Answer:
To understand Einstein's thought processes,
imagine yourself in the sealed box, being accelerated through interplanetary
space at 9.8m/s^2. You grab the flashlight that you keep on the bedside
table and shine a beam of light perpendicular to the acceleration vector. Since the box is accelerating upward, the path of the light beam
will appear to you to be bent downward, as the floor of the box rushes up
to meet the photons. However, thanks to the equivalence principle, we can
replace the accelerated box with a stationary box experiencing a constant gravitational acceleration. Since there's no way to distinguish between these
two cases, we are led to the conclusion that the paths of photons will be
curved downward in the presence of a gravitational field. Gravity affects
photons, Einstein concluded, even though they have no mass. Contemplating the curved path of the light beam.
Fermat's principle, which states that
light travels between two points along a path which minimizes the travel time required. In a vacuum, where the speed of light is constant, this translates into the requirement that light takes the shortest path between two points. In Euclidean, or flat, space, the shortest path between two points is a straight line. However, in the presence of gravity, the path taken by light is not a straight line. Thus, Einstein concluded, space is not Euclidean. The presence of mass, in Einstein's view, causes space to be curved.
