Evolution Lemmas

Background

The formulation below attempt to answer what is the origin of the concept of gene.

The statement of this article is that a concept of a gene as a unit of evolution originates naturally under the known laws of physics. The following is the formulation of the evolution principle that applies equally well to living and non-living elements, with the best example of the principle at work in the spontaneous symmetry break phenomena.

Gene equates to having a pseudo-stable property of unstable elements in the set. Example of pseudo-stable properties are particle properties such as electric charge if you an electron or color of your eyes if you are a person. An example of a set is a space of quantum fields for particles or species for humans.

Initial assumptions

We have a set of unstable elements that can potentially decay into a mix of more and less stable elements with different properties. Some properties of elements define how elements interact, other properties define how stable element within a given environment. One element can combine several properties essentially allowing "bundling" of properties within a given element.

Statement 1

The given property of unstable elements has a higher probability to persist through a drastic change in environment if it is shared by multiples of elements. Let us call this property "sharing" property.

Statement 2

Different elements have variations of the property. Each variation has a different interaction with the environment and have different probability to persist through environmental change.

Formulation

The property that has higher probability to persist through a change in environment becomes most dominant in the set.

Proof

Assuming an ability for multiple properties to exist in a single element, we will have a property that would make any other property to propagate to another element. Bundling this property with a) more stable and b) less stable properties, let the groups that propagate a) and b) properties be A and B groups correspondingly.

The property that has higher probability to persist, or "survive" the environmental change, combined with "sharing" property will lead to propagation of more stable property through the remaining elements making entire set of elements more stable and less likely to decay.

In our notation, the group A will become more and more bigger where group B will become smaller and smaller.

To prove it consider the opposite to be true, if in any stable system the group that decays faster, group B, would have alway be bigger than group A, then after all elements in group B have decayed, there group A by definition would also converge to zero and the entire set would disappear, which contradicts stability assumption.

In a stable system more stable elements propagate faster.

Empirical evidence and examples

The most striking example of more stable property becoming dominant is a spontaneous symmetry break phenomena in physics spanning fluid dynamics and Higgs mechanism.

In spontaneous symmetry breaking, the equations of motions of the system are invariant, but the system is not. This is because the ground state of the system is non-invariant. 

Small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. The slight fluctuations in the system would correspond to variants in the property of the elements. The system eventual decent into a symmetry break corresponds to a propagation of a small fluctuation to the rest of the system.

Verifiable consequences

By not requiring the property to be absolutely stable but only approximately stable I stipulate that the laws of physics are not invariant and can fluctuate or change very slowly.

Another consequence of this formulation is that the problem of fine tuning of this universe is naturally solved by requiring stability of the resulting properties of the system. If any laws of physics are allowed to mutate and adjust, then the most stable combination of forces will propagate and become our observable universe.