Lecture 2 | Quantum Entanglements, Part 1 (Stanford)

[@garydranch2014]

So greatful to Stanford U & Leonard Susskind for making available to the general public these lectures on multiple subjects of quantum mechanics and relativity theories, the nature of the very large and very small components of our universe. Now well into my seventh decade I come for the first time as a supplicant to the discipline of the study of physics. It is most gratifying to me that I am able to partake in the privilege of self-learning, inner-reflection and mental discipline that many others who hungered for such access to a community of knowledge have previously been denied. It is for this reason that I offer my utmost thanks and gratitude to the series producers, to Stanford University and to Professor Susskind for these priceless gifts that I am the beneficiary of. Bene facia!

[@MrFerdinandOo]

32:02 Bra-ket notation 33:44 - 38:05 complex numbers 43:30 complex conjugate (44:20 bra) 47:47 braket rule 49:16 50:43 quantum bit 1:14:25 observables

[@petergreen5337]

❤thank you

[@elifonkonsolakis2521]

I cannot explain with written words how much I enjoy these lectures, Ty prof Leonardo, (with Italian pronunciation ;-)

[@bear630]

Thank you for this. I cannot express to you how much I am enjoying this series of lectures. That they are available here is wonderful for someone like me.

[@xi7837]

this lecture series is probably a distant memory of yours but im the same I really like because as a child I can get the information for free

[@NazriB]

Lies again? Quaker Oats

[@cyb3rgh0stv7]

Eedsffz

[@xi7837]

@@Temmie_Dola Yes

[@lugia8888]

@@xi7837 he has such stupid complex variable notation lol

[@cicafittipaldi]

This professor is the brain rewiring master i have never in my life learned so much in so little time.

[@mauriciobarda]

Thanks a lot Standford and professor Susskind for these courses on modern physics. I'm really enjoying them a lot

[@aadeagle]

same here friend, Iam in field of biology and business but also interested in physics, very exciting. it was unfortunate that when i was in high school no one inspire me, but since then i'm fascinated with nature but confuse in physics. susskind is one of my hero along with feynman

[@jessestrehlow1979]

Thank you Stanford and Leonard for sharing such amazing knowlege.

[@mihastampek2018]

Oooooóóoooooooooooooooooooooooooooooooooooooóóóooóo

[@mihastampek2018]

Oooooóóoooooooooooooooooooooooooooooooooooooóóóooóo ooooóo

[@itis4peace]

Great pleasure! Excellent teacher. If any of you guys at Stanford are not taking advantage of Leonardo's lectures, you're against physics in time reverse, and going through physics dynamics in inertia stage. Greetings, Professor Susskind.

[@LukeTaylor101]

Seriously, i have no idea, how i landed no this video lecture. I was asleep when half way I heard the professor and woke up and realised i was studying Quantum Entanglements in my sleep. And..... this is Lecture 2. So you can imagine

[@hififlipper]

You woke up too early.

[@ZoeTheCat]

The Bra-Ket notation makes QM appear foreboding -- especially as you transition to Schrodinger eqtn examples. Susskind does a better job than most texts to demystify this notation. The same is true for Tensor notation within GR. I'm convinced that some Profs/Books just want to appear complicated rather than explain things in simple terms. Susskind follows Feynmans good example: "If you cannot explain things simply - you probably don't understand it very well."

[@sdsa007]

I've been learning quantum subjects piece-meal from various incomplete sources...... but now I am beginning to understand how the abstract math is fitting together in terms of a physical observation!... I am so happy for this!

[@parthoroychoudhury860]

I don't generally comment in lecture videos, but this explanation is just so cool! The way he explains this complicated subject, this is the best explanation quantum mechanics video I have found so far.

[@glennmain]

Thank you for the great vids Stanford and Leonard Susskind!

[@belkyhernandez8281]

Watching this in 2022. We have been in an anti intellectual period for the last 7 yrs, maybe more. So making this and other subjects available to everyone is more important than ever.

[@ddorman365]

I completely agree with you Lenny on what is necessary in thinking o understand Quantum Theory and your description of the juxtaposition of states is right on the mark, great job on describing 1/2 mono dimension, please hurry on to entanglement, peace and love, Doug.

