(Pseudo-)Riemannian Geometry

On X

2019

Eric Weinstein

@ericweinstein

1/ Sabine Hossenfelder has done an impressive job collecting and rebutting the arguments for building a new particle accelerator. I find them partially convincing. Let me give the big reasons that no one ever mentions as they are not in her list.

1:13 AM · Mar 28, 2019

Sabine Hossenfelder

@skdh

Nonsense arguments for building a bigger particle collider that I am tired of hearing (The Ultimate Collection)

http://backreaction.blogspot.com/2019/03/nonsense-arguments-for-building-bigger.html

5:32 PM · Mar 27, 2019

Eric Weinstein

@ericweinstein

2/

I) The physics community gave us both the hydrogen bomb and the Einsteinian speed limit. Humans who acquire the Bomb never lose the ability to make them and they only get cheaper with technology. Further, the speed limit of 'c' traps us on three rocks: Earth, Moon and Mars.

1:13 AM · Mar 28, 2019

Eric Weinstein

@ericweinstein

3/

The combination of these twin gifts likely doom humanity over the long run unless we can, somehow, get around the speed of light 'c'. For that we will need to make physics a *top* priority unless we want to pretend we are going to become wise, colonize Titan, etc..etc..

1:13 AM · Mar 28, 2019

Eric Weinstein

@ericweinstein

4/

II) Theoretical physics practically created the modern economy:

Chemistry
Semiconductors/Transistors
World Wide Web
Electrification
Wireless
Nuclear Power/Weapons
Molecular Biology

These are not simply taxpayer dollars. They began as Physics Dollars. We are being absurd.

1:13 AM · Mar 28, 2019

Eric Weinstein

@ericweinstein

End/

III) We are at the end of this thread...but also at the end of what may be the last chapter of physics. The three main equations (Dirac, Einstein, Yang Mills) are provably, in some sense, the best possible. No one would walk out just before learning the end of our story.

1:13 AM · Mar 28, 2019

Calcifer

@StefanTarr

I) "We gotta get FTL"
II) "Might be unexpected bonuses"
III) *appeals to emotion*

1:26 AM · Mar 28, 2019

Eric Weinstein

@ericweinstein

I) Not exactly FTL...but that is fair from what I wrote. I was using shorthand. Guilty.

II) No. We have obligations to this community. We don't allow them to fully participate so they have economic rights that we are abusing. This is a foreign idea to most.

III) No: Meaning.

1:26 AM · Mar 28, 2019

Fourliquin

@Fourliquin

Curious... I just reviewed the 'Dirac Sea' issue last night.

@EricRWeinstein , could you 'lightly' outline the 'provably the best possible' claim? w/o definitions for dark matter/ energy/ fluid, etc. how can we be near the end of the 'story'? thx

1:41 AM · Mar 28, 2019

Eric Weinstein

@ericweinstein

Briefly: A) Dirac operator actually generates K-theory.

B) Einstein theory from Hilbert Lagrangian is simplest possible Lagrangian in pseudo-riemannian geometry (just scalar curvature).

C) YangMills Lagrangian simplest in Ehresmannian geometry (just norm square of curvature).

1:48 AM · Mar 28, 2019

Wyvern

@David2APatriot

Lord Kelvin called from the past.

1:20 AM · Mar 28, 2019

Eric Weinstein

@ericweinstein

You should answer his call because he clearly doesn’t have my number. He’s a few digits off.

1:50 AM · Mar 28, 2019

2021

Eric Weinstein

@ericweinstein

I subscribe to an unpopular position. Consider 3 kinds of 🌎:

A) Ones with no life or at least no life within striking distance of the source code (ToE).

B) Worlds that are on the verge of gaining the source code but are confined to a terrestrial surface.

C) Root level access.

2:15 AM · Jun 29, 2021

Misha Mansoor

@mishaperiphery

I see your point, but I would ask, wouldn’t there be a difference between basic recognition and categorization, and actively studying and interacting? One would assume that other species would still be resource and time limited, therefore forced to prioritize their attention?

9:03 PM · Jun 28, 2021

Eric Weinstein

@ericweinstein

Now, if you can jack into the cosmos as ‘Root’ it MAY facilitate stuff that’s unimaginable (e.g. dimension hacking) yet only one remaining big upgrade away from being able to fuse nuclei. Which is where we are now.

I’d guess all civilizations that are Root care about each other.

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

The following is pure speculation (Tutored by experience w/ GU):

I think we sent a signal to the cosmos in 1945 and then on Nov. 1, 1952. Fusing Nuclei is what you do JUST before you become root. If this is right, we let the cosmos know “Earth is root adjacent” w/o awareness.

