This episode of Space Time explores the strange phenomenon of time and space switching roles when an object crosses the event horizon of a black hole. According to the mathematics, specifically the Schwarzschild metric, the coordinate that once represented distance (R) becomes time-like, while the coordinate that once represented time (T) becomes space-like. This means that below the event horizon, the direction of time is no longer separate from the spatial dimensions, and the concept of causality is severely distorted.
The episode explains that in flat space-time, the space-time interval is defined as the distance between two events, and it is always negative for causal movement. However, when a black hole is introduced, the space-time interval becomes more complex, and the direction of time is no longer fixed.
The episode also explores the consequences of this time-space switching, including the fact that the future light cone of an observer below the event horizon is severely distorted, and the direction of time is no longer clearly defined. The episode also discusses the concept of time crystals, which are systems that exhibit periodic behavior in time, but notes that these systems are not truly equilibrium systems and require external energy to maintain their oscillations.
Overall, the episode provides a detailed and technical explanation of the strange effects of black holes on space-time, and how our understanding of time and space is severely distorted in these extreme environments.
Here are the key facts extracted from the text:
1. The space-time interval is a quantity that governs the flow of cause and effect in a relative universe.
2. In flat space-time, the space-time interval is defined as the difference between the square of the distance and the square of the time.
3. The space-time interval is the same for all observers, regardless of their relative motion.
4. The space-time interval must be zero or negative if one event causes another event.
5. The space-time interval is negative in the direction of forward temporal evolution.
6. The time-like coordinate (T) must always increase to maintain causality.
7. The introduction of a black hole changes the behavior of time in space-time.
8. The Schwarzschild metric describes the space-time interval near a non-rotating, uncharged black hole.
9. The event horizon of a black hole is the boundary beyond which nothing, including light, can escape.
10. Below the event horizon, the space-time interval becomes negative, and the time-like coordinate becomes space-like.
11. The radial dimension (R) becomes time-like below the event horizon.
12. The singularity at the center of a black hole is a future time, not a central place.
13. The Penrose diagram is a useful tool for visualizing the extreme stretching of space and time near a black hole.
14. The lines of constant space and time are curved in the Penrose diagram, and light cones remain upright.
15. The concept of "time crystals" refers to quantum systems whose internal interactions result in a periodic change from one state to another and back again.
16. Time crystals do not require input energy to keep oscillating, but they are not sustainable in equilibrium.
17. The oscillations in time crystals are in resonance with an external electromagnetic field frequency.
18. The term "time crystal" is used to describe any system that has a pattern of internal states that repeats over time.