"While classifying emergent particle behaviors might not seem fundamental, some experts, including Xiao-Gang Wen of the Massachusetts Institute of Technology, say the new rules of emergent phases show how the elementary particles themselves might arise from an underlying network of entangled bits of quantum information, which Wen calls the “qubit ocean.”"
To everybody (especially physicists) who think, elementary particles could be really quasiparticles of a qubit-based medium at Planck scale, maybe this is the (Quantum-Gravity) GUT you are looking for, if you could consider the ideas below, for just few minutes:
This is the GUT problem really:
All the physical experiments and observations in history are telling us that Universe acts,
according to Quantum Mechanics (which is discrete and probabilistic) at smallest scales,
and according to Relativity (which continuous and deterministic) at largest scales.
Is there a more fundamental theory that combines both QM and Relativity into one?
Here is an answer proposal to consider:
Whenever we want to solve a really big and complicated problem, how about first we try to simplify it as much as possible? Is there any known simple analogy (toy model) for the GUT problem?
What if really there is?
There is a known (by computer scientists) simple 2d/3d Cellular Automaton called FHP. It is used for (basic) 2d/3d fluid simulations. It creates a toy universe (matrix) of cells. Each cell can be empty or contain a particle or (a particle size part of) an obstacle. Later computer software tracks all particle movements and collisions (with each other and/or any obstacles present). In this kind of fluid mechanics simulations, at smallest scales/resolutions (close to particle size), physics of the toy universe looks discrete and probabilistic (which is similar to Quantum Mechanics), and at largest scales, physics of the toy universe (which is Navier-Stokes physics), looks continuous and deterministic (which is similar to Relativity).
If so, then realize that those kind of (CA) fluid simulations actually create a new layer/level of reality/physics, as an emergent property! So if a very simple toy model can do that, why not our big and complicated Universe also could?
Okay but where is the GUT in above ideas one may ask:
Let's first assume, all elementary particles are quasiparticles of a qubit-based medium (at Planck scale). Then we can assume further that our theory (GUT) explains (all of) Quantum Mechanics and what is matter/antimatter. But even if so, then how we can explain Relativity (and what is spacetime)? Remember how FHP creates a new layer/level of reality/physics, as an emergent property? (And that it creates a continuous and deterministic universe (at largest scales) from discrete and probabilistic universe (at smallest scales).) Then what if the continuous and deterministic universe (at largest scales) of Relativity is created by the discrete and probabilistic universe (at smallest scales) of Quantum Mechanics?
Then one may still ask:
Okay, matter at largest scales can be explained by QM, but how spacetime can be explained from QM? What is spacetime is made of (at smallest scales), according to QM? This is what it really says, isn't it? Spacetime is made of quantum vacuum, which is made of virtual particles keep popping in and out of existence, everywhere in our Universe. Then isn't that really means, our perception of spacetime (and all of its properties according to Relativity), must be created by quantum vacuum? (Which would mean that virtual particles are creating spacetime, just like real particles are creating matter.) (Also realize if spacetime is quantum vacuum then Casimir Force is artificial gravity!)
Now realize that, if these above are assumed/accepted to be true, then finding the answers for many other big problems in physics is really not that hard to work out:
For example, what is the true nature of time, what is a Black Hole is made of, what is Dark Matter?
I think FHP model can answer a lot about true nature of time!
Only thing BHs could be really made of is Planck particles! (But if they are not made of any particles then they could be only pure balls of max dense spacetime!)
I think what all DM experiments/observations are really telling us is that DM is not made of particles (matter). Now remember that our GUT above tells us that everything in the Universe is matter or spacetime! And if so, then, isn't that mean, if DM is not any form of matter/particle, then it must be made of spacetime! Then what if, DM filaments of the Cosmic Web of our Universe, are really higher density regions of spacetime?
Okay then what really is gravitational field?
If spacetime is an emergent property medium created by virtual particle medium of quantum vacuum,
and since gravitational fields modify spacetime curvature, then what we call gravitational field must be a previously unknown type of vacuum polarization!
Okay if we really defined a full GUT above for unification of QM and Relativity, is that mean we really have a TOE here?
No, because remember these chains of reasoning all started by assuming, all elementary particles are quasiparticles of a qubit-based medium (at Planck scale).
That is the missing part to have a full TOE candidate here, otherwise it is a GUT!
Also where is the explanation for Dark Energy and expansion of Universe?
If we look at our Universe at largest scales, we see the cosmic web of Dark Matter expanding.
