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Comment by yakult | Hacker News Reader

Wild guessing from someone who has no background in physics:

1. Simulating QM-level events is NP-complete.

2.Assuming P=/=NP, a machine that simulates a volume of size X in QM-correct terms must be exponentially larger than X.

3. This includes X itself.

4. Therefore, the universe is taking sweeping shortcuts that look like classical mechanics at large scale. These are not 'our' computational shortcuts, they're actually how things work at a fundamental level.

5. ...maybe if we build a big enough quantum computer we can overflow the universe's buffer.

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> 1. Simulating QM-level events is NP-complete.

Unlikely. Check out "Can NP-complete problems be solved efficiently in the physical universe?" (http://www.scottaaronson.com/papers/npcomplete.pdf) and "BQP and the Polynomial Hierarchy" (http://www.scottaaronson.com/papers/bqpph.pdf).

There's, of course, also Wikipedia ( https://en.wikipedia.org/wiki/BQP).

You're missing step 0, which is assuming that our universe is a simulation. Also, you're making a lot of assumptions about the laws of physics and what is computationally feasible in the universe that that computer is running in.

I'm not assuming simulation. It's more of "if the universe can pack something that can predict the outcome of an NP-complete system (that is, the universe itself) in real-time into a relatively very tiny space, then either it's cheating or P=NP."

As for the assumptions, I agree. Hence it's wild guessing.

Then I misunderstood originally.

If you're not assuming the universe is simulated and is instead "fundamental" (whatever that means), then who are you to put limits on its processing power?'

I think you have a level-confusion here - the universe isn't packing computational machinery into itself. Remember that space-time is a part of this universe. If something is computing our universe, it has to hold the representation of space-time, too. The computation machinery isn't in here with us.

If 'fundamental' stuff gets to break P=/= NP, then I don't see why we can't do it in a computer, if only by aping the design. But then P=NP and things get weird.

I'm not sure why you keep mentioning NP and P. A problem being exponential doesn't mean it can't be computed. Maybe the universe does the calculations the hard way.

> 5. ...maybe if we build a big enough quantum computer we can overflow the universe's buffer.

Except black holes are a thing.

Depends on how it's optimized. If a star gets sucked into a black hole but nobody sees it, does it truly make hawking radiation?

(Next stop: solipsism.)

P=NP. We just can't read the meta-meta-rules surrounding QM yet.

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