Algis Džiugys (Dziugys): Is our world virtual? Mechanical solution

Summary: This article discusses theory and experiment, which either might prove or deny the possibility that our personalities and the world around us can be a computer model of virtual reality.

Algis Džiugys

Lithuanian Energy Institute, Breslaujos 3, 3035 Kaunas, 6^th March, 2000

According to nowadays physics our individualities are virtual people (virtuals), functioning in very complicated biological machines, however, to be sure that our bodies and the environment are real. After creation of computers and artificial intelligence, humans started to wonder if they are not a part of some giant computer program themselves, because there are no known obstacles for creating a computer and a program, which would compose virtual people and their virtual environment as much complicated as we are and our world that we observe.

Let us try to imagine that such giant computer exists and it is operating on the similar or the same basis of our ordinary computers and it simulates our world including us. As we are sure that our world is real and it is possible that the creators could have made an effort to make us not realize that we are programs. Therefore, we, virtuals, would discover world's laws that would be presented by the computer and would think that in our possibly real world those processes are real and must be such. Because of that, it is hardly possible that through exploration of our world we would find gaps that would show real origin of our virtual world. However, real world should be without inner contradictions, which is doubtful in artificial virtual world.

So, according to nowadays physics the world is made from basic elementary particles. If those elementary particles are just computer models and computer is not infinitively "big", then for the calculation of single particle movement and interaction with other particles, computer is using numbers saved within the computer memory with information bytes which number depends on how accurate the numerical simulation must be. That means that the movement of particles is estimated by finite accuracy due to rounding-off errors, because for the absolute accuracy infinite number of bytes for definition of every single particle is needed. Meanwhile, in our real world, nature describes particles and their movement by using the same particles and their movement is estimated by absolute accuracy.

The movement and interactions of the particles in virtual world are described by specific laws. However, due to the limited modelling accuracy, particles are behaving differently from how laws describing their behaviour. This will be explained by an example in Fig.1. Behaving by the laws, the particle 1 should move from point A to point B and there impact the other particle 2 and then move to point C as it is showed by continuous line in Fig.1. If we calculated particle’s path analytically by using the laws of our world, we could calculate it as exact as we want. However, if the giant computer is modelling the events of virtual world digitally, then its modelled particle’ movement is going to be different from the expected one (as it is showed with dotted line in Fig.1) due to rounding-off errors. But if we, virtuals, are still sure that our world is real, then we will think of these round-off errors are as naturally regular (which are indeed natural) and the laws that define our world we will be describe in a bit different way than those which computer uses in order to model our world. For example, even if we accidentally discover a law used by simulating computer, we will construct additional theory of inventing something similar as Heisenberg's uncertainty principle or certain particles, which quickly appear and disappear (as virtual particles in nowadays physics), and while interacting with other particles, alter its path. These alterations, however, would not help us in any way, because if we do not know the real law, we do not know that those are the alterations.

Figure 1. Partilce’s theoretical path (continuous line) and digitally modelled path (dotted line)

If to think simplified, the main laws describing the world are two main laws of physics that describe the movement of objects in classical mechanics (Newton laws) and quantum mechanics (Schrodinger equation), and which are absolutely deterministic and reversible in time. Determinism means that if we know the state of particle at the beginning, we will be able to calculate it any time later. Reversibility in time means that if the particle 1 is in point C and then we reverse time back, the particle should go back to point A. Time reversibility also means that if the particle 1 is in the point C and we would reverse the momentum of all particles, then all the particles would go back to the initial points through the same paths. However, the round-offs of modelling of the virtual world are not reversible, what means if reversed time in modelling or reversed the momentum of particles, then particles would move back through different paths than they did before.

In order to understand it better, let’s digitally to model the virtual world, which is composed of 100 stretchy balls that move in a box without energy dissipation, the same way real atoms move. This particles system is very sensitive to round-offs, because even the smallest change of particle’s momentum alters the path of particles due to many impacts with other particles and then the calculated system state will be different from the theoretical one obtained by analytical calculations. Hence, at the initial moment, t₀ balls are placed in order, as it is shown in Fig.2 (a), give them randomly chosen velocity, then we define their dynamics and interactions by mechanical laws and begin estimating their movement. In the moment of virtual world’s time t₁ > t₀ we get the image as it is shown in Fig.2 (b). In digital experiment, it is easy to reverse time or reverse the momentum of all the particles at once, which has been done in the moment of t₁ (Fig.2 (c)). If we reversed the momentum and continued on calculating the time span t₁ ‑ t₀, we will get the particles placed as it is shown in Fig.2 (d), and those particles will be almost in the same state as in Fig.2 (a), because time span t₁ ‑ t₀ was enough small and the accuracy of calculation was sufficient too. But if reversed the momentum at the moment t₂ >> t₁ (Fig.3 (b-c)), then after the time span t₂ ‑ t₀, we will get the 3 (d) image, which will barely remind of initial state due to exponential growth of round-offs.

Let’s assume that we are able to do a real experiment with randomly chosen system of particles and we are able to reverse time or the momentum of all particles at once. And if we were able to get the same initial state from any status of the system, we could say that our world is not a model of a computer that is known to us. Then we could rest assure that we are not the programs until someone would come up with a computer that would operate on a different basis (for example, modelling the world by integer numbers).

But what if the particles did not go back to the initial state? There are some possibilities why:

We are a part of virtual world. We try to find the “gap” in the operational system as soon as possible, so we could save ourselves in the “disc”, until the Great Programmer did not turn off the computer.
We are not virtuals, but randomness exists and that is why the laws of the world are not deterministic and not reversible in time.
We are not virtuals, laws are deterministic, but not reversible in time due to reasons that are still not known to us, for example, due to discrete nature of space and/or time.