Mr Eagleman came up with a cunning device: the "perceptual chronometer", a wristwatch-like device which flicked blindingly fast between two LED screens.
Normally the flicker would be so fast Jesse could only see a blur. But if time slowed down for him, he might be able to discern the two different screens and read a random number on one of them.
"There's no way to fake this test," says Dr Eagleman, "because if time is not running more slowly, they can't see the sequence."
All Jesse had to do was jump, and read. As he ascended the 33ft metal cage no-one seemed to believe this curious experiment might work.
When Jesse landed, he noted he had seen "98". Dr Eagleman checked. In fact the number was 96. Not quite spot-on, but the two numbers look very similar on a digital screen.
Further jumps got similar results - all suggesting that time did seem to slow down for Jesse during the jump.
So time actually does slow down or speed up based on what you are doing. This is very interesting, because when I was in a car wreck it seems like I have about 10 seconds of memory, but I know it lasted maybe half a second. And now I know that time actually did last for that long.
Also, some times before I get a good chance on scoring a goal in hockey time slows down, so maybe the greatest sports players aren't the ones with the best physical abilities, but the ones that are able to slow time down the most during important events.
Do you have any other cases of time slowing down?