Lecture 1 | The Theoretical Minimum

(January 9, 2012) Leonard Susskind provides an introduction to quantum mechanics.

Stanford University:

Stanford Continuing Studies:

Stanford University Channel on YouTube:

[supytalp-unroc]

I have no diplomas, --> bad student and lack of maturity when I was a teen. Yet I found a thirst for knowledge in my 20s, decided to start from scratch all the science and math. Two years ago I finally reached the confidence to start learning about quantum physics. I bought the book, did the math on paper It's been my only book for two years I never skipped a page until I was fully able to play and understand the mechanics involved. I watched the lectures many Times. And I come here just to say thank you.

Unfortunately I'll never work in physics, I am too old and still without a diploma, I have managed to make a great career in IA and machine learning. To each his own path eh?

Living in this era of knowledge, where you can learn from home, find communities to help you improve, is the greatest gift we have. Stanford and Leonard Susskind I thank you again for making this class available and henceforth contributing to what is the best about the world we live in. I felt, even though this video is old, that a heartfelt comment here was needed.

Thank you again. (a friendly Swiss fellow)

[Domk]

I have no clue what any of this means but for some reason I’m fascinated by hearing him talk so I’ve nearly finished the whole thing

[smajidy]

Lecture 1
0:00:00 to 0:11:35 - Transition from classical to quantum mechanics
0:11:35 to 0:20:00 - The state of a system in classical mechanics
0:20:00 to 1:01:21 - The results of measurements on a qubit
1:01:22 to 1:15:10 - Vector space
1:15:11 to 1:24:12 - Dual of the vector space
1:24:13 to 1:46:31 - Inner products

[NoActuallyGo-KCUF-Yourself]

I love that Lenny is so old-school that no matter how white the white board is, he still calls it a "blackboard."

[RalphDratman]

I'm surprised and pleased that this is online. I bought the Kindle book a few months ago, without knowing there is a set of free online lectures by the author. Thank you to Stanford and Leonard Susskind for making these lectures available.

[TEKim-lkop]

I'm so happy this is online. He is a great teacher - simplifying as much as possible. Visuals help immensely.

[DenisDmitriev]

Special thanks goes to camera operator, who predicts all the movements not even causing a real headache.

[amritkumarpatel]

Sir Leonard suskind wait for me for some years. I will definitely meet you in Stanford. I am currently at 7th. :)

[MichaelHarrisIreland]

Tks Stanford, what a privilege to listen to this. And Susskind is an amazing teacher. I'm blown away by getting a glimpse into the theoretical minimum which I knew little or nothing about.

[ashkansnake]

NOTES:
Systems have states
A set of states can include subsets
Inclusive (union) and exclusive (intersection) propositions can be made
The space of the states of a system in QM doesn't follow the set logic
It's a vector space
An apparatus detects the status of Q-bit that like a coin (with H and T) could be in two states, 1 for pointing up or -1 for down, only one of them at any given time
Both the apparatus and the Q-bit have a sense of direction of their own
The directions of the apparatus and Q-bit in relation to one another, determines and changes the probability of the results
Observing the system once prepares the result and will give you the same answer until the detector has been turned off and on again,
If the internal vector of the apparatus lies in the same axis as the Q-bits we get the same answer over and over again, which is its component, meaning if we rotate the apparatus 180 deg, we get -1 in which the negative sign indicates the opposite direction
Also even when we start with the apparatus on it's side (internal vector and Q-bit are in different axes) results are the same as long as the system is not disturbed.
However 90 deg rotation of the apparatus around any axis makes the results random with probability of 50% for each, averaging at 0
Results of an angled apparatus are also random but they average in the component of the initial axis along the rotated internal vector (Cos of the angle apparatus makes with its initial axis)

Mathematical vector space contains objects that aren't ordinary
Vector space is a collection of mathematical objects
In the vector space numbers are one dimensional and complex numbers are two dimensional
Vector a is written as: |a>
You can add vectors: |a>+|b>=|c>
Vectors could be multiplied with complex numbers in the complex vector space: z|a> = |a'>
Vector's components are represented in the form of columns in brackets
Addition: n'th row of one column adds to the n'th of the other
Multiplication: the number is multiplied with all of the rows in the column
Complex conjugate vector <a| is a duel version of |a> that has a one to one correspondence with its elements
Complex conjugate vectors lies in complex conjugate vector space
Duel of a vector sum is the sum of their individual duels
Duel of a vector |a> multiplied with a complex number z is <a|z* where z* is the complex conjugate of z
Duel vectors are written as a row in brackets (horizontally) and the elements are complex conjugates (singed with *) of their original
Inner product of two vectors is like dot product: <b| . |a>= <b|a> (=/ <a|b>)
However: <a|b>=<b|a>* (1)
Same rule as dot product, resulting in a number: Sum of multiplications of N'th element of the row vector (in this case <b|) with the N'th element of the column vector (in this case |a>)
<b| . |a> = <b|a> = α1. β1* + α2. β2*
<a| . |b> = <a|b> = α1*. β1 + α2*. β2
Using postulate (1) must be true that: <a|a> = <a|a>* which means it's always real (its imaginary component is zero so the conjugate doesn't change it) and always positive (the real part is being multiplied by itself), resulting in the square of the vector's length (using Pythagorean theorem) T
<a|a> = <a|a>* = α1.α1* + α2. α2*
The orthogonality causes the inner product to be zero (because: cos 90 deg=0)
Maximum number of mutually perpendicular non-zero vectors in a space determines the dimension of it

[matusfrisik]

What cookies does he use to eat? I want them.

[francescos]

Thanks so much prof. Susskind as a student and undegraduate in architecture I appreciate . Thanks.

[sconeofark]

I can visualize five dimensional space time.., but don't you Dare ask me what I was doing when I saw it.

[arthurmee]

I agree ErnestYAlumni. I also enjoyProf. Susskind's  dry humour like the bit where he says in answer to a question at about 54:50 "They might have got the Qbits from a Qbit store!" . . . humour helps the process of learning. ;-)

[helencardrick]

I was so spooked when the guy asked a question at 30:00

[ErnestYAlumni]

I really enjoy Susskind's lecture because even as a practitioner and expert, I like how he gets to the heart of the physical idea and it is wonderful that he is taking the time and effort to educate in this venue for continuing education.

[MrAlfred]

You know shit's getting serious when Paul Dirac comes back from beyond the grave to set things straight.

[DavidTJames-yqdr]

@5:14 what an awesome sermon. I am loving these lectures. I am pissed that, in my far reaches of the world, this exposure and influence has been denied me via my class, cast, socio-econ, and generational & physical demographic. More knowledge. more brains. I am hungry to intuitively know more. I love Educaton X Generation :D Thank you Stanford and Prof+Team

[capitanmission]

Thnks Stanford and Mr Susskind, his teaching is gold, i guess he learned a lot from mr Feynmann :P

[rahulban]

I don't know, he looks *sus kinda* 😅