There has not yet been a single math foundation of our reality, rather there have been two rather incompatible maths and yet both depend on the realities of continuous space and time. The math of relativistic gravity shows the direction and velocity of discrete macroscopic objects as they move through continuous space and time in one determinate direction. The math of quantum charge, in contrast, shows the direction and velocity of discrete microscopic objects jump in many directions and even forward and back in time, ostensively through that same continuous space and time. Whereas a gravity outcome is determinate and certain, a quantum outcome is probabilistic and uncertain. While gravity outcomes are determinate and not subject to free choice, quantum outcomes are subject to free choice.

A gravity clock always ticks forward, but a quantum clock can tick in either or both forward and reverse. Each quantum moment is then a superposition of the past along with many possible future moments. The discrete moments in quantum time superposition eventually phase decay into the reality that agrees with gravity time, but before that, quantum time represents a fundamental confusion between gravity past and gravity future.

For a determinate gravity path in space, there is a determinate path from precursor to outcome that has some chaotic noise along the way. Every infinitely divisible step on the path is determinate and so there is no free choice since there is no quantum phase decay despite an infinity of steps. Precursors completely determine each outcome and there is no entanglement of the quantum phases of any other outcomes. This means there is a shortest path called a geodesic whose outcome does not change unless there are outside forces that act. A Hamilton-Jacobi equation then predicts any action by using the difference in kinetic and potential energies, called the Lagrangian.

A probabilistic quantum path does not follow a single determinate geodesic path, but rather each step of a quantum walk is a result not only of precursors, but also a superposition of the quantum phase of many possible discrete outcomes. The steps in a quantum path are limited by the fundamental granularity of the universe. Each step therefore involves a free choice that entangles those many outcomes and so the path is always probabilistic and never determinate. A quantum outcome is not only determined by its precursors, but also by the phase entanglement of other outcomes.

There is actually no way to predict gravity and charge with a single equation in continuous time and space. While the Hamilton-Jacobi equation determines each gravity path according to the difference in kinetic and potential energy, the quantum Hamiltonian Schrödinger equation determines each quantum path according to a total energy (i.e. relativistic mass) and includes quantum phase. Unlike the energy difference that determines gravity paths, the total quantum energy includes quantum phase entanglement. This means that the quantum phase of the mass of an action is orthogonal to the quantum phase of the action itself.

The entanglement of quantum phase between two two gravity bodies means that the precursors of continuous time and space determine gravity outcomes. The math foundation of our reality is actually based on the discrete matter action of outcomes from precursors. Instead of the two notions of gravity and charge based on continuous space and time, the notions of time and space actually emerge from our primitive reality of quantum matter and action. For discrete quantum charge, it is easy to show how discrete outcomes are the progeny of discrete matter and action precursors. The archetypes of continuous time and space then emerge from discrete matter action outcomes of quantum single photon charge. Time emerges from electron spin period while space emerges from electron charge radius and the Hamiltonian Schrödinger equation and the total energy is the math, but quantum phase links matter and action.

For discrete quantum gravity, the archetypes of continuous time and space emerge from the quantum charge as electron spin period and radius. While single photon exchange bonds charges, photon pairs as biphoton exchanges determine the outcomes of quantum gravity. This means that instead of just the Hamiltonian and the total energy of single photon exchange, it is the action Hamiltonian-Jacobi equation of the kinetic and potential energies difference of biphoton exchange that is the math of quantum gravity.

The kinetic and potential energy difference of that biphoton exchange then determines a unique direction in time and space for each outcome. For example, if KE=PE, the difference or action is zero and the direction is then unchanged for biphoton exchange just as for classical relativity, but a quantum action can spontaneously emit a photon and then change direction since it is a single photon exchange.

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