Have we ever observed electron in gravitational interaction?

Question

So, as the title suggests have we ever observed electron in gravitational interaction? If we did have we ever observed a positron (or any other antiparticle) in gravitational interaction? Is there any difference between particle and antiparticle in gravity?

Answer 1

This is half way between answer and comment: the main aim is to direct you to weak equivalence principle tests as one area where such questions are explored.

Experiments to test the equivalence principle are able to detect many aspects of gravity. For example, if the electron had a gravitational interaction different from the one implied by its inertial mass, then this could in principle show up in a weak equivalence principle test, and I think existing experiments are sensitive enough to rule this out quite thoroughly.

Answer 2

Two electrons "touching each other" will gravitationally attract each other with $$G \frac {m_e^{~2}}{(2~r_e)^2} \approx 10^{−42}~\text{N}$$ force. Needles to say that gravitationally interacting elementary particles is out-of-scope of today's (and tomorrow's) research technologies. Add Coulomb force with a lot higher repelling force magnitude, Heisenberg uncertainty principle, which could mess-up interaction energy temporarily and you'll see that it's only possible to see gravitational interaction of HUGE gravity sources like merging black holes, etc.

EDIT

More real scenario is to measure particle interaction with Earth gravitational field. For example if say, neutron in a particle accelerator would be accelerated to $v=0.99999999999999999~c$ speed, then per

$$ G \frac {m_n \cdot M_{earth}}{\sqrt{1−(v/c)^{^2}}~R_{earth}^2} \approx 10^{−18}~\text{N}$$

it will experience $1aN~(\text{ato-Newton})$ micro force towards Earth center. This may or may not be measured, but measuring threshold of this scheme is certainly lower than in direct particle-to-particle case.

Finally, indirectly we already know that particles are affected by Earth gravitational field. Consider air density equation vs altitude barometric formula:

$$ \rho =\rho _{b}\exp \left[{\frac {-g_{0}M\left(h-h_{b}\right)}{R^{*}T_{b}}}\right] $$

Notice gravitational potential energy term $\to g_{0}M\Delta h$, so air get's more sparse up the hills (or higher in atmosphere), right? It is so because air molecules statistical average kinetic energy (term $T_b$ related to air temperature) can't withstand crushing force of Earth gravity, so air molecules simply tend to group more densely by the Earth surface. If molecules would not experience own weight force, then in an isothermal atmosphere would be $\rho = \text{const}$, besides without a stopping gravity, air would quickly evaporate into an outer-space, leaving Earth without atmosphere.

Answer 3

Actually, the charge of the electron was originally measured with the help of gravity. Oil drops were blown in a small device with an upward magnetic field, and electrons were sitting on the top of the oil drops. There is a relation between the charge sitting on the oil vs the mass of the oil drop, that you can get if you measure the "falling speed" of the oil drops. It turns out, that the observed values are clearly quantized, and the corresponding factor is the electron's charge. Its a very old measurement by Millikan, who got nobel prize for it. We repeated it in the lab during my BSc. It was one of the fun lab sittings.

Answer 4

Individual neutrons and atoms have been observed in free-fall as has been anti-hydrogen. There are three approaches: generate cold beams (i.e. low momentum spread), follow the trajectories; trap the particles, then turn off the trap and watch them fall; trap them, then use a laser to kick them upward (aka atomic fountains), and study macroscopic properties such as the height that they reach or, with lower excitations, the resulting absorption spectra, see e.g. here. Electrons, or charged particles in general, are usually easier to study than neutral particles because electromagnetic fields are so easy to produce. But in this case any electrical field would perturb the measurement because of the relative weakness of gravity, so actually experiments with neutral particles (or atoms) are simpler. One way around that is to use singly-ionized heavy atoms, where experiments have been suggested

Answer 5

Consider the equivalence principle tests by the Kasevich group at Stanford. Here is a blog-level introduction, and a bibliography.

The method is to drop ultra-cold clouds of rubidium-85 and -87 atoms, and look for interference effects. They claim a goal precision of $10^{-15}g$ difference in acceleration between the two species, and in this 2020 publication find no equivalence principle violations at the part-per-trillion level.

It's not immediately obvious (to me, skimming the linked paper) whether the rubidium experiments would count as a measurement of gravitation on electrons, since the number of (protons plus electrons) is the same in the two isotopes and the precision of the measurement arises from the differential technique. You can probably mine references-of-references until you come to a recent literature review.

The gravitational behavior of antimatter is the subject of several experiments using the cold antihydrogen source at CERN; see this Wikipedia article and links therein.