My problem with Quantum Mechanics is always the internal visualization element. I have to be able to visualize in my head what Im working with. How do you visualize 'wave' functions? If the math doesnt mean more than the numbers I have a hard time with it. I have to see what its supposed to look like at the beginning and then work from there. I dont understand how you can do that with most of this stuff.
And instinctively you are able to accurately express the oxymoronic truth that encapsulates the entire process of creation. Being that as we create our Present Now and Past and Future , we totally annihilate the now and replace it with the new now singularity... for example I just did that in a practical action as I had to cut a comment completely and replace it with an updated copy of the same comment... that is what life is. The past now is wiped out and replaced by the present now which came from the future now... constantly refreshing our old past reality with our new present reality which will be replaced by our future reality which was created by our present reality which is the only reality that can ever exist because the past does not exist anymore 0 The future does not exist yet 0 The Now always exists as the 1 Singularity that keeps changing form 1010101010 satisfying the law of the conservation of energy.
@@thetruthchannel349 > Someone said that as the photon flies along, it contains a little arrow that goes around and around. If the photon splits up and goes by more than one route to a detection site, the little arrow goes around and around along each route, and where they come together, those add up, and so they could cancel. So your detection site could see nothing; it might be in the middle of a dark band of the interference fringe.
Finally something at my level! I'm an engineer. The average "laymans" explaination is too layman. The average specialist explanation assumes you spend all your time doing physics - and have read all these books and papers. Thank you.
Exactly, I got indulged in this video because of the Math that is rarely shown on YT. On the other hand, articles assume you are well versed in the subject and you are willing to spend hours researching the technical jargon..lol
I think you would like the lessons of Leonard Susskind on the Stanford University Channel on TH-cam as well. He explained this. They do take time, though!
It's amazing how linear algebra underpins quantum mechanics, machine learning, digital signal processing, error correcting codes, computer graphics, and so much else. It's a great example of how learning the underlying math allows one to understand so many seemingly different fields of knowledge. Great video.
I just found amazing that tomorrow i have 2 exams in the same day, quantic mechanics and machine learning and you managed to mention both right in the start ahahah
I actually have a Master degree in Physics from ETH Zürich ( 25 years ago) , but had my Professor explained me the basis of QM like this I would have had much less problems and sleepless nights :-) ! ( now in the right videos comments)
Schrodinger's cat is just Hegel's cat in disguise:- Thesis is dual to anti-thesis -- the time independent Hegelian dialectic. Being is dual to non-being creates or synthesizes becoming -- Plato. Hegel's cat: Alive (thesis, being) is dual to not alive (anti-thesis, non being) -- Schrodinger's cat. Plato discovered Schrodinger's cat 2500 years ago, he was a smart dude. All vectors are dual, they are defined by two dual points, the origin and the arrow head. Vectors are dual to co-vectors (forms). Dirac notation is based upon inner or dot products. The inner product is dual to the cross product. Probability leads to projection, prediction or syntropy. Syntropy is dual to increasing entropy -- the 4th law of thermodynamics. "By imagination and reason we turn experience into foresight (prediction)" -- Spinoza. Syntropy is the convergence or integration of ideas to form predictions or expectation. Teleological physics (syntropy) is dual to non-teleological physics (entropy). "Always two there are" -- Yoda. Symmetry is dual to conservation -- the duality of Noether's theorem.
Sabine, to me you are the best Physicist on TH-cam! The no-nonsense style, concise and clear structure of the episodes and the intellectual rigour and honesty - you’re doing something that, as far as I know, is in very short supply here. Keep up the good work, we need people who have deep understanding and can also explain as clearly as you can! I love your channel. Also, I’m not German but I enjoy hearing the correct pronunciation of German names on the Internet.
This has very quickly become one of my favorite youtube channels ever. Concise explanations of scientific theories without climbing aboard the hype train or spending an hour explaining the double slit experiment for the millionth time. Thank you! On that note, I would love to get your thoughts on the delayed-choice quantum eraser experiment.
