# Has the ballistic motion of an electron in gravitational field ever been measured?

Reading this question I thought of an argument that an electron's trajectory would bend in the gravitational field despite the electron's being incapable of strong interaction; this would then disprove the conjecture stated in that question. But then I couldn't find any references to actual experiments that have been done to measure this ballistic motion of an electron in gravitational field.

Has such motion actually been measured?

• Why do you restrict the question to electrons? – my2cts Jul 4 '20 at 22:21
• @my2cts OK, any lepton could do I suppose. I just first thought of an electron because it's the most abundant of those we can easily interact with. – Ruslan Jul 4 '20 at 22:29
• sciencedirect.com/science/article/pii/S0370269315006723 – Árpád Szendrei Jul 4 '20 at 22:38
• I was thinking broader. Why not ask this for all matter? – my2cts Jul 4 '20 at 22:38
• @my2cts just read the question I linked to. The context requires a lepton. – Ruslan Jul 4 '20 at 22:39

After searching online for a while, I found this paper, entitled "EXPERIMENTAL COMPARISON OF THE GRAVITATIONAL FORCE ON FREELY FALLING ELECTRONS AND METALLIC ELECTRONS". The paper refers to two earlier papers:

1.F.C.Witteborn, L.V.Knight,and W.M. Fairbank, in Proceedings of the Ninth International Conference on Low Temperature Physics, edited by J.G.Daunt, D.0. Edwards, F.J. Milford, and M. Yaqub {Plenum Press, New York, 1965), p.1248.

1. F.C.Witteborn, thesis, Stanford University, 1965 (unpublished).

There are a bunch of related papers here.

Bottom line: it appears that measurements have been done.

• Well, I'll be damned, I didn't think it would be possible to emit such low-velocity free electrons, but I stand corrected. Quite the clever setup! – Tom Feng Jul 5 '20 at 2:03
• Hmm, the first paper seems to only measure the difference between gravitational acceleration of electrons in vacuum and those in metal. It doesn't measure absolute gravitational acceleration, instead finds that the difference is very small. This doesn't seem to be a conclusive evidence of electrons being affected by gravitational field. – Ruslan Jul 5 '20 at 9:46
• @Ruslan Read the conclusion in the last line. – my2cts Jul 5 '20 at 10:52
• @my2cts "We conclude that the force of gravity on electrons inside a metal is the same as that on electrons in a vacuum." So what? This doesn't preclude zero $g$. – Ruslan Jul 5 '20 at 11:09

EDIT: see the answer by S. McGrew. Turns out there's some clever methods of releasing extremely low energy free electrons, which makes gravitational effects just measureable.

Let's think about the size of the effect you're looking for.

Suppose you sputter off an electron with a very low energy of around 1 eV. This corresponds to an electron velocity of about 600 km/s. If you set up a vacuum chamber 1 km long, the electron travels across it in around 1.5 ms. In that time, gravity on Earth's surface will have deflected it by under 30 microns - 0.03 mm! Actual electron emissions are much higher energy, especially for long-chamber situations - most particle accelerators operate with energies in the MeV range, which gives deflections a thousand times less. More or less, this is completely impractical to measure, since this will be many orders of magnitude smaller than your beam width.