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

Is there anyone in the cosmos listening? Perhaps not. But we are all acting as if living on a terrestrial surface with the ability to fuse nuclei is some totally normal thing due to <70 years of good luck. Which is insane.

Now what if I’m right in the above and the cosmos cares?

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

The idea of a newly space-time-faring unwise civilization with fresh root level access is a nightmare. And no one but no one on earth takes this seriously anymore. After 1952 fundamental physics went on progressing normally for ~20yrs. So after that it’s been~50yrs of stagnation.

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

In those ~50yrs we learned to stop worrying. About Fusion-weapons, interstellar travel, a cosmos that listens or even our ability to progress to the end. In 1984, physicists were talking about the end of physics without irony. They then failed, while failing to report failure.

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

So they told another story: “String theory didn’t fail!! It may take 100s of years to figure it out!” That is “If we String Theorists can’t make progress, a Theory of Everything is now far over the Horizon for everyone else.” But that’s not logically necessary. I say we’re close.

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

It makes sense to worry about *every* small boutique program: Lisi, Wolfram, Barbour, LQG, Tegmark, ConnesLott, Octonions, amplitudhedron, etc. Our science/defense establishment doesn’t seem to get this idea: after 50yrs of no progress it seems too abstract to practical men.

2:15 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

I learned from my buddy @SamHarrisOrg that he thought 👽 would be Millenia ahead of us. Look at Nov 1, 1952 from Nov 1 1902: you don’t have powered flight, know what relativity or the quantum is, know that neutrons exist, know about anti-matter, etc.

From ‘02, ‘52 IS millennia.

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

Well, we may or may not have a major update in our future. And if it unlocks dimension hacking, looking glass matter, VEV/potential hacking, multi-temporal pseudo-Riemannian metrics, Dark Chemisty, Dark Light, additional families, RaritaSchwinger fields, etc then we get upgraded.

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

And I believe all at once.

What does that mean? I honestly don’t know.

But Imagine you sent a chainsaw, a Bugatti, Ibogaine, “My-1st-Crisper”, and an F-18 to a badly behaved 5yr old child for a birthday present w a simple card: “Enjoy!” We’d worry specifically b/c immaturity.

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

That’s what NDT has most wrong. He thinks we are far behind anything that could visit us, but that ISN’T backed up by science. He’d have to explain why we aren’t “root adjacent” right now or that root buys us nothing. Well?

Think of the relationship of Iran to nukes for example.

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

Iran is now Nuke adjacent. And their facilities and scientists keep running into mysterious problems. Why? Surely not because Iran is too insignificant to her more advanced neighbors. That would mirror NDT’s argument. My argument is that root level access to nuclei *suffices*.

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

Am I saying “Aliens are here”? Of course not. But the “Root Adjacency Hypothesis” is not properly discussed almost anywhere. Which defies all explanation.

Perhaps everyone else is right & I’m wrong. Absolutely! But it’s common for the world to make a crazy dumb idea a consensus.

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

And I think NDT is enforcing a dangerous “Copernican” consensus that we are too insignificant to even monitor or visit, to go along with “We’ve had Nukes for 70 years without losing a city. I wouldn’t worry. What could possibly go wrong.”

This is just a human rationality flaw.🙏

2:16 AM · Jun 29, 2021

Eric Weinstein

@ericweinstein

Physics’ Overton Window.

We can talk about CRAZY stuff that’s irrelevant to our lives & never progresses: Boltzmann Brains, Many Worlds, String Theory Unification, AdS, Super-partners, etc.

We can’t talk about anything that COULD suddenly change everything. UAP, other TOEs, etc

5:34 PM · Jul 9, 2021

Eric Weinstein

@ericweinstein

My point isn’t at all that low probability topics are likely to change everything. It’s that we feel *safe* knowing certain crazy ideas always seem to lead nowhere. But we feel unsafe when we don’t know if what we’re looking at *could* surprise us by suddenly changing our world.

5:43 PM · Jul 9, 2021

Eric Weinstein

@ericweinstein

An example: In GU, relativity theory is recovered from the Observerse which is constructed around two separate spaces X and Y. Einstein’s Spacetime (a signature (1,3) 4-manifold with pseudo Riemannian metric) is recovered from observations of Y by X.

6:11 PM · Jul 9, 2021

Eric Weinstein

@ericweinstein

Another example. Some see spacetime as the commutative limit of a non-commutative manifold. That would be beyond relativity.

Others see topology changing operators that allow agents to change spacetime topologically. Again that would be beyond the usual relativity theory.