[@deathtotruthers1]

Agreed. This is the single best explanation of quantum mechanics (for idiots like me) I've ever found. And I've been looking for a long time. When I retire, I plan to go back to school and get a BS in physics. But until then, this will do.

[@axelkolm3894]

These lectures are really helpful. Thanks for uploading them

[@jcbmack]

These lectures accomplish in a gentle way teaching the fundamentals.

[@AntKneeLeafEllipse]

This is wild: a little more than half way, you say "Let's take a break," and it happened just after I took off my glasses to rub my eyes. As if you were talking directly to me. What's the probability of that?? This is pretty incredible, and I'm very grateful for this resource.

[@jannisalexakis6436]

He is perfect in communicating knowledge!

[@cochisewolf]

Professor Susskind is excellent. I would have to agree with another comment, one sure way to improve the presentation would be to not allow questions to be asked until it was over. I had an instructor once who told everyone to hold off any questions till the end of the lecture at which time he would devote time to them.

[@aadeagle]

i'd heard the feynman lectures, its easily understood in layman's term, but i think prof. susskind explanation is much better, he's not talking like we physicist... but makes you feel like he is one of you, emphatically and patiently explaining physics concisely. a true modern day LEONARDO... I WISH HE COULD PLAY BONGO

[@ThinkTank255]

Hey, don't blame him for your own mental shortcomings. It is a very clear presentation. This is EXTREMELY basic stuff. It's intended for people that have at least a BASIC understanding of quantum mechanics and a BASIC understanding of mathematics. He has another video series on quantum mechanics. You should probably watch that first.

[@pharmahuascasoul]

ThinkTank255 you so smart

[@avitalmorgenstern]

NOW I GET IT! Thank you prof. Leonardo

[@SomeGuy-nr9id]

5:30 the mathematical term is a normalized vector or a unit length vector. Were all the components multiplied by themselves then added together sum to 1 which is valid across any number of dimensions. This part i know from doing so much graphical programming you work with tons of matrices and sometimes have to dive pretty deep into understanding them. Pretty much all the properties of the ideas have been named so they can be identified to explain or talk about harder concepts for manipulations. Cause you know video games.

[@majiddehghani4974]

Mr suskid is very patient in his teaching method

[@physicsjagat]

You are great teacher,all the series are excellent

[@am101171]

Vectors is just a way to represent things with several values. If you walk to your kitchen you do so at a certain speed but also with a certain direction, say an step a second with direction from the living room to the kitchen, that is a vector basically. If you multiply your vector by 2 (the scalar 2) you end up with 2 steps per second from the living room to the kitchen.addition: If your mom walks at same speed from the kitchen to the living room then bumps into you no one is going anywhere.

[@Holobrine]

I love how a complex number times its conjugate gets you a form identical to the Pythagorean theorem.

[@jessestrehlow1979]

Complex numbers are just vectors that can be written in polar form using sin and cos. For example. 3+4i has a magnitude of 3^2+4^2)^(.5)=5 and the direction is 5cos(¥)+5sin(¥)= arctan(img/real)=arctan (y/x)=tan-1[4÷3]=36.8°

[@AlecBrady]

Because you square the vector (i.e. form the inner product of the vector with itself) to get the probabilities. So total prob=1/rt(2)*1/rt(2)+1/rt(2)*1/rt(2) =1/2+1/2 =1

[@TheOvermaster]

@HyperBorealOperator Correct me if I'm wrong - but I believe it was a statistical mechanics course - so there is no loss of continuity by skipping (in this case, we can't watch it) part 2.

[@eschuber8]

this video looks like the pixels are following the uncertainty principle, wow, the quality is not so hot

[@dragonjake6968]

really now the pixel of a video doesn't guarantee quality learning its what you can take from it and besides if you listen to the video its all well done

[@ximecreature]

Susskind doesn't use the board so much. So long I can still have access to content of this quality, I'm not going to complain about the pixel density

[@NoActuallyGo-KCUF-Yourself]

But it looks like the vectors are moving, man!

