It is supposed that the smallest posible black hole (BH) has mass of Planck's mass. But obviously one nucleon (or an electron) also acts with gravitational force. If we assume that the smallest possible BH has really Planck's mass, is here any contradiction that a electron acts with gravitational force? Admittedly, elementary particles are not (supposed) as BHs, but how it is possible that one particle alone give gravitational force? Does this also not contradict to the calculations which gives that BH do not exist? It is clear that in gravitational field a path is curved for every elementary particle, for instance, for a photon which flies close to the sun. But how we can be assured that a photon which flies close to single electron, has curved path? How we can be assured that here it is not the similar effect of QM, as at the small quantum BH calculation? I suppose according to the above assumption, that only enough large group of particles gives gravitational force, but not every particle alone? Where I am wrong?
no. can you think of a reason there might be a 'contradiction'? Maybe you mean at Planck scale, time and space, etc become jumbled all together??...so gravity might be different?? Not impossible....Some think space reduces to two dimension at Planck scale....unproven so far as I know.... Anything with mass or energy or pressure has some associated gravity...even a photon without any mass; so both black holes and electrons exhibit gravitational attraction. Further, an electron is usually many,many times larger than a theoretical black hole; electrons have been experimentally verified, but maybe not their ultimate 'structure'; microscopic black holes have not, but I think they are seeking evidence in the Large Hadron Collider. I don't know if that has been experimentally verified, but if so, I would not be surprised. One could start by flying light, photons, past an atom...with multiple electrons and a nucleus, then if you could measure a deflection, you could move to smaller, lighter, atoms.....and see if you could get accurate enough measurements to make a reliable detection. We do know light is deflected by our sun, and by dark matter-energy in galaxies....its called gravitational lensing. Once you find anything with maass, or energy, we are confident it exhibits gravity. In fact it appears that even the 'empty' space of of the universe has some gravitational effects....negative pressure which causes expansion of the universe: Now THAT seems crazy!!! Here is another insight: one single electron has a fixed gravitational attraction...say, whatever value it is measured at. If you sit on earth and measure the attraction, or sit on the electron and measure the 'opposite' attraction, you'll get the same result. But now if instead of one electron, you pass an atom with a cloud of electrons past the earth, and compare that atom with one that has been 'heated'...that has energy added so the electrons have increased energy levels....the hot and the cold atoms have different gravitational attraction....because they have different energy...Oddly, a smaller black hole is hotter than a big one.....and radiates MORE....!!
It is still hard to measure the deflection of light caused by the earth. I doubt that there is a chance to see the deflection caused by gravity of a single particle within any reasonable future time scale. In addition, there are so many effects which are much stronger, including QED effects, gravitation from the measurement apparatus, diffraction, ... But there is no reason why this should not exist. Energy density can bend the spacetime, even if it is not dense enough to be a black hole. >> but I think they are seeking evidence in the Large Hadron Collider. Unless there are at least 2-3 small extra dimensions or some other new stuff, the energy is too low to produce them.
I think that here is not necessary to measure this. I only ask theoretically, how the (known) effects of quantum gravity influence on this. Some similar quantum gravity effects are, that BHs smaller than Planck mass do not exist, (calculations are known) that gravitational uncertainty of distance (GUD) is always larger than Planck's distance etc. Naty, I will study still one article of quantum gravity uncertainy and then will ask further questions. A preliminary question: It is clear that group of electrons acts gravitationally, but how one electron acts gravitationally. Its gravitational force is much weaker than force of one Planckian BH. Thus effects of this force are maybe smaller than GUD, thus that they do not exist? Thanks for long answers.
There is no problem with a force* weaker than that applied by a black hole. *better: coupling strength An electron can exchange gravitons like any other particle, too - assuming gravity can be expressed in this way at all. Smaller mass and energy is usually related to larger distances, not smaller ones. Therefore, the planck distance is not important for the electron.
I shall assume here the role devoted to dreamers and poets. Concerning not the deflection of light by the earth but the deflection of electrons by protons and neutrons around any nucleus: "Is it reasonable to think that "orbitals" are the signature of gravity at nuclear scale?" I mean the classical representation of gravity is resulting in orbits like the one of the earth around the sun. Are atomic orbitals (e.g.90% probability to find an electron everywhere around the nucleus) not the natural illustration of how gravity interact with "matter" at this scale? In some way, don't we still have a part of what we are looking for in front of our eyes? Is there not a link between quantum gravity and atomic orbitals? If not: where is my error? (Not the same scale?...)
>> Are atomic orbitals (e.g.90% probability to find an electron everywhere around the nucleus) not the natural illustration of how gravity interact with "matter" at this scale? No, as this is the electromagnetic force and independent of gravity.
A photon's path close to an electron or on any distance from it is curved. Any little cuvature means that it gives a small momentum to electron. This means that it gives one momentum to electron (on a small path or on all path). One very small momentum means uncertainty of this momentum and uncertainty of their mutual distance. So this means unprecissenes of curvature due to uncertainty principle and it is important also at small curvatures, even it more important at small curvatures.
Sorry, what do you mean? A momentum change can be smaller than an uncertainty given by some distribution of the electron. >> So this means unprecissenes of curvature due to uncertainty principle Due to the nature of wave functions. So what?