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I know that atoms and entire molecules and even sets of hundreds of molecules can be in superpositions of position eigenstates.

Viruses are the smallest living organisms (if they can even be called organisms) with the smallest being 20 nanometers.

Can viruses, analogous to a set of hundreds of molecules be in a nontrivial superposition of position eigenstates?

I don't even know if you could calculate this with current quantum theory and maybe this a silly question as well.

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    $\begingroup$ Any quantum state can be expressed as a superposition of some basis states. $$\lvert \psi \rangle = \sum_{a^\prime} \lvert a^\prime \rangle\langle a^\prime \vert \psi \rangle$$ $\endgroup$ – Sandejo Sep 19 at 21:36
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    $\begingroup$ Are you asking whether the state space of a virus can have more than zero dimensions? If so, the answer is (of course) yes. If not, what did you actually mean to ask? $\endgroup$ – WillO Sep 19 at 23:14
  • $\begingroup$ To quote a famous experimentalist: “The only things that limits the size of the object in superposition is the size of your grant.” $\endgroup$ – ZeroTheHero Sep 20 at 1:18
  • $\begingroup$ maybe the last part of this answer of mine might help physics.stackexchange.com/questions/572079/… $\endgroup$ – anna v Sep 20 at 4:00
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    $\begingroup$ I‘m wondering were the downvotes came from? That’s a legit question, isn’t it? $\endgroup$ – Hartmut Braun Sep 20 at 6:18
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In 2009, a group of German and Spanish researchers proposed a model for superposition of living organisms 1. Basically, the proposal was to isolate the virus in a vacuum chamber, using a laser-generated electromagnetic field, while another laser beam would be used to achieve the lowest possible energy state. Thus, a single photon would be used to put the virus into a quantum superposition of two states; moving or static.

If I am not mistaken, experimentally the model has not yet been tested, or at least the tests have not been publicly evidenced.

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  • $\begingroup$ Very interesting. I never heard of such an experiment. Do you know the link to the study? I might want to check it out myself. $\endgroup$ – Tachyon Sep 19 at 21:48
  • $\begingroup$ @Tachyon the link is embedded in the answer, just click on the number "1". $\endgroup$ – July H. Sep 19 at 21:50
  • $\begingroup$ Oh, that wasn't noticeable to me. Thanks! $\endgroup$ – Tachyon Sep 19 at 21:51
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You can treat a large organism as a superposition of quantum states. However, in such large systems there are many many many interactions. The result of treating a large organism as a superposition of states, and using the quantum time evolution function quickly results in a set of states which, if measured, would be tremendously correlated.

If you wanted to calculate it, the power tool you would want would be the Central Limit Theorem, which states that if you take draws from a random variable (measure the state of your organism), the distribution you draw from becomes increasingly normal and the standard deviation decreases linearly with the number of measurements.

As many of the interactions within an organism are well-modeled as classical (meaning we made sense of them without resorting to quantum mechanics), these interactions act as measurments in this sense. Thus your virus, with its 4 million atoms, will quickly converge on a easy-to-analyize average behavior with a statistical deviation of perhaps 0.0000001% within microseconds. Why do I choose that percentage? Well, in the physics community, a certainty of 99.9999% constitutes a "discovery" that is so unlikely to be due to random chance that the community is okay with ignoring that likelihood.

In other words, the behavior of a virus sized object in normal thermal conditions is so predictable by looking at the mean behavior, that you could claim that a virus does that behavior (as opposed to saying there's random variance around that behavior), and be credited with a "discovery" in the physics community sense.

Now if you had a large object in a known quantum state, you might be able to interact with it in a way which exhibits that quantumness in a way that wasn't predictable classically. However, this is an extreme corner case. We don't know how to put such a large object into a specific quantum state with current technology, and the particular interactions which exhibit this behavior (rather than collapsing back onto the classical behaviors) would be narrow indeed.

We currently do not believe large organisms need to be modeled in that way, although there are a handful who argue there may be small-scale quantum behaviors in the brain.

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As in the case of Schrodinger's Cat, any macroscopic object can be put in a superposition of quantum states. The difficult part is to prove it by experiment. The only way to prove that an object is in a superposition of quantum states is to produce a large number of identical objects in the same identical superposition, and perform measurements on all of them. However, it is nearly impossible to force a complex object like a virus - or a cat - into a known quantum state, much less force it into a given superposition of known quantum states; so to produce a large number of such objects that are all in precisely the same superposition of states is, at least with respect to today's technology, effectively impossible.

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The current mainstream physics hypothesis is that quantum mechanics is the underlying level of reality from which all other physics models/theories emerge.

In this view the answer is yes, ultimately one wavefunction should describe the whole universe theoretically, and some fancy models/theories have evolved based on such a premise, as the many worlds interpretation. So a superposition of two viruses should be in a single wavefunction will show quantum effects.

The difference between model/theory and experiment is that experimental errors limit the ability to measure these quantum effects in the laboratory. Considering that avogadro's number is $NA = 6.02214076×10^{23} mol{^−1}$ and our experiments have the accuracy of a few decimal places one does not expect quantum effects to show above nanometer dimensions.

It is true though that quantum effects appear macroscopically in superfluidity and superconductivity. Thus there is speculation about superconductivity in brain,for example. In my opinion this type of research has a better chance of finding quantum mechanical effects with living organisms than experiments with viruses, that are in the region of decoherence as far as our measurements can go.

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