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The '''Theory of Geometric Unity''' is an attempt by Eric Weinstein to produce a unified field theory by recovering the different, seemingly incompatible geometries of fundamental physics from a general structure with minimal assumptions. This structure is a mapping from a manifold | The '''Theory of Geometric Unity''' is an attempt by Eric Weinstein to produce a unified field theory by recovering the different, seemingly incompatible geometries of fundamental physics from a general structure with minimal assumptions. This structure is a mapping from a manifold <math>X^4</math> to a manifold <math>Y</math> called the [[Observerse|observerse]], which replaces Einstein's spacetime. For the latest updates on the theory, visit '''https://geometricunity.org/'''. | ||
This page currently summarizes information surrounding the theory | This page currently summarizes information surrounding the theory. | ||
__TOC__ | __TOC__ | ||
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== Concepts == | == Concepts == | ||
=== Observerse === | === Observerse === | ||
The '''observerse''' is the central mathematical object in the [[Theory of Geometric Unity]]. It is a mapping from a four-dimensional manifold | The '''observerse''' is the central mathematical object in the [[Theory of Geometric Unity]]. It is a mapping from a four-dimensional manifold <math>X^4</math> to a manifold <math>Y</math>, which replaces Einstein's spacetime. There are four different constructions of the observerse: exogenous, bundle-theoretic, endogenous, and tautological. Each generates a possible Geometric Unity theory. | ||
Read more at [[Observerse|observerse]]. | Read more at [[Observerse|observerse]]. | ||
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=== Problem Nr. 1: Einstein's Theory of General Relativity is not a proper Gauge Theory === | === Problem Nr. 1: Einstein's Theory of General Relativity is not a proper Gauge Theory === | ||
* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection | * From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection <math>\nabla</math> of the metric <math>P_E(F_{\nabla})</math> | ||
* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection | * From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection <math>d^\star_A F_A</math> | ||
'''Idea:''' What if the | '''Idea:''' What if the <math>F</math>'s are the same in both contexts? | ||
Further, supposing these | Further, supposing these <math>F</math>'s are the same, then why apply two different operators? | ||
'''Thus the question becomes:''' Is there any opportunity to combine these two operators? | '''Thus the question becomes:''' Is there any opportunity to combine these two operators? | ||
A problem is that the hallmark of the Yang-Mills theory is the freedom to choose the data, the internal quantum numbers that give all the particles their personalities beyond the mass and the spin. We can allow the gauge group of symmetries to act on both sides of the equation, but the key problem is that: | A problem is that the hallmark of the Yang-Mills theory is the freedom to choose the data, the internal quantum numbers that give all the particles their personalities beyond the mass and the spin. We can allow the gauge group of symmetries to act on both sides of the equation, but the key problem is that: <math>P_E(F_{\nabla h}) \neq h^{-1} P_E(F_{\nabla}) h </math>. If we act on connections on the right and then take the Einstein projection, this is not equal to first taking the projection and then conjugating with the gauge action. The gauge rotation is only acting on one of the two factors. Yet the projection is making use of both of them. So there is a fundamental incompatibility in the claim that Einstein's theory is a gauge theory relies more on analogy than an exact mapping between the two theories. | ||
=== Problem Nr. 2: Spinors are sensitive to the metric === | === Problem Nr. 2: Spinors are sensitive to the metric === | ||
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<blockquote> | <blockquote> | ||
"So if we're going to take the spin-2 | "So if we're going to take the spin-2 <math>G_{\mu\nu}</math> field to be quantum mechanical, if it blinks out and does whatever the quantum does between observations. In the case of the photon, it is saying that the waves may blink out, but the ocean need not blink out. In the case of the Dirac theory, it is the ocean, the medium, in which the waves live that becomes uncertain itself. So even if you're comfortable with the quantum, to me, this becomes a bridge too far. So the question is: "How do we liberate the definition?" | ||
How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It is responsible for a volume form; for differential operators; it's responsible for measurement; it's responsible for being a dynamical field, part of the field content of the system." | How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It is responsible for a volume form; for differential operators; it's responsible for measurement; it's responsible for being a dynamical field, part of the field content of the system." | ||
</blockquote> | </blockquote> | ||
Latest revision as of 20:53, 19 February 2023
The Theory of Geometric Unity is an attempt by Eric Weinstein to produce a unified field theory by recovering the different, seemingly incompatible geometries of fundamental physics from a general structure with minimal assumptions. This structure is a mapping from a manifold [math]\displaystyle{ X^4 }[/math] to a manifold [math]\displaystyle{ Y }[/math] called the observerse, which replaces Einstein's spacetime. For the latest updates on the theory, visit https://geometricunity.org/.
