General Relativity (GR) predicts a gravitational deflection angle of light which is twice what Newtonian gravitational acceleration predicts. This "doubled" angle was experimentally verified.

GR also predicts that massive relativistic particles moving close to the speed of light are bent by the same "twice the non-relativistic Newton angle". Was this ever directly experimentally verified ?

Remark 1 : According to this paper, "the effect of gravity on relativistic massive particles was never studied experimentally".

Remark 2 : According to this link, "The orbits of protons in the (LHC) have to be adjusted regularly to account for the gravitational effect of the moon.". I don't know how true this story is. But, if true, maybe the moon could be used to test "the" equivalence principle at a relativistic quantum level.

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    $\begingroup$ Not sure, but you can check this authoritative reference: arxiv.org/abs/1403.7377 $\endgroup$
    – Avantgarde
    Sep 4, 2018 at 15:17
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    $\begingroup$ "General Relativity (GR) predicts a gravitational deflection angle of light which is twice what Newtonian gravitational acceleration predicts." Newtonian gravity doesn't deflect light at all, it only acts on rest mass and not energy or momentum. $\endgroup$
    – ohwilleke
    Sep 5, 2018 at 2:18
  • $\begingroup$ @ohwilleke Newtonian gravitational deflection of light is a thought experiment based on the fact that gravitational acceleration of a point particle doesn't depend on it's mass. There's is plenty of literature on this topic, e.g. arxiv.org/abs/physics/0508030. $\endgroup$
    – Noé AC
    Sep 5, 2018 at 2:22

1 Answer 1


In this article the effect of tidal earth movements on the LHC beam is discussed:

Geological movements like Earth tides may change the circumference by up to 1 mm with 12 hours . Due to the limited accuracy of the tidal prediction (at level of a few percent) and to the presence of other slow ground movements, it is not possible to accurately predict changes to $C_c$ to better than $≈0.1 mm$.

It is in page 6 of an esoteric document , and I am quoting it to show that accuracies of microns are hard, and lead to this article, discussing neutral beams, where the effect of electromagnetic interactions is minimized:

According to (3.6), in order to focus a neutral beam into a 1 m radius at 1000 km, one would, for example, need a beam with an initial radius of 20 cm and an emittance of $2×10^−7$m·rad.

The quote is to show that there exists a balistic effect of gravity that is too small to affect beams at LHC, which at best can work with micron accuracies. Possible 1000km experiments cannot be with charged tracks within our technology (maybe in space).

Any corrections for tides are done by the "feel" of the operator of the beam, as the objective is to get the beams to collide, and for protons the electromagnetic effects will be stronger than any gravitational at the level of microns.

So any experimental verification of such claims, as twice the attraction of newtonian gravity, are not at present possible. There is an experiment which checks whether antihydrogen is attracted or repulsed, and sets limits, and that is as far as it goes with the present accelerators on interesting deviations of predictions.

  • $\begingroup$ Dear Anna v, we have never experimentally tested neutrino's deflection around massive objects? $\endgroup$ Sep 7, 2018 at 23:34
  • $\begingroup$ @ÁrpádSzendrei neutrinos are not only neutral but also only weakly interacting and of very small mass. That is why experiments are set up in kilometer distances. . It is not possible to get any measurement accuracy on such distances with beams on earth. , and cannot think of cosmological observations that might give a clue. Maybe comparing lensing of gamma ray bursts with lensing of a neutrino burst from the same source. $\endgroup$
    – anna v
    Sep 8, 2018 at 3:15

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