Some light quantum mechanics (with minutephysics)

The math of superposition and quantum states.
An equally valuable form of support is to simply share some of the videos.

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.

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:

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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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).

Various social media stuffs:

[eliayres]

No lie without the animation I would be totally lost. Such a powerful tool for education

[TrevorSchmahl]

It would actually be amazing if you did a video series explicitly going through Maxwells equations, their meanings and derivations! More physics!

[erik]

after a month, the Bob Ross of math is back

[imnotcringed]

I'm in grade 5 and watching this randomly and understand a little bit of it.

[OOchriOO]

THANK YOU both for finally making an accessible video on QM that actually dives into the mathematics instead of just saying "wow QM is weird! Look, the cat is alive AND dead! A zombie!".
You are a gift to the divulgation of science, people need to know what physics really is. Keep up the good work.

[LazerLord]

Holy crap...

I finally understand (a bit) what polarization *actually* is.

[proteincomputer]

Hey, i don't know if you're going to read this, but here it is. Me and my friends are graduate students in physics, we live in Brazil and we ADORE your videos. You really helped us how to understand a bunch of stuff ( the topology videos are amazing, thank you for that ).
I guess you'd like to know that your work is recognized here in Brazil. Everytime a new video is launched, we watch it with the excitement of a game of thrones episode.
So, this is it. Thank you for this incredible work, and always remember you fave a bunch of brazilian physicist fans.
Abraços!

[jamesmason]

3blue1brown says that he might make a video on maxwells equations
Me: I

[Pulsar]

For those of you who want to start learning quantum mechanics, I highly recommend the MIT course 8.04, by prof. Allan Adams. He's an amazing lecturer, and explains the topics with clarity and enthusiasm. The first few lectures are quite accessible, and they get progressively more advanced. Challenge yourself and see how far you're able to get. Link:

[dragoncurveenthusiast]

14:50 - 15:38 blew my mind.
Such an eye-opening moment! Incredible what the two of you are able to explain in a 22min video!!!
This is just beautiful.

[jeanpanachay]

omg 3b1b AND henry ?? I must be dreaming

[gizatsby]

wow, this is a really great video. that's all i can say really. it's just so well done.

[AlexTuduran]

I've been asking myself for years how introducing a third polarizing filter in between polarizing filters that cancel out each other makes them not to cancel. For me it was black magic, but it makes complete sense now.

And the fact that perceived intensity (amplitude) is the result of full amplitude turned on and off based on probability just works so well with the idea of energy being transferred in discrete steps and discrete amounts.

There's also another nice perspective on the subject. That is, because the Plank constant is so small compared to our perception of the world, the polarized filters could actually be called "temporal (quantum?) dithering filters", as what they do essentially is acting as on-off switches with a probability.

However, since the transfer speed of discrete quanta is so high, we perceive that probability as continuous intensity modulation and this is the very basis principle behind dithering.

[ComposingGloves]

How do you do such amazing graphics? The fields blew my mind!

[KyleKabasares_PhD]

I'm about to take quantum mechanics at the graduate level and this video cleared up so many questions I had as an undergrad in physics. Great job Henry and 3B1B!

[franzluggin]

-> Super-informative, serious maths and natural science content.
-> "Clicky stuffs"

Gets me every time.

[chrisbkirov]

18:33 The smoothest transition from Classical to Quantum Mechanics I've seen in a while: "Square of amplitude of a component shows percentage of total energy vs probability of measuring the total energy."

[lakshaymd]

And again I'm left speechless. Awesome video, hoping to see this become more of a series because this is by far the best introduction to quantum mechanics video I've seen until now

[cubicmetre]

I have come to the realization that I am actually learning things at university. Just began to understand complex numbers when I saw how they could form an equation to describe photon waves in this video. I am understanding!

So grateful we have access to resources such as this video online.

[ContinualImprovement]

Quantum mechanics Lite vs Quantum mechanics Pro 😁