen radiation belts are two regions around Earth caused by the planet’s magnetic field. The magnetic field traps energetic charged particles particles (electrons, protons) from the cosmos, solar wind, and reactions in the atmosphere in these two regions - the inner and outer belts (separate Q&A entry forthcoming for these sources of particles).

The trapping occurs because magnetic fields cause a force on charged particles as they move, so even though the details are somewhat more complicated, it’s similar to how we use gravity to “trap” satellites in orbit around Earth.
The reason there are two belts is because electrons and protons have the exact same charge, but the proton is roughly 1800 times more massive than the electron, so their typical orbital radius will be different. The inner belt is primarily protons, while the outer is primarily electrons.

Getting into speculative territory for me here, but I don’t think you can really recreate the exact circumstances of the Van Allen belt in a laboratory. However, we do use magnetic fields to manipulate charged particles all the time. In fact, this is one of the main ideas in CERN’s Large Hadron Collider. We use magnetic fields to “trap” the protons in a particular circular path while speeding them up to near the speed of light. More on this in the particle accelerator section.

Unanswered questions:

Supersymmetry

No question about this yet, but I’d like to write up about it when I have time later.

Edit 6/18 13:16 EST: Everything answered so far save for Supersymmetry, since that one will take some time/effort for me to write up. Stay tuned (and keep asking questions if you have any!).


#2

OK so here are the things I don’t understand/want to learn more about!

  • What’s the ‘Van Allen radiation belt’? and why are the conditions of it something you’d want to recreate?

  • What even is ‘computationalism’?

  • Quantum Electrodynamics-- WHAT? Can we start with the basics, what even are electrodynamics? And then how does the ‘quantum’ prefix tie in?

  • What does a particle accelerator do? And why is that useful?

  • Manifolds? what are those?

  • Abelian groups, same as above. This is so above me.

  • How do ‘boundaries’ play into this? I thought I knew what a boundary was, it’s a dividing line between two spaces, right? But now I’m confused.


#3

I guess I’m curious as to how they could possibly recreate one of the van allen radiation belts in their laboratory.

Is it possible?


#4

Computationalism is a school of thought that in the most basic terms says that all of reality is computation.

An analogy would be:
Your brain is the CPU of a system which runs the computation that is your being. Your mind, the quirks and knowledge that stuff is the program being computed.

Something to note Dr Hillary Putnam is a very important person in Computationalism.


#5

I can field a couple of these. The Van Allen radiation belts are areas of space near Earth in which high-energy particles like protons (hydrogen nuclei) are sort of trapped by the Earth’s magnetic field and accumulate. They form discrete bands which reflect the shape of the geomagnetic field, sort of like an onion.


#6

First answer is up (Van Allen). More forthcoming. I tried to address your question in there too, @boozecoyote.


#7

I am going to put this here rather than edit my first post to avoid confusion…


#8

A manifold is a surface and I believe (better math nerds than I please feel free to correct) that it is important that it is a closed surface, like a ball. I’m going to screw this up majorly, but the idea here is that we can describe a surface by how many “holes” are in it. A common example is that a doughnut and a coffee cup are the same shape, because each have exactly one hole in an otherwise uninterrupted surface. A 3d letter B or number 8 would be 2-manifold, because you could morph from one to the other without adding or removing any holes.


#9

Make sure you are not co-joining “Functionalism” and “Computationalism” as they are separate ideas. Computationalism has been around for 60 years but Functionalism has only been around for 40 years.

"Computationalism is the view that the functional organization of the brain is computational, or that neural states are computational states.

Functionalism is the view that the mind is the “functional organization” of the brain, or any other system that is functionally equivalent to the brain.

Putnam’s main example of a description of functional organization is the machine table of a Turing machine. For him, a functional organization is a set of functional states with their functional relations, where a functional state is defined by its causal relations to inputs, outputs, and other functional states (under normal conditions). Thus, under Putnam’s notion of functional organization, our two formulations of functionalism are equivalent.

The problem with this view is that it turns everything into a computer. For instance, some cosmologists study the evolution of galaxies using cellular automata. According to the received view of software implementation, this turns galaxies into hardware running the relevant cellular automata programs. If satisfying computational descriptions is sufficient for implementing them in the sense in which ordinary computers execute their programs, then everything is a computer executing its computational descriptions. This is not only counterintuitive—it also trivializes the notion of computer as well as the analogy at the origin of computational functionalism. If the mind is the software of the brain in the sense in which certain cellular automata are the software of galaxies, then the analogy between minds and computers becomes an analogy between minds and everything else."

http://www.umsl.edu/~piccininig/Computational_Functionalism.htm


#10

This is how they could make their own van alan. (recent news)


#11

I think I’ve got all of these answered (with help from @Orioncrush and @Dolnor for the Computationalism one) except for manifolds which I don’t know much about myself! Anything in the answers you’d like me to elaborate on?

Edit: Oh, I’m not sure what the meaning behind “boundary” could be. In physics/math, lots of theories make use of “boundary equations,” where the boundaries there are usually interfaces between two surfaces (e.g. the boundary of a charged metal sphere would be its surface, and the electric/magnetic fields produced by the sphere must have certain properties on that boundary).


