What are the prospects for the Causal Fermion System?

In summary: However, from a mathematical point of view, the principle of the fermionic projector is very attractive. It is a new model of space-time which should be valid down to the Planck scale and which can be studied in detail. It is also important to emphasize that the principle of the fermionic projector does not require any extra assumptions about the fundamental nature of space-time. In fact, the model is based on the usual quantum mechanics and does not require any extra parameters to be determined. In addition, it should be possible to extend the principle of the fermionic projector to include particles which are not fermions, like atoms and molecules.In
  • #1
Finny
107
31
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.]
 
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  • #2
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'.
 
  • #3

1. What is the Causal Fermion System?

The Causal Fermion System is a physical theory that aims to unify general relativity and quantum mechanics. It proposes that space-time is not fundamental, but emerges from the interactions of fundamental building blocks called fermions. These fermions are described by a mathematical entity called a causal fermion system and are responsible for the dynamics of space-time.

2. How does the Causal Fermion System differ from other theories?

Unlike traditional theories, the Causal Fermion System does not rely on a fixed space-time background. Instead, space-time emerges from the interactions of fermions, making it a background-independent theory. This approach also allows for the unification of gravity and quantum mechanics, which has been a major challenge in physics.

3. What are the potential applications of the Causal Fermion System?

The Causal Fermion System has the potential to provide a more complete understanding of the fundamental nature of the universe. It could also have practical applications, such as in the development of new technology or in the study of quantum computing. Additionally, it may help to resolve some long-standing problems in physics, such as the nature of dark matter and the cosmological constant.

4. What evidence supports the Causal Fermion System?

The Causal Fermion System is still a relatively new theory and is currently being tested and refined through mathematical calculations and simulations. So far, it has shown promise in providing solutions to some of the major issues in physics, but more research and experimentation are needed to fully validate its predictions.

5. What are the challenges facing the development of the Causal Fermion System?

One of the main challenges in the development of the Causal Fermion System is the complex mathematical framework used to describe it. This makes it difficult to translate the theory into practical applications or to test it experimentally. Additionally, the theory is still in its early stages and requires further development and testing to fully understand its implications and potential limitations.

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