Plato's Cave (physics)

Plato's Cave; the Source Code of the Gods (2018) is a non-fiction 'popular' text that describes a method for programming a Simulation Hypothesis model (the Universe as a Computer Simulation) at the  Planck level using mathematical objects for (Planck) mass, space, time and charge; the physical universe as a projection of the mathematical universe. The title comes from Plato's Allegory of the Cave as this projection examines the nature of our perceived physical mass-space-time 'cave-wall'.

This Simulation Hypothesis proposes that all of reality, the universe in its entirety, is in fact an artificial simulation, most likely a computer simulation in  "The Matrix" vogue. The simulation model described in the text posits that by using dimensionless geometrical objects instead of numbers and units (a numbering system and a system of units), self-aware structures inside the simulation may then perceive themselves as being within a physical reality. By operating at the Planck level (below the quantum level), this model is an attempt to determine the feasibility of a Full Universe Simulation where the Programmer (aka God) is external to the Universe.

“God vs. science debates tend to be restricted to the premise that a God does not rely on science and that science does not need a God. As science and God are thus seen as mutually exclusive there are few, if any, serious attempts to construct mathematical models of a universe whose principle axiom does require a God (an external Intelligence). In other words, if there is an Intelligence responsible for the 14 billion year old universe of modern physics, being the universe of Einstein and Dirac, and beginning with the big bang as the act of 'creation', then we must ask how it might be done? What construction technique could have been used to set the laws of physics in motion?”

Programming Plato's Cave
The Planck units are considered to be discrete and indivisible units and suitable for simulations, however programming at the Planck level where all events occur at unit Planck time poses certain challenges, it is necessary to replace probabilities with frequencies and as the universe does not exist in any material sense the sum universe; of energy, particles, charges, dimensions etc. must all cancel. Furthermore a Planck level simulation requires massive computing resources. The following summarize some of techniques (short-cuts) used to reduce complexity;

Planck units
In a geometrical model we need objects to represent mass, space, time and charge..., physics has a set of units known as the Planck units which can be appropriated.


 * The Planck units are assigned geometrical forms; mass $$M$$ = 1 (point), time $$T$$ = 2π (circle), length $$L$$ = torus, velocity $$V$$ = sphere, etc. and a rule set to define the relationships between them. These objects can then be combined together to form more complex objects (atoms to galaxies) whilst still retaining the underlying MLTA information, which can otherwise be lost in a purely numerical simulation.

Time

 * A discrete (digital) time as opposed to an analog (continuous) time is used; i.e.: FOR $$t$$ = 1 to ... gives $$t$$ values 1, 2, 3, ...; the universe (simulation) clock-rate $$t$$ is an incremental variable and not a continuous 'real-time'. Units of time $$t$$ measured as units of Planck time constitute absolute time.


 * For self-aware structures the time dimension would be a measure of change of state, if nothing moved there would be no means to measure this time and time would not change, universe time $$t$$ would however continue to increment.


 * Relativistic time is the time dimension as seen from the observer.

Planck black-hole

 * A geometrical entity that constitutes the Planck units; Planck mass, Planck time, Planck length is defined here as a Planck micro black-hole.


 * (Planck) mass-space-time and (Planck) charge-space-time continuum are used, from space and time we can calculate mass and charge. The ratios which define these continuum are embedded within the mathematical electron. The sum universe is dimensionless.

Expansion

 * For each increment of $$t$$ a Planck micro black-hole is added forcing the universe expansion (the expansion acting as a pilot wave) and so a dark energy is not required.


 * The velocity of this expansion is the origin of the speed of light, velocity is also an absolute, and so no object can travel faster than light.


 * Particle and object motion is a derivative of this expansion, in universe co-ordinates all particles and objects travel at, and only at, the speed of light. Relativity is the mathematics of perspective.


 * The arrow of time derives from the increment of $$t$$, if $$t$$ were to reverse, so too would the arrow of time.


 * As mass, space and charge are linked to time, then as the universe expands (adding time) it must also add mass, space and charge proportionately, the universe growing in size and mass as I type.


 * Photons, the means of information exchange, lack the mass point-state and so are not pulled by this expansion, consequently they can only travel along the 3-D universe surface.

Wave-particle duality

 * Wave-particle duality is replaced by a Planck-level electric wave-state to Planck-mass Planck-time point-state oscillation. Mass is a discrete rather than analog property of particles.

Gravity

 * Gravity can be simulated by linking all mass point-states with waves of angular momentum per unit of Planck-time.

"Science has a set of formulas that describe the universe and these are referred to as the Laws of Physics. To solve these formulas we use inputs such as the mass of the earth or of the electron, the distance from the earth to moon, the strength of gravity or of the ampere and so on ... these formulas often so complex that an advanced degree is required to understand them, science becoming the priesthood of the modern world. I use this term because nowhere in these formulas is there a number that refers to God, no formula such as 'E = God.c^2 ...', and so to understand the world around us we must instead turn to the formulas of science where God has no place. Ipso facto, we need science but science doesn't use and so doesn't need God."

"This however raises a philosophical question, why do electrons and planets know how to do whatever it is that they do? Neither the electron nor the moon would seem to know these laws of physics, they are not 'written in the stars', yet both electron and moon follow them diligently. Science has made simulations of our universe, they are incredibly complex and require super-computers to run. This is because our simulated electrons and planets don't instinctively know what to do, in the background these laws of physics dictate the simulation, hence the requirement for the super-computer."

"If I am tasked with writing a planetary orbital simulation program then nowhere in my computer program will I appear, the program consisting instead of planetary related data and formulas that manipulate that data ... yet the existence of the program source code itself is prima facie evidence of me the programmer. Likewise we may not find evidence of 'God' in the laws of physics, but if there is a source code from which these laws originated ... then could this be considered as prima facie evidence of 'The Programmer'."

Physics of Plato's Cave
The model is divided into 4 parts (4 articles)
 * The theory is focused on a mathematical electron fe that is used to construct the Planck units as geometrical objects from 2 dimensionless physical constants (α, Ω). To translate from dimensionless geometrical objects to the numerical SI Planck units requires 2 numerical scalars.
 * $$f_e = 4\pi^2(2^6 3 \pi^2 \alpha \Omega^5)^3 = .23895453...x10^{23}$$


 * The universe is an expanding hypersphere that increments in Planck size micro black holes in Planck-time steps and so for any chosen universe age in units of Planck time it is possible to calculate the mass and radiation density of the Planck  black-hole universe.


 * All motion derives from the constant expansion of the hyper-sphere, in hyper-sphere co-ordinates all particles and objects travel at the speed of light (velocity of expansion), time and velocity are thereby constants, however particle 3-D space has no means to measure this motion and so self-aware structures are restricted to relative motion, relativity as the mathematics of perspective.


 * Gravitational orbits are replaced by discrete gravitational orbitals ( gravitons) as units of orbital momentum. The orbital angular momentum of a planetary orbit and the rotational angular momentum of a planet becomes the sum of these orbitals, thereby resolving the problem of applying gravitational force between macro objects at the Planck level.

"Each formula presented in this text describes a particular function; consequently each formula has its own story to tell – and this story is the story of the universe itself ..."