  The textbook-accepted formulation of electromagnetic force was proposed by
Lorentz in the 19th century, but its validity has been challenged due to
incompatibility with the special relativity and momentum conservation. The
Einstein-Laub formulation, which can reconcile those conflicts, was suggested
as an alternative to the Lorentz formulation. However, intense debates on the
exact force are still going on due to lack of experimental evidence. Here, we
report the first experimental investigation of angular symmetry of optical
force inside a solid dielectric, aiming to distinguish the two formulations.
The experiments surprisingly show that the optical force exerted by a Gaussian
beam has components with the angular mode number of both 2 and 0, which cannot
be explained solely by the Lorentz or the Einstein-Laub formulation. Instead,
we found a modified Helmholtz theory by combining the Lorentz force with
additional electrostrictive force could explain our experimental results. Our
results represent a fundamental leap forward in determining the correct force
formulation, and will update the working principles of many applications
involving electromagnetic forces.
