Danish theoretical physicist Jesper Møller Grimstrup and danish mathematician Johannes Aastrup have been working on this fundamental theory since 2004.
I supported their Indiegogo campaign back in 2016 with a small donation and I bought Jesper's book last year, where he explains their journey so far on the theory in layman's terms (not a physics book).
More information about the theory and links to the papers:
https://jespergrimstrup.org/research...lonomytheory/
This stuff is waay out of my league and probably most people's leagues, except a few hundreds theoretical physicists in the world. But it sounds fascinating and I hope they succeed or get more people involved to help them.
From the latest newsletter (attached):
Quote:
OUR APPROACH
Since we met in 2004 Johannes and me have developed a new approach to a
fundamental theory, that takes its point of departure in Alain Connes work. And
during the past 34 years this work has materialised into something solid,
something that looks like a theory, which offers novel — and surprising! — answers
to the three questions that I listed above.
Our idea is to begin with something exceedingly simple. If a theory is to be
fundamental then we believe it must be based on a principle, that borders the trivial.
If the starting point has too much structure it will be exposed to further scientific
reductions; if it is to be final it must be based on something almost empty,
conceptually. And what can be more simple than the action of moving stuff around
in a 3dimensional space?
What we do is to start with a basic mathematical object, namely the algebra of
moving stuff around in space. Just that: moving stuff around. We then combine
this elementary mathematical object with a metric principle — basically we apply
the machinery of noncommutative geometry — and what comes out is a highly
interesting framework.
The idea is to derive everything from this algebra. And the exciting fact, that we are
right now busy analysing, is that a very rich mathematical structure does indeed
emerge from it.
This is exactly what we have been hoping for. After all, the standard model of
particle physics is complex, it involves a lot of structure. If we are to explain this
then we must come up with something that gives rise to a lot of mathematical
structure. And as I said, this is precisely what we are finding.
The million dollar question is, of course, whether the structure, that we find, will
eventually match the standard model of particle physics. We do not know the
answer to that question but things are beginning to look very promising:
First promising sign: Our theory automatically includes both bosonic and
fermionic quantum field theory — i.e. quantum field theory of forces and matter —
and it does so in a way that automatically takes Einsteins theory of general relativity
into account. Specifically: we are operating on a curved space. This means that an
answer to the second question about quantum field theory seems to emerge from
our framework.
Second promising sign: Key elements of Einsteins theory of relativity are
automatically included in our framework (we think its the full package, but I’d better
not write that until I’m certain). And most interestingly, it is not quantised. If we are
right then gravity does not appear to a quantum theory. This goes against
everything that theoretical physicists have been thinking for almost a century.
Third promising sign: Our framework includes a big fat arrow that points in the
direction of Connes’ work on the standard model. Connes has shown that the
standard model of particle physics can be understood as a purely geometrical
theory if one employs the machinery of noncommutative geometry. This result is
based on a particular type of mathematics and we begin to see signs that our
framework produces precisely this type of math.
All together it looks like a candidate for a fundamental theory. In fact, that is what
we believe we have found. Time will tell if we are right.
Note that our theory actually offers an answer to the question “why quantum?”. The
quantum aspect itself — the canonical commutation relations (i.e. the Heisenberg
uncertainty relations), both bosonic and fermionic, as well as time evolution (the
Hamilton operator) — is in our framework an output. It emerges from the basic
ansatz of ‘moving stuff around’ combined with a metric principle. I think this is
incredibly cool.
There are of course a number of open questions. Lot of them, in fact. I’ll tell you
more about them in my next newsletter, where I should be able to tell you about our
solution to the “fermion problem”.
