Are we in the Matrix?

A while ago one of my friends recommended this  for a topic for one of my posts and since it's my only request to date I wouldn't I oblige?

Well, he asked me to try to prove that the world that we all live in is not some complex computer simulation without our knowledge. I'm not going to say that this question includes the same history as the movies with a civil war between humanity and machine with the eventual victory and complete domination of the machines and using us as a power source to replace the sun, then creating a simulation for our minds to meander in and the eventual rise of a human rebel army using a chosen one to bring the end of the machines. The question is not about the history our current state of the real world if this situation were to be true, just that the world we see around is not the "real" world but just a computer simulation built by an intelligent civilization (one could say the "real" universe is just a simulation as well by some paranormal force, maybe some sort of god figure).

Although computers have decreased in size unimaginably in the past decades, where computers the size of a room are thousands of times less powerful than any standard smartphone today, and the trend still continues to this day and computer simulations become ever more realistic and graphics and physics become better each year, I do not think computers will ever become powerful enough to simulate the world to such detail that such an inquisitive species with such advanced technology would not be able to detect such a major detail  of the universe.

If this would be a simulation than it would be an extremely detailed one as scientists can detect events that occur on the extremely microscopic scale and have not seen any "pixels" as of yet. This simulation would have to calculate the position of every subatomic particle that makes up every atom of the known universe, which I hope I won't have to say how many atoms make up the known universe. Plus every subatomic particle the buzzes around space randomly which are probably even more numerous. Well maybe this simulation only works down to such details on earth and in space there are "efficiencies" where there the rules aren't so complex. So how big of a computer would be needed to simulate the Earth?

Well lets start about how much we would need to compute an atom. In modern computers computers store the state of all of it's data in transistors that holds a charge or not, the 1's and 0's of binary. The decreasing size of computers is the decreases in the size of transistors. Now matter how small transistors get they will always be made out of multiple atoms (I'm not willing to say how small because I'm sure scientists from the fifties would never believe how small computers have gotten today), and can only only hold two states. An atom however can be in multiple states with each subatomic particle storing a lot of information. To accommodate more than two states computers string up eight bits (a one or zero) into a byte. A byte could store one of 256 states (two to the power of eight) and x bytes linked up can store 256 to the power of x states. So if it takes (ARBITRARY NUMBER WARNING) one megabyte, 8,388,608 bits, would take up that many transistors and that number times each atom in a transistor, lets say 1,000, gives you how many atoms it would calculate the state of an atom, more than eight billion. So a hard drive that would store the single state of the earth would be more than 6000 times the volume of the sun and I'm giving plenty of leeway because I think an atom holds a lot more information then that and transistors will never get that small.

In the future we might be able to make quantum computers which instead storing the two states of an electron it can hold thirty two quantum states so one transistor could hold five bits of info dividing the size of our Earth hard drive by five. So if we are using the same numbers as above the Earth hard drive would be 1200 times the volume of the sun. Well that is progress so maybe we can keep going forward. Maybe we could keep making a single transistor hold more and more states and decreasing the size of hard drives this way. Lets say we check the state of an atom itself in a transistor rather than an electron if thats even possible. So if we can have a transistor hold every state an atom can hold than we just need one transistor per atom of the Earth, well we're down to 1000 times the volume of the Earth if we have our 1000 atoms per transistor ratio. If we can keep shrinking down the resistor to one atom for each transistor than we have a hard drive the size of the earth and that is with out wires, casings, or any other components.

A good logical way to see this problem is how can we get anymore information from an atom than how much an atom contains. So the smallest a hard drive can be for the Earth is the size of the Earth and the smallest a computer that can store the data of the of the Universe would be the size of the Universe and thats just to store the data not to mention the actual CPU that will actually change the data stored over time and I don't even want to understand how many calculations a computer would need to do per second to run at real time (I guess the computer could go extremely slow and could alter the way the brain perceives time to make it seem to go normally but I don't think it would because the lifetime would be significantly decreased).

So you can see why I find it a little hard for this entire complex, beautiful and flawless world could be a simulation. Thousands of years of scrutiny of the human civilization has not found a single glitch, bug, or short cut and modern telescopes peer thousands a millions and billions of light years into the Universe completely fitting perfectly with our understanding of the Universe and our findings here on Earth. With the vastness and complexity of the observed Universe there is no way a mortal civilization can make a computer simulation of what we observe around us.