[@ApteraEV2024]

L😆L!!! 👍

[@dweeper1020]

Don't think of the electron pointing up or down (this is just a convenience he uses), think of it as the spin state - spinning around it's axis (either spinning in one direction or the other). All elementary particles have a spin quantum number. These spins create a magnetic dipole moment that "point" in a certain direction depending upon the direction of spin. You can find more details on spin state in wikipedia.

[@F00dTube]

At around 1:27 on guy in the audience makes the remark that P(+) - P(-) isn't the expectancy value and that when both Probabilities are equal the total probability is 0. The formula should be 1P(+) + -1P(-).In this case it works because the absolute value of each possibility is 1.

[@philipolson4842]

The first lecture mentioned reviewing calculus would be a plus. This took an extra week.

[@MEpianist]

Big THANKS to KZbin, Stanford & Prof. Suskind! Although I disagree with your decision to edit out the questions...

[@am101171]

The vector space is your house in this example. Hope it helps.

[@fpgaguy]

thank you so much for providing this

[@cochisewolf]

I've had a few classes where there were people, usually one or two, that asked so many questions that we couldn't get through the subject. So those of us who actually studied and met the prereqs suffered. I agree there should be a Q&A period after class for those not resourceful enough to find the answers on their own.

[@Ymirheim]

@Lodine66 Actually I found most of the questions intelligent and insightful which is what you get when the students are not undergraduates.

[@MrWorshipMe]

I would change it to 60% :) - and only if we talk about experimental physics PhDs - most theoretical physicists are one notch above the rest. And after going through all of Feynman's and Susskind's lectures - I would recommend trying to tackle Penrose's "The complete guide to the laws of the universe", which takes you even more into the depths of theory and math of QM and GR.

[@An_Idiot_in_the_Wild]

Penrose's books are absolutely brilliant.

[@leighbarton7064]

It was a quick comment, not a Doctoral Thesis. The Professor wanted a term to describe angular direction, other than vector. Azimuth, elevation, declination, XY, and Z axis are all map reading and navigational terms that apply.

[@BrianJoeSandy]

The state is really in projective space, not vector space. A and -A are different in vector space but the same in projective space. So A-B and B-A are the same state likewise A+B and -A-B. Actually we should be in complex space (vector and projective) so multiplication by e^(i pi x) doesn't alter the state either.

[@Pidxr]

It's too bad these videos are either so highly compressed or just filmed at low resolution as to be distracting.

[@jojolafrite90]

Yeah, sure it's not the point. But at this point it's actually too bad and disappointing.

[@dweeper1020]

QUESTION: If we prepare the electron to be horizontal and put it in a vertical magentic field, there is a 50% probability that it will emit an electron. If it does, we know it is now aligned with the magentic field. If it does NOT, what alignment is the electron in (or can we ever know). Please only respond if you KNOW if the answer, not if you think you know it. I'd like to know.

[@NoActuallyGo-KCUF-Yourself]

If it's like most science classes I've taken, it doesn't start to get hard until over half-way through the course.

[@scotty369]

#giza, Thoth was doing this very easy I suspect right down to the cubit! Quantum, electrons, photons, quarks all from light, water, hydrogen, and dc power.

[@wladwlad]

a huge THANK YOU to stanford for making these available, i am fascinated both by the bold step and by the content. finally spending hours on youtube will be actually worth it :) btw. shmector really rules :)

[@boomfist]

I love how at 1:13:10 the wrinkles on his wonderful forehead actually crank the encryption algorithm into rendering interference.

[@skillabr1832]

It's video compression. Because there is complex movement, the delta in the picture does not get adequately captured when passed through the compression algorithm. Thus, you get a blurry image.

