A Theory of Everything
Discovering a fundamental mathematical principle that could explain the entire universe.
EINSTEIN spent the last 30 years of his life searching for an answer to the deepest question about the universe: does a fundamental principle, that governs all of reality, exist? He was searching for a unified field theory but he did not succeed.
In 2013 we, the theoretical physicist Jesper Møller Grimstrup and the mathematician Johannes Aastrup, discovered a simple mathematical principle, which we believe could be exactly what Einstein was searching for.
In a recent series of +2011+and+not++arXiv:1203.6164&of=hb&action_search=Search&sf=earliestdate&so=d&rm=&rg=25⪼=0″ rel=”noopener nofollow”>publications* we have shown that this principle, which we found after 10 years of research, entails a rich mathematical theory – we call it QUANTUM HOLONOMY THEORY – that shows signs of being a unified theory of quantum gravity. If our hypothesis is true it will revolutionize not only physics but science in general and beyond.
The purpose of this crowdfunding campaign is to secure the funding needed to further analyze this mathematical principle and the theory it entails and to determine if this really is a ‘theory of everything’.
The principle, which we discovered, is an algebra that essentially encodes how objects are moved in an abstract space.
This elementary algebra simultaneously includes the fundamental premise of a quantum theory of gravity and a mathematical mechanism known to be related to a unification of the fundamental forces. This means that this algebra includes key elements of a unified theory of quantum gravity – the holy grail of modern physics.
Surprisingly, this algebra has never been studied before.
We found this algebra after many years of analysis, where we applied methods ofmodern mathematics to the questions of how to quantize Einsteins theory of general relativity and how to unify the four fundamental forces of Nature.
The reconciliation of quantum mechanics with Einsteins theory of relativity is the most important unsolved problem in modern theoretical physics and is believed to hold the key to some of the deepest mysteries about the universe and its origin.
Why is this algebra so remarkable?
There are three features, which makes this algebra exceedingly interesting to study:
- It is so elementary, that it seems completely immune to further reductions in the sense of being explained by other, deeper mathematical principles.
- It gives rise to a rich mathematical structure, that links together several modern research programs in theoretical physics and mathematics.
- It is so utterly natural.
Our analysis shows that this algebra generates a complex mathematical theory, which we call+2011+and+not++arXiv:1203.6164&of=hb&action_search=Search&sf=earliestdate&so=d&rm=&rg=25⪼=0″ rel=”noopener nofollow”> quantum holonomy theory. This theory has a number of remarkable features:
- It is a candidate for a quantum theory of gravity.
- It includes matter with the correct coupling to gravity.
- It produces a key mathematical mechanism that is known to generate gauge degrees of freedom, i.e. fundamental forces.
- It shows promising signs of being internally consistent.
These achievements are highly non-trivial and make quantum holonomy theory an exciting candidate for a unified theory of quantum gravity.
Our results are either published in top international journals such asCommunications in Mathematical Physics and Classical and Quantum Gravity or presently in the peer review process. For more information on quantum holonomy theory please check out this homepage or +2011+and+not++arXiv:1203.6164&of=hb&action_search=Search&sf=earliestdate&so=d&rm=&rg=25⪼=0″ rel=”noopener nofollow”>these papers*.
There are two natural milestones for this project:
- A consistent theory. A mathematical proof that quantum holonomy theory is internally consistent. In physics-lingo this means proving that the constraint algebra closes off-shell.
- Proof of unification. Unambiguous proof that quantum holonomy theory is a theory of unification of the fundamental forces. In physics-lingo this means a clear connection to the non-commutative formulation of the Standard Model of Particle Physics.
If just one of these goals are met it will be clear that quantum holonomy theory is one of the most promising candidate for a final theory that is known today.
The goal of this crowdfunding campaign is to meet at least one of these milestones.We believe that this is possible within five years.
Why is this research important?
With quantum holonomy theory we propose a completely new approach to one of the greatest scientific problems ever. We have already shown that the theory is a serious candidate for a final theory. We believe that it is imperative to further analyze this framework.