#12

this is all making me feel very nerdy :woman_scientist:

I won’t pretend to totally understand everything you’ve posted, but I feel like I have a better grip on it now.


#13

I am very interested in the concept of solar wind (actually in all space weather) - we are coming to a point where as we develop more digital and EM dependent tech, we have more and more interactions with certain events from space. I wonder if certain space weather events not only could be harnessed (power, communication, etc) but might disrupt what they are working on.

With the Van Allen belt - what if you can create a barrier as described here - http://www.nature.com/nature/journal/v515/n7528/abs/nature13956.html orrrr flip side, what if you need to get through these barriers?

what are specific questions about solar wind? That term is actually a very general often misused term (kinda like tidal waves are not linked to tides :slight_smile:


#14

also for Van Allen - I believe a third belt sometimes exists - http://adsabs.harvard.edu/abs/2017EGUGA..1910776M and https://www.nasa.gov/mission_pages/rbsp/news/third-belt.html


#15

I’m trying to investigate the barcode right now, I’ll try to do justice to solar wind later and let you know so you can look it over!


#16

QED = Quantum Electrodynamics

ELI5: Theory of radiation such as radiowaves, microwaves, and lightwaves. Describes how light and matter interact with each other. First successful marriage of Theory of Relativity and Quantum Mechanics.

I will reproduce part of Wikipedia here. I have a PhD in Quantum Physics so I can vouch for the following information to be correct:

(1) Precursor to QED = Electromagnetism (https://en.wikipedia.org/wiki/Maxwell’s_equations)
Maxwell’s equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. They underpin all electric, optical and radio technologies, including power generation, electric motors, wireless communication, cameras, televisions, computers etc. Maxwell’s equations describe how electric and magnetic fields are generated by charges, currents, and changes of each other. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations, and first proposed that light is an electromagnetic phenomenon.

(2) Actual QED (https://en.wikipedia.org/wiki/Quantum_electrodynamics)
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.


#17

As we build these definitions - I am keeping Quantum Mechanics in the back of my mind and how they link to these topics (such as https://en.wikipedia.org/wiki/Sub-Riemannian_manifold) so glad you are bringing in some quantum background. I have had a gut feeling quantum principles would be important all the way back when we started with Radio (EM waves) on Project WT

As a PS - with color, radio and so on, has anyone made a chart of what EM wavelengths we have encountered thus far in waking titan?


#18

That Dr. Putnam won’t leave us alone!

I found a definition on a Quora question that helped me understand manifolds better:

Let me start this with an example.
Example 1:
Suppose there’s a road around the equator. You travel around it in a car. As far as you can see, the road goes on forever. But after travelling long enough, you realize that you came back to the place you started!
Locally, it looks like a straight line even though it is not!

Example 2:
Extend example 1 to the whole of earth. When you look around, earth looks like an infinite plane. But, actually, it is the surface of a sphere. Hence, locally it looks like an infinite plane.

This concept is called local topological equivalence. The infinite line and the circle (equator) look similar when we look at them closely enough.

The infinite line is called ℝ1 (Every point is defined by 1 real number).
Infinite plane is called ℝ2 (Every point is define by n real numbers). This can be extended to get ℝn.

Any geometric object which is locally topologically equivalent to ℝn is called a manifold.

It seems that manifolds help describe and model curved space-time and other aspects of the universe with more normal Euclidean geometry.

I also found this article on the use of manifolds in procedural generation to be “able to output variations that smoothly transition between states”. I know it’s probably just coincidence, but I love coincidences like that.


#19

Manifolds are nothing but geometrical objects. R0 would be a zero-dimensional object (i.e. a dot, with no extension in any direction). R1 is just a straight line, which can be modelled by the the real-number line, i.e. all numbers you can think of.

If you make a dot at point 0, then extending a line from that dot infinitely in the left direction, and then the same to the right - you get a line with infinite length. This is R1. The set of real numbers.

Next step: 2 dimensions. The most basic 2D shape is a plane. Think x-y coordinate system that you learned in high-school. As you only needed one number to locate any point in R1 (for example, the number -5 indicates 5 steps to the left), in 2D you need two numbers. You need a number going left/right and then another number going up/down. So you get a (x,y) coordinate. This is R2.

Next step: 3 dimensions. This is space as we know it. Ordinary space with left/right, and up/down and also front/back. You need three numbers to locate a point in 3D space, so you get a (x,y,z) coordinate, where z indicates the number of steps in the front/back direction.

Now, MANIFOLDS is just an extension of ordinary space into ANY dimensions. In mathematics and physics, it is very normal to have 4, 5, or even 11 dimensional spaces to work with. Sometimes these dimensions are merely mathematical constructs (Einstein’s theory of relativity is a good example, in which time is the fourth dimension) and sometimes these dimensions are to be interpreted as actual spatial dimensions (String theory with its 11 dimensions is a good example of that).


#20

Edited a link to this in the manifolds section and moved it to “answered.” Thanks!