If Dark Matter is higher density regions of spacetime, then expansion of Universe maybe kind of like the surface of a boiling soup, or the inside of a rising dough. So what maybe causing our Universe to expand could be a currently unknown internal energy conversion process (like how a dough rise), or it could be because of addition of (negative) energy to our Universe (like a boiling soup) from outside of it (if really exists).
https://www.quantamagazine.org/mathematicians-find-wrinkle-in-famed-fluid-equations-20171221/
Realize that whether real world fluids made of atoms, or computer world fluids made of particles in a matrix of cells, fully continuous world of Navier-Stokes could really only happen, if particle size making a fluid is zero. So fully continuous world of Navier-Stokes is always the limit case for infinite resolution fluid dynamics/simulation. Since FHP is much more simple than real world fluids, how about we try to understand Navier-Stokes using FHP CA, instead of real world fluids?
Imagine if we started with an FHP matrix of N by N with M particles and described them mathematically as a set of discrete particle equations, later, we assumed N and M values goes to infinity and that gives us the continuous Navier-Stokes equations in 2d. Realize that continuous Navier-Stokes equations are really the boundary condition of a math problem, asking exact mathematical explanation, for how they are created from a (simplest possible, like FHP) discrete particle world, as an emergent property. Also realize that Quantum-Gravity GUT problem also could seen as a mathematical emergent property problem, use continuous equations of (General) Relativity as the boundary condition at infinite resolution, start from discrete equations of Quantum Mechanics.
Further realize that TOE problem also could seen as a mathematical emergent property problem,
that asks, use continuous mathematical structure descriptions of elementary quantum particles as the boundary condition (at infinite resolution), start from discrete equations of particles/qubits at Planck scale. Realize then the TOE emergent property problem naturally mathematically must harder than the GUT emergent property problem. That is because, in the GUT problem, we have the set of boundary conditions for both ends (discrete at left vs continuous at right, where resolution increases from left to right) of a mathematical emergent property problem. (Realize it is also the same problem situation for Navier-Stokes emergent property problem. If we use FHP then we have the set of boundary conditions for both ends (discrete at left vs continuous at right, where resolution increases from left to right) of a mathematical emergent property problem.) But in the TOE problem realize, we have only the set of boundary conditions for the right side (equations of continuous mathematical structure of elementary particles), and asked to find the left side, discrete equations of particles/qubits at Planck scale.
Also realize that, in the mathematical setup of the GUT and the TOE emergent property problems, for the GUT, QM is the boundary condition for the left (discrete) side, and for the TOE, QM is the boundary condition for the right (continuous) side. That means for the GUT problem, QM needs to be mathematically defined as a set of discrete particle dynamics (movement and collision rules) equations (which are fully known today?). That means for the TOE problem, QM needs to be mathematically defined as a set of continuous elementary particle structure equations, which would be the set of elementary particle definition equations of Standard Model. (Standard Model would really have no choice but mathematically define structure of each elementary particle as continuous, since it does not assume existence of a deeper level of reality at an even smaller scale (Planck scale).
Of course currently it is unknown whether set of elementary particles in Standard Model is really complete or not. (My prediction is a least one more elementary particle waiting to be discovered: Planck particle, which BHs are maybe made of.) (How about gravition: I think if it really exists, it must be a quasiparticle of quantum vacuum that creates spacetime as an emergent property, not really an elementary quantum particle of Standard Model.)
Also realize that, in the general mathematical setup of emergent property problems, like the Navier-Stokes problem, the (Quantum-Gravity) GUT problem, the TOE problem, in the general case, there are three different problem setup cases:
1) The set of discrete particle mechanics equations are provided for the left (discrete math) side, as a boundary condition, and we are asked to find the set of continuous field mechanics equations for the right (continuous math) side.
2) The set of continuous field mechanics equations are provided for the right (continuous math) side, as a boundary condition, and we are asked to find the set of discrete particle mechanics equations for the left (discrete math) side.
3) Both sets of equations (a set of discrete equations for left and a set of continuous equations for right) are provided, as the boundary conditions, and we are asked to find (mathematically), how the set of discrete equations at left side creates the set of continuous equations at right side, as its emergent property, and vice versa.
Also realize that, we have (at least currently), no standard mathematical notation system that can express any kind of particular emergent property problem (so that we could try to find general solution equation(s)/algorithm(s)).