A final theory is expected to provide answers to some of the deepest questions in modern physics:
- What happened at t=0 at the big bang?
- What is dark matter and dark energy?
- What happens at the singularity of a black hole?
- Are the laws of physics unique?
- Will the universe expand forever?
Curiosity is part of what makes us human. Science is about the big questions, the fundamental “Why?” that seizes us when we gaze into the night sky. This is an integral part of our cultural DNA.
We believe very deeply in our research and in the aspiration towards a final theory. We have given everything we’ve got to get this far.
Jesper Møller Grimstrup: I am a 44-year old danish theoretical physicist. I was educated at universities in Aarhus and Copenhagen in Denmark, the ETH Zürich in Switzerland and at the Technical University of Vienna, Austria, where I received my Ph.D. I am an expert in theoretical high-energy physics, quantum gravity and non-commutative geometry.
I held a research position in theoretical physics at the Niels Bohr Institute in Copenhagen until 2011, when I was no longer able to obtain funding for my research. Since then I have financed my research with savings and by selling my flat in Copenhagen.
Johannes Aastrup: I am an assistant professor in mathematics at the Leibniz University of Hannover, Germany. I was born in 1974 in Denmark and was educated at the University of Copenhagen, Denmark, where I received my Ph.D. in 2002. I am an expert in geometric analysis, non-commutative geometry, operator algebras and mathematical physics.
For further information we refer to our home-pages, where our CV’s and publications are available.
– Professor Matilde Marcolli, Caltech, US
– Professor Adam Rennie, MSI, Australia
– Professor Raimar Wulkenhaar, Münster University, Germany
Essentially, what we have to offer is our research and we now invite you to play a role and take part in our adventure. We promise to do our very best! We have the following rewards for our backers:
- A popular book about our research. As our project develops Jesper will dedicate time to write a book for a general audience about our work. Jesper: “This book will be about the why and whereto’s, about the big questions and the big picture. I will explain how we came upon the ideas that lead us to quantum holonomy theory – a story that starts in the the militarized zone of Aksai Chin in the Tibetan Himalayas and involves both Kafka, Kierkegaard and the sci-fi movie Dark City; I will write about the background: Einsteins theory of general relativity and quantum mechanics and why most physicists believe that a theory, which combine these two, must exist; and I will write about quantum holonomy theory itself, the basic ideas and their implications. I will also write about what impact I believe the possible discovery of a final theory will have on society and on our perception of the world. Above all I will write about our fascination and love for our work. This book will be our main reward to our backers, either as an e-book or a proper book”.
- Official acknowledgement. It is customary to acknowledge financial support in scientific publications. We pledge to acknowledge in detail the largest donations in our future publications. Thus, if you choose this option your name will appear in some of the top international scientific journals – listed in the acknowledgement section of our papers or on the front page.
- A newsletter. Everyone who supports us will receive a newsletter with updates on our research, new publications and general trends in modern physics.
- Scientific interaction. All our supporters are welcome to interact with us with questions, suggestions, thoughts on science, the universe and everything in it.
This project has been a long time in the making. We spent more than a decade of research until we found what we were searching for. It is difficult to sustain funding for such a long period for a research project, that is far away from mainstream physics.
Our research has taken us into completely unchartered territory. We combine two very different and highly specialized research directions – non-commutative geometry and canonical quantum gravity –, neither of which are mainstream. It takes time for a new research direction to reach the level of impact required to secure a steady flow of funding.
This leaves us in the unusual situation where we have obtained very strong results while at the same time are running out of money. Unless we get external funding we will not be able to continue our work. This is the reason why we now ask the crowdfunding community for support.
If you would like to have additional information about our previous and present funding situation you are welcome to contact us. You can also find more information on our home-pages.
How we will spend the money
The funding raised in this campaign will primarily be used to finance research time for Jesper Møller Grimstrup. In plain english this means salary. To make the funding last as long as possible Jesper will make do with a very modest salary.
