“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 (the Intelligent Design hypothesis). However, 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?”
Science has a set of mathematical formulas used to describe the universe and these are commonly referred to as the Laws of Physics. The planets for example follow predictable paths and so science can calculate what the night sky should look like in 100 years. To solve these formulas of physics science uses inputs such as the mass of the earth or the electron, the distance from the earth to moon, the strength of gravity, the speed of light 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 for nowhere in these formulas is there a number that refers to a God (in the creator of the universe context), there is no formula such as 'E = God.c2' for example ..., and so while our understanding of the world requires the formulas of science, science doesn't use and so doesn't require a 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 are programmed into the simulation, hence the requirement for the super-computer.
However, although those super-computer simulations are restricted to the Laws of Physics, the existence of the simulation source code itself is evidence of the programmer(s) who wrote it. Likewise science may not find evidence of a 'God' in the laws of physics, but if there is a source code from which these laws originated (a deeper set of laws than the laws of physics themselves) ... then this could be considered as prima facie evidence of a 'Programmer God'.
Neil deGrasse Tyson put the odds at 50-50 that our entire existence is a program on someone else’s hard drive . David Chalmers noted “We in this universe can create simulated worlds and there’s nothing remotely spooky about that. Our creator isn’t especially spooky, it’s just some teenage hacker in the next universe up. Turn the tables, and we are essentially gods over our own computer creations   .
The full Simulation Hypothesis proposes that all of reality, including the Earth, the universe and all life forms within, is in fact an artificial simulation, analogous to a computer simulation, that is programmed by an external 'hand', the 'God as a Programmer' approach. Such simulation models look for evidence of a 'source code' underlying the laws of physics. The principal difficulty with all Mathematical Universe Hypothesis is reconciling physical structures with mathematical structures, as mathematical structures (i.e.: the formulation of a spherical ball) can only represent physical structures (the actual ball).
The Planck scale refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the Standard Model, quantum field theory and general relativity are no longer reconcilable, and quantum effects of gravity are expected to dominate (quantum gravitational effects only appear at length scales near the Planck scale). Consequently simulation hypothesis models that include these effects must consider (if not begin with) the Planck scale .
The SI units is the only system of measurement with an official status in nearly every country in the world. The SI mksa units are; meter (length, m), kilogram (mass, kg), second (time, s), ampere (electric current, A)). The corresponding Planck units are Planck length, Planck mass, Planck time, Planck charge. Resolving these in terms of mathematical structures that are indistinguishable from physical structures is the primary challenge of simulation models.
A fundamental physical constant is a physical quantity that is generally believed to be both universal in nature and have a constant value in time. These can be divided into dimension-ed (with units; speed of light c, gravitational constant G, Planck constant h, elementary charge e, electron mass me, Boltzmann constant kB ...) and dimension-less (units = 1; fine structure constant α).
Mathematical electron modelEdit
The Mathematical Electron model is an example Simulation Hypothesis model that describes the universe in terms of programmable mathematical structures. It hypothesizes that all events occur at the Planck level  (and the quantum level reflects this) and that the Planck units for mass, length, time and charge are the base units of our physical universe and that these are geometrical objects embedded within an electron function (a unit-less mathematical electron , fe).
The quantum level is the point of intersection between the mathematical structures of the Planck level and our perceived physical reality . This is resolved by replacing wave-particle duality at the Planck level with an electric wave-state (duration of particle frequency) to a Planck mass (for 1 discrete unit of Planck time) point-state. In the point-state the particle has defined co-ordinates and so all particles simultaneously in the point-state per unit of Planck time may be measured relative to each other. It is from these mathematical structures being defined in terms of each other that gives the notion of the physical universe. Comprising measurable quantities, the physical universe is characterized by physical units; formally in terms of mass, length, time and charge.
Mass, length, time, chargeEdit
In this model, the units for mass, length, time and charge are assigned geometrical objects MTLA instead of numerical values as an object can encode the function (mass-ness, length-ness, time-ness, charge-ness) of the unit. They are not independent of each other but instead are chosen to interact together, for example mass becomes mass in the context of time, length and charge and so complex macro (geometrical) structures can emerge whilst retaining all the underlying (mass, space, time) information.
The electron (fe) is a mathematical structure, the geometry of 2 unit-less constants (α, Ω) and so is also unit-less (units = 1). The geometrical objects MTLA are embedded within the electron, consequently these units must overlap and cancel according to a particular ratio as defined by this electron fe. In the following table are listed the objects MTLA and the unit relationships un between them.
