Basically, a strong gravity source, like our earth’s core will slow down space-time. They have taken cesium (or atomic) clocks in pairs (to prove the result was not just getting out of sync with each other), and taken one pair really low, like sea level, and another pair really high up into an observatory. When they were both brought back to the same level, the pair from the observatory were shown to be ahead of the pair from the lower height. Admittedly they were fractions of a second off, but the point still stands. Now if we change the high point from an observatory on a mountain to orbit around our planet, that pair would be even more ahead of the sea level pair, even though they were in sync at the beginning of the experiment.
This information we can then extrapolate to a black hole, something that has gravity so intense that not even light can escape it. As long as we do not go past the black hole’s event horizon (the edge of the gravity pull where light no longer can escape) a clock there will move so slow that we might see years pass before they see a second pass.
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