This explanation is interesting. Thanks for sharing it. While reading it, I got the impression that the simulation is not fully quantum mechanical, but rather classical with select quantum mechanical effects.
Which parts of quantum mechanics are idealised away and how do we know that not including them won't significantly reduce the quality of the result?
Are you possibly using stochastical noise in the simulations and repeat them multiple times, in the hope that whatever disturbance caused by the idealisation of the model is covered by the noise?
That's a good question and there are a number of ways to try to tackle this. One of the main reasons you cannot do QM simulations directly is that the high quality methods can cost Omega(n^6/eps) to get eps. relative accuracy (you can do better with DFT, but then you're making your life hard in other way). At a high-level (and I mean, 50,000 ft. level), here are the simplest way:
1) Do quantum mechanics simulations of interactions of a small number of atoms — two amino acids, two ethanol molecules. Then fit a classical function to the surface E[energy(radius between molecules, angles)], where this expectation operator is the quantum one (over some separable Hilbert space). Now use the approximation for E[energy(r, a)] to act as your classical potential.
- Upshot: You use quantum mechanics to decide a classical potential for you (e.g. you chose the classical potential that factors into pairs such that each pair energy is 'closest' in the Hilbert space metric to the quantum surface)
- Downside: You're doing this for small N — this ignores triplet and higher interactions. You're missing the variance and other higher moments (which is usually fine for biology, FWIW, but not for, say, the Aharanov-Bohm effect).
2) Path Integral methods: This involves running classical simulation for T timesteps, then sampling the 'quantum-sensitive pieces' (e.g. highly polar parts) in a stochastic way. This works because Wick rotation lets you go from Hamiltonian evolution operator e^{i L}, for a Lagrangian density L, to e^{-L} [0]. You can sample the last density via stochastic methods to add a SDE-like correction to your classical simulation. This way, you simulate the classical trajectory and have the quantum portions 'randomly' kick that trajectory based on a real Lagrangian.
3) DFT-augmented potentials: A little more annoying to describe, but think of this as a combination of the first two methods. A lot of the "Neural Network for MD" stuff falls closer in this category [1]
[0] Yes, assume L is absolutely continuous with regards to whatever metric-measure space and base measure you're defined over :) Physics is more flexible than math, so you can make such assumption and avoid thinking about nuclear spaces and atomic measures until really needed
> Upshot: You use quantum mechanics to decide a classical potential for you (e.g. you chose the classical potential that factors into pairs such that each pair energy is 'closest' in the Hilbert space metric to the quantum rest) - Downside: You're missing the variance.
Couldn't the quantum mechanical state become multimodal such that the classical approximation picks a state that is far away from the physical reality?
And, couldn't this multimodality excaberate during the actual physical process and possibly arrive at a number of probable outcomes which are never predicted by the simulation? Is there more than hope that that doesn't happen?
Yes, for sure. In practice (and not at the 50,000 ft. level), you do try to include the multimodalities — you don't _really_ just use E[quantum_energy(r)]. But you ARE still reliant on some computable/smooth/Lipschitz moment and/or expectation from the quantum surface. The semi-heuristic argument for why you get away with this in biological simulation is somewhat heuristic, but of the following form:
- Most quantum field theories are described by of the form L(E), where E is an energy level ["effective field theory"] and the Lagragian changes as E change.
- When E is low, L(E) is classical mechanics & EM
- When E is around 1GeV, L(E) is the aforementioned plus QED
- When E is around 100GeV, L(E) has the aforementioned plus some QCD
- When E is at 1 TeV, L(E) has the aforementioned plus Higgs-like stuff
Now biology is on the lowest end of that scale, so you mainly have to deal with QED and perturbative electronic expansion. These electronic expansions are the most important part — you need them to get hydrogen bonding + electrodynamic molecular interactions correct — BUT they are highly local.
This locality is what you take advantage of when you normalize — you find from QM that the potentials only matter when the two charged/polar molecules are close, so you try to make a classical potential that has quantum 'jumps' when these things are close.
Do you miss the purely quantum stuff? Aharanov-Bohm, Chern classes, and the like? Of course. But from a practical standpoint, you do get the structures that you measure from experiment to be correct because the 'cool' quantum with 'tons' of states is less important for pedestrian things at low energy scale.
It is still hard to get right though! There's a lot of entropy you need to localize correctly and in some sense, you have to make sure you get the modes as a function of local particle positions correct.
The final thing to point out is that the Wick rotated path integral stuff works for biology much better than for real HEP-type of stuff because molecules are contained at low energies — those tunneling probabilities are O(h E), and log(E) is still dwarfed by -log(h) so you _can_ safely ignore them.
This is not true for things like circuits, however, because the lithography at EUV scales (3nm -_-) does have tunneling issues at high field strengths.
tl;dr: Biology has some saving graces that give you good approximations. Are they perfect? No, but if you find a time that I have to compute a vanishing first Chern class in a noisy, ugly biological system, then you deserve a Nobel Prize!
Copyright does not deserve voluntary submission anyways. It is an unjust and ever stricter becoming legal framework to give life support to an industry that is unwilling to adjust to new technological realities.
