(from Christoph Schiller’s “MOTION MOUNTAIN
If a description of motion claims to be final, it must explain all aspects of motion. But a full explanation must be unmodifiable. This is an important point that is rarely discussed.
Theoretical and mathematical physicists are fond of generalizing models. If you have a description of a part of nature, they will try to find more general cases. For any candidate unified description, they will try to explore the model in more than three dimensions, with more than three generations of quarks, with more involved gauge symmetries, with different types of supersymmetry, with more Higgs doublets, or with additional heavy neutrinos.
If a description of nature is final, generalizations must be impossible. If a candidate unified theory could be generalized, it would not be final.
Where does this fondness for generalization come from? In history of physics, generalizations often led to advances and discoveries. In the past, generalizations often led to descriptions that had a wider range of validity. As a result, generalizations became the way to search for new discoveries. Indeed, in the history of physics, the old theory often was a special case of the new theory. This relation was so common that usually, approximation and special case were taken to be synonyms. General relativity and the standard model must be approximations of the final theory.
But can either general relativity or the standard model of particle physics be special cases of the final, unified theory? Or, equivalently: Can the unified theory be a generalization of existing theories? The answer is no. The two existing theories cannot be special cases of the final theory. If the unified theory were a generalization of the two existing theories, it could not explain any of the open issues! Indeed, given that general relativity or the standard model of particle physics cannot explain the open issues in physics, any generalization of them cannot either. Generalizations have no explanatory power.
In short, the final, unified description of motion must neither allow generalization nor must it itself be a generalization of either the standard model or of general relativity. The unified theory cannot be generalized and cannot be specialized; the unified theory must be unmodifiable. This requirement is extremely strong; you may check that it eliminates most past attempts at unification. For example, this requirement suggests to eliminate grand unification, supersymmetry and higher dimensions as aspects of the final theory: indeed, these ideas are modifiable and they generalize the standard model of elementary
particles; thus, these ideas lack explanatory power. In short, a theory that is not final cannot be unified.
Of the few candidate descriptions that satisfy the requirements, it seems that the simplest is the one that uses featureless fluctuating strands. In this approach, strands, not points, are assumed to be the fundamental constituents of vacuum, matter and radiation.
Nature is made of unobservable, fluctuating strands. Everything observed in nature – vacuum, fermions, bosons and horizons – is made of strands. Strands are the common and extended constituents of nature. Even though strands are unobservable, all observations are due to strands. To describe all observations, the strand model uses only one basic postulate or fundamental principle: Planck units are defined through crossing switches of strands.
Every observation is a sequence of crossing switches of unobservable strands. In turn, crossing switches are automatic consequences of the shape fluctuations of strands. We will show below that all the continuous quantities we are used to – physical space, physical time, gauge fields and wave functions – result from averaging crossing switches over the background space.
Nature is built from fluctuating featureless strands. The strands are featureless: they have no mass, no tension, no stiffness, no branches, no fixed length, no ends, and they cannot be cut or pushed through each other. Strands have no measurable property at all: strands are unobservable. Only crossing switches are observable. Featureless strands are thus among the simplest possible extended constituents.
Strands are one-dimensional curves in three-dimensional space that reach the border of space. In practice, the border of space has one of two possible meanings. Whenever space is assumed to be flat, the border of space is spatial infinity. Whenever we take into account the properties of the universe as a whole, the border of space is the cosmic horizon. Imagining the strands as having Planck diameter does not make them observable, as this measurement result cannot be realized. In low energy situations, a vanishing strand diameter is an excellent approximation. In a purist definition, strands have no defined diameter at all – neither the Planck length nor zero. Funnels might be a better visualization of this puristic definition. To keep the introduction as intuitive as possible, we stick with the idea of very thin strands.
Events are observable crossing switches of unobservable strands.
A tangle is a configuration one or more strands with a particular topology.
We will discover that the classification of tangles leads to the elementary particles that make up the standard model of particle physics. We will also discover that strand fluctuations and the induced crossing switches in every physical system lead to the evolution equations and the Lagrangians of quantum field theory and of general relativity. In this way, strands describe every physical process observed in nature, including all known interactions and every type of motion.
Does the strand model reproduce all the paradoxical results of modern physics? Yes, it does. The strand model implies that vacuum cannot be distinguished from matter at Planck scales: both are made of strands. The strand model implies that observables are not real numbers at Planck scales. The strand model implies that the universe and the vacuum are the same, when explored at high precision: both are made of one strand. The strand model also implies that the number of particles in the universe is not clearly defined and that nature is not a set.
If strands really describe all of nature, they must explain the inverse square dependence with distance of the electrostatic and of the gravitational interaction. But that is not sufficient. If the strand model is a final, unified description, it must provide complete precision. First of all, the model must describe all experiments. This is the case, as will be shown below, because the strand model contains both general relativity and the standard model of particle physics.
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