# Do viruses suffer from quantum de-localization?

Consider some microscopic life form. It should obviously be localized in space, in the quantum-mechanical sense, if it is treated as a single particle (though it is composite). If its characteristic length is $l$, then its wavefunction would de-localize in the typical timescale $$\tau = \frac{ml^2}{\hbar}$$

If we estimate this for a virus (~typical diameter 100 nm), and assume roughly water mass density, we obtain $$\tau \approx \frac{1 \frac{g}{cm^3}\cdot(100\ nm)^5}{\hbar} \approx100\ seconds$$ So technically speaking, after about two minutes, the virus had doubled its uncertainty in position. Even if the mass assumption is off by two orders of magnitude, we still obtain everyday timescales. How should this estimate be interpreted? Was is observed in biology?

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Don't forget they aren't just sat there doing nothing, they are 'absorbing' and losing other small molecules constantly as part of their growth and survival, constantly replacing parts of themselves – RhysW Apr 19 '13 at 9:58
I edited the title, because "microbial" usually refers to bacteria, which are quite a bit bigger than the scale you're talking about here. I hope that's ok. – Nathaniel Apr 19 '13 at 12:40

An experiment to put a virus into a superposition of states was described in this Arxiv preprint. As far as I know the experiment has not been done yet, but I would guess most of us believe it will work and that a virus does indeed obey the principles of quantum mechanics just like a sub atomic-particle. After all a considerably larger object than a virus has been placed into a superposition of states, though this was under rather special circumstances.

However it's unlikely we will ever observe quantum behaviour for a virus in water. This is because while an isolated virus can be described by a basically simple wavefunction, if the virus interacts with anything, e.g. water molecules, it's wavefunction becomes entangled with the wavefunction of whatever it interacts with. For a virus in water we would have to observe quantum behaviour of the virus and the water it's in. This increases the size and complexity of the system to be point where it would rapidly decohere and return to classical behaviour.

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"if it is treated as a single particle" - but of course a virus is not. If one particle in a composite system suddenly decides to randomize its location, the other particles around it will be in the way. Forces will (mostly) try to pull it back. For the whole system to spread apart or shift position, every particle must, by incredible coincidence, jiggle out of their positions just the right way.

The delocalization timescale of a particle is related to the probability of the particle being not where it original was, per some tiny unit time. For a bunch of particle involved in one system, the delocalization probability per unit time for the whole, is the probability of particle #1 moving off, AND the probability of particle #2 moving off, AND the probability of particle #3.... which multiplies out to a very small probability.

At least, this is one crude wordy hand-waving way to explain why viruses, nanoparticle and large molecules stay in one piece and move about in a mostly classical sort of way. There are more mathematically refined ways to explain it.

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