# Fermilab

## Inquiring Minds

What are experiments confirming an existence of gravitational mass of "elementary" particles?

What are experiments confirming an existence of the gravitational mass of "elemetary" particles (e.g.protons, electrons, neutrons ect.)? Where can I find the detailed dscriptions of these experiments?

Yours sincerely Pr. Taran

Dear Pr. Taran,

There have been numerous experiments measuring the gravitational mass of macroscopic objects dating back to experiments by Eotvos 1889 and 1922 where he used a torsion balance to measure the gravitational mass. Other types of experiments involve Free-fall and pendulum experiments. References to these can be found in many books on general relativity such as "Gravitation and Cosmology", Steven Weinberg and "Gravitation and Inertia", Ignazio Ciufolini, John ArchiBald Wheeler.

Experiments involving elementary particles are fewer and less accurate than the their macroscopic counterpart. These experiments are generally free-fall experiments. The most successful of these experiments measure the gravitational mass of the neutron. A beam of slow moving neutrons are reflected off of a liquid. If the neutrons hit the surface of the liquid at a critical energy (equal to potential of neutrons in the liquid) then they will be reflected by the liquid which acts as a mirror. It will obey the following relation:

Nb_f = (\gamma * m^2 * g_0 * h_0)/(2*pi* planks constant)

m = gravitational mass h_0 = critical height ( height which the particle was released in which critical energy was reached)

\gamma = (m_i/m)(g_f/g_0) where m_i is the inertial mass. g_f is the gravitational acceleration of the free falling neutron and g_0 is the gravitational acceleration of bulk matter.

b_f = scattering length N = atoms per cm^3

The parameter b_f can be measured independent of gravity (b_0). If these two are different then this would imply that \gamma is different from one and show that the gravitational and inertial masses are different. Experimentally, if it is found that \gamma = 1.00016 +- 0.00025 (L. Koester 1976) and \gamma = 1.00038 +- 0.00025 (Jorg Schmiedmayer 1989)

see L. Koester; 'Verification of the equivalence of gravitational and inertial mass for the neutron', Physical Review D, Volume 14, Number 4, 15 August 1976.

see Jorg Schmeidmayer; 'The Equivalence of the Gravitational and Inertial Mass of the Neutron', Nuclear Instruments and Methods in Physics Research A284 (1989) 59-62

There have been similar experiments to find the gravitational mass of charged particles such as the electron. The difficulty here is that the charge of the electron is much higher that the gravitational force and must be shielded. See:

F.C. Wittenborn and W.M. Fairbanks, Physical Review Letter 19 (1967) 1049; Rev. Sci. Instrum. 48 (1977) 1.

The gravitational mass difference between the neutral kaon and its anti-kaon counterpart was also calculated by various people. See:

I.R. Kenyon, "A Recalculation of the Gravitational Mass Difference between the K_0 and \bar{K_0} Mesons", Physics Letters B, Vol. 237, Number 2, 15 March 1990. p274-277.

Russell Gilmartin