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10/03/2017

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Craig

I would be very skeptical of an easy refutation of the argument without an actual attempt to get into the details of the argument. So unless you understand the actual argument (and not just the Cosmos write-up of it), I would assume that, yes, you are missing something.

Marcus Arvan

Fair enough - but here's a key passage from the actual paper:

"Having a “sign problem” thus means that no local transformation that removes the signs and phases is possible. Notably, the definition of a sign problem must involve the notion of locality [see also the study of Hastings (7)]. By performing a nonlocal transformation on the physical degrees of freedom, one can always diagonalize the Hamiltonian and obtain a classical partition function. However, such a transformation requires computational resources that scale exponentially with the system size. Therefore, for a meaningful definition of the sign problem, one has to add an additional requirement, that is, that the degrees of freedom σ, that enter the Boltzmann weights must be expressed as local combinations of the physical ones or, more precisely, that σ are given by finite depth local quantum circuits acting on the physical degrees of freedom. For the sake of clarity in this work, we do not address the possibility of nonlocal approaches to QMC, such as determinant QMC or cluster algorithms (8–10)."

Basically, then, the actual argument in the paper appears to be:

(1) Local simulations of QMC are impossible due to computational obstruction to local transformations in QMC (quantum mechanics) (note: everyone already knows this, as Bell's Theorem establishes quantum non-locality).

(2) There's *no* such computational obstruction to non-local transformations (which are known to be algorithmically possible given standard QMC).

(3) However, non-local transformations require an immense amount of processing power.

But (4) "in this work, we do not address the possibility of nonlocal approaches to QMC, such as determinant QMC or cluster algorithms (8–10)."

In other words, they argue that (A) simulating QMC assuming locality is impossible (which everyone already knows due to Bell's Theorem), (B) simulating QMC non-locally would require a ton of processing power, and (C) they did *not test* the possibility of non-local simulations in their paper.

Which is a fancier way of putting my point in the OP. They didn't show that non-local simulations of QMC are impossible - only that non-local simulations require a ton of processing power.

Pendaran

Who cares what's physically possible? If we're living in a simulation, our entire 'physics' could be made up. In the real world who knows what's possible! Not only could there be orders of magnitude more atoms, but there could be no atoms at all. Atoms could be purely part of the simulation.

Maybe this is another way of saying what you're saying?

Marcus Arvan

Hi Pendaran: That's fairly close.

We actually know that interpretations of quantum mechanics assuming locality are *logically* possible. Violations of Bell's theorem demonstrate that there is no possible way to render QMC consistent with locality. However, this has long been known - and so isn't a problem for simulation theory. All it means is that we know QMC is a non-local theory. So, the real question for simulation theory is whether it is possible to compute that!

The problem then is that, by explicitly setting aside non-locality, the authors have given no reason to think that's impossible. It would of course take a ton of processing power - but again, who would have thought otherwise to begin with! It was already known that the quantum wave-function has something like 10 to the 50th power possible solutions - so of course simulating our world would require a ridiculous amount of processing power. But what of it? As you note--and as the authors don't rule out--we have no idea whether "physics", whatever it might be in the "higher" reality, wouldn't be able to pull it off.

And indeed, this is so much as explicitly admitted here (http://www.newsweek.com/are-we-living-computer-simulation-scientists-prove-elon-musk-wrong-677251 ):

"While achieving this on classical computers is impossible, the research does not entirely rule out that an effective method for massive-scale simulations might one day be possible through advances in ultra-powerful quantum computers, however the researchers note that currently no efficient simulation algorithms are known.

The reason that such algorithms have yet to be discovered, Ringel and Kovrizhin argue, is that they are currently outside the realm of what can currently be imagined within the laws of theoretical physics. For now, the simulation hypothesis will have to remain within the scope of science fiction."

Pendaran

I agree with your assessment of the paper.

Rollo Burgess

Thanks Pendaran for your point re atoms etc. Hear hear.

A number of these simulation arguments that one sees seem to draw inferences based upon our knowledge of the physics and computer science of *this* world and apply them to the world in which the simulation we live in would be running. This is clearly nonsense.

We are entitled to assume

1. That pure mathematics and basic logical principles would apply in the world ‘1 up’ (the ability to make this assumption is actually a pretty good modern definition of a priori I think).
2. And that in some way the ‘1 up’ world contains a capability to create the ‘simulation’ (per hypothesis).

We are entitled to draw absolutely no inferences whatever concerning anything about the world ‘1 up’ other than these.

To be clear – it is as likely that the ‘simulation’, if we live in such, was created by a process analogous to magic and by a being analogous to a wizard as it is that it was created using something analogous to a computer. (Actually one of the features of a lot of the very crude simulations that we run ourselves is that we deliberately create worlds that work very differently to ours… e.g. World of Warcraft etc.)

Balazs

By definition we cannot tell if we live in a simulation. No matter how much science you throw at it, it will be the science of the simulation. It seems that we are still hopelessly stuck at the notion that humans are the centre of the universe.

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