Hypothetical Eclipse Calculation

[mahonskey]

TL;DR Summary

Hypothetical: Approximately how far from earth would a star the size of the sun have to be for an object the size of a quantum particle to cause a total eclipse of that star when orbiting the earth at a distance equal to that from earth to the center of the moon?

Hypothetical: Approximately how far from Earth would a star the size of the sun have to be for an object the size of a quantum particle to cause a total eclipse of that star when orbiting the Earth at a distance equal to that of Earth to the center fro the moon?

 

[PeterDonis]

an object the size of a quantum particle

A quantum particle does not have a definite size. You need to either pick an object that does, or just pick a size directly, for your question to be answerable.

 

[anuttarasammyak]

Say there is a particle between a star and eyes of an observer
D: diameter of the star
d: diameter of the particle
R: distance from the eyes to the star
r: distance from the eyes to the particle
$$D/R=d/r$$
This is the preliminary evaluation with no quantum nor GR effects considered.

EDIT: I would add diffraction, dispersion by air and field of view of an eye to the factors to be considered.

 

[mahonskey]

A quantum particle does not have a definite size. You need to either pick an object that does, or just pick a size directly, for your question to be answerable.

Alright, let's just say an electron. Classical electron radius.

 

[PeterDonis]

Classical electron radius.

Then you can plug that into the formula given in post #3.

 

[PeterDonis]

This is the preliminary evaluation with no quantum nor GR effects considered.

It should be noted that this formula, strictly speaking, is for a single "eye" receiving the light at a point--more precisely, in a region smaller in diameter than the particle. That is not actually true for a single human eye and a particle with a diameter as small as the classical electron radius; the individual light sensors in the human eye are much larger than that. But we could imagine some idealized detector the size of an atomic nucleus, or smaller.

 

[mahonskey]

It should be noted that this formula, strictly speaking, is for a single "eye" receiving the light at a point--more precisely, in a region smaller in diameter than the particle. That is not actually true for a single human eye and a particle with a diameter as small as the classical electron radius; the individual light sensors in the human eye are much larger than that. But we could imagine some idealized detector the size of an atomic nucleus, or smaller.

You don't happen to know the smallest diameter detectable by the human eye, do you?

 

[PeterDonis]

You don't happen to know the smallest diameter detectable by the human eye, do you?

Not off the top of my head, no, but I would guess that if "detectable" means "resolvable by a single cell in the retina, if we attached idealized detectors to it" it's around 1 micron ($10^{-6}$ meters), since that's my rough estimate of the size of the cells involved. That's about 9 orders of magnitude larger than the classical electron radius.

If "detectable" means "actually perceivable consciously by the human whose eye it is", the answer is probably 1 or 2 orders of magnitude larger; IIRC a human hair is about 100 microns (1/10 millimeter) wide, and that's a rough proxy for the smallest diameter we can consciously perceive.

 

[Ibix]

This is the preliminary evaluation with no quantum nor GR effects considered.

EDIT: I would add diffraction,

For an obstacle comparable in size to the wavelength of light you most definitely need to consider diffraction. And the far field diffraction pattern, at least, includes a bright spot in the middle.

For an obstacle much smaller than the wavelength of light (like an electron), I don't think it would have any material effect at all. It's a bit like asking if you can deflect a tsunami by holding a shield up infront of you. Even if you were strong enough not to get swept off your feet the wave would just wash over you and keep going.