Here is the paragraph:
>If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Spacetime is a **pseudo-Riemannian manifold** *M*, endowed with a **metric tensor** and governed by geometrical laws. (ii) Over *M* is a **vector bundle** *X* with a **non-abelian gauge group** *G*. (iii) **Fermions** are sections of **(Ŝ +⊗VR)⊕(Ŝ ⊗VR¯)(Ŝ+⊗VR)⊕(Ŝ⊗VR¯)**. ***R*** and ***R*****¯** are not **isomorphic**; their failure to be **isomorphic** explains why the light fermions are light and presumably has its origins in representation difference Δ in some underlying theory. All of this must be supplemented with the understanding that the geometrical laws obeyed by the **metric tensor**, the **gauge fields**, and the **fermions** are to be interpreted in quantum mechanical terms.
>
>Edward Witten, “Physics and Geometry”
According to Eric Weinstein (who I know is a controversial figure, but let’s leave that aside for now), this is the most beautiful and important paragraph written in the English language. You can watch him talk about it [here](https://youtu.be/vdW9XDBuxjU?t=3079) or take a deep dive into his [Wiki](https://theportal.wiki/wiki/Graph,_Wall,_Tome).
Could someone (1) literally translate the paragraph so a layman can grasp the gist of it, switching the specific jargon **in bold** with simplified plain English translations? Just assume I have no formal education in math or physics, so feel free to edit the flow of the paragraph for clarity’s sake. For example, something like:
>If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Spacetime is a ~~pseudo-Riemannian manifold~~ ***flexible*** ***3-dimension space*** *M*, endowed with a ~~metric tensor~~ **composite list of contingent quantities** and governed by geometrical laws… etc.
And (2) briefly explain the importance of this paragraph in the big picture of physics?
In: Physics
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PhD student in theoretical physics here. This paragraph describes what the whole universe really is and what everything in the universe is fundamentally made of. It touches on a lot of very advanced ideas in mathematics, but I’ll do my best to unpack it. Warning: It’ll be long.
**(i)** Age-old question: What does the whole universe look like if you stand “outside” of it? Is it like a flat plane that extends in all directions forever? Is it like a ball, where if you walk in one direction for a while, you’ll return to your original position? Or is it like a large twisted pretzel with holes? In mathematics, we call these different shapes, flat or curved, **manifolds**.
To describe a “pretzel” or a “flat plane”, we need to say where the shape is “rounded” or “curved”, like a blind man touching an elephant, telling his friend where the round belly is and where the trunk is sticking out. We call this description a **metric tensor** on the manifold.
What this point tells us is that our universe has all sorts of bumps and troughs here and there, and everything in the universe—the Sun, the Moon, galaxies—move around according to where the bumps and troughs are, like a small ant on a pretzel trying to walk in a “straight line” but inadvertently walking in circles. In other words, the Earth goes in circles around the Sun (and stars around galaxies) because it follows **geometrical laws** of “how to walk on an irregular bumpy manifold”.
It turns out that clocks run at different speeds depending on where they’re placed in the universe, whether it’s at the bottom of a trough or on flat ground. Physicists figured out that that’s because space isn’t the only thing getting curved and twisted in our universe; time is too. Normal run-of-the-mill manifolds don’t do the job anymore. This is when **pseudo-Riemannian manifolds** come in to describe our universe, where both time and space are twisted with each other, into curved **spacetime**. Don’t even try to imagine what that looks like; we can’t either. All this is described in more detail in this [Introduction to General Relativity](https://en.wikipedia.org/wiki/Introduction_to_general_relativity).
**(ii)** Another age-old question: Magnets, how do they work? Also, what makes rocks stick together and not fall apart? Physicists have figured out that these forces are due to these things called **fields**, which are invisible but permeate everywhere in the entire universe. Take the electromagnetic field as an example. It is everywhere. Closer to a magnet, where the field is stronger, a second magnet gets attracted to the first one very quickly; farther from the magnet, where the field is weaker, the second magnet barely moves at all.
Remember from (i) that our universe is a curved shape called a manifold? Well, the electromagnetic field (and other fields for other forces) is everywhere on this manifold. In mathematics, we call that a **fibre bundle over the manifold**. (Pardon the strange name. If you try to imagine little hairs on a pretzel indicating how strong the field is at each point on the pretzel, it ends up looking like a bundle of fibres.)
Now we need to know how the electromagnetic field makes the magnet move around, how it makes your microwave cook your food, and how light comes out of a lightning. All of this is described by a very special kind of theory called **gauge theory**. What you need to know is that every gauge theory comes with a mathematical structure called a **group**. The simpler the group, the simpler the the interaction between the corresponding force and matter is, and vice versa. The simplest group is an **Abelian group**, which is what describes the electromagnetic field.