(If we had a standard mathematical notation that can express any emergent property problem, then someday maybe we could use advanced quantum computers, to extremely fast search between all possible sets of solution symbols, and try to find solutions (expressing valid, discrete or continuous equation sets), containing the minimal number of symbols (of our (future) standard mathematical notation). Meaning, then, we would be looking for minimal length strings, made of our standard mathematical notation symbols, which are valid mathematical solutions, for the problems we have, like the Navier-Stokes, the GUT, the TOE emergent property problems.)
Also realize that, in the emergent property problem case 3, since we have both boundary conditions (discrete and continuous sets of equations), and the solution (discrete or continuous set of equations, whichever we want), depends on what resolution (scale level) we choose. For example, if the mathematical emergent property problem setup is the GUT, and if we choose a scale any close to an average human size, we should expect to get the discrete equations of Quantum Mechanics which are approximating the continuous equations of Newton Physics at that scale, or the continuous equations of Relativity which are approximating the continuous equations of Newton Physics at that scale.
Then realize that, the (Quantum-Gravity) GUT (emergent property problem) is already solved:
Because we have the both sets of (discrete and continuous) equations defined as boundary conditions (at left discrete Quantum Mechanics (Particle Dynamics) equations, and at right continuous Relativity equations (at infinite resolution scale limit)). We also know that at intermediate scales (like close to human size scales), equations of Quantum Mechanics reduce to an approximation of Newton Mechanics, and equations of Relativity also reduce to an approximation of Newton Mechanics, just as we would expect based on all the physics we experimented/observed at those scales (and that is actually how we (including Newton) discovered Newton Mechanics. So it can be said that we already know, as we look at how the reality/Universe physically/mathematically works, in different size scales, going from average size of elementary particles to average size of the galaxies for example, we can theoretically/experimentally/observationally show that, at lowest scales, reality works following purely/perfectly discrete rules of Quantum (Particle) Mechanics, and at the highest scales, reality works following purely/perfectly continuous rules of Relativity (Field) Mechanics. And, at any size scale, in between the both extreme limit cases, we already know that the physics at that selected size scale depends only on, if that size scale is closer to pure/perfect, Quantum physics side at left, or the Relativity physics side at right. So it should be possible to determine how exactly the scale variable value determines the exact mathematical nature of physics at that (any selected) scale.
Is the scale variable of the GUT emergent property problem, operate like a linear weight variable like: Physics(scale)=scale*Relativity+(1-scale)*Quantum, where scale is between 0 and 1 (after normalized from being in between average particle size scale and average galaxy size scale).
(Or normalization scale could be chosen to be between smallest particle size (Planck particle size) and size of the whole Universe. So the choice of the normalization scale, determines the scale range of the emergent problem, and what scales its solutions would apply.)
Then some important questions:
Is the scale really works linearly, like in above equation, in our real Universe? (Or it works a non-linear way (currently unknown)?
Is the scale works the same way for all kinds of mathematical emergent property problems?
One way to answer would be, if we setup many simple emergent property problems, each with both boundary conditions given, and try to find out how scale changes the physics, at different scale values, and try to find a fitting curve, from those scale point physics. Then in the end, we could clearly see if scale changes the physics always linearly or non-linearly, and with always the same general equation (curve), or not.
One such simplified emergent property problem is clearly FHP. Imagine, if we analyzed the physical behaviors (mechanics) of FHP fluid simulations, going from single particle scale resolution to large scale, nearly continuous looking, fluid dynamics. And if we checked/determined the physics is what share (of the whole) discrete particle physics and what other share (of the whole) is continuous field (Navier-Stokes) physics.
For example, if the scale variable really works the same linear way, for all emergent property problems, as the way suggested for the GUT problem above, then it would mean, this is the general equation for it:
Physics(scale)=scale*B+(1-scale)*A, where scale is normalized to be between 0 and 1.
A: discrete (particle) physics/mechanics/dynamics
B: continuous (field) physics/mechanics/dynamics
Of course, if someday we can define/express all mathematical emergent property problems in a standard general way, then it maybe possible to find the general equation of scale, applying to any emergent property problem (physical system), if really exists, (instead of trying to do curve fitting).
I think General Emergent Property Problem is quite possibly the greatest unsolved problem in all of mathematics, physics, computer science. (Realize its utmost importance in physics and realize solving even a special (maybe the simplest) case of it, is a Millennium Problem!)
