Quantum Field Simulator

 

Welcome to Smart Black Box

Quantum Field Theory (QFT) or is it just a simulation theory? Whether you call it a quantum field theory or a simulation theory, both do calculations based on mathematics. The existence of the universe and where we come from has amazed me for years. Now that there are more ideas from people around the world, the idea of what reality is has evolved in an interesting way. So many ideas you've never thought of before. Even among people around the world with no scientific or philosophical background, they have ideas about reality and even parallel realities. As many have thought, we already live in an illusionary reality or a simulation. But this illusion feels very real to me.

 

Einstein once said:

“Reality is merely an illusion, albeit a very persistent one.”

 

This quote got my brain cells working really hard. If reality is an illusion, then the universe must be an imagination. I'm not sure if this statement is true, but it feels right to me.

So I started this quest for what we are really made of. It is actually not wrong to say that we live in an illusionary world. Maybe we live in a computer simulation that is so good we don't even notice it. But the paradox is that the computer that simulates this reality must be made of 'something'. So what is this 'something' made of, a simulation in a simulation and you can go on forever. Scientists are beginning to believe that consciousness has something to do with this. Such as an observation that affects the outcome of the double slit experiment. But consciousness is a problem for scientists, because how do you measure consciousness? Let alone what is consciousness? This is another topic that I won't go into in depth because I want to talk about how reality is likely constructed and simulated. The simulator I have been working on since mid-2022 is just an approximation of how I think about how reality works. It is far from complete, but it is a start.

 

But there's also the aether theory, which has been criticized by many scientists and replaced by the quantum field theory, but I think there are some elements in both theories that make sense. The aether theory states that the medium must be a continuous space that carries the electromagnetic waves. And this medium is made of an invisible substance or field that is beyond our reach.

 

The proposed field is the carrier of electromagnetic waves, see above the entire electromagnetic spectrum.

 

I agree with the idea of an invisible substance or a field, but I have to disagree with the idea of a continuous space. Because a continuous space might work with mathematical equations, but in practice it doesn't make any sense at all. Because infinity large or infinity small is impossible to compute. The concept of infinity has amazed me for years, but I have to come to the conclusion that this is not always practical. The QFT, on the other hand, is more practical. But I can't follow the proposed equations that can be found on the internet, because this is way over my head. The idea of the quantum field is represented as a discrete space and consists of mass points connected by a spring. The distance between the points is known. Each point interacts with its neighbors to determine its location in space and therefore creates a wave that propagates through space. This is a very interesting idea.

So the QFT doesn't actually describe what the field is made of, but rather a concept of what it could be. Can we then say that both aether and QFT say that the field is made of an invisible substance or an imaginary substance? What I believe is that this substance is invisible to us from our perspective as a human that lives in a 3D world. But from the creator's point of view, seen from beyond our 3D reality, this field can be perceived. But the question is: "if there is a creator, then who creates the creator of our reality?". I know, some would say: "it's some guy sitting behind his computer, presses some buttons and he is playing a game!". I do have some idea about this paradox, but that requires a more detailed explanation and for now QFT is already difficult enough.

To simulate this field, one could use the proposed point of masses and springs in a 3D matrix. You could do this with complex formula's, but what if this can be simulated with a very simple formula. And I think I may have found a way to simulate this. I have discovered this formula by trial and error. The application and source code can be downloaded on my Github page. This application was initially developed to simulate the double-slit experiment to see if it can be done with this theory.

 

​​You can download the application at: https://github.com/dqnguyen59/QuantumFieldSimulator/releases Or download Java source code at: https://github.com/dqnguyen59/QuantumFieldSimulator ​Recommended graphics cards: NVIDIA RTX2080Ti, AMD Radeon RX6800 or higher. ​Watch video tutorial on YouTube:

 

 

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The Quantum Field Formula

Before we talk about the formula, first we have to ask the following questions. How is the field constructed? And what are the rules to make it work?

​​I believe that the field consists of a substance, which I call "a field of nodes", where each node has a number of properties that follow the rules of the laws of motion as we know them in physics. These properties are location, acceleration and velocity. The nodes are placed in a matrix form, where each node is connected to its neighbors. Each node can only have 6 neighbors, right, up, front, left, down and back. It takes energy to change a node's position and just like when a node changes position, it will distribute its energy evenly among its neighbors. And because of this effect it will cause a wave. The distance between the nodes must be the smallest ever, but not infinitely small. To give you an idea of how small this is, there are billions, billions, billions and billions of nodes that fit in the diameter of a hydrogen atom. How many nodes to be exact? See calculation below:

 

$\text{Planck length: } {1.616255} \times {10}^{-35} m$

$\text{Hydrogen atom}: {1.06} \times {10}^{-10} m$

$\text{Nodes } = \frac{Hydrogen atom} {Planck length} = \frac {{1.06} \times {10}^{-10}} {{1.616255} \times {10}^{-35}}$

$\text{Nodes } = {6.558}×{10}^{24}$ (6558000000000000000000000)

 

These smallest units (length, time, mass and temperature) have been postulated by Max Planck.

The video above is an example of what the field looks like when only one node oscillates in the center, say in a circular motion. The central node gives its energy to its neighbors and the neighbors also give its energy to its neighbors, and so on.