6:11 PM · Jul 9, 2021

Eric Weinstein

@ericweinstein

But in standard Relativity theory as an effective theory, I don’t think about FTL. Sorry.

6:11 PM · Jul 9, 2021

2024

Eric Weinstein

@ericweinstein

Q: Is a “Harald trumpet” expanding while resting on a shelf?

A: No. It just sorta sits there. Neither growing nor shrinking.

Q: Well then, is the cross-sectional circumference of its surface expanding as you travel down its tubing length from mouthpiece to bell?

A: Yes.

Q: Do mathematicians have an intrinsic way to describe this without having to artificially locate the trumpet in any particular place, or do they have to have it sit in a three dimensional space?

A: They use something called a Riemannian metric (or Pseudo-Riemannian metric) so they can study the trumpet as having a curved 2 dimensional surface without having to stick the trumpet artificially in a three dimensional space as in the picture.

Q: So is that the confusion? It’s just bad language?

A: Yes. The Universe is not expanding. The size of its cross-sections as measured by the intrinsic Riemannian volume, is what is expanding as you travel down its tube from the Big Bang (mouthpiece) towards the present (the bell).

Q: How can that be?? I was just watching Professor X and he said “The universe…”

A: I don’t know what to tell you. Sorry.

12:47 AM · Nov 30, 2024

Physics In History

@PhysInHistory

If the Universe is Expanding, What is it Expanding Into? ✍️

5:01 PM · Nov 29, 2024

2025

Eric Weinstein

@ericweinstein

@HeathHimself Shhh. Have you noticed that you are like close to the only one who caught that? Explain that!

He just made that up. And no one noticed or bothered to check. And it is ALWAYS like this and has been for 40 years. I have no explanation. It’s completely beyond my comprehension.

11:14 AM · May 28, 2025

Eric Weinstein

@ericweinstein

That’s just it. I keep saying that the community is pretending. But it is actually lying.

Pretending there is no crisis.

Pretending that I am not in and out of physics departments all the time.

Pretending GU makes no predictions. Like in section 11.3 on pages 52 and 53 for example.

And we can quietly be here discussing this while Sean says he has read the draft in front of over half a million people that GU doesn’t make any predictions within it. Confident that no one will actually speak out with page numbers and screen shots and say “You do realize you are lying? Either about having read the draft or about the explicit predictions within it.”

Imagine you send a paper for peer review and you get Sean Carroll as your anonymous reviewer. He says he read it and there is nothing of interest. No Lagrangians. No predictions.

It has been *exactly* like this for 40 years. No one can believe it until they experience it. It has no explanation.

3:02 PM · May 28, 2025

Eric Weinstein

@ericweinstein

@codingquark @HeathHimself GU is both the most anti-interesting theory in history as well as the only theory that cannot be steelmanned.

3:05 PM · May 28, 2025

Eric Weinstein

@ericweinstein

Right? But it is always exactly like this.

Everything works backwards from the narrative. And the narrative is that our main job is to quantize a spin 2 field to get quantum gravity. And that our leading theory is thus String Theory / M-Theory and everything else is pointless because we are too many orders of magnitude away from the Planck Scale and there is no guarantee of UV completeness.

Which is absurd. It’s a story. It’s not reality.

7:59 PM · May 28, 2025

Eric Weinstein

@ericweinstein

@niederhaus17566 @HeathHimself If GU were right, that narrative would be wrong. And that narrative is the entire world to those who have devoted their lives to it for >40 years.

So GU must be madness. Which it is not.

8:00 PM · May 28, 2025

Eric Weinstein

@ericweinstein

Not that you said anything wrong, but let me advance a different perspective. Sean’s work is a an undisclosed *direct* competitor to GU. Attached in a screenshot are the first three lines of his 1990 abstract.

Let me put them in the language of GU.

“The Chern-Simons Lagrangian has been studied previously in (2+1)-dimensional spacetime, where it is both gauge and Lorentz invariant. We the authors believe that outside of this special dimension, there is a fundamental trade off where we must either violate Ehresmannian Bundle Geometry (Gauge Theory of Particle Theory) or the pointwise Lorentz Invariance of Riemannian Geometry (Einstein’s General theory of Relativity). It appears to the authors that the right way to construct an analogous term in 3+1 dimensions is to create a Chern Simons-like term which couples the dual electromagnetic tensor to an artificial external four-vector which has no supporting evidence or motivation and violates both Einstein’s Special and General theories of Relativity. If we take this four-vector to be fixed, the term is gauge invariant but not Lorentz invariant throwing out one of the two pillars of modern physics. We do it anyway, because we believe the above mentioned tradeoff precludes any other approach.”