The electromagnetic field also keeps rocks together and strong. But if you chop a rock into little pieces, you get to the atom, made of neutrons, protons, and electrons. Neutrons and protons are in turn made of even smaller particles called quarks. What keeps the quarks together in a neutron or a proton is the strong nuclear force, caused by the **gluon field**. Neutrons and protons can also turn into each other, emitting radiation that makes some cancer treatments possible. This is due to the weak nuclear force, caused by the **W and Z boson fields**.
These fields are also described by gauge theories, so they’re called **gauge fields**, but their interaction with matter is so complicated that their corresponding groups are **non-Abelian groups**, which is as complicated as you can get when it comes to groups.
**(iii)** One final age-old question: What’s stuff made of? What’s the smallest bit of matter? As I said before, chopping things down to the smallest pieces gives you electrons and quarks. These particles (and a few others) all belong to a class of particles called **fermions**. The special thing about fermions is that every fermion has a left-handed and a right-handed version, just like gloves—they look alike, but are mirror reflections of each other.
The gluon field doesn’t care whether the fermion is left or right-handed. It doesn’t discriminate. (Be like gluon.) You might think the electromagnetic field and the W and Z boson fields are good guys too, but no, they like to interact more with the left-handed fermions than the right-handed ones. This is what the formula means.
The correct formula is (Ŝ+⊗VR)⊕(Ŝ−⊗VR̃). (Unfortunately, Reddit doesn’t support subscripts.) It basically says the left-handed fermion Ŝ+ interacts with all the gauge fields in this way (VR), while the right-handed fermion Ŝ− interacts with the gauge fields in a different way (VR̃). It is important that VR and VR̃ are **not isomorphic**, which is just a snobby way of saying “they’re different”.
We know that the electron, along with another fermion called the neutrino, is lighter than the quarks. We don’t yet know why that is the case, but every new idea physicists have come up with over the years involves the difference between the way gauge fields interact with left-handed and right-handed fermions (**representation difference**). If one of those ideas turns out to be correct, then it is the **underlying theory** that we all dream about.
Finally, if all of the above is not complicated enough, God plays a joke on us by making everything **quantum mechanical**. In short, this means that the same particle can be in several different places at the same time, and particles are randomly popping in and out of existence everywhere, all the time.
**Personal thoughts:** The paragraph is certainly very concise, mostly because it takes entire textbooks to truly describe the mathematical terms in each of the three bullet points. It is also very beautiful, because it tells you in precise mathematical terms what you’d need if your job were to create another universe. However, it’s like describing an elaborate wedding cake by listing all its ingredients.
“The most beautiful paragraph in physics” is a bit of a stretch. Sure, it encapsulates what our universe is, deep down. But it doesn’t capture any of the emergent phenomena—how these particles come together into complex atoms and molecules, how atoms form beautiful crystals and rocks, how rocks form planets, how stars and dust form galaxies, how too much stuff makes a black hole… Physics is a vast subject with countless interesting questions to study, and “what is the fundamental structure of the universe” is just one of them.
**TL;DR:** Our universe has curved spacetime in which matter, made of very small particles called fermions, interacts through forces controlled by gauge fields. The interaction is different for left-handed and right-handed fermions. The paragraph is beautiful because it tells us what blueprint God had in mind when creating our universe.
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Okay, let me give it a try. Note: I am not a physicist or mathematician, but i have read a bit of differential geometry. So this is probably wrong in subtle ways. Cool? Cool! I will try i) and ii)
For simplicity, imagine our universe being flat like a piece of paper. And do it in a very specific way: we live on a line and the second dimension is time. so if you move along your 1d position universe, this is represented by a curve on the 2d plane.
You can bend this paper-universe, but not fold, rip or tear it. The sides of the paper might be glued together, for example to form a doughnut. i) and ii) together mean, that you can look at a very small part of your bent piece of paper and pretend it to be flat. you can do that simply by pressing down with your finger to straighten it out. In this flat part (Which might be very tiny) you can measure distances and angles with your normal geometrical tools. Most likely you can’t do it everywhere at the same time (e.g. on a doughnut). So for big distances, measuring distances and angles can become complicated, because you need to flatten the parts differently to straighten them out.
Physically this means that for slow objects which are close together, everything looks normal, so you can for example measure distances and speed easily. for very fast objects, the object position changes a lot in a small amount of time which in our 2d paper universe means that it has a large distance and you might get into trouble trying to flatten out the universe enough to be able to measure distances properly.