Excellent explanation! As a Science teacher myself, I love when someone can break down seemingly incomprehensible concepts into understandble smaller chunks.
It’s important to realize that the wave function is not |psi> but is psi(x)=. |psi> is the state vector, and is independent of x. It depends only on the various quantum numbers of the problem and perhaps on time.
this were 8 minutes which answered a lot of questions which i never dared to even try to find out, because I thought I would never even get a clue of what these brackets mean. Thank you so much!
ON THE ABSOLUTE PHYSICAL EQUIVALENCY AND BALANCING OF E=MC2 AND F=MA: It is a very great truth in physics that the ability of thought to DESCRIBE OR reconfigure sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (THOUGHTS ARE INVISIBLE.) INDEED, E=mc2 IS DIRECTLY and fundamentally derived from F=ma; AS time dilation proves that electromagnetism/ENERGY IS GRAVITY. Therefore, ultimately and truly, time is possible/potential AND actual IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In fact, INSTANTANEITY is FUNDAMENTAL to the FULL and proper understanding of physics/physical experience; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. GREAT !!! BALANCE AND completeness go hand in hand. It all CLEARLY makes perfect sense. (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Gravity IS ELECTROMAGNETISM/ENERGY. By Frank DiMeglio
Great introduction, Dr. Bee!. I cannot emphasize the importance of using the Dirac bra-ket notation too much, as it greatly simplifies the mathematics of QM. My favorite elementary text is Sakurai's Modern Quantum Mechanics, whose first three chapters provide everything one needs to know about the notation and its applications.
I was literally taking a break from reading Sakurai's first chapter and watched this video. Excellent explanation. I appreciate the part on the density matrix, I guess that's where things get really exciting.
The missing part is that for a complex number z, we have zz* = |z|^2 which is a real number, positive or null. It was somewhat implied but it was never written.
I am a final year Bsc physics student who was very worried about their understanding of QM, something just didn't click for me. You just summarized everything that needed clearing up for me within 8min, I feel like all the lectures I have witnessed finally made complete sense. I am shocked and honestly a little in love. I never write comments on yt videos but WOW and THANK YOU... THANK YOU SO MUCH.
In this video I understood something which I never understood by watching 100rds of videos!!! Thankyou so much for this simple and powerful explaination! It would be amazing if you write a book on quantum mechanics,,,hope to see that soon....!!!
same for me with Science Asylum. The method of explanation is SO important. The more clearly someone understands a subject, the more clearly they can explain it. Even better if they use graphics.
@@yahiakandil4086 Lost in Math. It's pretty good. It's about Sabine's quest to understand why physicists are obsessed with the notion that physics must be beautiful, and her impressions of how that has backfired in modern physics. It's a refreshingly honest take on the shortcomings of modern academia.
@@1ucasvb "Beauty is in the eye of the beholder." Historically speaking, physics has gotten more "beautiful" over the centuries. Part of that is discovering new symmetries (which means we can merge two fields together) and part of it is simply notational improvements. The real reason physicists chase 'beauty' so much these days is that we don't really have anything else to look for. The LHC confirming the Higgs to be basically what we expected means we don't have any real leads for the next step to take. We know there _is_ a next step because of the fundamental incompatibility between QM and GR, but we're not going to be able to directly probe those energy levels likely in the next few hundred years, if ever. Short of a miracle new collider design or a complete fluke with some astronomical event, we're stuck with just poking around at the energy scales we have available and hoping to prod something out to give us a hint. In the meantime physicists want to stay employed, and our only real "hint" for what's next is following the history of unification. Maybe the planned LHC upgrades will prod out something new like those elusive SUSY particles we keep expecting, but really there's not much guarantee that anything exists between the Higgs and the energy levels where we expect GUT to occur, and even that is likely a good couple of collider generations (not just upgrades) away still. Which could be a century or more given how long it takes to design, fund and build such immense projects.