 

\begin{array}{rcl} \Large \text{Quantum Field Formula} \end{array} \begin{array}{rcl} \vec{a} & = & \text{node acceleration} \\ \vec{v} & = & \text{node velocity} \\ \vec{p} & = & \text{node position} \\ N & = & \text{neighbor node position} \\   &   & \left\{ N \in \mathbb{R}^n \hspace{0.15cm}|\hspace{0.15cm} \tiny Right, Up, Front, Left, Down, Back \normalsize \right\} \\ r & = & \text{constant radiation} \\   &   & \left\{ r \in \mathbb{R} \right\} \\ k & = & \text{constant wave speed} \\   &   & \left\{ k \in \mathbb{R} \text{ | } 0 \ge k \le 1 \right\} \\   &   & \\ \vec{a} & = & avg\small{(N, \vec{p})}\normalsize \\ avg\small{(N, \vec{p})}\normalsize & = & \Large \frac {k^2} {\left| N \right|} \sum \limits_{\vec{n} \in N} {\vec{n} - \vec{p}} \\         &   & \\ \vec{v} & = & nVel\small{(\vec{v},\vec{a})}\normalsize \\ nVel\small{(\vec{v},\vec{a})}\normalsize & = & \Large \left( {\vec{v}} + {\vec{a}} \right) {r} \\         &   & \\ \vec{p} & = & nPos\small{(\vec{p},\vec{v},\vec{a})}\normalsize \\ nPos\small{(\vec{p},\vec{v},\vec{a})}\normalsize & = & \Large {\vec{p}} + {\vec{v}} + \frac {1} {2} {\vec{a}} \\ \end{array}

 

​This is the formula (above) I discovered through trial and error. ​A very simple formula, without using any complicated math. For each node acceleration is calculated first. The new velocity is calculated with acceleration and its previous velocity as inputs. And the new position is calculated with acceleration, velocity and its previous position as inputs. ​This formula is actually derived from the physics formula of motion below.

 

\begin{array}{rcl} \Large \text{Motion Formula} \end{array} \begin{array}{rcl} a & = & \text{acceleration} \\ v_{\tiny 0} & = & \text{initial velocity} \\ v & = & \text{velocity} \\ x_{\tiny 0} & = & \text{initial position} \\ x & = & \text{position} \\ t & = & \text{time} \\   &   &   \\ v & = & v_{\tiny 0} + a \times t \\   &   &   \\ x & = & x_{\tiny 0} + v_{\tiny 0} \times t + {\frac{1}2} a \times t^2 \\ \end{array}

 

The calculation for the velocity and position are different, because time (t) is missing in my formula. ​There's a very good reason for that. ​Since we are working with Planck units, then we can say that one Planck-time is one frame and one Planck-length is the distance between the nodes. ​Which means t can be considered as 1, so t can be eliminated from the formula. ​The reason why the formula works is because of the calculation of acceleration. ​​The acceleration is calculated by averaging the distance of the node and its neighbors. ​​The calculated speed and position will be used when the next frame is calculated. ​​This way, each node updates its properties with each frame, and by executing these frames in quick succession, you see a wavy animation of the field. ​​Since each node is affected by the changes of its neighbors, it will create a rippling effect through space. ​The speed of the ripple can then be calculated. ​This ripple is similar to electromagnetic waves and so the speed of the ripple can also be compared to the speed of light. The constant k determines the speed of the ripple or the speed of light. This constant can be set between 0.0 and 1.0 and the lower the value the lower the speed. But also, the lower the value the higher the amplitude it will have. ​The radiation (r) is optional and will cause the wave to fade or even amplify. The constant r is by default 1.0. If this value is less than 1.0, then the wave will fade. And if the value is greater then 1.0, then the wave will amplify. ​​​​But amplifying the wave makes no sense at all, because it makes the wave infinitely large. ​​During the development of the application, the wave seems to fade, while the radiation is set to 1.0. ​This was tested when the wave was initiated once and since the wave is always contained in a box (with reflection), you would expect the wave to continue indefinitely. ​This may have been caused by the use of the Double data type. ​This data type has a length of 32 bits and an accuracy of 4.9E-324. But this imperfection can be compensated by empirically finding a radiation slightly higher than 1.0. Perhaps using integers would be a better choice as it eliminates these accuracy errors. The nodes do not actually move through space to an arbitrary position which may be very far away, but only oscillate within their limited area using their fixed location as a base. It is the nature of the interactions between the nodes that creates a wave through the field of nodes, or in other words through space.

 

 

Video tutorial: How to simulate a double-slit experiment?

 

The application is capable of creating walls. ​A wall contains nodes that are fixed and therefore immovable. Such nodes cannot be affected by other nodes. ​​However, a fixed node affects other nodes that are not fixed. ​A node that is near a fixed node will have more difficulty changing its position than a node that is further away from a fixed node. ​Walls are like mirrors and reflect the wave that hits them, which can be seen in the simulation. ​If you make one slit in the wall, you can clearly see how the energy is dispersed at the opening of the slit. ​​If you make a double slit in the wall, you will clearly see an interference pattern like the picture above.​ The interference pattern occurred when the waves cancel each other out.​​

Although the formula I discovered with this simulation differs from the formula proposed in quantum field theory, I am surprised to see how this simple formula works so gracefully. ​​But I'm sure there is much more to discover, perhaps how an atom is constructed. ​The formula I discovered is far from complete, but I hope to find more in the future. ​​I'm amazed that the motion formula works just as well in the small-scale as Planck units as it does in our daily lives when we drive to work in our car.