Full Physics Theories

What must full theories of physics look like?

The basic idea is that the following is *not* a valid conclusion

(1) There exists a particle p1 whose motion in R³ is given by a time parameter t

(2) There exists a particle p2 whose motion in R³ is given by a time parameter t'

therefore

(3) There exists a system or set of particles {p1, p2}, whose state in (R³crosst)cross(R³crosst') is given by a time parameter t''.

This is much stronger than the assertion that p1 and p2 can't live in the "same" space. This is the assertion that there is no fact of the matter as to "the state" of p1 and p2. Instead, under reasonable assumptions, the ontologically consistent model is that p1 is a function of a timeline/parameter t_p1 and p2 is a function of a related but ontologically distinct timeline/parameter t_p2. t_p1 and t_p2 could be thought of as locally parallel in the geometry of p1 and p2's potential interactions, as specified from the timeline t_p1 on one hand and t_p2 on the other. But there is no objective evolution of "the state of both particles" (unless they form one ontological system, contra hypothesis), because that would require a third, "more objective" time parameter t_thirdSystem, contra to the hypothesis there are exactly two particles existing in this model.

Suppose there is a single system S evolving according to a time parameter t. Now suppose that, according to the ontology of the theory, S splits into two distinct (disjoint?) systems p1 and p2. Necessarily, the only possible "theories of physics" in this universe are the theories instantiated by p1 as it moves through t_p1 on hand and theories instantiated by p2 on the other hand. It is not possible for there to be a theory of physics that is not had by either p1 or else p2. It's not possible for either p1 or p2 to possess a theory of physics in both full variables t_p1 and t_p2 in this universe.

I'll consider two cases. The first is where there are just a set of relations between p1 and p2, and the second where p1 and p2 are evolving "in space".

Case 1

In the first case, p1 will evolve in t_p1. By assumption p2 is an ontologically distinct system. So all p1 can do is specify the possible future states of its interactions with p2, and it can do this using only information of t_p1 and 't_p2', where 't_p2' is p1's mathematical theory (or instantaneous theoretical projection) of t_p2 at time t_p1. The analogous things hold for p2. In this universe there is no such thing as the (full) state of both systems at a time t_p1 or a time t_p2 or a combined time (t_p1 and t_p2) or some other such.

Of course things aren’t completely random in this model: presumably if p1 and p2 have full theories T_p1 and T_p2 they may suppose (predict) the other particle is moving according to some subtheory T'_p1 and T'_p2 respectively, which makes T'_p1 and T'_p2 isomorphic as ontological objects and equal when regarded as mathematically formulated theories. p1 and p2 later recombine as judged (experimentally) by either p1 or p2 then form one system again and evolve according to one temporal parameter.

This is *not* 2-dimensional time. In that scenario (known to be wrong in models of physics, as I understand it) you could have one or more particles' movements parametrized by a communal temporal parameter space t₁crosst₂. That suggestion suffers from all the problems mentioned above, and has nothing to do with my topic.

What's interesting is that there is seemingly quantum behavior (ontologically) just from being consistent about a full theory of time.

Case 2.

Suppose p1 evolves according to t₁ in R³. What ontologically exists in this model is either 1. just the particle p1, or 2. the particle p1 and the points of space given by R³. But it won't matter for the following arguments.

Now suppose we add particle p2 to the scenario. The *incorrect* thing to do is just let p1 and p2 both be in R³, and evolve the system according to t₁ or at least some new temporal parameter t. If time full (for both p1 and p2) there is no objective fact of the matter about "the state of p1 and p2 in R³". Instead there is the theoretical situation as given by p1 as p1 moves along t_p1. The "theoretical situation" as given by p1 can be in terms of the variables t_p1 and 't_p2', but not t_p1 and t_p2. So the only possible theories of physics are p1's theory of the combined system, call it T_p1(t_p1, 't_p2') and p2's theory of the combined system T_p2(t_p2, 't_p1'). It would be ontologically inconsistent to say there is a physical system that exists as a point (value) of some third time parameter t_p1andp2. Therefore, a theory of physics that uses t_p1andp2 or even assumes it is equal to either t_p1 or else t_p2 cannot be fundamental.

What's interesting is if you consider p1's theory. All spatial interactions with p2 are specifiable by the 2-dimensional coordinate system on the sphere at distance 1 meter from p1 itself. p1 can specify the evolution of p2 in terms of t_p1 and 't_p2', but 't_p2' is really just an element of p1's theory about p2, so I'll assume it is part of the theory to begin with. So p1's theory evolves according to t_p1, i.e. T_p1 (t_p1) is p1's theory of p2's evolution on p1's co-evolving sphere. The radial distance to p2 can be given by another variable. And similarly for p2. So, we have the theories

1. T_p1(t_p1) gives the predicted locations of p2 in the variables (angle 1, angle 2, radial distance)

2. T_p2(t_p2) gives the predicted locations of p1 (on p2's sphere) in the variables (angle' 1, angle' 2, radial distance')

We can model this on the 16-dimensional manifold

(t_p1)cross(angle1 values, angle 2 values, radial values)

cross

(t_p2)cross(angle' 1 values, angle' 2 values, radial distance' values)

with lots of dimensional reductions, depending on the physical laws and geometry between t_p1 and t_p2 et. al.

Another interesting thing is that "a physical state" on M is non-local. If the points of R³ are taken to ontologically exist in the same way the particles do, then each one will have a separate (but normally parallel) temporal evolution, and the collection of all such theories is equivalent to a classical theory of the system {p1, p2}, probably.

An interesting case (but only one case) is where p1, p2, ... are Super Universal Turning Machines. If they start out with representations of their environments, including the initial states of the other machines, then they can evolve into a Nash equilibrium in which their states are constant or cyclic. This has the interpretation that none of the pi will change their mind about the universe from then on.