it’s time for a newsletter. A few things have happened since my last newsletter, both concerning my work with Johannes Aastrup and concerning other things. In the following I will try to cover it all.
Also, I am going to write something about our research from a birds eye perspective: the broad strategy and what it all means. I will start my newsletter with this part.
So, that is the plan, let’s get started!
Gravity vs quantum
About a century ago two new theories were discovered: quantum mechanics and general relativity. These two theories come with each their new framework. On the quantum side we have quantum operators and commutator relations; on the gravity side we have geometry.
And ever since it has been an open question how these two frameworks should fit in with one another? They don’t seem to coexist easily, so what do we do?
The question is really about quantum field theory. That is, the quantum theory that describes fields such as the electro-magnetic field for instance. The question is how the framework of quantum field theory and the framework of gravity relate to one another.
It has been a widely accepted assumption that what one has to do is to apply the framework of quantum field theory — or at least the basic concepts of quantum theory — to the framework of general relativity. That is, the geometry of space time, the metric field, should somehow be turned into a quantum theory with the metric as a quantum operator.
So: to apply quantum field theory to gravity.
What Johannes and myself during our decade long walk-about have stumbled upon is the exact opposite. We didn’t see this at first, it is something that we were lead to over the years; our analysis took us to a place we didn’t expect to find. In fact, we resisted it for several years: it wasn’t what we wanted and thus we tried to avoid it. But eventually we realised what it meant.
What we found is that the way these two frameworks — the quantum and the geometrical — fit together may be the complete opposite of what we have all been thinking these past some hundred years.
That is: we should apply gravity to quantum theory.
What does that mean? Well, a key object in quantum field theory is what is called a configuration space. A configuration space is the huge, infinite dimensional space of all possible configurations of a given field. It could be the electro-magnetic field, in which case the configuration space contains all possible ways the electro-magnetic field can be formed. This is, to put it mildly, an insanely large space.
In fact, quantum field theory is in a certain sense quantum mechanics on this huge configuration space.
Now, what Johannes and I have found is that this space has a geometry. What we suggest is that we should construct a gravitational theory on the configuration space.
This may sound crazy but that is because we are used to thinking about general relativity in terms of curvature of space and time. But really, gravity is simply geometry and many spaces can have a geometry. In particular, what we find is that the configuration space has a geometry too.
So, what is all this good for? Well, it turns out that when you sit down and formulate a geometrical theory on a configuration space (and this is what we have been doing for the past many years) then you soon encounter mathematics that we already know: it is the mathematics that we know from general relativity and from the standard model of particle physics.
It is important to say that we have not yet crossed the goal post yet: we don’t have a proof that all this gives us exactly what we are hoping for.
But what we do know is this: from the simple ansatz of a geometry of the configuration space we find both fermionic and bosonic quantum field theory (that is, matter and forces) as well as a curved 3-dimensional space. It looks like gravity of space-time is there too**, and most importantly, we see certain mathematical structures that look like the structures we encounter in the standard model.
That is: it looks like a framework of unification. And not merely unification of the forces but a larger type of unification, namely a unification of quantum field theory and gravity.
This up-side-down point of view has greatly surprised me. It is so simple and yet nobody saw it before we stumbled across it. And it offers a very simple solution to a problem that seemed almost insurmountable, namely the construction of a quantum theory of gravity.
One of the problems of formulating a quantum theory of gravity is that gravity is not a force like the three others (the strong and the electro-weak forces) because gravity is the background upon which everything else happens. A quantum theory is also formulated with respect to a background — space and time — and that is what makes all this so hard: because if we are going to construct a quantum theory of the background itself, of gravity, then with respect to what background are we going to construct it? Clearly, there cannot be any. This is the problem of background independence — a headache that has lasted decades.
But the solution that Johannes and I suggest solves all this. There is no theory of quantum gravity, the geometry of space remains classical. It is not quantised. I find this idea very appealing; it fascinates me.
I will write more about this in future newsletters and elsewhere. We have just opened the box; I am sure more interesting stuff will emerge as we begin to investigate things more closely.
My book is out
My book SHELL BEACH – the search for the final theory is finally out, both as an ebook and as a paperback.
In the book, which I wrote as a perk for the 2016 crowdfunding campaign, I have tried to write several intertwined stories, both about science in general, about our search for a final theory, and about my own work and my own story. Those of you who ordered my book during the crowdfunding campaign should have received at least an e-book by now. I will deliver the paperback to those who ordered an english copy later this year.
If you would like to help me getting my book out in the world then please rate it on Amazon or write a review. This would help me greatly. Thanks a lot to those of you who already did so.
By the way, the mathematician and blogger Peter Woit wrote about my book on his blog “Not Even Wrong”.
A video about our work
Recently the american science-communicator Arvin Ash made a video of our work. I find this video quite good, it explains the basic idea without going into technical details. So if you have not already seen it I recommend it to you.
The metric nature of matter
A few month ago I wrote a guest post on the noncommutative geometry blog (it belongs to Masoud Khalkhali and Alain Connes) about our recent work. The point that I wanted to emphasise is how we find a framework, which unites most of the key elements of theoretical high-energy physics, from a conceptually very simple ansatz.
Mostly theoretical physics is about complex analysis, technical computations and proof of theorems. It may sound strange but theoretical physics is rarely about explaining new concepts and painting the broad picture. It is difficult to find a platform where you can actually do that; that is why I wrote this guest post.
For those of you who understand Danish, I have published a few items about physics in various Danish outlets during the past months. First of all, I wrote an Op-Ed in the danish paper Berlingske, where I discuss String Theory and the strange fact that although this theory has not been able to produce any falsifiable physical statements it has completely dominated theoretical high-energy physics for more than four decades — and continues to do so.
It is a remarkable fact that instead of abandoning the theory leading scientist have instead been willing to abandon a key principles of science, namely falsifiability. I believe that it will be the task of future historians and sociologist to explain how things could go so wrong. In a situation where high-energy physics is in need of new ideas and where one might expect an explosion in creativity with researchers venturing out in many different directions and with heated debates about fundamental ideas, concepts, and assumptions, the exact opposite has in fact happened. There has been a contraction, people have grouped themselves in a very small number of research groups centred around a small number of fairly old ideas. And new ideas are simply not welcomed.
One explanation for this odd situation is the incentive structure. The manner in which research funding and positions are handed out favours those, who work on mainstream ideas: what matters is the number of publications and citations and you get more citations if you work on a topic that many others work on as well. And you get very few citations if you work on a completely new idea that is far away from mainstream. Thus, young researchers get punished for being creative and bold; they get rewarded for being conformists.
I have written more about this on my blog, see for instance this post.
Also, I wrote a piece on the popular science portal videnskab.dk about the standard model of particle physics and the way it is seem from a string theory point of view and from the point of view of noncommutative geometry. The difference between the two is whether the standard model — and thus the universe that we so happily inhabit — is ultimately a coincidence or whether it is unique. According to string theory it is a coincidence; according to noncommutative geometry it is not.
It is my intention and aspiration to start writing also for English language outlets. I have some communications with science magazines about this; I hope it will materialise.
Have a nice summer!
With this I end my newsletter. I wish you all a nice spring and summer — and if you live on the southern hemisphere, I wish you the opposite! — and I expect to write the next newsletter sometime in the fall 2021. I hope this year will be considerably better than the last and in particular I hope that you are all safe and healthy!
Take good care, may the horse be with you!
** The reason why I am hesitant to say that gravity – that is, the curvature of space and time – comes out of our construction is that although we have the curvature of space itself we are not yet certain about the curvature of time. We think it is all in there somewhere but we are not completely certain yet.