I am trying to build an ultra-lilliput world.

Let's assume that sentient beings can exist on objects of the size of a proton.

  1. Would they be able to observe the atom where the proton belongs, its electrons and maybe (part of) the molecule where the atom is bonded?
  2. Would they be able to infere the existence of the supramolecular world? If so, how?
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    $\begingroup$ If you don't have intense knowledge in quantum mechanics, I highly suggest you think about this twice. You could write a book just to answer that question. $\endgroup$ – PatJ Feb 15 '17 at 15:27
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    $\begingroup$ Not to mention that these little beings are built of things we don't know anything about. We don't know what their sensory capabilities are, what they live on or even how to communicate with them. $\endgroup$ – Green Feb 15 '17 at 15:33
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    $\begingroup$ If they knew where they were they literally wouldn't be able to tell if they were coming or going. $\endgroup$ – Lio Elbammalf Feb 15 '17 at 15:43
  • $\begingroup$ There have been such tales written in the time og Bohr. I even saw it on Mork and Mindy (season 2 opener, 2 parter) $\endgroup$ – JDługosz Feb 15 '17 at 19:00

If only you had asked that question in a fantasy theme instead of science fiction ...

Anyhow. Based on science alone, here are the answers.

1- Would they be able to observe the atom where the proton belongs, its electrons and maybe (part of) the molecule where the atom is bonded?

No. You see things only when light coming from them falls on your eyes. It happens that usually light (photons) interact with the electrons of an atom and not the protons. And then again, it is not that light reflects from electrons, it is that electrons absorb and then re-emit photons of light. So no. The beings will see nothing for 99.999% of their lives. However, if they have other senses (like fine tuned gravitation and electric charge sensing etc), then they would be able to build a very accurate charge-mass model of the world around them. However, they would not know how big or small things are around them.

2- Would they be able to infere the existence of the supramolecular world? If so, how?

This falls not into science, but into philosophy. If they are intelligent then many of their kind (the philosophers) would go on to argue that the universe is bigger than the planet (proton) they are living on and that the universe is far, far more vast than they could ever imagine.

Although we are at least 27 orders of magnitude bigger than those beings, the same applies to us, too ...

Important Note: When you talk about individuals living on a proton, most scientists would immediately denounce the prospect. At subatomic level, things get very, very complex. For example, if the proton (on which they are living) happens to be in the LHC and goes on to collide with another proton at relativistic speeds, would those creatures survive?

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Beings smaller than a proton? Science based?

Then I'm afraid the answer to any question you might ask about them is no.

Could they see the other protons?

A photon with high enough frequency that it would stand a chance of interacting with something so small would be far more than enough to send them flying at near the speed of light (assuming their mass is negligible compared to that of a proton). So, no.

Could they interfere with the supra-molecular world?

If they have such a small size and mass that they can live on a proton without weighing it down, then no.

And now for some questions you didn't ask, but maybe you should have:

Could they live on a proton?

No, protons aren't little solid spheres that have any kind of surface. They are quantum mechanical objects that can be here and there with no definitive boundaries.

What would they even be made of?

There's nothing even theoretically consistent with quantum field theory that could possibly allow for complex beings of that size. And you'd have to invent entire new sets of other forces and fields to account for it. Solidly in the realm of fantasy rather than science fiction.

Could they even know what they themselves are doing?

As Lio Elbammalf pointed out in a comment, due to Heisenberg's uncertainty principle, and due to how small they are, if they could know that they were in a particular place on a proton, they'd have no idea if they were coming or going or how fast. This isn't a matter of some problem with instrumentation or limited resolution of their eyes. It's an issue with the fundamental uncertainty of the things in this universe. When something's position is know to a significant enough degree, it doesn't even make any sense to say it has a particular momentum or vice versa.

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