Hi everyone,
there has been a new development in my research project with Johannes Aastrup since I sent you my latest newsletter last month. It turns out that the core elements of Einsteins theory of general relativity emerge from our construction, something that Johannes and myself did not realise until a few weeks ago. In this short update I will bring you up to date on all of this.
The cornerstone of Einsteins theory of general relativity
In the beginning of September as Johannes and myself were finishing our most recent paper we also discussed the possibility that Einsteins theory of general relativity might emerge from our construction. As you will remember from my last newsletter, we have already shown that the basic building blocks of bosonic and fermionic quantum field theory emerges from the geometrical construction over a configuration space, which we have been developing over the past two decades, and thus it was natural to ask whether or not Einsteins theory might also emerge.
There are good reasons to believe that this should be the case and Johannes and myself did put a fair amount of energy into this question. I spent two weeks in September in Hannover working with Johannes, and during those weeks we spent several days discussing this question. Sometimes our discussions became heated, but the bottomline was that we did not see it.
But sometimes it takes a long time to see the obvious. And once we saw it, it really was obvious. In a certain limit the cornerstone of Einsteins theory really does emerge: a dynamical metric on three-dimensional space emerges exactly where one would expect it.
Why is this important?
The reason why this is important is that with this result we appear to be very close to have a solution to the ancient problem of reconciling general relativity with quantum theory. This problem has haunted theoretical physicists for almost a century. Now, Johannes and myself have already shown that key elements of quantum theory — in particular: of quantum field theory — emerges from our geometrical framework, and now we know that the central element of general relativity also emerges from it. This means that our geometrical construction really does appear to reconcile Einsteins theory with quantum theory.
All the basic characteristics of a fundamental theory
With this new development things look very promising. We now have a mathematical theory, which has the following key characteristics:
- It is based on an extremely simple principle. This is the mathematics of empty space, or, in mathematical terms, the HD-algebra, which encode how stuff is moved around in empty space. The central idea is to consider the geometry of the configuration space that is associated to this algebra. This starting point has a very high degree of uniqueness.
- It exist as a rigorous piece of mathematics. This was the main result of our latest paper: we proved that our construction actually exists mathematically1.
- It generates the key building blocks of quantum field theory. Over the past 5 – 6 years we have shown how the key mathematical ingredients of both bosonic and fermionic quantum field theory emerges from our construction, i.e. the canonical commutation and anti-commutation relations, the Hamilton operators and the bosonic and fermionic Fock spaces.
- It generates the key building block of Einsteins theory of general relativity. This is what is new. We can now demonstrate how a dynamical metric (i.e. a geometry of three-dimensional space that evolves in time) emerges in the same limit as quantum field theory.
- It contains elements of unification and a possible connection to the standard model. This part has not been fully investigated yet, but we know that our framework involves an additional mechanism of unification. This mechanisms has to do with the basic characteristics of the HD-algebra. In technical terms, it involves what is known as inner automorphisms, something which in the case of the standard model is known to give rise to the entire bosonic sector. Also, the mathematics, which we use, is very similar to the mathematics, which the physicist Ali Chamseddine and the mathematician Alain Connes used in their formulation of the standard model of particle physics, namely the machinery of noncommutative geometry. We do not yet know if there is an actual connection to the standard model, but that is what we suspect.
Concerning general relativity, then we are not quite there yet. We still do not know if it really is Einsteins theory we find. It looks like it, but we still need to check a number of things2. But the fact that we get a dynamical metric out is highly encouraging and non-trivial. It is in my opinion a very important milestone.
A resubmitted paper and a thank you
Johannes and I have now updated and rewritten our latest paper and resubmitted it to the physics arXiv. We have withdrawn the old version of the paper and replaced it with the new version, which has a new title.
Let me end this update with a huge thank you to those of you, who support my work. I rely 100% on the support of private donors. Without your support I would not be able to carry out this work. Thank you so much.
If some of you would like to support my work you can do so via Paypal or alternatively by contacting me to get my bank details. I need all the help I can get, everything counts.
With this I wish you all the best. I hope life is treating you well, take good care,
Kind regards, Jesper
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- There are still a number of details concerning existence, which needs to be worked out, as is pointed out in the paper. For instance, issues concerning higher commutators between the Dirac-type operator and the HD-algebra. Nevertheless, the fact remains that we have well defined operators acting in a well defined Hilbert space. ↩︎
- Technically: we need to check to what extend the dynamical metric in three-dimensional space gives rise to a four dimensional metric in space-time, and, if it does, what signature that metric will have. The signature of a metric encodes how spatial and temporal distances are measured. In the case of general relativity the signature corresponds to Minkowski space, and thus what we are looking for is the origin of the Minkowski signature. ↩︎
Jesper møller grimstrup 