The more money we raise the more time we will have for research. We are deeply grateful for any support. We here formulate two additional stretch goals:
- If a miracle happens and we manage to raise 200.000 $ we will buy Johannes Aastrup extra research time.
- If two miracles happen and we raise 400.000 $ we will hire additional researchers to join us.
More about the PHYSICS
Let us finally provide a little more information on quantum holonomy theory. This part will involve a certain level of technicality.
The algebra, which we call the Quantum Holonomy-Diffeomorphism (QHD) algebra, is build of two types of elements:
- so-called holonomy-diffeomorphisms on a 3-dimensional space. A holonomy-diffeomorphisms is the mathematical entity, that moves stuff in space.
- certain translation operators that shift the way the holonomy-diffeomorphisms operate.
The first thing to note about the QHD algebra is that an infinitesimal version of its central algebraic relation is identical to what is called the canonical commutation relation of canonical quantum gravity formulated with Ashtekar variables. This means that a theory build over the QHD algebra automatically involves the kinematics of quantum gravity, i.e. the basic requirement for a quantization of Einsteins theory general relativity.
Furthermore, the QHD algebra is non-commutative, which means that it naturally falls within the framework of non-commutative geometry, a branch of modern mathematics, which has proven to be highly relevant for the question of how to unify the four fundamental forces of Nature. In our work we have shown that the QHD algebra in a semi-classical limit produces a so-called almost-commutative algebra, which is the key ingredient in a unification scheme due to Alain Connes and Ali Chamseddine. In that formulation the emergence of gauge and Higgs sectors – i.e. fundamental forces and masses – can be traced back to this almost-commutative algebra.
All together this means that the QHD algebra has a mathematical structure that makes it extremely interesting to study in the context of a unified theory of quantum gravity. It naturally combines the two most important ingredients for a fundamental theory.
Building the he theory
Once we have the QHD algebra we need to build a theory around it. The first ingredient we require is a Hilbert space, which is the mathematical stage on which the algebra acts in order to produce the numbers, which may eventually be measured in experiments.
To do this we first find a quantum state on the QHD algebra – this is the prerequisite for a Hilbert space. Once we have a single quantum state on the algebra we can use what is known as the GNS construction to build a Hilbert space.
Once we have a Hilbert space we have essentially a quantum theory.
Incidentally, the states we find are semi-classical, which implies that each semi-classical approximation entails a different Hilbert space. This also means that this theory already has a well-defined semi-classical approximation, an issue that has remained largely unsolved within other non-perturbative approaches to quantum theory of gravity.
Furthermore, it is an important result that the semi-classical limit of an operator, which resembles a curvature operator, produces the Hamiltonian of general relativity formulated in terms of Ashtekar variables. This means that Einsteins theory of general relativity emerges from this operator.
In addition to all this we also find states in the kinematical Hilbert space, which produces what is known as the Dirac Hamiltonian in the semi-classical limit. This means that the theory also includes matter with the correct gravitational coupling.
With this brief tour we have a rough outline of quantum holonomy theory. We hope that it will be clear that the QHD algebra is worthy of further analysis. For more information please go to this homepage or contact us.
- Homepage Jesper Grimstrup
- Homepage Johannes Aastrup
- Publications: Jesper Grimstrup
- Publications: Johannes Aastrup
- Researchgate: Jesper Grimstrup
- Public ORCID account (Jesper Grimstrup)
- Academia.edu (Jesper Grimstrup)
- LinkedIn profile (Jesper Grimstrup)
- In the news (in danish)
Risks & Challenges
In fundamental research there are no guarantees of success. Often things turn out different than anticipated and sometimes new directions of research open op where old ideas failed. And there is always the possibility that you are working yourself down the wrong alley. This is what fundamental research is like. If we knew beforehand we would not need to look.
In the course of our own research careers we have encountered numerous setbacks. Every time this happens we pause, think, and push on. Like all researcher do.
We are however certain that no-matter what happens this project will generate a steady flow of scientific output.
If we obtain additional research funding during the timespan of this crowdfunding campaign we shall save the received money for later scientific use.