[@bean8287]

Around 20:00 in, when talking about the state of the electron as either spin up or down, how do you actually know that the electron is spin up or down per se. If you are determining this by whether a photon is radiated or not, and they are all radiated with the same energy, then how do you know that the electron has actually completely re-aligned itself with the magnetic field, and not simply made a partial alignment, corresponding with the amount of emitted energy. It seems like the only way to know for sure is to wait and see whether more radiation is emitted, implying the electron made another incremental rotation. But such an experiment would be tricky, because just because you don't detect radiation yet, could mean there might be some in the future. Perhaps my answer lies ahead in this video/series, I'll have to see, hopefully in the meantime someone could fill in the gap for me. Edit: Ahh looks like I only needed to wait another minute, as he explains that you would not detect further photons after the first one, I will have to do some research after watching this to see the specifics of the experiment!

[@musicalfringe]

This is to the best of my understanding - someone please correct me if I blunder. The electron never partially re-aligns. It either remains in its original (indeterminate) state or emits and aligns completely. Particle spin axis seems to be an example of something that's fundamentally discrete in a very counterintuitive way in QM. Partial measurements or even ambiguous post-measurement states don't seem to be allowed. If my thinking is right, indeterminacy of spin only appears when you (a) change the measurement axis relative to the particle's last-measured spin axis, (b) allow enough time between measurements for the particle's interaction with the environment to push its state away from the last-measured state. Ignoring case (b), the indeterminacy only ever appears in the form of the next measurement being probabilistic to the degree that its axis is perpendicular to the previous measurement axis. After that, though, the spin axis is once again completely known.

[@drumstruck751]

can you get the stars to make sense within a year of orbit acceleration with two long hot seasons and two short cold seasons. That way we can make sense why winter is shorter than summer. meaning summer is the long part of the oval when were closest to the sun, winter is in the quickly changing portion of the oval.

[@apollion888]

I fucking love this guy, Susskind rocks!

[@ukvaishnav]

@av733 not really but if you have done little idea of linear algebra and ket-bra notation (which is just the vector space in different suit) then go ahead you'll hardly have problem. If you don't then first finish the Quantum Mechanics lectures.

[@shakagenghis]

conceptually this is very helpful. up/down could be yellow/purple- some states x and y that are connected observationally to a certain behavior. Very helpful. I really should have watched the whole lecture before I asked the question, but nevertheless I appreciate the help.

[@ldl1949]

also I have questions for him: 1. if the electron is pointing up (to the south)? and then you reverse the magnets the electron will release a photon... and also by what I understood from him if you keep reversing the magnets you will always get a photon because it definitely moves. and in the states between there is a variating probability then maybe we can not measure the amount of energy in the so called ""single photon released""?

[@gricka31]

well questions are always helpful, often for multiple people, but they should be asked at the end of the lecture, because they are often resolved later on in the lecture

[@StephanLuik1]

A very nice explanation. However, I wonder if it could have been done in a quarter of the time if students actually knew complex numbers and matrix multiplication rules?

[@FlashJockey1]

so if you prepare an electron for say, an angle of 90°, you measure it's spin... one half of the time you get the same amount of energy that radiates if it was prepared for 180°, where does that radiated energy come from?

[@F00dTube]

Correct in this case it works. But what if we had a die(1-6). Than the outcome would be very different: 1P(1) + 2P(2) + 3P(3) etc. So only in this case, with only two possibilities and with 1 and -1 having the same absolute values, subtracting the probability will work. So the confusion for the student is understandable.

[@phycogsmithomniscience309]

it makes sense to me , the electron radiates the same energy no mater what to make a adjustment or it is not required to make that adjustment.

[@bindon8581]

In order to account for the arbitary mass of the electron to the proton, I postulate the electron is created by the proton. [ it's needed to balance or neutralise the charge, monopoles not having been found in nature ]. There are free electrons, of course; they've been been knocked free from their creator, the proton. That's how we can get electricity. The valence bonds are weaker on the outer quantum bands, as we see in metals. [ the neutron's mass is slightly more than the combined mass of a proton, an electron and a neutrino. As a result, free neutrons (neutrons that are not tied up in the nucleus of an atom) spontaneously decay with a half life of about 10 minutes. If the neutron were very slightly less massive, then it could not decay without energy input. If its mass were lower by 1%, then isolated protons would decay instead of neutrons, and very few atoms heavier than lithium could form. That's an indication of why the electron mass ratio to the proton is approximately 1836.15. I hate to say, like Fred Hoyle, that this is "a done deal" or pre-programmed, but I will. Anyone who wants to fall back on multiverses I'm calling a "romancer".

