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I am curious what efforts have been made to date to define virtual computer worlds based on the physics we know in the real world?

I think it would be awesome to say start off with an atom defining a class atom with characteristics atomic number, weight, etc. then model how these atoms interact and try to build up Helium, Hydrogen, Oxygen, etc. Tie this into a computer graphics engine and voila. ; ) I know this is major over simplification and you could go down to quarks or something else but you get the idea. I am curious about exploring discussion about what the bottlenecks are here.

Maybe modeling the interactions between virtual atoms is impossible (too large a number to compute on today's hardware). Maybe quantum computing has advantages here? Maybe there are efforts out there to model interacts between larger molecular constructs then... or even an abstraction the size of a human cell? Would be interesting to discuss what is theoretically possible here.

What got me thinking about this was in the context of Artificial Intelligence. If you could take a snapshot of the physical world and load it into this hypothetical model... what would that mean, i.e. a brain of sorts?

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You just sort of cropdusted several broad topics here. As for modeling of single molecules, I know there are a few chemical reaction simulators among other things. For large scale virtual interactions of particles you could look into voxels maybe. Several supercomputers are used to model out physical situations (jaguar), read up on them some. –  a sandwhich Nov 8 '12 at 2:53
Not sure this question can lead to any concise answer. One thing you have to keep in mind is that every level of your hierarchy involves further simplifications. It would be computationally prohibitive to model a cell via protein-protein interactions, to find a protein's shape based on molecular structure (though this is an active field of inquiry), to model amino acids with all the details of every atom's electronic orbital structure, etc. Unlike in computer science, physics can't just build up structure from well-understood pieces. At least not easily. –  Chris White Nov 8 '12 at 3:43
The cropdusting was rather intentional. : ) Good discussion so far. Thanks for the voxel recommendation. –  Ryan R. Nov 9 '12 at 3:59
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4 Answers

up vote 2 down vote accepted

Let's do actual numbers. You ask whether interactions between atoms would already kill you off? Nope, it's even worse.

Let's take the iron atom. It has 26 electrons. That means in real space your wavefunction is a function of 26 3d coordinates, $\Psi = \Psi(\vec{x}_1, \dots, \vec{x}_{26})$.

Assume we are happy with an extremely crude real space grid. Say, 10 points in each direction. That means $10^3 = 1000$ points per coordinate. That means that we have to store $1000^{26}$ entries to write down just that one wavefunction.

That is the same as $10^{3\cdot 26} =10^{78}$.

We need $\sim 20$ bits for each entry, so let's bump up the exponent to 79.

This number is higher than the number of atoms in the universe, so there's no chance in hell to get a computer model of the physical world that starts at the atomic level. This is why simpler models are so important in condensed matter physics.

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Excellent! Only to add that the whole wavefunction also depends on the spin variables $\Psi=\Psi(\{x_j\},\{\sigma_j\})$. –  juanrga Nov 10 '12 at 12:10
Good answer! Going to accept this. Would be curious about other discussion involving looking at the bottlenecks of modeling from the atom up, i.e. if we were able to discretize the interaction of atoms to some level of precision how bad is computing the more macro interaction to say... get to a static object the size of a chair? Say N cycles per second per atom. Do we also hit a bottleneck here? If you could model this wave function, does the rest of physics fall into place? Where else is this impossible? Just playing devils advocate. ; ) –  Ryan R. Nov 15 '12 at 0:21
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There are several conundrums one faces in computational science. The first is that you must make simplifications to have any hope of running a computation that is feasible given technological limitations, and for the same reason you must limit the scope of what you are simulating to some subsystem of the universe.

But here's the more subtle conundrum: even with infinite computational resources, what exactly would you learn by recreating a virtual universe? You'd just get a copy of what already exists. The art is in making as many simplifications as you can that still allow you to capture the complexity you seek to model. Only when you've done that have you really learned anything.

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These computations are extremely time-consuming.

Even with the most advanced methods, computers, and severe approximations, one is currently not able to simulate by molecular simulation more than a few microseconds of a single protein molecule, let alone a world!

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Virtual computer worlds (virtual reality, games...) are almost exclusively based on a subset of classical physics.

Quantum mechanical methods are both time and memory intensive. Accurate quantum chemical methods can be applied only to small molecular systems and they scale poorly. For instance a CCSD(T) energy calculation for an alanine-alanine amino acid pair would require about two years to complete and scales by a factor of 128 when the size of the system is doubled; i.e. the computation of two pairs would require about 256 years to complete. Consider that a single molecule of DNA can have millions of pairs and you can start to get an idea of the complexity. And all of this is for a stationary system! A dynamical study is much much more demanding. Due to the lack of powerful enough supercomputers, scientists use crude molecular simulations based in classical mechanics plus empirical optimizations for the study of some aspects of large molecules and still they only can simulate them during a short interval.

Note that it is not a simple question of time. Storing the standard equation used in NMR for a relatively 'large' quantum system (1000 levels) requires of the order of 7 Gib of memory. No known computer has enough memory to solve the equation.

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