# What are the prospects for the Causal Fermion System?

## Main Question or Discussion Point

Wikipedia:
The theory of causal fermion systems is an approach to describe fundamental physics. It gives quantum mechanics,general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory.

It seems possible this might be progress. A step toward a ‘theory of everything’….On the other hand, these guys might be waaaaay out there as I saw there were only three citations.

What do you think? I did not find discussions in these forums. I really like the concept that spacetime and particles and forces within emerge from a unified framework. They are not such distinct entities as we currently portray them.

Here is a quick summary of the theory:

https://en.wikipedia.org/wiki/Causal_fermion_system

Instead of introducing physical objects on a preexisting space-time manifold, the general concept is to derive space-time as well as all the objects therein as secondary objects from the structures of an underlying causal fermion system………..

Taking the concept seriously that the states of the Dirac sea form an integral part of the physical system, one finds that many structures (like the causal and metricstructures as well as the bosonic fields) can be recovered from the wave functions of the sea states. This leads to the idea that the wave functions of all occupied states (including the sea states) should be regarded as the basic physical objects…….

The physical picture is that one causal fermion system describes a space-time together with all structures and objects therein (like the causal and the metric structures, wave functions and quantum fields). In order to single out the physically admissible causal fermion systems, one must formulate physical equations. In analogy to theLagrangianformulation ofclassical field theory, the physical equations for causal fermion systems are formulated via a variational principle, the so-calledcausal action principle. Since one works with different basic objects, the causal action principle has a novel mathematical structure where one minimizes a positive action under variations of the universal measure.

There is another description here:

http://arxiv.org/abs/1502.03587

“ The general structure of the theory of causal fermion systems can be understood in analogy to general relativity. In general relativity, our universe is described by a four-dimensional space-time (Lorentzian manifold) together with particles and fields.

However, not every configuration of Lorentzian metric, particles and fields is considered
to be “physical” in the sense that it could be realized in nature. Namely, for the configuration to be physically realizable, the Einstein equations must hold. Moreover, the particles must satisfy the equations of motion, and the additional fields must obey the field equations (like Maxwell’s equations). This means that in general relativity, there are two conceptual parts: on the one hand one has mathematical objects describing possible configurations, and on the other hand there is a principle which singles out the physical configurations………"

[The video link at the end of the Wikipedia article gets very mathematical within just two or three minutes and I could not understand the dialogue with the German accent.]

Related Beyond the Standard Model News on Phys.org
I found a 2008 paper by one of the authors which explains the basis of their concept: the emergence of spacetime leads to spontaneous symmetry breaking and 'structures' [particles, forces,relationships] we can recognize.
So this has been developing longer than I realized. It seems maybe analogous to, but more general than, for example, causal dynamic triangulation which also involves evolving spacetime.

http://arxiv.org/abs/0712.0685
From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives
Felix Finster

"...The principle of the fermionic projector [4] proposes a new model of space-time, which should be valid down to the Planck scale. This model is introduced as a system of quantum mechanical wave functions defined on a finite number of space-time points and is referred to as a fermion system in discrete space-time. The interaction is described via a variational principle where we minimize an action defined for the ensemble of wave functions. A-priori, there are no relations between the space-time points; in particular, there is no nearest-neighbor relation and no notion of causality. The idea is that these additional structures should be generated spontaneously. More precisely, in order to minimize the action, the wave functions form specific configurations; this can be visualized as a “self-organization” of the particles. As a consequence of this self-organization, the wave functions induce non-trivial relations between the space-time points.

"...important physical principles are missing in our framework. In particular, our definitions involve no locality and no causality, and not even relations like the nearest-neighbor relations on a lattice. The idea is that these additional structures, which are of course essential for the formulation of physics, should emerge as a consequence of a spontaneous symmetry breaking and a self organization of the particles as described by a variational principle. Before explaining in more detail how this is supposed to work.............

Of course 'the devil is always in the details'.