Why is it hard to realistically simulate collisions and gravity in computers?

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Jam Smith
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Hello everyone,
Last night I was reading about gravity and I come across one debate. I tried to search about it but got confused. I hope some one can help me.

The question is:

Why is it so hard to realistically simulate the collisions of particles, gravity all the forces that go on around us daily in a computer?
 

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Jam Smith said:
Why is it so hard to realistically simulate the collisions of particles, gravity all the forces that go on around us daily in a computer?
Your question is completely unclear. EXACTLY what is it you want to see simulated? A single particle-pair interaction is one thing. Simulation of everything involved in, say, a single human being is quite another.
 
Jam Smith said:
Hello everyone,
Last night I was reading about gravity and I come across one debate. I tried to search about it but got confused. I hope some one can help me.

The question is:

Why is it so hard to realistically simulate the collisions of particles, gravity all the forces that go on around us daily in a computer?

Start with the 3-body problem and figure out why getting an analytic solution for the most general situation (i.e. without any kind of simplification or restriction) is impossible.

https://www.wired.com/2016/06/way-solve-three-body-problem/

Now imagine how this gets progressively more difficult with 4, 5, 6... Avogadro's number of particles.

Zz.
 
One way of simulating the motion is to start with an initial state and calculate the state a small time step in the future. Then repeat with the new state. Depending on how you do the time integration, you normally accumulate small errors which scale with some power of the size of the time step. In addition, you have a limited machine precision which introduces errors. These errors will cascade into your future states. The more chaotic your system is, the more sensitive you are to these errors.
 
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ZapperZ said:
Start with the 3-body problem and figure out why getting an analytic solution for the most general situation (i.e. without any kind of simplification or restriction) is impossible.

https://www.wired.com/2016/06/way-solve-three-body-problem/

Now imagine how this gets progressively more difficult with 4, 5, 6... Avogadro's number of particles.

Zz.

Hello Zz,
I am amazed after visiting this link. I found many books but this information is quite unique and also helps me to solve my doubts.
 
Khashishi said:
One way of simulating the motion is to start with an initial state and calculate the state a small time step in the future. Then repeat with the new state. Depending on how you do the time integration, you normally accumulate small errors which scale with some power of the size of the time step. In addition, you have a limited machine precision which introduces errors. These errors will cascade into your future states. The more chaotic your system is, the more sensitive you are to these errors.

How can we predict, these areas of chaotic starting conditions without an error approach?