Bundles

This article is a stub. You can help us by editing this page and expanding it.

2009

Eric Weinstein

@EricRWeinstein

Meanwhile, as for the Euler Class, we often meet it as a *top* class for the tangent bundle thereby prohibiting seeing it as a square root.

2:41 AM · Sep 4, 2009

Eric Weinstein

@EricRWeinstein

Additionally, Vilfredo Pareto's move towards ordinal utility can be seen as imparting a non-abelian bundle structure to welfare.

4:33 AM · Oct 5, 2009

2010

Eric Weinstein

@EricRWeinstein

Note to Geometers: A depiction of a fiber bundle is shared by both the US Senate seal and the Fascist Flag.

Odd, that.

8:20 PM · Jan 2, 2010

Eric Weinstein

@EricRWeinstein

GU: Don't conflate Spin 0 fields valued in the adjoint bundle / non-linear sigma models w/ higgs at LHC. Nature uses Spin 0 alternatively.

6:21 AM · Jan 27, 2010

Eric Weinstein

@EricRWeinstein

The definition of "tangent bundle" is a good example of how mathematical precision makes even the visual incomprehensible.

1:43 PM · Mar 13, 2010

Eric Weinstein

@EricRWeinstein

The definition of 'line bundle' is a good example of how mathematical precision makes even the incomprehensible physics 'anomaly' visual.

1:48 PM · Mar 13, 2010

2018

Eric Weinstein

@EricRWeinstein

@mkealz @jisheppard So far as we know, the universe we live in is generated by a principal fiber bundle. This is essentially the only visual mature example we have to show you one without equations. I didn’t explain it. I pointed to it.

If someone I trusted said these words to me, I’d invest in it.

5:42 PM · Nov 20, 2018

2019

Eric Weinstein

@EricRWeinstein

@GTAlien @SamHarrisOrg Love Toronto. I’d do a gig there in a heartbeat if I could bundle it with a trip to @Perimeter and/or @FieldsInstitute to geek out.

1:43 PM · Feb 6, 2019

Eric Weinstein

@EricRWeinstein

My personal & overly condensed view of mathematics and physics in the 20th century would be summarized like this.

Mathematics began as a stool on the three legs of Algebra, Calculus, and Geometry where the last appeared to many to be the weakest leg. It turned out otherwise.

5:53 PM · Nov 23, 2019

Eric Weinstein

@EricRWeinstein

Repeatedly we find that any important problem from math or physics which we consider to be outside geometry/topology has a hidden geometrical nature to it. And there are only so many times you fall for that before you start to see geometry absolutely everywhere.

5:53 PM · Nov 23, 2019

Eric Weinstein

@EricRWeinstein

As for Weinberg, he is one of three people I can make the case for as our “Greatest Living Physicist”. I’ve met him. But he still has big bets which are undecided (e.g. asymptotic safety). Witten is somehow even smarter but less accomplished in standard predictive theory. But...

5:53 PM · Nov 23, 2019

Eric Weinstein

@EricRWeinstein

I would say the one who awes me most is...CN Yang. I don’t understand why I never hear his name as candidate. He has at least 3 of the greatest achievements: chirality for the weak force (w/ Lee), non-Abelian maxwell theory (w/ Mills), and the bundle revolution (w/ Simons/Wu).

5:53 PM · Nov 23, 2019

2020

Eric Weinstein

@EricRWeinstein

Melanie, you‘re one of my favorite stable wave collections co-propagating along the base-space of this twisted chiral Spinor bundle we call reality.

It seems a crime to waste our time discussing “Many-Worlds” or “String Theory” over the geometric beauty of our existence. Thanks!

5:10 PM · Jan 25, 2020

Eric Weinstein

@EricRWeinstein

Gauge Symmetry is essentially the study of horizontal cross-sections to those circles pictured in the GIF under *variable* amounts of rotation of the circles themselves.

Don’t know why no one seems to say things like that...but that’s what it is.

7:15 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

As for the “definition” given...

1st: The GIF pictured is a bundle, but NOT a vector bundle. It is called a Principal Bundle. If you want a vector bundle think Möbius band.

2nd: The horizontal cross section I mentioned are used to create the differential operators they mention.

7:24 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

3rd: The “functions” which get differentiated by the operators are called “Sections”. They are not pictured here.

Hope this helps. But you are looking at an actual gauge theoretic structure. This is the real thing and not an analogy. That’s why I use it to explain this all. 🙏

7:24 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@katoi In fact it is. This bundle pictured is the 720 degree double cover of the 360 degree regular rotation bundle.