This page currently summarizes information surrounding the theory.
Motivations[edit]
Source Code and the End of Physics[edit]
In his answer to the last Edge.org annual question "What is the Last Question?", Eric responded:
Does something unprecedented happen when we finally learn our own source code?
The source code, or a theory of everything, would mean the end of theoretical discovery at the most fundamental level of physics; all new discovery would take place at levels of more complexity.
Twin Nuclei Problem of Cell and Atom[edit]
Geometric Unity is hoped to solve the Twin Nuclei Problem by finding a means of breaking the Einsteinian speed limit, the speed of light, so that human life can spread across the cosmos. Eric says that does not necessarily imply faster-than-light travel or other concepts in that vein, and that he does not know whether this hope will bear fruit. A theory of everything, though, would provide definite means of exploring possible ways around Einstein's constraint.
New April Fools' Day Tradition[edit]
The release of updates to Geometric Unity on (or around) April 1st is to establish a new April Fools' Day tradition. The tradition was conceived in recognition that many ideas may never be expressed due to social pressures and the risk to livelihood and reputation. To address that, it is proposed that on one day a year, people should be allowed to put forward competent, partial ideas that would normally tarnish one's reputation or destroy one's career. Then let the "fools" develop their ideas for a year, and report back, with the choice of abandoning the idea without reputational cost or continuing their pursuit.
Eric first outlined this idea in two Twitter threads in the Spring of 2018, and discussed it further at the beginning of A Portal Special Presentation- Geometric Unity: A First Look. During the video's preface, in relation to Geometric Unity, he said, "[If] there is a fool, it is certainly me, because I have sat on this theory for almost 40 years."
History[edit]
Eric Weinstein first began developing the theory in the mid to late 1980s while he was a PhD student at Harvard University.
2013 First Presentation[edit]
Geometric Unity was first presented in three Simonyi Special Lectures delivered over the course of a week at the University of Oxford. The lectures were organized by Marcus du Sautoy, the Simonyi Professor for the Public Understanding of Science. The lectures provided a broad overview of the mathematical structures in the theory’s endogenous version, discussed where current effective theories are recovered in those structures, and showed general predictions based on those structures.
2016 Private Talk at FQXi[edit]
Three years after the first presentation at Oxford, Eric gave a private talk on Geometric Unity at FQXi.
2020 Video Release of First Presentation[edit]
A Portal Special Presentation- Geometric Unity: A First Look was uploaded on April 2nd, 2020 as a general introduction to Geometric Unity. The video is divided into three sections: a preface, the lecture proper, and a supplementary PowerPoint presentation. The preface provides context based on historical and contemporary events and introduces the concept of a theory of everything. The lecture shown is a recording of the first lecture given at the University of Oxford. The PowerPoint reviews the lecture’s major concepts in a more up-to-date notation.
2021 Manuscript and Presentation[edit]
In April, Eric will be presenting Geometric Unity on the Joe Rogan Experience and releasing a manuscript.
Eric Discussing Geometric Unity[edit]
Appearances where Eric discusses Geometric Unity are listed below.