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Alright, Lets assume that I have a computer with limited calculation speed (1-4GHz) but unlimited parallel processing capability and unlimited memory capacity to go with it. Under this assumption could the universe be simulated in real time with perfect (near-Perfect?) accuracy? Would a prediction algorithm be need to make it run in real time? Could it be made to run in faster then real time? How many calculations would it take approximately?

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I'd say no.

First of all, you would have to know all the properties of every particle in the universe. While this information would fit into your infinite amount of memory, you cannot measure the moment and the position of even a single electron because of the uncertainty principle.

Also, according to the current models, particles are described by wave functions, and all you can do is predict the possibility of a particle showing up somewhere. So if you would run your simulation, and check how this-or-that electron travels in the first second of the simulation, all you could get is a fuzzy graph on the possibilities of that electron being here and there.

Also, our models of the universe can't be described as a simple function of time. You can't create a function that takes a positive real number (time) and spits out a huge vector of particle parameters (well, probability distributions).

All you can do is to run a calculation that approximates the solution. Since certain parts (or all?) of the universe are tend to be sensitive to the initial conditions (your measurements), even the slightest error in the measurement would drive your calculations away quickly from the behaviour of the real universe. Since you cannot possibly measure all parameters of even a single particle, you cannot ever create a simulation that does exactly what the universe does. Even if we suppose that we can somehow download the "database of the universe" with all information there is, this is a serious practical limitation, since you have to calculate with absolute and perfect accuracy, never rounding any number during the simulation.

What surprising is that with a very real computer (like the one you are using right now), with real data, sometimes you can get surprisingly close to a simulation you described. You can create quite interesting simulations of planets moving around. Simulating the solar system for example is not a big deal today. With a fair amount of programming knowledge and using only the Newtonian principles, you can write a model, fill it with data from some astronomy web site, and tell quite precisely where the planet Mars will be a year later. So simulating the positions of planets looks easy.

However, it is quite impossible to tell whether it will rain a year later, since any model of the weather (and the "real" weather too) is very, very sensitive to the initial conditions, and no matter how precisely you measure the temperature, atmospheric pressure, etc, you won't get much closer to the truth.

Maybe the greatest obstacle would be the actual model of the universe. The best model of all matter and forces is the modestly titled Standard Model. This completely excludes the description of gravity, does not predict or describe neutrinos with mass, and fails to account for the "dark matter" that seems to fill the universe. Actually, there seems to be much more dark matter than readily detectable everyday matter: some 85% of our universe is nothing but that mysterious stuff. Also, we don't know why the universe's expansing is accelerating, what is the "dark energy" that drives that expansion.

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I think infinite computation would be needed to consider virtual particles.

Consider the paper Tenth-Order QED Contribution to the Electron g-2.

Just to calculate the QED contribution to the electron g-factor, an infinite number of Feynman diagrams need to be considered.

The paper explains that for the 8th order contribution, 891 Feynman diagrams need to be considered and for the 10th order 12672 diagrams need to be considered. There are an infinite number of orders of contribution.

$$g_e/2 = 1 + C_2(\frac{\alpha}{\pi}) + C_4(\frac{\alpha}{\pi})^2 + C_6(\frac{\alpha}{\pi})^3 + C_8(\frac{\alpha}{\pi})^4 + ...$$

"it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time" Richard Feynman, The Character of Physical Law.

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