This is the “Spin double cover of the orthonormal frame bundle of the sphere.”

If you will.

7:26 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@Chrisfalchen That concept of a bundle structure is our most fundamental picture of reality.

7:27 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@natanlidukhover Circles are 1-dimensional manifolds depicted in 2-dimensional planes. Mathematicians count dimensions differently.

7:29 PM · Nov 14, 2020

Eric Weinstein

@EricRWeinstein

@NoGodOnlyReason Because it is likely the most familiar of any designs that one can put on a round sphere. It’s merely an aid to show that there is a regular two dimensional sphere in this three dimensional mix.

7:51 PM · Nov 14, 2020

2022

Eric Weinstein

@EricRWeinstein

Huh. Let’s see…

Standard Model: Fiber Bundle

General Relativity: Fiber Bundle

Our universe: Derived from SM+GR

So…uh…yeah. So far. Crazy right?

Weird flex, but it checked out.

1:02 AM · Jan 7, 2022

Eric Weinstein

@EricRWeinstein

In essence this is happening every time “you” move. When you see spectators doing “The Wave” the spectators are the medium. They don’t move with the wave.

You are a wave. You excite a totally different portion of the medium wherever you go. That medium is called a vector bundle.

5:41 PM · Mar 11, 2022

Eric Weinstein

@EricRWeinstein

@CreatedInTheD The atom moves through space. But as a wave. If a wave moves through a small oil slick, the oil slick doesn’t move with the wave. It briefly rises & falls in place when excited. The medium doesn’t move. The thing that moves is the atom. The thing that stays is the Vector bundle.

5:25 PM · Mar 12, 2022

Eric Weinstein

@EricRWeinstein

A surprisingly deep simple question.

There appears to be a mysterious circle at every point in spacetime which physicists accept but cannot explain. And, every type of particle is endowed w/ a mysterious complementary ⭕️. The spacetime ⭕️ rotates the particle’s sympathetically.

9:05 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

The charge on the particle is the gearing ratio of the spacetime ⭕️ with the particle’s ⭕️. It’s like a bicycle where the pedal gear⚙️ is the spacetime ⭕️ and the particle ⭕️ is the rear wheel ⚙️. Positive charge is clockwise drive. Negative charge is counterclockwise.

9:05 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

An electrically neutral particle is like a particle not having a chain hooked up between the pedal and wheel. So a +2/3 Up Quark will be driven around 2 times clockwise for every three times an electron goes counter-clockwise with charge -1=-3/3.

That may sound weird. So be it.

9:05 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

@TEMguru That U(1) is the circle at every point in space time. It’s minimal gauge coupling via a character is the chain between the gears. C’mon.

10:03 PM · Jul 28, 2022

Eric Weinstein

@EricRWeinstein

Uh. That’s *exactly* how it’s done. There is a principal U(1) (circle) bundle. But it isn’t the U(1) that you refer to which is weak-hypercharge. And the analogy makes perfect sense based on internal quantum number

\chi_n:U(1) —> Aut(C)

before tensoring with the spinor bundles.

2:48 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

Let me just say that there is a community of academics who throw a lot of nasty anti-collegial scientific shade that just isn’t scientifically accurate. Don’t know what to do about that. These people try to cast a spell of Fear Uncertainty and Doubt.

I stand by what I say here.

2:53 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 Let me help you then. You have a group:

G=SU(3) x SU(2) x U(1)

And a homomorphism:

rho: G —> U(16)

So

Spin(1,3) x G —> SL(2,C) x U(16)

represents on C^2 tensor C^16, and its conjugate, to give one generation of the Fermions (with Right handed neutrinos assumed). With me?

3:11 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 Now the U(1) ⭕️ of the original description lives inside the SU(2) x U(1) via bundle reduction or symmetry breaking as you see fit. The gearing ratio I mentioned is simply the integer indexing all irreducible representations of U(1) which are all 1-dimensional characters. Clear?

3:14 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 Every U(1) character can be visualized as two circular gears connected by a chain with some integer ratio of the circumferences. Negative integer representations are ones with the chain having a half twist. The trivial representation has no chain at all.

Hope that helps.

3:19 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 @FrankWilczek Not true at all. @FrankWilczek correctly points out that there is something super compelling about SO(10) Grand Unified Theory. Both space time and internal representations are spinorial if this is true.

I just don’t know from what position you’re speaking so authoritatively.

3:24 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@sluitel34 @FrankWilczek This should be in any book that discusses the standard model via groups, representations, bundles, etc.