For example, the following unit relationships cancel;
The electron wave-state has the units (ampere*meter), the units for the magnetic-monopole. After .23895453... x1023tp (units of Planck time), the (A*L)3 units combine with a unit of time T, and cancel (units (A*L)3/T = 1) exposing a unit of Planck mass for a unit of Planck time (the point-state). As the electron is defined by this wave-state to point-state oscillation, it does not exist at any single unit of (Planck) time, rather time is 1 of the dimensions of the physical electron.
3-D space is traditionally measured in meters although what is actually being measured is the distance between 2 points irrespective of the medium (space or air or water ...). If we assign space a physical component of ampere-meters (an aether) then electrons will not move through space, rather they will oscillate through space, 3-D space and the electron wave-state both composed of the same (AL)3 medium, there is no distinction, and so the sum universe itself may also be unit-less. In essence this means that although we may quantify physical structures from within the boundaries of the universe, if we combine all the mass, space, charge etc (the measurable units of a universe) together, they would sum to 1 (regardless of the age of the universe). Thus in order for a universe to create time (the time required to read this page for example), an equivalent mass and space must also be created to balance these units = 1 ratios, that universe thereby growing larger and more massive as it ages. Should time reverse, the universe must likewise shrink in size and mass accordingly. Asking what lies outside such a universe would then have no more meaning than a set of accounting data asking what lies outside their Microsoft excel spreadsheet, although the answer presumably would be "the real world".
If the particle point-state is a unit of Planck mass then we have a model for a black-hole electron (an electron centered around a micro Planck black-hole). When the wave-state (A*L)3/T units collapse this black-hole center is exposed (for 1 unit of Planck time). The electron now is mass. Mass is not a constant property of the particle, rather the particle mass is the average mass, the average occurrence of the point-state. We can measure the energy of the electron with the formula E = hv where h is a constant and v is the frequency of h (a v = 10Hz wave will have less energy than a v = 1000Hz wave). As for every wave-state there is a corresponding point-state, then E = hv = (m)v. E = mc2 cannot be used here as it requires mass to be a constant property of the particle, c2 has no frequency component.
The simulation universe macro-structure uses an expanding (digital time) 4-axis hyper-sphere into which particles are embedded . This hyper-sphere expands (the arrow of time) in discrete steps (the simulation clock-rate) in micro Planck black-hole increments measured in units of Planck time with the velocity of expansion as the speed of light. Particle motion is driven by the expansion of the hyper-sphere, all particles travel at, and only at, the speed of expansion (the speed of light) in hyper-sphere co-ordinate terms.
In the electric wave-state the particle is locally undefined, in the mass-gravity point-state the particle has defined hyper-sphere co-ordinates, each point can then be referenced against each other, consequently mass-gravity is the domain of the observable macro-world.
Particles are assigned N-S axis with motion in the hyper-sphere directed along that axis. Thus by changing the N-S axis (through a transfer of momentum), particles will appear to have motion relative to each other although still travelling at the speed of light in hyper-sphere co-ordinates.
As photons (the electromagnetic spectrum) do not have a point-state they have no mass and therefore do not have fixed co-ordinates in the hyper-sphere and so unlike particles they are not pulled by the hyper-sphere expansion and so can only travel laterally along the hyper-sphere. Consequently they are time-stamped, they do not age, a photon emitted from a distant galaxy a billion years ago is a billion years old. As the principal source of information regarding the observable universe comes predominately from the electromagnetic spectrum, and as this information can only transverse the hyper-sphere laterally, it is possible to infer the hyper-sphere expansion, but not directly measure it. It is akin to 2-D satellite photos of planes on/above an airport without a knowledge of the height dimension.
The mathematics of perspective is a technique used to project a 3-D image onto a 2-D screen (i.e.: a photograph or a landscape painting). Because of the lateral motion of the electromagnetic spectrum within the hyper-sphere, visible 3-D space is a projected image from the 4-axis hyper-sphere, the relativity formulas translating between the hyper-sphere co-ordinates and 3-D space. Observed 3-D space is a measure of relative object positions and the time dimension of science measures the change in state = change of information (change in relative position) of particles to each other and so derives from, but does not equate to, the universe clock-rate (digital time).
All particles that are simultaneously mass (in the point-state) at any given unit of time (digital time) are linked to all other particles also in the point-state by a gravitational orbital akin to atomic orbitals. A gravitational orbit between objects (planets for example) is simply the sum of all the particle-particle orbitals (the particles that comprise those objects). Thus it is in principle not necessary to have direct information regarding the orbiting objects to calculate their respective orbits. If the electron is an electric wave for .23895453... x1023tp and then mass for only 1tp and gravity occurs only between mass points, then gravity for that electron can occur only once every .23895453... x1023tp. Gravity only appears weak because it so seldom occurs.