This is an amazing video. I am a biologist with a master's in physics: I always had trouble with mathematics but come to realize that it only takes a simple explanation from someone at the correct speed and structure of ideas. Everyone is different. I wished I had seen this video when I started my master's. Thank you, I can't believe how well you explain these concepts!
Nature uses QM frequently in biology, especially in chemical reactions, processing of light, and capturing energy from the Sun. Most non-biologists don't know this.
Whenever I come across a video claiming in its title that "Quantum Mechanics (or any other fancy, popular scientific term) were not so difficult" I find myself thinking about misleading titles and how they are supposed to generate traffic. The explanations in this video, just as in all the other videos on the matter, are neatly arranged versions of standard textbook contents. While I do appreciate the effort that goes into scripting and producing these videos I am always missing an advice of caution. The fact that the mathematical basics of Quantum Mechanics are comparatively simple does not imply anything really, least of all that Quantum Mechanics are not so difficult. The brief glimpses on "vector spaces", "dual spaces", "inner products", etc. provided in this video are merely first steps into a massive subrealm of mathematics. I agree that anyone who is interested in Quantum Mechanics has to work on their mathematical abilities although I highly recommend using these videos as a motivation to acknowledge, rather than to deny, the difficulties of theoretical physics and maths. The net information seldom surpasses party-trick quality standards and that is all well because being too complex to be legitimately summarised in any video (of finite length and information density) is in the nature of things!
Broseph you are incorrect about the value of this presentation. I have multiple degrees including physics (see a comment a cpl days after yours) and what is sorely lacking in many formal instances is SIMPLE CONTEXT. It annoyed me the abstract manner I was "taught" QM (I wasn't taught anything I was "read") You are correct about the whole other branch of mathematics and solid foundation needed before tackling any of this QM stuff. If you are doing an undergrad physics degree like 2/3rds of it will be maths for the first 2 years, then in years 3-4 you get the pleasure of using said maths. Fourier transforms, separating the variables, deriving and solving Schrodinger's equation, Maxwell's equations, of course general relativity and Lorentian transforms (pretty easy in comparison to the rest). Then after all that some twat will "read" to you and introduce entirely new notation and processes, talking to you about Laplace this, Dirac that, and asking, "is this Hermetian"? Bitch it would help if you told me what type of Hermit crabs first. Oh you weren't talking about crabs or lap-dancing clubs but some random maths you are reading to me for the very first time in my life. Reading me maths. No don't try and work out what's happening or what any of this stuff is, just copy and paste, the lecturer is paid to "read" not "teach"
@@Pax_Veritas I'm not entirely sure whether your comment is directed at me since I don't know who Broseph is. However, I'll just go ahead and pretend you were targeting my comment. In that case I feel like you misunderstood my critique - I do agree that simple explanations and teachings are both often missing at university and important for scientists in training. I just don't agree with the way in which many attempts at simlpe explanations seem to downplay stuff in the same breath. In my opinion presenting a smart, intuitive and simple ACCESS to a difficult subject loses its added value when it is sold to be the "real deal". Also, congratulations on your multiple degrees including physics! Good job! Finally, I'm not sure what happened to you in that last paragraph and it's hard to judge one's emotional state via a TH-cam comment section. Still I sense some measure of frustration - is that right? In that case: Hang in there, mate! Everything's gonna be okay! :-)
The way Sabine Hossenfelder presents information is comfortable to view. I perceive the nonverbal hand gestures as offering knowledge. Thank you for sharing
In this theory the mathematics of quantum mechanics represents geometry, the Planck Constant ħ=h/2π is linked to 2π circular geometry representing a two dimensional aspect of 4π spherical three-dimensional geometry. We have to square the wave function Ψ² representing the radius being squared r² because the process is relative to the two-dimensional spherical 4π surface. We then see 4π in Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π representing our probabilistic temporal three dimensions life. The charge of the electron e² and the speed of light c² are both squared for the same geometrical reason. We have this concept because the electromagnetic force forms a continuous exchange of energy forming what we experience as time. The spontaneous absorption and emission of light photon ∆E=hf energy is forming potential photon energy into the kinetic energy of electrons. Kinetic Eₖ=½mv² energy is the energy of what is actually happening. An uncertain probabilistic future is continuously coming into existence with the exchange of photon energy.