3:25 AM · Jul 29, 2022

Eric Weinstein

@EricRWeinstein

@WKCosmo @PasseVivant It’s a decent first answer for dynamics as in Hamiltonian systems. But there are a lot of places where symmetries intrude where that simple answer seems less convincing. Principal bundle structure groups for example. Or discrete symmetries. Etc. Etc.

10:03 PM · Aug 4, 2022

Eric Weinstein

@EricRWeinstein

@WKCosmo @PasseVivant Uh, no. Is “Structure group of a principal bundle” or “Discrete group” buzzwords to you? That doesn’t sound like a physicist to me.

Sorry. I’ll move on. I thought this was a Professional conversation. Be well. Bye.

10:18 PM · Aug 5, 2022

Eric Weinstein

@EricRWeinstein

According to physics, you’re a wave. A conscious wave.

As a conscious wave, you were curious as a child. The most natural question for a conscious wave is probably “If I’m but a conscious wave, in what medium am I an excitation?”

Yet most waves never ask this question.

Why? 🙏

11:13 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

The short answer is “You appear to be a wave in a structure called a Fiber Bundle.” of which many have never heard.

I talk about Fiber Bundles a lot because they appear to underlie all of existence, and am thus very confused by physicists who don’t discuss them. It’s so odd.

11:28 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

For years this has been the leading image of a fiber bundle on Google Image search. This I take as proof that the human race is slightly insane: Our leading image of the underlying medium of existence itself looks to me like a bandaid/plaster that has been ripped off a hairy arm.

11:28 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

We created this picture so that you would have a picture of what a “Fiber Bundle with Gauge Potential” actually is. So that everyone could see in what type of structure they actually vibrate.

So far as I know, this is the only animation of its kind:

11:39 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

Would love to get back to explaining things about the true wonder of our existence.

If you are fascinated by Entanglement, Quantum Weirdness, Relativity Theory, The Multiverse, String Theory etc, most of you would be better served studying fiber bundles:

11:48 PM · Aug 28, 2022

Eric Weinstein

@EricRWeinstein

@McLuhanStates @LueElizondo There is a lot of loose talk about dimensionality. Keep in mind that I have zero direct evidence of the phenomena. So this is wildly premature.

My interest here is that GU replaces one manifold with two in a bundle structure and adds BOTH temporal and spatial dimensions.

11:24 PM · Oct 24, 2022

Eric Weinstein

@EricRWeinstein

Q5: So let’s see. Inflation is a field like temperature. But a field in a fiber bundle over ♾-dimensional path spaces of loops of preferences/prices valued in non-commuting groups leading to non linearities not addressed by economists? What about actual geography!”

A5: Fair. 👍

4:05 PM · Nov 6, 2022

2024

Eric Weinstein

@EricRWeinstein

Buckaroo?

Ok. But….Also a layperson’s term for flatland viewing an ambient space for an embedded/immersed sub-manifold. Also for a Kaluza Klein theory or a general fiber bundle projection. Or for worm holes and non trivial topology. Etc

In other words, it means almost nothing.

6:55 PM · Feb 15, 2024

Curt Jaimungal

@TOEwithCurt

I'm confused. This lecture doesn't negate the geometric foundations of GR. Einstein differentiates between how gravity and electromagnetism relate to the structure of space, all the while pointing to his ultimate goal of unification. As for the rest of the original article linked, I'm unsure how the quotes from Einstein support the author's title. GR is indeed a geometric theory; however, Einstein's viewpoint was that its geometric nature doesn't singularly distinguish it from the broader domain of physics, where geometry has always played a fundamental role. If anything, Einstein is saying not to confuse the map with the territory.

6:39 PM · Mar 27, 2024

Eric Weinstein

@EricRWeinstein

He is correctly anticipating the Simons-Yang discovery of the “Wu Yang dictionary”.

Maxwell became Yang Mills Yang Mills became Simons Yang. Simons Yang became the Wu Yang Dictionary. Wu Yang was (except for one entry) was Ehressmann fiber bundle geometry.

Think of metric geometry, fiber geometry and symplectic geometry as the geometry of symmetric metric 2-tensors, fiber bundle connections and anti-symmetric 2 tensors respectively.

6:52 PM · Mar 27, 2024

Eric Weinstein

@EricRWeinstein

[Note for Curt: This is the whole point of Geometric Unity. They are three geometries. Which are all one geometry, and that is only possible in the rarest of circumstances. Which we are in oddly.

Metric Geometry: General Relativity GR Fiber Geometry: Standard Model SM Symplectic Geometry: Hamiltonian Quantization of the SM. ]

6:53 PM · Mar 27, 2024