Realize that, it is actually a Cellular Automaton problem. For example, in the case of TOE, at right (continuous) side, we have the set of elementary particle (continuous) structure definitions of Standard Model. We are asked to find, the unknown set of discrete equations (maybe zero or any number of valid solutions possible), that would create the right side perfectly as an emergent property, at infinite resolution. So in special case of the TOE problem, we are asked to find any/all/simplest/shortest (Planck scale) Cellular Automaton definition, that would be able to create all elementary particles of Standard Model perfectly, at infinite resolution limit. Also realize that any such Cellular Automaton would need to be qubit-based, because of quantum nature of elementary particles of Standard Model! (For that Cellular Automaton what we need is the full set of all possible cell states and the full set of cell state transition rules.) (Why it needs to be Planck scale, because that is where (the scale) our known physics equations breakdown and become invalid solutions! And our basic laws of physics indicate Planck Units are the base measurement units of our Universe!)
What if we done that and created a quantum computer simulation of our (any solution we can find) Cellular Automaton and discovered it does not look like really matching to our Universe, what then? I think that would mean Standard Model is incomplete?!
Also realize that, even though it could be said the GUT problem is already solved, for a true test of it, and also to establish validity of the whole Emergent Property idea, we would need to convert all known quantum elementary particle mechanics/dynamics (movement and collision rules) into a Cellular Automaton definition form. Later, we would need to do, either mathematically show that our CA would recreate full General Relativity at infinite scale resolution limit, and/or create a computer simulation, and look at the action, at as large scales (at as large resolutions) possible, and try to determine, if the action, really matches to General Relativity (field mechanics/dynamics), or not! (The action would also need to match Newton Mechanics at its valid scales!) (Also realize that any such Cellular Automaton would need to be qubit-based, because of quantum nature of elementary particles of Quantum Mechanics!)
Also realize that, in the case of the GUT problem, our Cellular Automaton (CA) solution, would need to include mechanics/dynamics of all elementary particles, including both matter and antimatter, including both real and virtual, including both negative and positive energy versions!
(Similarly in the the TOE problem, the set of continuous particle structure definitions (Standard Model) would need to be able to express all elementary particles, including both matter and antimatter, including both real and virtual, including both negative and positive energy versions!)
Obviously, if we solved both the GUT and the TOE emergent property problems, and showed their validity thru simulations, experiments, observations, then it would mean our reality created by a quantum cellular automata operating at Planck scale, and it creates QM at higher scales, and it creates Relativity at even higher scales, in our Universe!
And since the TOE CA is would need to be based on a crystal-like solid matrix of cells (which creates elementary quantum particles as its quasiparticles), and if we also consider expansion of our Universe, it would mean our Universe/Reality is like an expanding bubble/sphere of information, essentially! (But what if fluid/gas-based (no solid (ordered/random) matrix/grid) CA solutions are also possible?)
Do we really have the complete solution for the (Quantum-Gravity) GUT emergent property problem? It actually still depends. If we look at CA (FHP/LBM) used for fluid simulations, which we now know are actually physical models, capable of numerically solving the Navier-Stokes emergent property problem, they require a full set of movement and collision rules to handle mechanics/dynamics of their particles. In the GUT problem, we need the full set of discrete equations defining movements of all kinds of elementary quantum particles (would composite particles use the same rules or require their own set of rules?), and also need the full set of discrete equations defining collisions of all kinds of elementary quantum particles (would composite particles use the same rules or require their own set of rules?) (Amplituhedron?).
Is beauty really important in mathematics, physics, computer science? Can beauty really guide us towards the truth? I think it really depends on the sense of beauty of a scientist. Personally for me, if our Universe/Reality is really created by a very advanced Planck Scale CA-based Quantum Computer, I think it would be absolutely beautiful! (For the TOE CA, my sense of beauty tells me, it would be best, if each Planck Scale cell state represented by a Sedenion (16D number) (which is also can be seen/used as 2 Octonions (8D numbers), or 4 Quaternions, or 8 Complex Numbers, or 16 Real Numbers).)(And imagine, if each of those 16 real numbers was a physical qutrit (using Balanced Ternary (-1, 0, 1) state values).) (Why Universe would want/need to use qutrits (using Balanced Ternary), instead of qubits (using Binary)? Because both the TOE CA and the GUT CA would need to be able to represent both positive and negative energy particles or fields, and also neither.) (Why Universe would want/need to use Sedenions and all the others? Because, I think, when number of dimensions of numbers/variables/constants, used in mathematical/physical equations/formulas, increases/doubles, their expressive/computational/solution powers also increases/doubles. Think about how much mathematical/physical progress was made because of discovery of Complex Numbers. And also I think many experiments and observations show that our Universe does not really disappoint, when it comes to realizing even most extreme conditions/possibilities :-)
(20180113)
So, if, both 2d/3d FHP CA and LBM CA (particle physics) are creating Navier-Stokes (field physics) as their emergent property, they are both valid solutions for the Navier-Stokes emergent property problem, and there is no difference between them? (Also, both FHP CA and LBM CA algorithms have many different versions for simulating different fluids/gases.) Actually, each different version would create a different version of 2d/3d general Navier-Stokes equations/physics, as its emergent property! For example, if LBM CA is considered, values of its free parameters (constants) selected, determine, values of the global constants of the fluid/gas created, as the emergent property.