[@inox1ck]

The electron vector can still be explained classically. if you imagine the vector being elastic not rigid, it bends up to a point, then if you force it further it yields the energy then it straighten itself up. Another way is unless the electron is ready to emit the energy it continues the precession indefinitely. This is still quantum but it is imanginable

[@inox1ck]

Actually the first statement doesn't explain what happens.

[@Jodoi1]

@pete2331 From Prof. Susskind's intro in this video, this appears to be the second part - I think it has been labelled incorrectly.

[@WPMcNeill]

If you find the idea of a single electron being held in place by a nail distractingly artificial, try reading about the Stern-Gerlach experiment, which is the actual way spin was first observed.

[@brad1368]

I've been watching a lot of Prof. Susskind's videos and he almost always has a coffee and some little bag of treats...does anyone know what he is eating? It appears to be the same thing each time and it looks pretty good.

[@captainhampton]

How did the people in this class....get in this class? I love Susskind, and I know he's fully capable of teaching at a faster pace. Wish his class would allow that.

[@SamTheSciencerAtheist]

You can do that with a Quantum Dot, and there has been many experiments that studied Quantum tunneling of a single electron in Quantum Dots. In Quantum Dots, you basically make a two dimensional gas of electrons (electrons confined in two dimensions, like x and y, and then you control them with static electric fields and you can do very nice things with that system. Just google "Quantum Dots", and learn more about the miracles of physics ;)

[@PetraCarExpo]

Amazing series!

[@mnfchen]

This lecture series is a bit slow, but gotta be patient. I went through Linear Algebra in college, and these people obviously haven't =/ Great lecture btw!!

[@MrWorshipMe]

Feynman is the only other person I know who explained it as clearly - but he did it in a more interesting and fun manner... Still Susskind is very good :)

[@naimulhaq9626]

Every electron is a magnet with a magnetic moment. While watching Cosmology Lectures, by Leonardo, I can remember him explaining how a lots of magnetic monopoles that vanished with inflation, and consequently became difficult to find or detect. Is it possible that the magnetic moment of electrons are the result of some amalgamation of electrical and magnetic fields,due to the lost Leonardo's monopoles?

[@NathanOkun]

The "average:" value should be called the "balance" value, like the center of gravity of the results. Not a possible actual measurable value is implied.

[@TehAl3X]

@1HumanKind To answer your question: everyone is entitled to a chance to learn.

[@Svenskivsk]

I think what he is saying is that there are only two states an electron can have (in this situation), and if the electron is prepared at a different angle it changes the probability that the electron will emit a photon of definite energy, correct?

[@kadigan1979]

@fragmentsoferik It was just a very simple example of assigning a value to each result of a test. Assigning +1 and -1 to each state is arbitrary. It's not of much interest in the case of a coin, other than to say that the average expected value is 0 - you see the same number of occurrences of each result, which sums to 0. A more interesting example might be if you bet on the coin and receive $5 for a head (P+) = 5 and lose $10 for a tail (P-) = -10, in which case your average value is -$5.

[@hossboll]

1. duas direções possiveis p/ apontamento do vetor do e: cima ou baixo. no in between: quantum bit. 2. dependendo da config. fisica - disposição do campo/do e - , ha maior ou menor probabilidade de emissão do foton na transicao. quanto mais o e estiver alinhado com o campo (n->s), menor a prob de emissão do foton. (problema: qual o "referencial" do e? campo grav. terra? para haver dif. probs faz-se necessario haver diferentes percepcoes do espaço (?).)

[@beingnonbeing]

If you mean while the camera pans, YES. I find it maddening.

[@kamrannasir3871]

Now, someone else asked the same question in lecture 8, where we are discussing pure and mixed states, this is something which is easily misunderstood by some.

[@qigong1001]

I question the intelligence of those against questioning.

