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I've recently made myself more familiar with Laughlin and Pines' "quantum protectorate" arguments (1, 2), which seems built on Anderson's famous More is Different article (3). This does seem in disagreement with Dirac's 1929 sentiments, (4):

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

(though I know not everyone agrees with this, e.g. this chemistry SE thread) and perhaps these arguments are still considered speculative. However, there are a few mentions of the failures of ab initio methods (which seems quite reductionist to me), and it seems implied that they cannot be enough to predict some effects in condensed matter, especially superconductivity.

My question is, to what extent is this true, and how would one typically try to model matter that is in some "protectorate," e.g. superconductivity?

In these cases, are ab initio methods not suitable (and say, even with incredible computing power, still not suitable?)? Would (for example) renormalisation group methods be more reliable than ab initio methods? If they fail, is this a failure of our reductionist model ("theory of everything"), or is it a failure of our approximations in solving the reductionist model? Is there reason to believe that we can't, for example, recover the Josephson effect (which relies on spontaneous symmetry breaking) by direct solution of the Schrödinger equation (with our technology, but also in principle, i.e. if we imagine a world where we can solve such a large system with FCI/QMC)? Similarly, on the more extreme "patently absurd" end, protein functionality and the human brain: these are obviously inaccessible just in terms of computing power, though I suppose asking questions about ab initio neuroscience quickly turns into poppycock.

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    $\begingroup$ +10. Welcome to our new community, and thanks for the very interesting contribution! We hope to see much more of you in the future!!! I removed the second question because we have a policy to ask only one question per question. The question about when we abandon ab initio methods and resort to model Hamiltonians, is an entirely different can of worms and needs to be asked separately. The part about FCI not being exact due to the BO approximation wasn't really necessary because you can also do FCI without the BO approximation. $\endgroup$ – Nike Dattani Feb 5 at 19:35
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    $\begingroup$ Thank you, you added a lot more clarity to me question :) And thanks for the answer. I shall make a separate post about model Hamiltonians. $\endgroup$ – tmph Feb 5 at 23:45
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    $\begingroup$ uh, this is a key point: historical perspective. this is a literally ~90 year old quote by dirac about "computation". the word literally had a completely different meaning at the time. Turings paper was written 1936 before general purpose computers existed. computers completely "change the equation" of what is feasible to compute. the founding fathers of QM could not conceive of the possibility, it was like science fiction in their era. diracs ideas are still valid but take on an utterly different meaning in 21st century. $\endgroup$ – vzn Feb 6 at 15:46
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It's a very good question, and we may get several answers here from people with various different perspectives, but here is mine:

In every case so far where we are certain that computations have been done thoroughly enough, known quantum field theories have been able to reproduce experiments when gravity is not strong enough to play a role. For example, QED (quantum electrodynamics) is a quantum field theory, and from it we can "derive" both the Schrödinger equation and Dirac equation, as the first and second terms of an expansion of operators proportional to different powers of the fine structure constant. Another example of a quantum field theory is QFD (quantum flavordynamics) which is able to treat the electro-weak force, and hasn't yet failed to do so for any experiments which were simple enough to reproduce with present-day computing power and human desire. Likewise the same can be said of QCD (quantum chromodynamics, or quantum colordynamics) for the strong force.

So you asked whether or not our known quantum field theories (such as QED, QFD, QCD) can successfully predict superconductivity and consciousness of the brain if we had access to enough computing power and motivation to do so. It's an interesting question, but one for philosophy, because it is not possible to test it using the scientific method, because we do not have enough computing power to run such an experiment (we do have the capability to do laboratory experiments that observe superconductivity, but we don't have enough computing power to properly conduct the experiment on the other front, which is to see if completely thorough ab initio calculations will match the laboratory experiment).

I do not see any reason why superconductivity should not be possible to predict with an ab initio calculation if we had enough computing power, but ab initio calculations are so far away from being able to treat systems with so many electrons without making a lot of approximations, so we really do not know whether or not something comes up that we've missed in QED for example. From an Occam's razor perspective, I would be surprised if we were missing something in quantum theory which is needed in order to predict superconductivity, because if we were missing something then why (does it seem like) it is only superconductivity that we can't predict? But that is a question for philosophy. There was a related question that was asked by one of the moderators in this community, and it is not surprising that it didn't get an answer: What's the largest system we can study based on "fundamental limits to computation"?

As for human consciousness, we have to first know what it is, before we can try to predict it using an ab initio method. So in that case, yes we do need more than just the laws of quantum physics (and maybe also gravity), in order to predict human consciousness, because we also have to know what it is that the calculation is looking for.

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  • $\begingroup$ Both the first two citations in my question mention examples of failures in ab initio calculations, e.g. Pines, "ab-initio computations have failed completely to explain [cuprate superconductor] phenomenology; indeed it would appear that not only has deduction from microscopics not been able to explain the wealth of crossover behavior found in the underdoped cuprates, but that as a matter of principle it probably cannot explain it, much less calculate the high transition temperatures found at optimal doping." $\endgroup$ – tmph Feb 7 at 3:41
  • $\begingroup$ Based on your second paragraph, would I be right that your argument is that these "alleged" ab initio computations that they cite use too many approximations? (Also they don't just mentioned superconductors, but also 3He) $\endgroup$ – tmph Feb 7 at 3:47
  • $\begingroup$ We do not have enough computing power for an ab initio study of cuprate superconductors to predict Tc, without making fairly significant approximations in the amount of electron correlation treated (for example). You can call this a "failure" of ab initio calculations to explain cuprate superconductivity (keep in mind that high-Tc superconductivity remains an unsolved problem whether using ab initio methods or anything else, so this "failure" needs to be taken with the appropriate grain of salt), but there's still 0 evidence of a sufficiently thorough ab initio calculation failing. $\endgroup$ – Nike Dattani Feb 7 at 4:49
  • $\begingroup$ Fair enough, thank you for addressing that. While I am convinced by your argument, I am curious about any different perspectives. $\endgroup$ – tmph Feb 7 at 16:03

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