Comment by strainer | Hacker News Reader

Comment by strainer | Hacker News Reader

In a physical simulation, you can't simply set the timestep to -1 to recover previous states for the sole reason that each step adds inaccuracy to the model by way of rounding error.

Like this saying "There is nothing in the form of the laws of nature at the fundamental microscopic level that distinguishes a direction of time." There is nothing in the simulation which prefers to step time by 1 or -1 , but the unavoidable rounding error means it can't step exactly backward. I guess its intimately attached to the fact it cant step exactly forward.

This is why the shattered virtual object wont rearrange perfectly going backwards - it didnt smash perfectly when it was going forward.

I had an idea for making previous states recoverable by applying extra rounding between every timestep, but now I suspect this will not entirely work either, as some least significant imprecision occuring during the timestep will still occasionally trip the more significantly rounded 'interstep' state values, irrecoverably.

Rounding errors aside, you can still experience information loss when stepping time. Any observed state which could have resulted from more than one previous states (by the rules of your simulation) represents an irreversible transition.

This was an interesting point which I missed at the time. However this situation would only occur extremely rarely in the normal running where the timestep is set small enough to produce reasonably accurate/continuous behaviour. Basically a state is so intricate and detailed that a coincidence of that kind is difficult to envisage, among multiple bodies, holding space and velocity values. And since going forwards or backwards in time always produces a single solution, (rather than multiple solutions) the idea of multiple plausible inputs still seems reliant on rounding error to me or numerical oddities which get more unlikely the more precision and smaller timestep is employed.

If the simulation was quantized, say like using integers of a large enough size to encompass all things in your simulation, it would be fully reversible I believe. Of course I'm speaking from my limited understanding of physics engines in computers today like bullet or equivalent. Isn't floating point just like a compression for large numbers in limited bits, and the only reason it would not be reversible? The other potential non-reversibility is the fact that the physics engine uses some sort of integration like adding up forces at each time step unlike the universe which I believe is instant. (verlet integration? Google says that is reversible.)

I do see floating point as like automatically compressed integers, but unlike simulations such as, Conway's game of life, the operations in a physics simulation produce real number values even if we begin with integer state, due to square roots and divisions mainly. I think whatever strength of integer or floated precision used to store results, it will never be possible to tell whether a certain parameter was eg. 328480284374964325 or 328480284374964326. And we need to be able to tell exactly what the input state for any output state must be, in order to have reversibility.

Perhaps the simulation isn't time reversible, but that doesn't say anything about the reversibility of the laws of physics and the reversibility of the universe. I.e., reversing the entire universe would still run the simulation backwards, correctly, because it takes place at a lower level.

However, I think the point of the article is that given a deterministic universe, even though it doesn't "run" forwards or backwards but just exists throughout space-time, observers inside the universe can still observe an "arrow of time" in the direction of more stability.

Yes. Or restated, that it's almost only ever possible to form memories of a universe that has increased in entropy.

Im not sure. Simulated observers could also observe the direction of time progression; that orders in the past become irrecoverable to them is a mechanistic result of infinite precision not being preserved from one moment to the next.

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