This episode of Space Time explores the concept of time and space switching roles in the mathematics of black holes. When an object crosses the event horizon of a black hole, the coordinates of space and time change. The radial distance from the center of the black hole, which was once a space-like coordinate, becomes time-like, and the time coordinate becomes space-like. This means that the object's future is no longer ahead in time, but rather inward, towards the center of the black hole.
The episode uses the Schwarzschild metric to describe the space-time around a non-rotating, uncharged black hole. The metric shows that the space-time interval becomes negative below the event horizon, which means that the flow of time is reversed.
The episode also explores the concept of time crystals, which are quantum systems that exhibit periodic changes in their internal states. The host discusses how time crystals are different from regular crystals and how they can be used to study the behavior of quantum systems.
The episode concludes with a discussion on the importance of understanding the universe and how it can be challenging, but ultimately rewarding. The host encourages viewers to persist in their efforts to understand complex scientific concepts, even if they seem difficult at first.
Here are the key facts extracted from the text:
1. The episode is sponsored by Crunchyroll.
2. The topic of the episode is the switching of roles between space and time in the mathematics of black holes.
3. The space-time interval is a quantity that governs the flow of cause and effect in the universe.
4. The space-time interval is defined differently for flat space and for space with gravity.
5. The Schwarzschild solution to Einstein's field equations describes the space-time interval for a non-rotating, uncharged black hole.
6. The event horizon of a black hole is a boundary beyond which nothing, including light, can escape.
7. Inside the event horizon, the space-time interval becomes negative, and the coordinate R, which once represented a distance, becomes time-like.
8. The coordinate T, which once represented time, becomes space-like.
9. The Penrose diagram is a useful tool for visualizing the extreme stretching of space and time near a black hole.
10. The diagram shows how the light cones of observers change as they approach the event horizon.
11. Inside the event horizon, the future light cone of an observer encompasses more and more of the event horizon.
12. The past light cone of an observer encompasses light that has been struggling to escape from the black hole.
13. The singularity at the center of the black hole becomes a future time, not a central place.
14. The Swarzchild metric gives two separate space-time maps, one for above and one for below the event horizon.
15. The coordinates play different roles in those regions.
16. Time crystals are quantum systems whose internal interactions result in a periodic change from one state to another and then back again.
17. Time crystals were first proposed by physicist Frank Wilczek in 2012.
18. The term "time crystal" is used to refer to any system that has a pattern of internal states that repeats in time.
19. Time crystals do not require any input energy to keep them oscillating.
20. The oscillating state of a time crystal is an equilibrium state.
21. Time crystals can be used to study the behavior of quantum systems in the presence of external forces.