This has consequences, for example you will have difficulties to compare distances of objects that are fast with distances of objects that are slow. To be able to create a theory, we need a way to compare behaviors at different points (i can observe something at my current speed/position/time. How would it look like at a different speed/position/time?). Luckily, there is a tool to do this and it is called a gauge-group. But it behaves in unintuitive ways.
so the important part here is the existence of these tools because they allow the description in a way that is not depending on where you are, when you are and how fast you are. you can develop a theory at a certain point and the gauge-group will tell you how it will look like somewhere else.
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Picture two Parallel straight lines, an inch apart. One of them is time as we perceive it, the other is the actual time in the universe. Space and time are related and effect each other. Now imagine a massive celestial body was outside our solar system, that’s gravity was strong enough to to pull us in. The universal line starts to curve. We perceive time the same, in the straight line. However, our time will not line up with the other line anymore, and the the measurements between the two change, they go from one inch to another size. The maths to work out the new distance follows the same rules as geometry.
Now, picture that in three dimensions, where you won’t have lines, you’ll have 3D shapes that as you approach or go through will change the distance between the two lines.
It’s essentially an over complicated version of how the planet with high gravity effected time in interstellar. The interesting part is that it follows the same rules as geometry.
Eric is hell bent on trying to make this sound like revolutionary science. When in reality it’s more of an “ah, interesting”.
For the record, I believe he’s been refusing to publish this for decades, and refused to speak about it publicly because of the “danger to humanity”.
Keep in mind Eric works for a private think tank in California funded by some very questionable people, who had close ties to Jeffrey Epstein. He goes on Joe Rogan and acts like that frustrated academic striving for a better tomorrow but in reality he is a pawn of the “legacy” media he criticises, and has quite effectively capitalised on Rogans nativity by brown nosing him.
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1) Space is flexible with time, in a specific squishy way. Call it “M” because we’ll refer to it later. The squishiness of space and time follows a specific set of rules for 3D manipuation, called a “pseudo-Riemannian manifold”. The way it squishes is called a tensor, and it follows geometrical laws. There are a bunch of formulas involved in that manipulation, but it means you can convert between time and space, that stuff in space affects time, and stuff in time affects space.
2) There are a bunch of values well call “X” that can modify space and time. They represent forces and fields. They follow special ordering rules, and form a gauge group. You can use these values X to modify the squishy thing in the first point. These things represent energy and motion. They have specific ordering requirements, and they cannot be easily reversed. As an ELI5 of that if you have 3 and you subtract 3 you don’t always get 0; if you want to get zero again you have to do extra steps. These explain the relationship of how you can squish space and time around to change their shapes.
3) Subatomic particles that make up matter, called fermions, that all meet a general pattern. This things make up mass. The pattern formula has multiple solutions, and includes both a positive side and negative side. Even though it has two sides, they’re not opposites from each other like you would have +3 and -3 that are equal and map to each other, the two opposite sides are not isomorphic. These things still have some big questions to be answered, but they explain how you can manipulate matter and space. (There is another set, called bozons, that have a similar relationship with energy).
So an ELI5 rewrite:
> We can see three fundamental things about the universe: (1) Space and time are squishy according to a set of rules. We have math that predicts it. (2) Squishing space and time depends on ordering and a second set of rules, and any squishes generally cannot be easily undone. We have math for predicting this, too. (3) Subatomic particles another set of rules that build all matter, but we only have most of the math to model it, not quite all of it for a complete model.
> Putting those three topics together gives all our current rules for space, time, energy, motion, and mass, and conversions between them.
Using those general words describes the relationship of all the various conversions and systems we know in physics. The next picture in the video shows a clip of a wall that depicts a bunch of the relationships. Some are well known, like how E=mc^2 is the relationship between energy and matter and explains things like why converting matter into energy in an atomic bomb creates huge amounts of energy. Others explain relationships with space and distance, and relationships with time. They all inter-relate, something that relates with space and distance and time also must relate with motion and force.
I don’t think it’s particularly beautiful, but I can see why he likes it as a short summary of our current physics models.
Imagine that I gave you a map, drawn on paper, and some basic geometry tools, like a protractor and a pair of compasses. Now suppose I told you that any question about the world, anything at all, could be answered by making geometric measurements on the map. That would be pretty amazing, right?
Well, this paragraph is saying that that’s basically how it is. All of the fundamental forces of nature can be explained by geometry. The map is at least four dimensional, and Pythagoras’s theorem doesn’t apply the way you think it does, and the algebra is horrendously complicated, but it’s all geometry.
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