Professor T. N. Palmer, a contemporary of Steven Hawking, has proposed a new law of physics. It is the **Invariant Set Postulate** (ISP) which, if it is true, will have profound implications in the understanding of the fundamental nature of the universe. It also claims to resolve the paradoxes of QM, i. e. superposition, wave-particle duality, the measurement problem and non-locality. Essentially, the ISP proposes that the fundamental geometry of physical reality from the quantum to the cosmic scale, is fractal in nature.

From the abstract of his paper published by The Royal Society, UK, on the Invariant Set Postulate

A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I, invariant under the action of some subordinate deterministic causal dynamics DI.

Reconciling Einstein with QM:

On the one hand, consistent with Einstein’s view, the Invariant Set Postulate indicates that quantum theory is incomplete in the sense that it is blind to the fractal structure of the invariant set and hence DI. With respect to DI, physics is both deterministic (no dice) and locally causal (no spooky effects).

On the other hand, the Invariant Set Postulate provides an objective basis for understanding why the observer is a partner in the very concept of reality. From the Invariant Set Postulate, it is not meaningful to regard an individual quantum system as having any intrinsic properties independent of the invariant set on which the whole world state evolves. The invariant set is, in part, characterized by the experiments which inform humans about it. Hence, the Invariant Set Postulate implies that it is not meaningful to regard a quantum sub-system as having any intrinsic properties independent of the measurements performed on the quantum system. Since experimenters play a role in determining the nature of these measurements, they manifestly also play a key role in defining the very concept of reality. This is one of the key tenets of the Copenhagen interpretation.

On free will:

However, by the Invariant Set Postulate, this is not the case. We humans are conscious beings. As such, we acknowledge as ‘real’ the physical world around us. Hence, by the Invariant Set Postulate, we acknowledge the reality of I. That is, we acknowledge the reality of something which is fundamentally non-algorithmic. As stressed by Penrose (1989), no automaton would be capable of this!

On gravity:

If the geometry of I is to be considered primitive, then the geometric properties of the invariant set which lead to certain regions being relatively stable and other regions unstable should be considered a generalization of the notion introduced by Einstein that the phenomenon we call ‘gravity’ is merely a manifestation of some more primitive notion of geometry—here the geometry of a dynamically invariant subset of state space.

Conclusion:

Principles of invariance and symmetry form the bedrock of physics. Based on a type of dynamical invariance, a new law of physics is proposed, directly relevant at the cosmological level. Specifically, the Invariant Set Postulate subordinates the notion of the differential equation and elevates as primitive, a dynamically invariant fractal geometry in the state space of the universe.

And the TOE?:

It is proposed that the introduction of global geometric and topological methods in state space may similarly transform our understanding of quantum gravitational physics. Combining these rather different forms of geometry may provide the missing element needed to advance the search for a unified theory of physics.

So, it seems that at the most fundamental level, fractal geometry rules, but we have free will. OK?