[@kamrannasir3871]

he says that the average value of the die is sum of the probabilities, times the sum of each observable, but why do we have to write the sum of probabilities when it is just equal to 1 ! i am referring to the formula at 1:22:00

[@ComradeSpookfessor]

When lectures talk about crazy things I normally just Google them. Although I understood it perfectly, you mustn't have.

[@pranav.dilsephysics]

It's amazing ✨

[@LaureanoLuna]

1:20:12 Not the expected value, not the average but the expected value of the average, i.e. the expected average.

[@SalimMaroun-fb5rd]

Thank you you are the man

[@Holobrine]

17:20 What if you measured how long the electron takes to release a photon? Maybe it has to build up the energy first somehow.

[@DoaaElshahat--]

Yes, it has to absorb some energy from the EM field.

[@ernestorodriguez6445]

When you measure the direction of the electron, how long do you have to wait till it emits a photon? Is it always the same time? Are we sure that if we leave the electron exposed to the field it will never emit the photon if it didn't after some time?

[@hamzaabrar2724]

Hi, I have an MPhil degree in Physics. I have taken six courses of Prof. Susskind which are "Classical Mechanics," "Quantum Entanglements Part 1," "Special Theory of Relativity," "General Theory of Relativity," "Cosmology," and "Statistical Mechanics". I have also taken handwritten notes of him in all the details and currently I'm typing his notes on Latex. Kindly let me know in the comments which lectures of him do you want the notes of and I will make them for you on Latex. Cheers!!

[@mastercard02]

Thanks @hamzzbrar2724, I'm following the Quantum Entanglements Part 1. It would be so kind of you to share your Latex links on these course!

[@Achrononmaster]

@43:00 Oops! Lenny is wrong here. Hilbert spaces are not "absolutely essential" for quantum mechanics. If you want to do real-valued QM rather than use a complex vector space, then you have the option of doing QM in geometric (Clifford) algebra. In fact GA is a lot nicer. No matrices, and the operators are the same objects as the states, all are multivectors, and the unit imaginary has a lovely geometric interpretation, it is the spacetime pseudoscalar (a unit oriented 4-volume). Any time you want to you can use a GA -> Hilb dictionary isomorphism to translate from geometric algebra back to matrix algebra. See the work of Hestenes, Lasenby, Doran, et al.

[@simoncrase5360]

While I admire Hestenes' Reforming the Mathematical Language of Physics geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf, LS is correct if you want to communicate with people about QM. GA may well be clearer, but the overwhelming majority of physicists are used to Hilbert spaces. It may well be the case that QM would have been easier to understand if Dirac and Heisenberg knew GA, but we've gone down this path for a century, and I think it's too late to change.

[@schmetterling4477]

Misner, Thorne, Wheeler introduced a geometric interpretation of tensors in their book "Graviation" in the 1970s, but if you want to calculate something, you still have to pick a coordinate system and fall back to tensors with components. You can find tons of general geometric theorems about Hamiltonian flow in books about the topic written by mathematical physicists, but if you want to calculate a spacecraft trajectory through the Saturn system, then you still have to run numerical integration on a powerful computer. New concepts are only great if they reveal something new and useful at the structural level. Not sure that applies here. What am I learning about physics here that I didn't get before?

[@quahntasy]

*Who else is here in 2020*

[@JohnSmith-vm8rx]

2021

[@steebh7870]

2022 bb

[@ЕвгенийВовж]

GDI

[@ЕвгенийВовж]

@@steebh7870 dsssc

[@ЕвгенийВовж]

4r

[@stewartcalder8941]

So what happens to the conservation of energy in the milliseconds between the field being switched on and the elctron flipping to its stable UP state? (I still have an hour left to watch)

[@roxiefaye144]

I'm curious what you doing now

[@apostolismoschopoulos1876]

@@roxiefaye144 I thought of the same thing lol. There are times as these when I encounter comments from 9 years old that I'm wondering what do these people do today?