And I think, that means, in general, global constants of each emergent property (at right side of the problem setup) is determined by global constants of the CA (at left side of the problem setup). This would imply, for example, it must be possible to calculate any global constants in (General) Relativity equations, using the global constants in Quantum Mechanics equations (when it redefined as a CA). And, similarly, it must be possible to calculate any global constants in Quantum Mechanics equations (when redefined as an Emergent Property (EP)), using the global constants in the TOE CA.
I think, there are big mathematical questions waiting to be answered about General Emergent Property Problem, for example:
Since, we can always calculate the constants at right side, from the constants at left side, can we also always calculate the constants at left side from the constants at right side? (Is the relationship always one-to-one; can it be one-to-many; can it be many-to-one?)
As the resolution/scale goes to infinity, are the values of constants for the emergent property, always converge to constant values? Can they diverge to +/- infinity? Can they change periodically, chaotically, or like a fractal (deterministic/non-deterministic) curve?
(20180114)
If spacetime is an emergent property created by virtual particles of quantum vacuum,
what is the total energy in unit volume of quantum vacuum?
I think, that must be the total energy of all elementary particles currently in existence in that volume in any given moment in time. (Also think that calculating it, would require knowing creation probabilities, and average durations, for all virtual elementary particles (assuming Standard Model is complete).)
If quantum vacuum is always creating positive energy elementary particles (always as matter-antimatter pairs?), then it would mean quantum vacuum energy is positive.
If quantum vacuum is always creating both positive and negative energy elementary particles (always as pairs?), then it would mean quantum vacuum energy is zero (neutral/signless).
If quantum vacuum energy is positive, then Dark Energy (which causes expansion of Universe), also must be positive. (Because, if it was negative, then it would cancel out quantum vacuum energy and make Universe contract, instead of expand.)
And, if quantum vacuum energy is neutral, then Dark Energy must be a neutral form of energy, also. (If it was really zero then it would mean Universe will expand forever to infinite size! But, I think, if our reality is created by a CA Quantum Computer matrix/grid of Planck scale cells, then our Universe is really an expanding ball of information. Meaning, all forms of matter and energy are just information. And, all our experiments and observations show that energy is always conserved. Meaning, information must be always conserved by the CA Quantum Computer matrix/grid creating our reality. (All known conservation laws would be also, ultimately, because of the conservation of information law of our reality.) And, if information is always conserved, it would mean, information would not be created out of nothing by our reality (so it must be provided initially for Big Bang to happen).) So, if quantum vacuum energy is calculated to be zero, it would not mean quantum vacuum has no energy (and so it can be created infinitely), but it would mean quantum vacuum energy and Dark Energy are neutral/signless forms of energy.
Also realize that, in the emergent property problem case 3, since we have both boundary conditions (discrete and continuous sets of equations), and the solution (discrete or continuous set of equations, whichever we want), depends on what resolution (scale level) we choose. For example, if the mathematical emergent property problem setup is the GUT, and if we choose a scale any close to an average human size, we should expect to get the discrete equations of Quantum Mechanics which are approximating the continuous equations of Newton Physics at that scale, or the continuous equations of Relativity which are approximating the continuous equations of Newton Physics at that scale.
Then realize that, the (Quantum-Gravity) GUT (emergent property problem) is already solved:
Because we have the both sets of (discrete and continuous) equations defined as boundary conditions (at left discrete Quantum Mechanics (Particle Dynamics) equations, and at right continuous Relativity equations (at infinite resolution scale limit)). We also know that at intermediate scales (like close to human size scales), equations of Quantum Mechanics reduce to an approximation of Newton Mechanics, and equations of Relativity also reduce to an approximation of Newton Mechanics, just as we would expect based on all the physics we experimented/observed at those scales (and that is actually how we (including Newton) discovered Newton Mechanics. So it can be said that we already know, as we look at how the reality/Universe physically/mathematically works, in different size scales, going from average size of elementary particles to average size of the galaxies for example, we can theoretically/experimentally/observationally show that, at lowest scales, reality works following purely/perfectly discrete rules of Quantum (Particle) Mechanics, and at the highest scales, reality works following purely/perfectly continuous rules of Relativity (Field) Mechanics. And, at any size scale, in between the both extreme limit cases, we already know that the physics at that selected size scale depends only on, if that size scale is closer to pure/perfect, Quantum physics side at left, or the Relativity physics side at right. So it should be possible to determine how exactly the scale variable value determines the exact mathematical nature of physics at that (any selected) scale.
