The Unification of Symmetry and Conservation Sergio Pissanetzky

1. 1 The Unification of Symmetry and Conservation Sergio Pissanetzky

2. The Unification of Symmetry and Conservation – Sergio Pissanetzky 2 THE THEORY • I propose a new Theory of Mechanics. • One fundamental principle: Causality. • One postulate: the action functional. • Discrete, scale free. • Describes the system in “high resolution.” • The granularity of descriptionis adjustable. • There are no assumptions of smoothness. • Applies to all dynamical systems.

3. The Unification of Symmetry and Conservation – Sergio Pissanetzky 3 PLACING THE THEORY E B F A C G H D Statistical methods: probabilities. Differential methods: smoothness. Causal Mechanicsis general.

4. The Unification of Symmetry and Conservation – Sergio Pissanetzky 4 MODEL • The model is a causal set. • If not familiar with causal sets think of a computer program. • The action functional is the metricfor causal sets. • System specified by variables, states, transitions, trajectories: • variables  elements • transitions  causal relations • trajectories  legal permutations • However, the transition probabilities are irrelevant.

5. The Unification of Symmetry and Conservation – Sergio Pissanetzky 5 PRINCIPLE OF SYMMETRY • A causal set always has a symmetry of the action. • The symmetry is represented by the legal permutations. • A causal set always has a conservation law. • A causal set always has a conserved quantity. • Hence, the principle of symmetry follows from causality. • All conserved quantities are determined by the theory.

6. The Unification of Symmetry and Conservation – Sergio Pissanetzky 6 PRINCIPLE OF LEAST-ACTION • The action functional is the natural metric of causal sets. • The action depends on the trajectory. • The trajectory is represented by a permutation. • The subset of least-action permutations is a grupoid. • The grupoid has a group-theoretical block system. • The block system is the unique conserved quantity. • Hence, least-action also follows from causality.

7. The Unification of Symmetry and Conservation – Sergio Pissanetzky 7 PREDICTIONS • The theory applies to all systems, even the brain. • In 2011, I predicted optimally short dendritic trees in the mammalian brain. • At that time a non-optimal 4/3 power law was accepted. • In 2012, Cuntz proposed a 2/3 optimally short power law. • Hence, the prediction is confirmed. • This is a major success for the theory. • The theory also applies in Physics. • Predicted Noether’s theorem as a particular case of the theory. • Already proved a small part of Noether’s theorem.

8. The Unification of Symmetry and Conservation – Sergio Pissanetzky 8 FEATURES • This theory has exceptional features. • It is simple, elegant, and general. • Has only one principle and one postulate. • Does not divide Physics into micro/macro scales. • Does not divide Physics into simple/complex systems. • No limit in the granularity of the description. • Infinitely many conserved quantities, all computable. • Satisfies Smolin rules for a scientific theory. • Is confirmable, falsifiable, and the hypothesis are the simplest among theories.

9. The Unification of Symmetry and Conservation – Sergio Pissanetzky 9 I call this theory: The theory of Causal Mechanics Sergio@SciControls.com www.SciControls.com