I don’t think we know anywhere near enough about quantum gravity to be sure of that.
Not that I’d be super-optimistic about “quantum gravitational computers” actually being any use relative to ordinary quantum computers—but in the absence of an actual working quantum theory of gravity I don’t see how we can know they wouldn’t make a difference in calef’s hypothetical world.
We actually know quite a bit about quantum gravity: it must fall under a quantum mechanical framework, and it needs to result in gravity, and gravitons haven’t been directly detected yet. This isn’t enough to determine what the theory is, but it is enough to say some things about it. The main two things are:
1: Since it’s just quantum mechanics, whatever it does, it’ll just set another Hamiltonian. If it changes the ground rules, then it’s not a theory of quantum gravity. It’s a theory of something else gravity.
2: Gravity is weak. Ridiculously weak. Simply getting the states to not mush up into a continuum will be more difficult by a factor for which ‘billions of times’ would be a drastic understatement.
In order for gravity to be even noticeable, let alone the main driver of action, you either need to have really really enormous amounts of stuff, or things have to be insanely high energy and short-ranged and short-lived (unification energies).
Either of these would utterly murder coherence. In the former case your device would be big enough (and/or slow enough) that even neutrino collisions would decohere it fairly comprehensively long before the first operation could complete. In the latter case your computer is exploding at nearly the speed of light every time you turn it on and incidentally requires a particle accelerator that makes CERN look like 5V power cable,
So, everything that makes gravity different from electromagnetism makes it much much worse for computing.
Not that I actually believe most of what I wrote above (just that it hasn’t yet been completely excluded), if QG introduced small nonlinearities to quantum mechanics, funthingscouldhappen, like superluminal signaling as well as the ability to solve NP-Complete and P#-Complete problems in polynomial time (which is probably better seen as a reason to believe that QG won’t have a nonlinearity).
Nonlinearities in quantum mechanics? Linearity is what makes quantum mechanics amplitude-independent. If you ruin that, then the laws of nature will change from moment to moment as the wavefunction moves to fill more and more of Fock space. Suffice it to say, QM’s leading order is 1, and any higher powers are way out of reach.
Unless, that is, worlds are top-level entities in your physical theory somehow, which then brings in the full weight of the ‘what does it have to do, kill a puppy’ rant against it.
I don’t think we know anywhere near enough about quantum gravity to be sure of that.
Not that I’d be super-optimistic about “quantum gravitational computers” actually being any use relative to ordinary quantum computers—but in the absence of an actual working quantum theory of gravity I don’t see how we can know they wouldn’t make a difference in calef’s hypothetical world.
We actually know quite a bit about quantum gravity: it must fall under a quantum mechanical framework, and it needs to result in gravity, and gravitons haven’t been directly detected yet. This isn’t enough to determine what the theory is, but it is enough to say some things about it. The main two things are:
1: Since it’s just quantum mechanics, whatever it does, it’ll just set another Hamiltonian. If it changes the ground rules, then it’s not a theory of quantum gravity. It’s a theory of something else gravity.
2: Gravity is weak. Ridiculously weak. Simply getting the states to not mush up into a continuum will be more difficult by a factor for which ‘billions of times’ would be a drastic understatement.
In order for gravity to be even noticeable, let alone the main driver of action, you either need to have really really enormous amounts of stuff, or things have to be insanely high energy and short-ranged and short-lived (unification energies).
Either of these would utterly murder coherence. In the former case your device would be big enough (and/or slow enough) that even neutrino collisions would decohere it fairly comprehensively long before the first operation could complete. In the latter case your computer is exploding at nearly the speed of light every time you turn it on and incidentally requires a particle accelerator that makes CERN look like 5V power cable,
So, everything that makes gravity different from electromagnetism makes it much much worse for computing.
Not that I actually believe most of what I wrote above (just that it hasn’t yet been completely excluded), if QG introduced small nonlinearities to quantum mechanics, fun things could happen, like superluminal signaling as well as the ability to solve NP-Complete and P#-Complete problems in polynomial time (which is probably better seen as a reason to believe that QG won’t have a nonlinearity).
Nonlinearities in quantum mechanics? Linearity is what makes quantum mechanics amplitude-independent. If you ruin that, then the laws of nature will change from moment to moment as the wavefunction moves to fill more and more of Fock space. Suffice it to say, QM’s leading order is 1, and any higher powers are way out of reach.
Unless, that is, worlds are top-level entities in your physical theory somehow, which then brings in the full weight of the ‘what does it have to do, kill a puppy’ rant against it.