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This question also stems from Anna's answer here: https://physics.stackexchange.com/a/578929/230132

Quoting her, she says an electron bound to a nucleus is not a quantum entity, the entire atom is. She adds that as such the two are not separable.

And she says this is also true of a molecule, i.e. it is one single quantum entity.

Clearly, a molecule can be very complex and have a size almost visible to the naked eye or low level microscopy.

Take DNA for example. To replicate it, a biological device will have to locate the interesting part of its code, free it from its constraints and start reading it.

How is that compatible with the idea of the molecule being a single quantum entity that is not separable to its constituents since those constituents are detected and dealt with separately in biological processes?

Does that mean the said quantum entity actually has so many parameters that in the end its description contains constituents?

Anyway, pursuing my thinking, keeping in mind the idea of a single quantum entity, although I am uncertain of its meaning, if this is synonymous with an elementary object, then does that mean there is instantaneous communication inside the molecule even though it has a size? If not, how can this still be considered a single entity?

Note: by instantaneous communication inside a molecule, I mean that what happens on one end of it is instantaneously known to the other side of the molecule, thus producing effects exceeding the speed of light, which seems erroneous to say the least.

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    $\begingroup$ I think of my yardstick as a single entity even though information does not travel instantly from one end of it to the other. $\endgroup$ – WillO Sep 16 '20 at 5:42
  • $\begingroup$ The question is about quantum entities. $\endgroup$ – Winston Sep 16 '20 at 5:43
  • $\begingroup$ What is a 'quantum entity" and why would information travel across it any differently than it travels across my yardstick? $\endgroup$ – WillO Sep 16 '20 at 5:46
  • $\begingroup$ Thanks for actually repeating the question. $\endgroup$ – Winston Sep 16 '20 at 5:47
  • $\begingroup$ What I'm gently trying to suggest is that your question is exactly as well motivated as "Does information travel instantaneously across yardstick entities?". Why would you expect in the first place that the answer might differ across different types of entities, and why is it any more natural to single out "quantum entities" than "yardstick entities" or "rhinoceros entities" for special inquiry? $\endgroup$ – WillO Sep 16 '20 at 5:54
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I think you took anna v's answer too literally. Atoms and molecules are not so much "single entities" as the elementary particles are. They are far from elementary. This means that, although the individual constituents like electrons and nuclei (or deeper, electrons, quarks and gluons) don't have their single-particle quantum states, they still do have their own probability distributions (both conditional—depending on other constituents' states—and average—where other constituents' coordinates are integrated out), and you can measure their instantaneous properties like positions or momenta (with the usual caveat of state collapse) individually.

Similarly, in non-eigenstates of its Hamiltonian, a "quantum entity" can have time-dependent probability distribution of positions of its constituents, see e.g. the animations of the electron cloud in a single-electron ion at the bottom of this answer. This makes it possible to not only treat a DNA molecule as an entity you could probe at a particular spot, but even single crystals, which are actually macromolecules, can be touched with fingers and felt as having e.g. different temperatures at different sides of the crystal.

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  • $\begingroup$ Thank you very much for your contribution here. So there is some separability, at least a mathematical one, of quantum entities? $\endgroup$ – Winston Sep 16 '20 at 8:55
  • $\begingroup$ @Exocytosis it's not called separability. Separability is the possibility of expression the wavefunction of e.g. two particles in the form $f(x_1)g(x_2)$. And inside the molecule/atom there is a way to interact with its constituents (unlike an electron, which doesn't have any constituents). $\endgroup$ – Ruslan Sep 16 '20 at 9:42

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