Is the scale variable of the GUT emergent property problem, operate like a linear weight variable like: Physics(scale)=scale*Relativity+(1-scale)*Quantum, where scale is between 0 and 1 (after normalized from being in between average particle size scale and average galaxy size scale).
(Or normalization scale could be chosen to be between smallest particle size (Planck particle size) and size of the whole Universe. So the choice of the normalization scale, determines the scale range of the emergent problem, and what scales its solutions would apply.)
Then some important questions:
Is the scale really works linearly, like in above equation, in our real Universe? (Or it works a non-linear way (currently unknown)?
Is the scale works the same way for all kinds of mathematical emergent property problems?
One way to answer would be, if we setup many simple emergent property problems, each with both boundary conditions given, and try to find out how scale changes the physics, at different scale values, and try to find a fitting curve, from those scale point physics. Then in the end, we could clearly see if scale changes the physics always linearly or non-linearly, and with always the same general equation (curve), or not.
One such simplified emergent property problem is clearly FHP. Imagine, if we analyzed the physical behaviors (mechanics) of FHP fluid simulations, going from single particle scale resolution to large scale, nearly continuous looking, fluid dynamics. And if we checked/determined the physics is what share (of the whole) discrete particle physics and what other share (of the whole) is continuous field (Navier-Stokes) physics.
For example, if the scale variable really works the same linear way, for all emergent property problems, as the way suggested for the GUT problem above, then it would mean, this is the general equation for it:
Physics(scale)=scale*B+(1-scale)*A, where scale is normalized to be between 0 and 1.
A: discrete (particle) physics/mechanics/dynamics
B: continuous (field) physics/mechanics/dynamics
I think General Emergent Property Problem is quite possibly the greatest unsolved problem in all of mathematics, physics, computer science. (Realize its utmost importance in physics and realize solving even a special (maybe the simplest) case of it, is a Millennium Problem!)
Realize that, it is actually a Cellular Automaton problem. For example, in the case of TOE, at right (continuous) side, we have the set of elementary particle (continuous) structure definitions of Standard Model. We are asked to find, the unknown set of discrete equations (maybe zero or any number of valid solutions possible), that would create the right side perfectly as an emergent property, at infinite resolution. So in special case of the TOE problem, we are asked to find any/all/simplest/shortest (Planck scale) Cellular Automaton definition, that would be able to create all elementary particles of Standard Model perfectly, at infinite resolution limit. Also realize that any such Cellular Automaton would need to be qubit-based, because of quantum nature of elementary particles of Standard Model! (For that Cellular Automaton what we need is the full set of all possible cell states and the full set of cell state transition rules.) (Why it needs to be Planck scale, because that is where (the scale) our known physics equations breakdown and become invalid solutions! And our basic laws of physics indicate Planck Units are the base measurement units of our Universe!)
What if we done that and created a quantum computer simulation of our (any solution we can find) Cellular Automaton and discovered it does not look like really matching to our Universe, what then? I think that would mean Standard Model is incomplete?!
Also realize that, even though it could be said the GUT problem is already solved, for a true test of it, and also to establish validity of the whole Emergent Property idea, we would need to convert all known quantum elementary particle mechanics/dynamics (movement and collision rules) into a Cellular Automaton definition form. Later, we would need to do, either mathematically show that our CA would recreate full General Relativity at infinite scale resolution limit, and/or create a computer simulation, and look at the action, at as large scales (at as large resolutions) possible, and try to determine, if the action, really matches to General Relativity (field mechanics/dynamics), or not! (The action would also need to match Newton Mechanics at its valid scales!) (Also realize that any such Cellular Automaton would need to be qubit-based, because of quantum nature of elementary particles of Quantum Mechanics!)
Also realize that, in the case of the GUT problem, our Cellular Automaton (CA) solution, would need to include mechanics/dynamics of all elementary particles, including both matter and antimatter, including both real and virtual, including both negative and positive energy versions!
