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I am writing a discrete event simulation engine. I am trying to figure out if there is anything that I cannot model. (As my system uses a time step as basic unit of change).

I can think of some phenomena Y that are only dependent on X... but then X is dependent on time. So in the end, Y is dependent on time.

In other words, I am trying to poke holes in my model, so that I can configure it optimally to be able to model as much as possible. Any suggestions on things are that are maximally time-independent would be very nice to hear.

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  • $\begingroup$ Hopefully people don't think this is a stupid question because I am serious! $\endgroup$
    – Alexander Mills
    Dec 7, 2022 at 0:26
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    $\begingroup$ This is extremely vague. What do you mean by "modeling something that does not depend on time"? In physics, there are many problems and solutions that do not depend on time, e.g. statics, or equilibrium thermodynamics. Questions and answers there do not involve any process in time, they are more about which states are equilibrium states, and whether such equilibrium states are stable, metastable, or unstable. $\endgroup$
    – Ján Lalinský
    Dec 7, 2022 at 0:31
  • $\begingroup$ How do things change, if there is no time component? Is time hidden somewhere in the equations, or perhaps cancels out in the equations? I think OP is pretty clear; I am happy to accept any answers that confirm or disconfirm OP. $\endgroup$
    – Alexander Mills
    Dec 7, 2022 at 0:33
  • $\begingroup$ If there is no time component, things do not change. $\endgroup$
    – Ján Lalinský
    Dec 7, 2022 at 0:36
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    $\begingroup$ If your system uses a single uniform time increment for all phenomena, you will miss all relativity, because you will be restricted to a single spacetime foliation. $\endgroup$
    – Stéphane Rollandin
    Dec 7, 2022 at 9:54

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Yes there are such questions and models in physics - statics (static mechanics), electrostatics (static EM theory) and equilibrium thermodynamics come to mind. These are often some kind of minimization problem.

Example:

We are given system of three weights of equal mass $m$ hanging off a single string at distance $l$ from each other when the string is straight. The string is hanging in gravity field on two pulleys that are fixed at the same height and separated by horizontal distance $d<2l$. Determine stable equilibrium configuration of this system (height of each weight).

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  • $\begingroup$ upvoted..not sure if your weight example works, but see my comment on OP about a triangle with changing angles? $\endgroup$
    – Alexander Mills
    Dec 7, 2022 at 2:39
  • $\begingroup$ What do you mean "works"? It is a regular physics problem that does not involve time in any way. Isn't that what you wanted? $\endgroup$
    – Ján Lalinský
    Dec 7, 2022 at 13:10
  • $\begingroup$ What I meant by "works" is I am not sure if the weight system is independent of time - seems like changes would be a function of time (such as gravitation force etc), m/s^2 anyone? Maybe I am missing something lol. My triangle example tho :) Also someone added a comment about relativity to OP. $\endgroup$
    – Alexander Mills
    Dec 7, 2022 at 18:03
  • $\begingroup$ Changes are functions of time only if we assume so. Change of some position in the equilibrium system are functions of changes of other positions, i.e. change of height of one body is function of change of distance $d$. There is no time unless we insert it into considerations. $\endgroup$
    – Ján Lalinský
    Dec 7, 2022 at 23:19

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