## 物理学：The Maths of General Relativity – Part 1/8

In this series, we build together the theory of general relativity. This first video focuses on the notions of worldline, proper time, and coordinate systems.

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# What are the Deep Laws of Nature?

What’s fundamental? What’s bedrock reality? What are the deep regularities, things that work the same—always, everywhere—across the universe? Are these regularities “laws”?  Where do they come from?

## 数学：四元数及四元数的可视化

How to think about this 4d number system in our 3d space.

Brought to you by you: http://3b1b.co/quaternion-thanks

Part 2: https://youtu.be/zjMuIxRvygQ

Interactive version of these visuals: http://3imaginary1real.com

Quanta article on quaternions: https://www.quantamagazine.org/the-st…

The math of Alice in Wonderland: https://www.newscientist.com/article/…

1.定义纯四元数

2.进行四元数运算

3.产生的一定是纯四元数，也就是说它的第一项为0，有如下形式：

4.中的后三项就是

***********************************************************************************************************

1.运算产生的结果也要是三维向量
2.存在一个元运算，任何三维向量进行元运算的结果就是其本身
3.对于任何一个运算，都存在一个逆运算，这两个运算的积是元运算
4.运算满足结合律

（不加说明，以下所说四元数全为单位四元数）

## 物理学：我们是不是可以这样理解量子力学？

The standard theory of quantum mechanics leaves a bit to be desired. As Richard Feynman put it, “I think I can safely say that no one understands quantum mechanics.” This is because observations of experiments have led us to a theory that contradicts common sense. The wave function contains all the information that is knowable about a particle, yet it can only be used to calculate probabilities of where a particle will likely turn up. It can’t give us an actual account of where the particle went or where it will be at some later time.

Some have suggested that this theory is incomplete. Maybe something is going on beneath the radar of standard quantum theory and somehow producing the appearance of randomness and uncertainty without actually being random or uncertain. Theories of this sort are called hidden variable theories because they propose entities that aren’t observable. One such theory is pilot wave theory, first proposed by de Broglie, but later developed by Bohm. The idea here is that a particle oscillates, creating a wave. It then interacts with the wave and this complex interaction determines its motion.

Experiments using silicone oil droplets on a vibrating bath provide a remarkable physical realization of pilot wave theories. They give us a physical picture of what the quantum world might look like if this is what’s going on – and this theory is still deterministic. The particle is never in two places at once and there is no randomness.

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Silicone oil droplets provide a physical realization of pilot wave theories.

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