(Similarly in the the TOE problem, the set of continuous particle structure definitions (Standard Model) would need to be able to express all elementary particles, including both matter and antimatter, including both real and virtual, including both negative and positive energy versions!)
Obviously, if we solved both the GUT and the TOE emergent property problems, and showed their validity thru simulations, experiments, observations, then it would mean our reality created by a quantum cellular automata operating at Planck scale, and it creates QM at higher scales, and it creates Relativity at even higher scales, in our Universe!
And since the TOE CA is would need to be based on a crystal-like solid matrix of cells (which creates elementary quantum particles as its quasiparticles), and if we also consider expansion of our Universe, it would mean our Universe/Reality is like an expanding bubble/sphere of information, essentially! (But what if fluid/gas-based (no solid (ordered/random) matrix/grid) CA solutions are also possible?)
Do we really have the complete solution for the (Quantum-Gravity) GUT emergent property problem? It actually still depends. If we look at CA (FHP/LBM) used for fluid simulations, which we now know are actually physical models, capable of numerically solving the Navier-Stokes emergent property problem, they require a full set of movement and collision rules to handle mechanics/dynamics of their particles. In the GUT problem, we need the full set of discrete equations defining movements of all kinds of elementary quantum particles (would composite particles use the same rules or require their own set of rules?), and also need the full set of discrete equations defining collisions of all kinds of elementary quantum particles (would composite particles use the same rules or require their own set of rules?) (Amplituhedron?).
Is beauty really important in mathematics, physics, computer science? Can beauty really guide us towards the truth? I think it really depends on the sense of beauty of a scientist. Personally for me, if our Universe/Reality is really created by a very advanced Planck Scale CA-based Quantum Computer, I think it would be absolutely beautiful! (For the TOE CA, my sense of beauty tells me, it would be best, if each Planck Scale cell state represented by a Sedenion (16D number) (which is also can be seen/used as 2 Octonions (8D numbers), or 4 Quaternions, or 8 Complex Numbers, or 16 Real Numbers).)(And imagine, if each of those 16 real numbers was a physical qutrit (using Balanced Ternary (-1, 0, 1) state values).) (Why Universe would want/need to use qutrits (using Balanced Ternary), instead of qubits (using Binary)? Because both the TOE CA and the GUT CA would need to be able to represent both positive and negative energy particles or fields, and also neither.) (Why Universe would want/need to use Sedenions and all the others? Because, I think, when number of dimensions of numbers/variables/constants, used in mathematical/physical equations/formulas, increases/doubles, their expressive/computational/solution powers also increases/doubles. Think about how much mathematical/physical progress was made because of discovery of Complex Numbers. And also I think many experiments and observations show that our Universe does not really disappoint, when it comes to realizing even most extreme conditions/possibilities :-)
(20180113)
So, if, both 2d/3d FHP CA and LBM CA (particle physics) are creating Navier-Stokes (field physics) as their emergent property, they are both valid solutions for the Navier-Stokes emergent property problem, and there is no difference between them? (Also, both FHP CA and LBM CA algorithms have many different versions for simulating different fluids/gases.) Actually, each different version would create a different version of 2d/3d general Navier-Stokes equations/physics, as its emergent property! For example, if LBM CA is considered, values of its free parameters (constants) selected, determine, values of the global constants of the fluid/gas created, as the emergent property.
And I think, that means, in general, global constants of each emergent property (at right side of the problem setup) is determined by global constants of the CA (at left side of the problem setup). This would imply, for example, it must be possible to calculate any global constants in (General) Relativity equations, using the global constants in Quantum Mechanics equations (when it redefined as a CA). And, similarly, it must be possible to calculate any global constants in Quantum Mechanics equations (when redefined as an Emergent Property (EP)), using the global constants in the TOE CA.
I think, there are big mathematical questions waiting to be answered about General Emergent Property Problem, for example:
Since, we can always calculate the constants at right side, from the constants at left side, can we also always calculate the constants at left side from the constants at right side? (Is the relationship always one-to-one; can it be one-to-many; can it be many-to-one?)
As the resolution/scale goes to infinity, are the values of constants for the emergent property, always converge to constant values? Can they diverge to +/- infinity? Can they change periodically, chaotically, or like a fractal (deterministic/non-deterministic) curve?
(20180114)
If spacetime is an emergent property created by virtual particles of quantum vacuum,
what is the total energy in unit volume of quantum vacuum?