Thank you. This video really emphasized what I already knew; to go beyond the high level videos on quantum mechanics I have to commit to honing my math skills. Otherwise it's like trying to learn a topic without having a good grasp on the language it's being taught in. And math is essentially a language.
I've always wonderd how even janitors in star trek have a firm grasp on quantum physics. I do not wonder anymore, your vidieos are pointing us into a future where this is possible (Maybe not Star Trek, but the 'Janitor builds a particle accelerator for funsies at home future'). And for that i am grateful. Not just for me, but to see that knowledge is finaly spreading to those that want to know regardless of birth of wealth. Just... THANK YOU
Very nice video. I really really very much appreciate the lesson and also how & where to go to find more about it in Brilliant. I'm glad that you don't assume your audience is Physics PhDs only. You are Great lady and teacher.
Now that was a high density information transfer - not a word wasted, yet completely clear, at least if you already know about linear algebra and complex numbers. Thank you.
You maam, are brilliant. Unlike so many other 'orthodox' scientists you mostly qualify your statements. Other scientists lack humility, stating ' conventional models of phenomena' as undisputed fact. Thanks for all you do in this respect.
I could spend every second of my life with you Madam Sabine and never get bored... Thank you so much for the videos . I've learnt a lot, a bit too complex such that I have to watch the videos twice to get it. But worth it. 😁 and I appreciate the time you take to share your knowledge with us... Watching from Lusaka, Zambia.
I think one should make a distinction between the state and the wavefunction. The state is an abstract mathematical object whereas the wavefunction is a complex function of spacial coordinates. If you want to obtain the wavefunction from the state you project it onto your spacial basis.
You have a gift for communicating the seemingly complex in a straightforward and clear style. Absolutely wonderful discussion. Thank you for taking the time and making the effort to do these. Very much appreciated!!!
I love when things become more technical, thank you Sabine to make them so simple, but not dumb. Btw, did you know that Max Born was the grandfather of Olivia Newton John?
6:27-6:33 This is THE prerequisite for understanding this vedio. In summary, this Lecture is a excellent reminder of how the basis vectors are reprsntd and works, if one hasnt been through transforming position-space rep to momentum-space rep then it will be hard to understand. We choose particular basis for diagonalizing our particular choice of Hamiltonian,for example.
Well, the real mental challenge arises from entanglement and/or second quantization (quantum field theory QFT) later. As in a superposition of a (possibly infinite) number of quantum states. For example, how many (non-physicist) people do know and can grasp that a laser state has a definite (electromagnetic) phase, but is actually a superposition of an indefinite number of (photon) quanta? Thus, even such a simple thing as a laser pointer already exceeds ordinary human intuition and understanding by far. Yes, we can describe such physical states mathematically in terms of Hilbert vectors, but one can easily put a question mark on what do we people understand about the nature of reality from that.
Reminds me of the first line in the Tao: "The real Tao is not the Tao that can be spoken about nor understood" or in your words "If you think you can understand the Tao, then you do not understand the Tao"
yeah well that was valid back then in the beginning days of QM, today more and more is understood as is also explained in vids like this. 500 yrs ago electricity was also something that one could think to understand but dont understand it at all... same goes for all new discovered natures features. of Einsteins theories it was close to the same....and now every simple soul can understand it simply. So Feynmans statement wears off over time. Thing is one needs to start thinking in different ways then one was used to and then it becomes more easy over time.
@Bertrand de Born are you always so unpolite by calling people idiots before you even know them ????? well you know what they say......... it takes one ...... to know one
I often worry about the situation where professional scientists go out of their way to explain what seem like complex concepts and do their best to clear up common misconceptions and some comments suggest science is wrong seem to me to come from these misconceptions and even worse it feels as if the time hasn't been taken to understand what had been said. I have taken a lot of time to deepen my understanding of physics over the last few years and it is thanks to this an many other channels that I have learnt much and realize that I still have even more to learn and I appreciate the work done here especially as I am a science teacher.
