The Final Theory - Part 1

(from Christoph Schiller’s “MOTION MOUNTAIN” vol. VI, www.motionmountain.net)

Requirements for a final theory

In our quest for the final, unified theory, we have deduced many requirements that such a theory must realize. All the requirements that we deduced are listed below. So far, this list is not found elsewhere in the literature.

Certain requirements follow from the property that the description must be final, others from the property that it must be unified, and still others from the property that it must describe nature. More specifically, every requirement appears when the expressions for the Compton wavelength and for the Schwarzschild radius are combined.

General requirements for a final and unified description of nature and of motion

Precision

must be complete; the unified description must describe all motion and explain all open issues of physics.

Modification

must be impossible, as the theory is final.

Fundamental principles

must be clear. (Otherwise the unified description is not falsifiable.)

Vacuum and particles

must not differ at Planck scales because of limits of measurement precision; vacuum and particles therefore must be described by common fundamental constituents.

Fundamental constituents

• must be extended and fluctuating, to explain black hole entropy, spin, space-time homogeneity and isotropy of space.
• must be as simple as possible, to satisfy Occam’s razor.
• must determine all observables.
• must be the only unobservable entities. (If they were observable, the theory would not be final; if more unobservable entities would exist, the theory would be fiction, not science.)

Non-locality

must be part of the description; non-locality must be negligible at everyday scales, but important at Planck scales.

Physical points and sets

must not exist, due to limits of measurement precision; points and sets only exist approximately, at everyday scales.

Evolution equations

must not exist, due to the lack of points and sets.

Physical systems

must not exist at Planck scales, due to limits of measurement precision; systems only exist approximately at everyday scales.

Universe

must not be a system, due to limits of measurement precision.

Planck’s natural units

must be limit values for each observable (within a factor of order one); infinitely large or small measurement values must not exist.

Planck scale description

must imply quantum field theory, the standard model of particle physics, general relativity and cosmology.

Planck’s natural units

must define all observables, including coupling constants.

Relation to experiment

must be as simple as possible, to satisfy Occam’s razor.

Background dependence

is required, as background independence is logically impossible.

Background space-time

must be equal to physical space-time at everyday scale, but must differ globally and at Planck scales.

Big bang

must not be an event, and thus not be a beginning, as this would contradict the non-existence of points and sets in nature.

Circularity of definitions of physical concepts

must be part of the final, unified description, as a consequence of being ‘precise talk about nature’.

Axiomatic description

must be impossible, as nature is not described by sets; Hilbert’s sixth problem must have no solution.

Dimensionality of space

must be undefined at Planck scales, as space is undefined there.

Symmetries

must be undefined at Planck scales, due to the limits to measurement precision.

Large and small scales

must be similar, due to the limits to measurement precision.

Looking at the requirements for a final theory, we note something astonishing.

Even though all requirements appear when quantum physics and general relativity are combined, each of these requirements contradicts both quantum physics and general relativity.

The final theory thus differs from both pillars of modern physics. A final theory cannot be found if we remain prisoners of either quantum theory or general relativity. To put it bluntly, each requirement for the final theory contradicts every result of twentieth century physics.