Could scientists perfectly simulate the entire universe in a computer, down to the last atom?
Category: Physics Published: September 15, 2014
By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and Associate Professor of Physics at West Texas A&M University
No. Even with an incredibly powerful computer, scientists could never perfectly simulate the entire universe in a computer. There are a few reasons for this.
1. The universe is non-deterministic.
On the fundamental level, the universe obeys quantum theory. Quantum theory is probabilistic and non-deterministic. This means that if you know everything there is to know about a certain electron at the current moment, and then perfectly apply all the equations of quantum theory to the electron, you cannot exactly predict where the electron will be in one minute. You can only predict the probability of the electron being at various locations. The probability distribution may give you a general idea of where the one electron will end up, and can even tell you the average location of many electrons, but quantum theory cannot tell you the actual, exact location of the electron. The problem is not with quantum theory. The problem is with the electron itself. Quantum objects like electrons are not hard little balls or classical waves. They are more complicated beasts that are somewhat particle-like and somewhat wave-like at the same time. Furthermore, quantum objects innately contain uncertainty in their properties. Electrons fundamentally don't have exact locations. They have locations that exist only up to a degree of definiteness as a result of their inherent uncertainty, which depends on the state of the electron.
The bottom line is that it is fundamentally impossible to predict exactly what a quantum object will do, because such certainty regarding the object does not exist in the first place. Even if we have all the information that exists, we can only calculate what a quantum object is most likely to do. Such is the nature of the quantum world. And since the entire universe is simply a collection of quantum objects, the universe itself cannot be exactly simulated. If you loaded into a computer all that there is to know about the entire universe at the current moment, down to every atom and particle; and if you perfectly implemented all the laws of physics into the computer, including quantum theory with its uncertainty principle; and then pressed "Go", the simulation would give you a certain predicted state for the universe in a million years. If you reset the computer and ran the exact same simulation again, you would get a slightly different result for a million years in the future. You would even get a very slightly different result for two seconds into the future, because the reality of the quantum nature of the universe will have been accurately built into your computer simulation. The simulated universe for two seconds into the future will accurately describe some physically plausible universe, it will just no longer exactly describe our universe. The more time that passes in the simulation, the less the simulated universe will match our physical universe, even though all information and physical laws have been perfectly programmed into the computer. Innate quantum uncertainty makes this result inevitable.
Note that quantum uncertainty does not render all computer simulations meaningless. It just means that scientists have to be content with less-than-perfect predictions. The greater the number of non-coherent interacting quantum objects that there are in a system, the lower the system's quantum uncertainty becomes, and the closer the system gets to acting deterministically. A baseball contains trillions upon trillions of non-coherent atoms, and therefore is ridiculously close to being deterministic. This fact allows a baseball outfielder to accurately predict where a ball will land based on its initial trajectory. The quantum uncertainty for a baseball is so low that a batted ball seems to land right where you expect it to. But, fundamentally, you cannot correctly predict the landing location of the baseball to infinite accuracy. However, for the purposes of catching the ball, you don't need anywhere close to infinite accuracy. In a similar way, computer simulations of lasers, cells, and galaxies can give us answers that are extremely close to accurate, even if we can't fundamentally know or predict the exact location and momentum of every atom and particle in the system.
2. The universe is most likely infinite.
In principle, it is impossible to directly observe an infinite object in a finite amount of time. However, we can make the reasonable deduction that an object is infinite if we mathematically approach infinity using a limiting procedure. For instance, the electric field created by an electric point charge is deduced to extend out infinitely in all directions. This infinite-extent property of the electric field can't be directly observed by humans, but it can be deduced. If you measure the electric field of a point charge that is 1 meter away to be 1000 mN/C, and then when the charge is 10 meters away you measure the field to be 10 mN/C, and then at 100 meters away the field is 0.1 mN/C, and so forth; then you see that the field strength depends on distance r according to 1/r2. According to this dependence, for large and larger distances, the field strength of a point charge gets smaller and smaller, but it never goes exactly to zero. Therefore the electric field extends out to infinity.
In a similar way, even though we can't directly observe the universe to be spatially infinite, all of our scientific measurements and theories seem to indicate that the universe is indeed infinite. If that is true, then that is another reason that a computer can't perfectly simulate the entire universe. Simulating an infinite universe would require infinite computing memory space. Note that this argument only limits simulating the entire universe. We could, in principle, simulate a portion of the universe, insofar as quantum uncertainty allows.
3. The computer is part of the universe.
The computer that is going to simulate the universe is also part of the universe. Therefore, if the computer is going to perfectly simulate the entire universe, it must also simulate itself. Not only that, the computer must simulate itself running a perfect simulation of the universe. Which, if it is perfect, must also contain a simulation of the computer. Therefore, the simulation must contain the computer running a simulation of the entire universe, which must contain the computer running a simulation of the entire universe, which must... and so on forever. In the field of computer science, this process is known as "infinite recursion", and it leads to your computer freezing up and never making any progress in its calculations. Therefore a computer that is making a simulation of the universe in which the computer resides can never make an exact simulation of the entire universe.
You may say that the simulation can just simulate the entire universe minus the computer itself in order to avoid infinite recursion and still end up with the correct simulation. But this approach will not give you a correct simulation because everything in the universe has the potential to interact with everything else. For instance, perhaps the computer blocks a falling meteorite from striking and killing a scientist in the room, who goes on to discover how to create black holes, and uses this knowledge to destroy Mars in a fit of psychosis. If the simulation omits the computer, then it will predict that the meteorite flies past where the computer should be and kills the scientist before his discovery. Therefore the simulation will falsely predict that Mars is still around a year later, when it really is not. In this way, omitting the computer itself from the simulation could lead to drastically wrong predictions.
4. We cannot know the state of the entire universe.
Due to the finite speed of light, and the fact that nothing can travel faster than light, we can only have knowledge of the parts of the universe that are close enough that there has been enough time since the Big Bang for the light from these parts to reach us. We call this part of the universe the "observable universe". We are fundamentally forbidden from knowing anything about regions of the universe outside of the observable universe. At the same time, these regions can still interact with our observable universe and change its evolution if we wait long enough. For instance, a star that is currently just outside of our observable universe could be headed right towards a moon that is on the edge, but just inside, our observable universe. After enough time, the star could enter our observable universe and consume the moon. But we have no way of predicting this event because of our fundamentally limited knowledge of the current state of the entire universe.