In a data world of 1's and 0's such as a computer game, characters within that game may analyse other parts of their 1's and 0's game, but they have no means to analyse the hard disk upon which they (and their game) are stored, for the hard disk is mechanical, is not part of their 1's and 0's world, it is a part of the 'real world'. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may not resemble the Laws that operate in the 'real world', assuming there even exist such laws. Thus any region where the laws of physics break down would be significant. A singularity inside a black hole is such a region.
The particle point-state would then be analogous to a storage address on a hard disk, the interface between the (simulation) data world and the real world, a massive black-hole the sum of its individual particle Planck black-hole constituents.
The surface of the massive black-hole is of the particle world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however, as the interface between the data world and the real world, does not exist in physical terms. Thus we may discuss the surface area of a spherical black-hole but not its volume.
Laws of PhysicsEdit
The scientific method is built upon testable hypothesis and reproducible results. Water has always boiled, under identical conditions, at 100°C. In a geometrical universe particles behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these patterns, the more complex the orbits, the more complex the formulas required to describe them (and so forth). If there is a source code from which these geometrical conditions were programmed there there may be non-repeating events, back-doors etc built into the code, a common practice with our computer games, these by definition would lie outside the laws of physics yet would be no less valid.
Our present level of technology uses digital computers, consequently computer simulations use digital time instead of analog (continuous) time. It may be that future technologies and/or Gods use analog computers, however evidence that our universe time is digital rather than analog would strongly suggest a simulation. Quantum spacetime and Quantum gravity models refer to Planck time as the smallest discrete unit of time. A digital time simulation universe argument would then be as follows;
FOR age = 1 TO the_end 'in units of Planck time, big bang = 1 FOR n = 1 TO all_particles 'all the particles in the simulation IF particle(n) = ... ........ NEXT n NEXT age
The variable age is the simulation clock-rate (the universe age) as measured in units of Planck time. For each age the n-loop calculations are performed, only when they are finished does age increment. As such, age is a (discrete) incremental variable and not a time dimension, for there is no 'time' interval between increments. Although the n-loop calculations may be extensive, self-aware structures from within the simulation would have no means to determine this, they would perceive themselves as being in a real-time. Information is exchanged by photons which are limited by the speed of light, therefore information exchanged in real time irrespective of distance could be construed as evidence of an 'n-loop'. The common example is the thought experiment; if the sun were to magically disappear, we would see this 8 mins later (the time taken for photons to reach the earth), but would we continue to orbit the sun for those 8 mins or would we immediately drift off into space. Could the effects of gravity as a particle black-hole to particle black-hole phenomena (as distinct from gravitational waves) update throughout the universe in real-time?
The dimension of time in physics would be a measure of relative motion and so although deriving from the variable age it would not be the same as age. If there were no motion, all particles and photons were still (no change of state), then the dimension time would not update, the variable age would however continue to increment. The analogy being pressing the pause button on a film, this would not affect the computer clock-rate itself.
- Programming relativity and gravity in a Planck unit Simulation Hypothesis
- Programming the Matrix via a Mathematical Electron, a Simulation Hypothesis Overview
- Mathematical electron
- Planck quantum gravity
- Planck black-hole
- Plato's Cave; the Source Code of God", online edition
- Simulation Argument -Nick Bostrom's website
- Our Mathematical Universe: My Quest for the Ultimate Nature of Reality -Max Tegmark
- Dirac-Kerr-Newman electron -Alexander Burinskii
- The Matrix, (1999 film)
- Pythagoras "all is number" - Stanford University
- Simulation Hypothesis
- Mathematical universe hypothesis
- Philosophy of mathematics
- Philosophy of physics
- Macleod, M.J. 2003-2019, "Plato's Cave; the Source Code of God", online edition
- Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/
- https://www.youtube.com/watch?v=yqbS5qJU8PA, David Chalmers, Serious Science
- The Matrix as Metaphysics, David Chalmers http://consc.net/papers/matrix.pdf
- Are We Living in a Computer Simulation?https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/
- Planck scale, Brian Greene; ""
- Planck scale, Brian Greene; ""
- Macleod, M.J. "Programming Planck units from a mathematical electron; a Simulation Hypothesis". Eur. Phys. J. Plus 113: 278. 22 March 2018. doi:10.1140/epjp/i2018-12094-x.
- Macleod, M.J. 2003-2019, "Plato's Cave; the Source Code of God", online edition
- Macleod, Malcolm; "Programming relativity and gravity in a Planck unit Simulation Hypothesis". RG. 26 March 2020. doi:10.13140/RG.2.2.31308.16004.