I have always found the connection curious. In video games, for example, you do exactly this - not calculate something unless it is being observed.

Who is to say the quantum effects are not actually artifacts of some optimizations in the simulation we are in?

That's not what quantum mechanics really does. The wavefunction, which is the core of a quantum calculation, "runs" all the time whether any part of it is observed or not. A given observable property of the wavefunction may not be predictable without looking, but that doesn't make the wavefunction any easier to simulate. And without the wavefunction running, we wouldn't observe the probabilities which we observe in experiments.

> The wavefunction, which is the core of a quantum calculation, "runs" all the time whether any part of it is observed or not.

The wave function doesn't really have to "run" to exist though... a wave doesn't actually have any influence on anything until it is collapsed. If nothing observes the wave, it won't have any affect at all. It will just be there, in some cosmic register, waiting for some dust cloud to inquire about it.

Consider a polygon in a game engine, which started at 0,0 and has a known velocity. You are at tick 4762, and that polygon is represented by a position function, but it doesn't actually "run" until you declare a tick, and do the math.

I dispute whether a wavefunction can influence things without collapsing, but putting that aside...

Your example of a polygon with a constant velocity is carefully chosen: that equation has an analytical solution, so you can calculate x(t) and "skip" forward in time. This is not possible in general, even in classical mechanics. If it were a system of more than two interacting particles, you wouldn't be able to fast-forward; you would have to calculate all the intermediate timesteps even if you only wanted the last one.

That's only because as a human being you deal with closed form solutions.

Who is to say that the "universe simulator" is only doing 21st century math?

If the universe simulator can solve iterative problems in O(1), then I question whether our concept of optimization is meaningful enough to it for this discussion to make sense.

This is a very interesting question. What if the universe is stateless and any state at time T can be calculated in O(1)

What if we just lack the expressiveness or the initial conditions to model a stateless universe?

A fun consequence of stateless universe would be that you can rewind, fast forward, loop, speed up, slow down time at no extra cost.

There are some physical systems (mathematically, "Hamiltonians") which have this "stateless" property. However, if the time/energy uncertainty principle is true, simulating time T in O(1) cannot be possible in general unless BQP=PSPACE (the unlikely idea that quantum computers can efficiently solve any problem that can be stored in polynomial amounts of memory). See this paper: https://arxiv.org/abs/1610.09619

> The wavefunction, which is the core of a quantum calculation, "runs" all the time whether any part of it is observed or not.

How can you tell?

See the last sentence of my comment: it's not consistent with experiments. The success of quantum mechanics as a predictive tool comes from acting as if the wavefunction is always present, no matter what aspect of it is measured.

There may be a whole different theory of physics which can replace quantum mechanics and doesn't have wavefunctions, and has completely different simulation requirements, but at that point you could postulate anything.

Or who's to say that they didn't try exact simulations and find it too boring?

There is running joke about general relativity and quantum mechanics being a demonstration of simulation hypothesis, i.e., floating point computations used to simulate our universe break down under very small and very large scales.

And mass slows down time because the load increases

Related to this, Second Life has a concept of time dilation which is the ratio of current simulator frame rate to ideal frame rate (30fps IIRC). As more avatars, scripts, and physically simulated objects were put in a simulator the time dilation increased.

Interesting, I first heard about this regarding EVE Online.

It's funny because it's true.

I actually really like this idea. I was in Blender and thought about how mipmapping has some surface similarities with the way the world works. Detail is only apparent once you can observe it. Maybe fields and waves are faster to calculate, where finite particles are difficult.

I'm just spewing nonsense, but this is the sort of stuff that makes for a great talk over a beer.

Because it only makes sense when you are drunk?

I don't know enough about this to comment, but is there any reason it is critically unsound to do so? (within the confines of said theory)

Yes, it is unsound. Quantum mechanics has features which aren't observable (the imaginary components of the wavefunction, the value of position and velocity at the same time, etc). However, this does not mean less computation, because in order to simulate the system you need to represent the whole wavefunction and everything that happens to it whether it's observable or not. Quantum mechanics is elegant in many ways, but low computational load is not one of them.

See Feynman on the subject: https://people.eecs.berkeley.edu/~christos/classics/Feynman....

Is it weird that the complexity gets me excited? The thorough needs of this kind of nature of computation is a thrill to dream about.

Thanks for the notes and the links. I've recently started to work my way through Feynman's lectures a I'm considering a return to school for physics particularly because of the excitement it brings me to be able to even just peek beneath the covers. I want to be able to rip them off the whole damned bed and leave the sleepers exposed! But I digress...

It's not weird, I'm right there with you. I love this stuff.