Watch on YouTube

Download is disabled.

1,048,935

27,099

262

Genre: Education

Family friendly? Yes

Wilson score: 0.9892

Rating: 4.9617000000000004 / 5

Engagement: 2.61%

3Blue1Brown

**Shared September 13, 2017**

The math of superposition and quantum states.

minutephysics channel: https://www.youtube.com/user/minuteph...

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

And by Brilliant: https://brilliant.org/3b1b

Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way.

This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of classical waves, specifically classical electromagnetic waves.

I will say, if you *do* want to go off and learn the math of quantum mechanics, you just can never have too much linear algebra, so check out the series I did at http://3b1b.co/essence-of-linear-algebra

Mistakes: As several astute commenters have pointed out, the force arrow is pointing the wrong way at 2:18. Thanks for the catch!

*Note on conventions: Throughout this video, I use a single-headed right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use double-headed arrows for describing polarization states, while single-headed arrows are typically reserved for the context of spin.

What's the difference? Well, using a double-headed arrow to represent the horizontal direction emphasizes that in a quantum mechanical context, there's no distinction between left and right. They each have the same measurable state: horizontal (e.g. they pass through horizontally oriented filters). Once you're in QM, these kets are typically vectors in a more abstract space where vectors are not necessarily spatial directions but instead represent any kind of state.

Because of how I chose to motivate things with classical waves, where it makes sense for this arrow to represent a unit vector in the right direction, rather than the more abstract idea of a horizontal state vector, I chose to stick with the single-headed notation throughout, though this runs slightly against convention.

Music by Vincent Rubinetti:

https://vincerubinetti.bandcamp.com/a...

------------------

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

Various social media stuffs:

Website: https://www.3blue1brown.com

Twitter: https://twitter.com/3Blue1Brown

Patreon: https://patreon.com/3blue1brown

Facebook: https://www.facebook.com/3blue1brown

Reddit: https://www.reddit.com/r/3Blue1Brown

26:21

But how does bitcoin actually work?

25:13

Thinking outside the 10-dimensional box

2:11:46

EM Waves

22:30

Why do prime numbers make these spirals?

17:05

The Essence of Calculus, Chapter 1

14:00

Curves we (mostly) don't learn in high school (and applications)

54:42

An Introduction to Quantum Biology - with Philip Ball

18:07

The more general uncertainty principle, beyond quantum

29:43

Pi hiding in prime regularities

21:44

Feynman's Lost Lecture (ft. 3Blue1Brown)

13:13

Music And Measure Theory

51:55

Rethinking Reality: Space, Time and Gravity

18:55

This is How Easy It Is to Lie With Statistics

19:55

Fractals are typically not self-similar

19:43

But what is the Fourier Transform? A visual introduction.

15:42

Divergence and curl: The language of Maxwell's equations, fluid flow, and more

42:47

Why Everything You Thought You Knew About Quantum Physics is Different - with Philip Ball

9:55

The hardest problem on the hardest test