Theodore Maiman, inventor of the laser
Let us begin by supposing that we have a positive, non-relativistic point charge, q, momentarily at the origin of an inertial rectangular coordinate system, and moving along the positive x-axis at constant speed v<<c. At point (0, y>0, 0) the electric field points away from q and has the value
Ey = q/4πε0y2. (1)
If we replace q with a row of n equally spaced point charges, all moving at constant speed v<<c along the x-axis, then Ey will be greater than the value in Eq. (1) by a factor of f(n,Dx) that depends upon n and the spacing (Dx) between the charges:
Ey = f(n,Dx)q/4πε0y2. (2)
Let us now replace the charges in Eq. (2) with photons of wavelength λ. According to gravitomagnetic theory a photon of wavelength λ has the real inertial mass
|m| = h/λc. (3)
And any test particle with inertial mass |mtest| has an equal magnitude imaginary gravitational mass, mtest. Thus (making the appropriate substitutions) the gravitational field of a row of photons should be
gy = f(n,Dx)Gih/λcy2. (4)
If we place a horizontally moving material particle with inertial mass |mtest| at y, then since this particle has a gravitational mass of mtest, the test particle should experience a small gravitational acceleration toward the line of photons:
ay = -|gy|. (5)
In brief, the line of photons should gravitationally attract the test particle quite as the Earth’s much greater gravitational field does. If the test particle is moving in the positive x-direction (as the photons are) then its path should curve slightly more toward the x=axis than it does with the photons absent.
Experimentally the row of photons can be provided by a laser beam. And the test particle can be one whose path can be traced on an impact screen placed at a suitably large x. When the laser beam is turned off, the test particle should have no acceleration in the -y direction (other than the one attributable to the Earth’s gravitational field). But when the laser beam is turned on, the test particle should have a small additional acceleration toward the laser beam. Its impact point on the screen should shift downward by a measurable amount.