[@YAHYEL-ANUNNAKI]

Teleportation Study Experiment. (working model) Take a very very thin, perfectly round hollow metal (copper, steel, etc) ball and put it on a flat glass table at least 5'x5' in once location of the table surface and call that (location A) then strike the ball with an object or with sound and measure its frequency vibration with sound or other devices, then put the ball in another place of the glass table and call that (location B) and measure the vibrational frequency of that ball in that location, then put the ball back in location A and infuse, bombard the ball with the location B frequency vibration, either sonically or electromagnetically, etc... The ball will either disappear and reappear on location B or it will move from location A to B physically and this depends on how precise the instruments used are measuring and infusing the new frequencies. Please save and share this experiment with as many people as possible. This experiment is how we will learn to map the vibrational frequencies equations of any location in our universe. (This is not a joke)

[@Eay5paev]

At 1h02'55'' he says "we'll come to that", talking about -A being the same physical state as A but A+B not being the same state as B-A. Where does he explain this? This issue has always puzzled me!

[@ddorman365]

Thank you Lenny, I think when we describe electron P- function bond to a atom configuration we might consider the electron to bond with one of, depending on how many partials are bonded together forming an atom will determine how many gluon radiation fields are expressed, the gluon radiation fields expressed by the nucleolus and the energy level of the electron will match with precession the corresponding energy level of the gluon radiation field it is bonded to, and if the energy level changes to either of these components there will be a corresponding change to the P- function configuration and it is the precession of the gluons in ASP Rp expression that there is found the radiation field with sufficient precession necessary to account for the precession of orbit of the electron, I think that the quarks have more freedom of movement and thus there radiation field accounts for the outer radiation field of the atom, the field that interacts with the Higgs field giving the atom its "hardness", ( I think, but I am not sure I have to think about , this was just a thought I had listing to your Lecture:), Catywompus, is that a word, Lenny? I think that the P- function of the electron( or wave function) is a 4th dimensional function and this proses occurs at the velocity of radiation so that to us it would appear to occur instantaneously. Lenny, is 13* the complex conaget of 11 dimensional space, our Y- cordante plus the 2 producing States?, peace and love, Doug.

[@jcovello]

Anyone know if: A: Putting the electron in magnetic field and watching for photon is hypothetical or really how the experiment if performed. B: If actual experiment we know there is a probability of photon being emitted but can we tell if electron gets reoriented in all situations or only when photon is emitted.

[@kevinldonnelly]

Information theory would forbid differing experiments giving infinitely varying energy photons

[@pengfeiDu83]

@ericpaterson If I understand the lecture, what you are talking about it what you imagine in a classical way, but that's wrong, in reality or quantum world, you have only two states, photon released or not, which means two states only: either 0(no energy released) or 1(released).

[@phewpow]

Is it possible that there are 1000 or x amount different kind of electrons, and that it's not probility, but that you just can't say which kind of electron you are handling at the moment?

[@musicalfringe]

That's known as a hidden-variable theory, and John Bell established mathematically that, although hidden variables aren't disallowed, explaining quantum behaviour through them changes the other assumptions allowed in your theory, e.g. locality.

[@eugenbarbula9661]

I would like to see a course, in which the ideas, concepts and tools of Quantum Mechanics are explained on the distribution of prime numbers, seems like the concepts would make a lot of sense, by mapping it to the prime numbers. A bit sequence would be a sequence of prime numbers in some choosen base and for some choosen multiple of that base, the concept of vector spaces can easily be shown, even the concept oh Hilbert Vector Space, with it's infinite dimension, finally makes some sense for if imagining it on the prime numbers, a matrix can be constructed by using n bitsequences of prime numbers for some choosen base and just adding them up to down into a form of matrix of some choosen size n*k, all kinds of symmetry properties should be possible to explain by finding examples of them at some positions on prime seqences, I think I would be able to understand Quantum Mechanics so much better, by getting it explained this way. I think the same is true for Machine Learning as well, where a lot of algorithms and different criteriums of optimality can be explained on prime numbers, where all kind of problems can be formulated with all kind of different metrics and sives which algorithms can learn on to improve themselfes.

[@leighbarton7064]

Vector entanglement can only occur as the result of the interaction of transluminal wavicles with a parallel polarization to the orbital Z axis relative to the direction of travel?