I think, that must be the total energy of all elementary particles currently in existence in that volume in any given moment in time. (Also think that calculating it, would require knowing creation probabilities, and average durations, for all virtual elementary particles (assuming Standard Model is complete).)
If quantum vacuum is always creating positive energy elementary particles (always as matter-antimatter pairs?), then it would mean quantum vacuum energy is positive.
If quantum vacuum is always creating both positive and negative energy elementary particles (always as pairs?), then it would mean quantum vacuum energy is zero (neutral/signless).
If quantum vacuum energy is positive, then Dark Energy (which causes expansion of Universe), also must be positive. (Because, if it was negative, then it would cancel out quantum vacuum energy and make Universe contract, instead of expand.)
And, if quantum vacuum energy is neutral, then Dark Energy must be a neutral form of energy, also. (If it was really zero then it would mean Universe will expand forever to infinite size! But, I think, if our reality is created by a CA Quantum Computer matrix/grid of Planck scale cells, then our Universe is really an expanding ball of information. Meaning, all forms of matter and energy are just information. And, all our experiments and observations show that energy is always conserved. Meaning, information must be always conserved by the CA Quantum Computer matrix/grid creating our reality. (All known conservation laws would be also, ultimately, because of the conservation of information law of our reality.) And, if information is always conserved, it would mean, information would not be created out of nothing by our reality (so it must be provided initially for Big Bang to happen).) So, if quantum vacuum energy is calculated to be zero, it would not mean quantum vacuum has no energy (and so it can be created infinitely), but it would mean quantum vacuum energy and Dark Energy are neutral/signless forms of energy.
I think, to better understand Big Bang, expansion of Universe, Dark Energy, we can further use 2d/3d FHP/LBM CA fluid simulations as simplified models/analogies. I think they are mostly used for fluid flow simulations, not for static fluid in a container. Realize, if the GUT CA and the TOE CA ideas are really correct, then our Universe also could be like a fluid flow simulation. In fluid flow simulations, using CA, there is a continuous incoming flow of new particles to be simulated. What if, each (stable) elementary quantum particle is always stable, even if it is a virtual particle? Imagine, if each elementary particle always can either have full necessary positive/negative energy to continuously exist (as told by Standard Model), or it would stay as same (stable) elementary particle, but as virtual. (And, if it is virtual, then it pops-in-out of existence (actually just appears and disappears, from our view/measurements), with a certain random uniform probability.) (And, imagine, when real (also virtual?) particles, collide and get destroyed (or decay), their total available positive/negative energy gets shared, between (always existing) virtual particles closest nearby, to get charged/absorbed to become real particles.)
And, if those above are correct, it would imply that our Universe could be really like a CA fluid flow simulation. Imagine, new quantum (stable/unstable) particles are uniformly and randomly keep getting fed (somehow) into our Universe/reality ball of real/virtual quantum particles, starting from the time of Big Bang. Imagine, if the incoming flow of particles (all/mostly) were real particles, for a certain time duration, at the beginning, which created matter later. Imagine, if the incoming flow of particles (all/mostly) were virtual particles, afterwards, until today and keep going (so they keep creating new spacetime!).
I think it is also possible that each and every virtual particle keeps appearing and disappearing from our reality in periodical oscillations, kind of like how any Neutrino oscillate. And if so, it could be that each virtual particle increases its frequency of periodical oscillations as it encounters and absorbs positive/negative more energy available from its local environment. (And if its frequency ever reaches a certain threshold (resonant?) value then it turns into a real particle.)
https://www.quantamagazine.org/what-makes-the-hardest-equations-in-physics-so-difficult-20180116/
How do we know if Navier-Stokes equations are always stable (fluid velocity never could go to infinity anywhere anytime)?
Remember (from above) that Navier-Stokes problem is an emergent property problem, and FHP CA and LBM CA are its special and general (valid) solutions (at infinite resolution/scale limit) (which is already known/proven). And realize that, one thing common, in both FHP CA and LBM CA, is that (all) particle velocities are always bounded!
Okay but how is that mean Navier-Stokes equations are always stable (fluid velocity never could go to infinity anywhere anytime)? That is because both in the real world and in computer fluid simulations, resolution (scale) is always finite! That is why fluid (particle) velocities can never add up to infinity anywhere anytime, since (all) particle velocities are always bounded (finite) numbers! (Keep in mind that, in the real world, all fluids are made of atoms/molecules, and in the computer simulations, all fluids are simulated grids of certain finite resolution.)
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