“Could we ourselves be in such a computer simulation? Could what we think of as the universe be some sort of vault of heaven rather than the real thing?”
— Martin Rees, Astronomer Royal —
In this chapter, we will sketch our basic understanding of nature, laws of physics, models, simulations and confusion among them.
3.1 Nature, laws of physics and models
The main method used throughout this work is a computer simulation of nature. This method is based on believe that nature is understandable and has a mathematical underpinning.
Natural philosophers or physicists discovered that nature behaves according to regular patterns. They discovered that the behavior of nature is mathematically describable. Marquis Pierre Simon Laplace[24] thought that if we knew where all bodies in the universe are at a particular time and knew what their velocities are then by applying the discovered laws of physics – such as Newton’s laws – we could find out where they would be located at any time in the future. He imagined the universe as a clock mechanism so that everything is predictable. Such a finitely complex universe could be modeled exactly, if we knew initial positions and velocities of all particles during the “Big Bang”. In addition, we would get through such a simulation not just an approximation, but the exact reproduction of the evolution of such universe.
Is a description of phenomena in nature by the laws of physics exact? Science is in the state of permanent change and development. A scientific community continuously updates the laws of physics that describe patterns of nature. For example, Albert Einstein showed that Newton’s laws of motion do not apply to objects traveling at speeds close to the speed of light. However, Einstein himself knew that his work will be challenged one day – and it has already happened in astronomical and cosmological observations. We are facing the problem of apparently striking lack of mass-energy in the universe, which we must find in order to vindicate current laws of physics. Probably there is some dark matter and dark energy of yet unknown kind, but maybe our current laws of physics do not apply on the scales of universe.
Laws of physics were created by men and are not a precise description of nature. Laws of physics are only an incomplete and limited description of nature. Laws of physics do not govern nature’s behavior as the notion can suggest.
Greek astronomers were the first who devised and tested mathematical models of heavens, how the universe is working. Such a first known scientific modeler was Eudoxus[25] who tried to model the motion of planets with the set of uniformly rotating crystal spheres that held the planets, while the Earth was at the center. Since Eudoxus, people are improving models to be in always better agreement with an observable reality.
Again, the model always represents only a certain idealization. Thus, we should be cautious to identify any real physical phenomenon with the corresponding mathematical model. The model is an imperfect image of nature’s behavior. Through, some physicists motivated by an enormous success of physics believe that we are capable to fully understand nature[26].
Models are sometimes intentionally simplified when we are confident that not all known facts are essential for our purpose of study (e.g. we can neglect people living on the Earth when we want to study the evolution of our galaxy even if we are able to model human social interactions).
3.2 Computer models and simulations
Computer modeling and simulations play an essential role in today physics. For a long time persisting division of natural sciences to the theoretical and experimental research is now out of play. With the advancement of computers, numerical[27] physics has become an increasingly important branch of physics, distinct from both experimental and theoretical physics, but borrowing parts of both (Nelson, 2000). Computational physics is a way of doing physics research, next to the experiment and theory.
Some characteristic problems accompany galaxy studies. There were theoretical attempts to create the universe in a laboratory[28]. However, even if it would be successful, this universe would be hard to study, because it would start expansion in its own space. Computers are used to create mathematical models of such complex phenomena and to explore them. Computer models and simulations are employed when it is impossible to perform the real world experiment. What we have learned from observations about the patterns of nature is programmed into a computer and through the process of numerical simulation is evolved; new results about nature’s behavior are obtained.
Simulation programs serve as an essential tool for contemporary astrophysics. It is impossible to imagine today’s astrophysics without computer simulations. Even a personal computer technology is on such a level that it can perform astrophysical simulations. These machines are able to mimic or simulate the evolution of the universe lasting billions of Earth years in short times of several hours or days of computer time.
There is no need for expensive material equipment. Moreover, the model is safe and indestructible. There is a multiplicity of situations to be explored and this can be done at ours discretion. In contrast to the real models, parameters can be easily changed. An enormous range of both length and time scales can be covered in simulations[29]. The complexity reduced to simple parts makes these computer simulations so close to reality[30].
Before using numerical models, we should always master underlying physics and explore analytical solutions as much as possible. A numerical computation is coming in cases where analytical solution cannot be found[31] or cannot be found by elementary means. The numerical computation can answer problems that are not solvable to exact solution. We are trying to turn an analytical problem into a numerical problem. However, the numerical problem has its own challenges so we end up with a different set of challenges and limitations.
Laws of physics are usually expressed by differential equations[32]. A simulation is a process numerically solving a set of differential equations. These differential equations are trying to express the behavior of nature. A numerical formulation of differential equations forms a computer model, which in turn determines the behavior of the computer simulation. The calculation with the computer model (simulation) consists of simultaneously solving a set of equations describing the physical processes involved in the model. This is executed repeatedly.
3.3 Modeling and simulating galaxy dynamics
Galaxy dynamics is one of the liveliest subfields of astrophysics. To understand the past, present and future of galaxies, looking at them is not sufficient. Why are not all galaxies the same? What causes spiral arms? Questions about how evolutionary changes occurred and about relationships between different events have become increasingly important. Since the galactic history occurred only once and doing the real experiment is impossible, computer simulations play an important role. Simulations can capture important elements of a process and can suggest avenues to explore further in the field.
However, it is hopeless to create models of galaxies only while sitting in offices with computer simulations. Simulations must be compared to real galaxies so that we can be sure that our results are not just nice pictures. It is impossible to observe directly the evolution of concrete single galaxy with a respect to the size of a temporal dimension. It is not possible to observe the galaxy forming or evolve; the processes are far too slow. Researchers may only observe many different galaxies, each caught at a different phase of its evolutionary history. Nevertheless, we are able to observe different galaxies in different phases of their evolution and study their interactions by observing distant galaxies.
Telescopes are probing the very earliest galaxies and computer simulations can extend our knowledge behind the real world observations. When we notice a pattern in nature, we are curious about it and attempt to investigate it. The numerical tool is often the only one available to the researcher studying the long-term evolution of galaxies. When we perform a computer simulation of galaxies, we hope to learn why real galaxies have the features we observe.