You’re suggesting copyright is obsolete because technical means of protecting content are so easy to circumvent.
That’s absurd, considering laws protecting rights that are easily protected by, for example, physical means are entirely unnecessary.
The only reason we have laws against burglary is to allow us the benefits of not living in a personal fortress. To turn this around and deny anyone going out in public without a personal protection detail the benefit of laws against being robbed or raped is indistinguishable from just scrapping all criminal law.
The other, more common and less interesting (but equally wrong), assumption you’re making is that there is some secret business model that thousands of publications and journalists have somehow missed to see. Or, alternatively, the strange situation of gleefully enjoying the decline of journalism, coming up with all sorts of accusations to deny that their work has any value for you or society, while simultaneously spending 8+ hours these days reading their work.
I'm saying that copyright is unjust. It violates fundamental individual freedoms of people like freedom of expression to achieve goals that do not justify that mean, and is therefore illegitimate.
The comparison to laws that protect people is invalid because copyright does not protect people. It grants governmentally enforced monopolies. Copyright has a legitimate goal. There is a value in certain activities for society and copyright is a governments intervention to increase that activity.
There are other things that are considered so important that the government takes action to provide them, like for example social security, health services and infrastructure. That is realized by taxation. I'm suggesting that the state should use taxation to ensure the activity of those who rely now on copyright so the restrictions of individual fundamental freedoms is gone.
Note that copyright has become even more restrictive with time. There are situations where people are forbidden from singing a song on a birthday party in public. This is an example of where the unjust restriction of individual freedoms becomes apparent.
And I'm saying that this injustice in some situations is so grave, that we should show civil disobedience and try to break and mock copyright when possible as a form of protest.
It is not stealing. It may be illegal, but it isn't stealing nor robbery. You may be violating the copyright law, but nobody is taken away any object and there is no threat of violence. When people get access to copyrighted works, then at first, it is good for people. Only then the idea is that the creators can't make a living by producing those works. We can solve that differently, without using copyright. Copyright is a weirdly anti-market and authoritarian concept where the government artificially makes something scarce by punishing supply. In any case, distributing stuff is not stealing. /rant
The company CureVac only denied rumours that it will be bought, it did nor deny claims that the Trump administration approached them and tried to buy exclusive access to the vaccine.
The company itself has put out a statement that it's false news. And Reuters has now edited their article and removed the part which said it was confirmed by government official.
I never said the US was trying to buy it for exclusive access, if that is the conspiracy theory you're alluding to. You need to bring it up with the one I replied to. They were making those claims, not me.
It's called a strawman's argument. You falsely claim something your opponent said and before you know it, everyone believes it.
>The conspiracy theory is that the German government conspired to spread a lie.
Are you on the wrong post? I never said they were spreading lies?
The only thing the German government did was confirm they and the US government were both in negotiations with CoreVac. They did NOT state that the US was looking for exclusive rights.
None of this goes against my initial post that this is a completely unsubstantiated article.
Edit: You can't cite the news as your source for the news, especially when the news itself says it is unconfirmed.
I quote from the article: "US President Trump is attempting to entice a German lab to develop a vaccine exclusively for the US, a German newspaper reported."
You are sharing the conspiracy theory that the Trump administration did not in fact try to secure exclusive access to the vaccine.
I don’t think you understand the term conspiracy theory nor do you understand how the burden of proof works.
I have already given many credible sources showing why your claim is false, the hacker news mods have removed these articles multiple times (including this very post). You have provided an unsubstantiated claim with no evidence. An extraordinary claim requires extraordinary evidence.
Which is reporting on the initial article which again just states that Germany said the US was trying to invest in the company, not that they were looking for an exclusive arrangement. Show me where Germany confirmed that the US was looking for an exclusive arrangement, we have multiple people saying this was not the case.
That's not what is said in the article of politico. Here is what is reported:
First, The allegation:
According to the article, Trump was trying to get the Tübingen-based CureVac company — which also has sites in Frankfurt and Boston — to move its research wing to the United States and develop the vaccine "for the U.S. only."
Then, the government acknowledgement:
A spokesperson for Germany's Health Ministry quoted in the article appeared to acknowledge the U.S. approach and said that Berlin was "very interested in ensuring that vaccines and active substances against the new coronavirus are also developed in Germany and Europe."
Who says this is incorrect? The alleged party? Because the company did not deny that it was approached by the US American government to sell exclusive access. It just denied that it will be bought, which is a different thing. Regarding the exclusivity it has declared that it will ensure that the vaccine will be available to the world, without neither confirming nor denying the allegation. The fact that they clarify that (source: https://www.curevac.com/news/curevac-focuses-on-the-developm...) the fact that the German government acted at all (multiple reports of that exist), and the fact that the CEO of the company was fired (the company has a press release about it) after meeting Trump are further evidence that indeed an exclusive deal was sought.
Which parts of quantum mechanics are idealised away and how do we know that not including them won't significantly reduce the quality of the result?
Are you possibly using stochastical noise in the simulations and repeat them multiple times, in the hope that whatever disturbance caused by the idealisation of the model is covered by the noise?