I personally knew Sean’s co-author Roman Jackiw decently well on this topic as he was at MIT. This was his perspective.

Why is Geometric Unity called Geometric Unity? Because we believe you can sacrifice neither geometry or the field will come to a standstill. It’s right there in the name. You need to have both Riemannian and Ehressmanian geometry to combine Gravity and Particle theory respectively.

Sean’s work is the DIRECT competitor of this GU theory. And GU sacrificed neither.

1:47 PM · May 29, 2025

Eric Weinstein

@ericweinstein

Odd right? He looked into a camera and said he read a draft that has a chapter called Lagrangians and said there were no lagrangians. He saw the tables of predictions and said there were no predictions. Etc.

I mean…that was incredible! There are over half a million views on that video too.

1:50 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@Areness_ @HeathHimself We are in too different games:

Sean is trying to win “The Vibe”.

I am trying to get the physics right.

Both are in play.

And I don’t initiate these fights. I just return fire when forced.

1:53 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@matthiasgisslar @HeathHimself Zero accountability. But no one is really reading each others papers which is why this is possible. He wouldn’t be able to do this in the world of 60 years ago. So he wouldn’t try.

The Vibe is all he cares about.

1:56 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@matthiasgisslar @HeathHimself BTW I am taking him at his word that he read the paper so he saw the table of contents and he read chapters 9, 10, 11 which are all about Lagrangians, Interactions and Predictions.

1:57 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@HeathHimself From @grok. Not that Grok is necessarily right or wrong. But interesting none the less.

2:02 PM · May 29, 2025

Eric Weinstein

@ericweinstein

It’s an interesting question. For 40 years the answer has been no. Precisely, no one capable without an obvious personal ax to grind will do so in public in a collegial fashion if steelmanning is expected and criticism is constructive.

Only trolls, stalkers, non-experts and people willing to lie about factual matters will do so in public. This is a consequence of the fact that the dominant 40+ year narrative is totally contradicted by GU. They correctly know what is on the line. And who it would enrage.

2:08 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@NeophyteOne @matthiasgisslar @HeathHimself Ha! Ok. Optics is king.

2:09 PM · May 29, 2025

Eric Weinstein

@ericweinstein

Well…first of all:

He is quite smart.

He knows a lot.

He isn’t stringy.

But his opinion isn’t respected so much as he is on the front line protecting much bigger people he doesn’t care to contradict.

Said differently, he is protecting his masters at all costs. And his reward is his “situation”. He finally has tenure. And he likely deserved it somewhere earlier. He does yeomans work and does it well. And they finally gave him something in his 50s. They treated him badly in my opinion.

2:13 PM · May 29, 2025

Eric Weinstein

@ericweinstein

Ah. It has two features that general Ehressmanian geometry generally lacks:

I) A distinguished Choice of Connection (The Levi Civita connection and the connections induced from it on associated bundles).

II) Tensor Decomposition coming from the lack of structure groups auxiliary to those of the tangent bundles.

So actually the specific sub geometry of (pseudo)-Riemannian geometry is an exchange of Gauge Symmetry and field content freedom for these two attributes.

Except in totally exotic cases. Like the one in which we oddly happen to live…but I digress.

2:27 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@IsZomg @HeathHimself @seanmcarroll Or he read it! Because even 45 seconds gets you to the table of contents. Here is page 3.

This is essentially what all physics people do. And I have no explanation for how this is possible.

2:30 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@Areness_ @HeathHimself *two

2:34 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@Elvhammer @Areness_ @HeathHimself It’s so…cheap. Drama. I hate it.

2:51 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@growthesque @AISpaceIdeas @matthiasgisslar @HeathHimself That sounds so sophisticated.

Except you forget what subject we are talking about. https://t.co/d6oIfrSeR5

4:54 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@growthesque @AISpaceIdeas @matthiasgisslar @HeathHimself Thanks for the clarification. But this is for the source code of the universe. It’s not the French literature department.

5:41 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@BMcGrewvy @HeathHimself He's quite smart and good at many things. He knows a lot about many different areas. He's a marvelous explainer. He has some creative ideas as well.

Making progress and being courageous and an ethical colleague are difficult for *many* people in a brutal field.

10:17 PM · May 29, 2025

Eric Weinstein

@ericweinstein

@williamhbhamill @Areness_ @HeathHimself Oh well. It was a good ride. And I would have gotten away with it too…if it weren’t for you meddeling kids.

10:40 PM · May 29, 2025

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