Super-Saturated Chemistry
inference-review.com
inference-review.com
Quantum mechanics can and does predict every element on the periodic table. Whether we can calculate what it predicts at the present time is a different matter entirely. In the words of Peter Gill, "The field of quantum chemistry has become an applied mathematics problem". Yes, it's well-known that naïve quantum chemistry fails to predict experimental results for a variety of reasons, but all of these reasons come back to the fact that we had to use approximations to solve difficult equations that otherwise could not be solved. If our predictions failed in some way fundamental to QM/QFT, every theoretical physicist alive would be shocked — it would be the biggest news in the field in over a century.
As better and better numerical approximation schemes are developed, the current issues with quantum chemistry will begin to disappear. Some people argue there are fundamental limits on what a classical computer can discover about quantum chemical systems, but then others argue that quantum computing will surmount these barriers (and others argue that it won't).
There is nothing a quantum Turing machine can compute that can not be computed by a classical Turing machine. However quantum Turing machines may be able to solve problems faster than classical Turing machines but, as far as I know, it is not known whether this is indeed the case. It is known that the speedup is at most exponential.
I'm not so sure. For example:
> The commutator of the Hamiltonian with the angular momentum of an electron does not vanish.8 Its eigenvalue is, therefore, not a constant of motion.
In fact, the Hamiltonian is invariant under rotations (the electron does not care about which way the protons in the nucleus are rotated), which is why the angular momentum even exists. (From the fact that the Lagrangian is invariant under rotation: Noether's theorem tells you that there is a conserved quantity associated with that invariance. It turns out that rotational invariance gives rise to angular momentum.)
I haven't checked his reference 8, but "Boston Studies Series in the Philosophy of Science" is not the first place I'd go to understand constants of the motion and how they relate to things that commute with the Hamiltonian.
As I recall, actual atomic Hamiltonians have terms like σ₁·σ₂. The reason involves some tricky correspondence between exchange and spin that I haven't thought about in a long time, and would have to look up.
I agree with the broader point that this essay is odd and confusing.
Yes, but that doesn't contradict what the article said. The article said, unpacking slightly, that the Hamiltonian operator does not commute with the "angular momentum of a single electron" operator. It only commutes with the "angular momentum of all the electrons taken together" operator.
Given that we can't confirm that, how do we actually know this?
While you are right that there is no a priori reason to dismiss that, it's not quite a bagged thing. Especially considering that we are missing some things for sure (neutrino mass, ...)
If we can't calculate what it predicts, then we don't know that what it predicts matches what we actually observe. We might believe, with high confidence, that QM, once we can calculate what it predicts, will in fact predict what we observe; but until we've actually done it, we don't know for sure.
[Edit: I see GFK_of_xmaspast already made this point.]
https://www.google.com/search?hl=en&source=hp&biw=&bih=&q=ph...
But seriously the guy sounds just like Ernst Mach (1838-1916) who cautioned against attributing reality to "molecules" (at that time not directly observed). I appreciate Professor Henry's viewpoint (chemistry is distinct from physics, in fact chemistry is better and chemistry is cool) but almost every part of his discussion uses the tools of _physics_ to support both sides.
Perhaps he's irritated by the unspoken idea that chemistry is merely the yet-to-be-straightened-out basement of physics, to be organized only after physics has found the missing strings. (And perhaps string theory is physicists' way of putting off the chemistry basement cleanup?8-))
http://science.sciencemag.org/content/354/6319/1570
but looks like it's occurring on their bench at will.
Anybody good enough at the quantum stuff to estimate how long it would take to predict this with just the math?
OK, that's a tall order, how about just mathematically describing this now-known reaction?
If not, then estimate how long it will take until things like this can be well modeled?
I get the impression that these are extraordinary bench chemists, and advanced quantum concepts might shed additional light.