(Pseudo-)Riemannian Geometry
On X
2019
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.
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
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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.
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..
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.
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.
I) "We gotta get FTL"
II) "Might be unexpected bonuses"
III) *appeals to emotion*
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.
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
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).
You should answer his call because he clearly doesnât have my number. Heâs a few digits off.
2021
I subscribe to an unpopular position. Consider 3 kinds of đ:
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.
I see your point, but I would ask, wouldnât 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?
Now, if you can jack into the cosmos as âRootâ it MAY facilitate stuff thatâs unimaginable (e.g. dimension hacking) yet only one remaining big upgrade away from being able to fuse nuclei. Which is where we are now.
Iâd guess all civilizations that are Root care about each other.
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 âEarth is root adjacentâ w/o awareness.
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 Iâm right in the above and the cosmos cares?
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 itâs been~50yrs of stagnation.
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.
So they told another story: âString theory didnât fail!! It may take 100s of years to figure it out!â That is âIf we String Theorists canât make progress, a Theory of Everything is now far over the Horizon for everyone else.â But thatâs not logically necessary. I say weâre close.
It makes sense to worry about *every* small boutique program: Lisi, Wolfram, Barbour, LQG, Tegmark, ConnesLott, Octonions, amplitudhedron, etc. Our science/defense establishment doesnât seem to get this idea: after 50yrs of no progress it seems too abstract to practical men.
I learned from my buddy @SamHarrisOrg that he thought đ˝ would be Millenia ahead of us. Look at Nov 1, 1952 from Nov 1 1902: you donât have powered flight, know what relativity or the quantum is, know that neutrons exist, know about anti-matter, etc.
From â02, â52 IS millennia.
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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.
And I believe all at once.
What does that mean? I honestly donât know.
But Imagine you sent a chainsaw, a Bugatti, Ibogaine, âMy-1st-Crisperâ, and an F-18 to a badly behaved 5yr old child for a birthday present w a simple card: âEnjoy!â Weâd worry specifically b/c immaturity.
Thatâs what NDT has most wrong. He thinks we are far behind anything that could visit us, but that ISNâT backed up by science. Heâd have to explain why we arenât âroot adjacentâ right now or that root buys us nothing. Well?
Think of the relationship of Iran to nukes for example.
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 NDTâs argument. My argument is that root level access to nuclei *suffices*.
Am I saying âAliens are hereâ? Of course not. But the âRoot Adjacency Hypothesisâ is not properly discussed almost anywhere. Which defies all explanation.
Perhaps everyone else is right & Iâm wrong. Absolutely! But itâs common for the world to make a crazy dumb idea a consensus.
And I think NDT is enforcing a dangerous âCopernicanâ consensus that we are too insignificant to even monitor or visit, to go along with âWeâve had Nukes for 70 years without losing a city. I wouldnât worry. What could possibly go wrong.â
This is just a human rationality flaw.đ
Physicsâ Overton Window.
We can talk about CRAZY stuff thatâs irrelevant to our lives & never progresses: Boltzmann Brains, Many Worlds, String Theory Unification, AdS, Super-partners, etc.
We canât talk about anything that COULD suddenly change everything. UAP, other TOEs, etc
My point isnât at all that low probability topics are likely to change everything. Itâs that we feel *safe* knowing certain crazy ideas always seem to lead nowhere. But we feel unsafe when we donât know if what weâre looking at *could* surprise us by suddenly changing our world.
An example: In GU, relativity theory is recovered from the Observerse which is constructed around two separate spaces X and Y. Einsteinâs Spacetime (a signature (1,3) 4-manifold with pseudo Riemannian metric) is recovered from observations of Y by X.
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.
But in standard Relativity theory as an effective theory, I donât think about FTL. Sorry.
2024
Q: Is a âHarald trumpetâ 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? Itâs 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 âThe universeâŚâ
A: I donât know what to tell you. Sorry.
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If the Universe is Expanding, What is it Expanding Into? âď¸
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2025
@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. Itâs completely beyond my comprehension.
Thatâs 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 doesnât make any predictions within it. Confident that no one will actually speak out with page numbers and screen shots and say âYou do realize you are lying? Either about having read the draft or about the explicit predictions within it.â
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.
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@codingquark @HeathHimself GU is both the most anti-interesting theory in history as well as the only theory that cannot be steelmanned.
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. Itâs a story. Itâs not reality.
@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.
Not that you said anything wrong, but let me advance a different perspective. Seanâs 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.
âThe 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 (Einsteinâs 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 Einsteinâs 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.â
I personally knew Seanâs 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. Itâs right there in the name. You need to have both Riemannian and Ehressmanian geometry to combine Gravity and Particle theory respectively.
Seanâs work is the DIRECT competitor of this GU theory. And GU sacrificed neither.
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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 meanâŚthat was incredible! There are over half a million views on that video too.
@Areness_ @HeathHimself We are in too different games:
Sean is trying to win âThe Vibeâ.
I am trying to get the physics right.
Both are in play.
And I donât initiate these fights. I just return fire when forced.
@matthiasgisslar @HeathHimself Zero accountability. But no one is really reading each others papers which is why this is possible. He wouldnât be able to do this in the world of 60 years ago. So he wouldnât try.
The Vibe is all he cares about.
@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.
@HeathHimself From @grok. Not that Grok is necessarily right or wrong. But interesting none the less.
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Itâs 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.
@NeophyteOne @matthiasgisslar @HeathHimself Ha! Ok. Optics is king.
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WellâŚfirst of all:
He is quite smart.
He knows a lot.
He isnât stringy.
But his opinion isnât respected so much as he is on the front line protecting much bigger people he doesnât care to contradict.
Said differently, he is protecting his masters at all costs. And his reward is his âsituationâ. 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.
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 liveâŚbut I digress.
@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.
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@Areness_ @HeathHimself *two
@Elvhammer @Areness_ @HeathHimself Itâs soâŚcheap. Drama. I hate it.
@growthesque @AISpaceIdeas @matthiasgisslar @HeathHimself That sounds so sophisticated.
Except you forget what subject we are talking about. https://t.co/d6oIfrSeR5
@growthesque @AISpaceIdeas @matthiasgisslar @HeathHimself Thanks for the clarification. But this is for the source code of the universe. Itâs not the French literature department.
@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.
@williamhbhamill @Areness_ @HeathHimself Oh well. It was a good ride. And I would have gotten away with it tooâŚif it werenât for you meddeling kids.
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