Simulation Computing Loophole? [closed]

Question

The story i'm working on is set on a near future where brain-computer interface has evolved enough for people to control virtual bodies in real time and feel every physical stimuli from the virtual world, that's why i'm researching on computer simulation and theorizing what might be feasible with future developments on quantum and hybrid electric-analog computers.

Could a computer that can simulate matter down to the quantum level simulate a computer bigger than itself, that in turn would simulate an even bigger computer, and on and on until we manage to compute anything?

Because if not, then the simulating computer would be very limited and could not simulate more matter than it uses to compute, and thus would require several workarounds for simulating full virtual reality environments, like ditching the volume of things and simulating only the surface of what you can perceive with your senses and ditch all the unnecessary rest.

Answer 1

Quantum mechanics says no

QM (specifically, the no-hiding theorem) dictates that information is always conserved. You can't create or destroy it.

Let's look at it more simply. Let's say you have a computer register than can store 64 bits. It cannot possibly store more information than 64 bits. It doesn't matter if it's qubits in a quantum computer—those only allow for a larger volume of information processing (i.e. computational speed). You cannot, within the laws of physics, store more information in less information.

Answer 2

You're putting a chest into a chest

Have you ever seen this in video games? Take a treasure chest item (or any item container), and put it inside another, very similar chest. That's what you're suggesting.

^{Yes, I know we can perform a chestception only once in this game, but it was the easiest to set-up 🐶}

Going further, you put inside the chest which is inside the chest another chest, all exactly similar. And another chest into the chest which is in the chest in the chest. Then another chest into another... Pifi, I need some time to breathe.

But if I can add as many treasure chests I want into my treasure chests, does it mean I can store any amount of chests and items I want in my main chest?

Well... In some games, virtually yes¹. But try this in real-life and you'll quickly face some disappointement getting even one inside. And if you add a smaller chest, you'll feel that you cannot hold as much things as when it was empty. It's because it's the volume -the space inside your main treasure chest- which tells us what it can hold, not some arbitrary slots you put your items in.

Your computers are exactly the same in this case. It's a treasure chest, and you put things in it. You can add another treasure chest, another simulation into it, but it will take some of the space of your main computer. It will actually reduce the total capacity and computing power, rather than increasing it.

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^{1: That is... Until you took all chests available in your game or crashed your computer because you looted so much items it can't handle all of them anymore.}

Answer 3

Simulation is a whole can of worms. The kind of operation you are seeking to do is known as fractal compression. It permits the infinite level of detail required to store the computer's image of itself, and the computer's image of its image of itself and so on.

One major issue you will run into is the Halting problem. You can rather quickly prove that a computer that reasons perfectly about itself must be subject to the halting problem, and thus it would be undecidable whether it actually is reasoning about itself perfectly or not. You may have a supercomputer with this property, and be completely unable to prove it has it!

When one leaves the digital realm, which it sounds like you are, now there are some solutions. In dynamic systems one can compute "fixed points," states that do not change. Your computer could hold one of these. Behaviors of these fixed points are often provable, thanks to the power of real numbers (rather than integers). Indeed, there's prior art for this in fiction. I'm a fan of the depiction in Westworld season 3, myself. In particular, it does a good job of showing how such a computer could operate by creating states that are easy for it to simulate. If you're looking for dystopian fiction, this is a fun topic to riff on.

Answer 4

Technically, the answer is yes, but not in the way you want.

My laptop computer (given sufficient disk space) can simulate a super computer, which has about 100,000 times as many processors as my laptop computer, has communications 10x faster, and takes up about 100,000 times more space than my laptop computer.

How? Well, the supercomputer, like matter, is built up of many smaller, identical parts. And like matter, they behave in very predictable ways. And even interact with each other in very predictable ways. These rules can easily fit into the memory of my laptop, and a team of a few dozen programmers can write a good simulator.

So what's the catch? Time. It would take my laptop about 10,000 times longer to simulate the supercomputer than just running the supercomputer.

One of the things we run on the supercomputer is quantum chemistry simulations. It takes the supercomputer 30 minutes to simulate 0.01 seconds of quantum chemistry. About 180,000 times as long as the actual quantum reaction would take. And that is just a few hundred atoms, the simulation time increases exponentially as the atoms increase, like double the atoms and the runtime goes up by 100x.

Simulation cannot be real time.

We already execute your strategy in real life. I work with engineers that design processors and chips. We've developed simulators for them, to test their circuits before they spend hundreds of thousands actually building them. Our simulators are nearly perfect on the physics and chemistry, so much so that if the simulator says the circuit will work, and won't overheat, and so on, it turns out that way when it is fabricated.

So they feed in exactly the same specifications they'd send to the fabricator, we build an internal simulation of all the circuits, and they can poke it and prod it and make it run in simulation.

But it takes hours for our state-of-the-art simulator to simulate what would be microseconds of real-life operations. That's enough on a processor, microseconds of circuit simulation is enough. That is thousands of cycles.

Your problem is not whether the simulation of a bigger thing by a smaller thing is possible. Your problem is time itself, and you cannot escape it: Simulation, especially of quantum phenomena, will always take at least thousands of times longer than reality.