Bending Space and Time

Someone asked me if I know how to bend space and/or time. It was asked as a joke, but I happen to know the answer. Space actually does bend, in the vicinity of matter, according to General Relativity. Light beams will appear to bend as they pass through the warped region. This phenomena is called gravitational lensing.

The resulting deflected is equal to the angle θ = 4GM/rc², where G is the gravitational constant, M is the mass of your object, c is the speed of light, and r is the distance from the light beam to the point source of the gravity.

Let's say, for example, that I want to bend your laser pointer with my body mass. You shine the laser 1 foot from my center of mass. I want to bend the light by just one degree. This small deflection should be observable if you bring your eye towards the laser pointer and look strait down the beam. In this hypothetical, how much do I weigh?

1° = 4GM/rc²

4GM = 1°rc²

M = 1°rc²/4G

M = 1.79 * 10²⁴kg

M = 30% mass of the Earth

Time to go on a diet.

What if you're shining a laser pointer at the mirror left on the Moon by the Apollo astronauts? I walk up and stand one foot from the beam, weighing 100kg. How far does my mass cause your laser beam to drift off target?

First, we have to find the angle of deflection caused by my mass.

θ = 4GM/rc²
θ = 5.58 * 10^-23°

Now, we do a little trigonometry to find drift off target, x. Let d represent the distance from the Earth to the Moon.

tan(θ) = x / d
x = d * tan(θ)
x = 3.91 * 10^-16 meters
x = 0.391 femtometers

A miniscule effect.