Haha. My linear algebra professor was a mathematician. Now I have to crack the old book from a different point of view. Thanks Sabine for a clear and concise reduction of a subject shrouded in mystery. Thanks I signed up for Brilliance. Hopefully it will will make it clear also. Not holding my breath.
great stuff! please do more of that kind - with equations. i've heard some popular science authors say that they avoid equations because it supposedly scares away readers. not so for me. i want to see the equations. there's way too little physics content out there at the math level of an engineer or scientist. it's mostly either full blown professional physicist level or level zero - and very rarely something in between. i also especially like the "theoretical minimum" books by leonard susskind (eagerly waiting for the next volume to come out). i really like to see more content at this level! (edit: and higher - maybe tensors at some point? :-))
I concur based on what I barely know about linear algebra so good work. I follow but struggle to correlate it to anything quantum but I understand it implicitly when it comes to complex ac circuit analysis. So I need more. Thanks.
I just took Quantum last quarter. For the most part, the math for Quantum 1 is pretty easy. There are no long differential equations. Most of my solutions were less than a page long. If you understand basic linear algebra, given enough time, you can get a basic understanding of it. You have to remember that it's very abstract, so it is hard to model in your brain if you don't understand that math,;and that is mostly due to using Hilbert Space, which isn't really a space like you are used to.
I am finishing my quantum mechanics course this week and I am so disappointed to just find your channel now. I appreciate how clearly you explain concepts. Thank you, I look forward to your Brilliant instruction.
Nice lecture! During the covid shutdown, I revisited QM to re-acquaint myself since university some decades ago. I struggled with it back then, being overwhelmed in electrical engineering coursework. But - Dirac was a genius and using Bra-Ket notation really makes this a lot easier.
I thank Sabine Hossenfelder and Leonard Suskind have inspired me to study QM. I don't think I would ever get interested in the subject, and start doing the math rather than just reading theory.
WHY THE MOON CONSTITUTES A CLEARLY BALANCED QUANTUM GRAVITATIONAL FORM IN ACCORDANCE WITH E=MC2 AS F=MA: What is the THE MOON is necessarily invariant AND terrestrial (a LAND relation) in accordance with the fundamental fact that E=mc2 IS F=ma, as ELECTROMAGNETISM/energy is gravity. So, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE. Therefore, the rotation of WHAT IS THE MOON matches it's revolution. Therefore, the Moon is moving AND not moving IN BALANCE in conjunction with invisible AND VISIBLE SPACE in fundamental equilibrium AND BALANCE; AS E=mc2 IS then F=ma. THE MOON is ALSO manifest or shaped in balance WITH THE EYE. The Moon IS THEN manifest ON BALANCE as what is ALMOST invisible in RELATION to/with the BLUE SKY, AS the dome of a person's EYE is ALSO visible on BALANCE. Magnificent. Notice that the shape or curvature of what is the Moon matches that of what is the EARTH/ground (given what is a clear horizon, of course). SO, the ORANGE SUN is CLEARLY proven to be FUNDAMENTALLY in accordance WITH the setting, WHITENED, AND fully illuminated Moon; AS the INVARIANT form of what is the TERRESTRIAL or LAND BASED Moon is then clearly proven ON BALANCE. It is CLEARLY predictable that there will then also be the experience of less gravity in relation to what is the Moon. Importantly, BALANCE AND completeness go hand in hand. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. So, it is also CLEARLY explained why objects fall at the SAME RATE (neglecting air resistance, of course), AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. Great !!! It ALL CLEARLY makes perfect sense. Notice that the Earth is also BLUE (as water), AND the Earth is also ORANGE (as lava). The composition of lunar rocks is, in fact, practically identical to that of Earth rocks. Notice the black space of what is THE EYE. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. GREAT !!! (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) SO, it ALL CLEARLY makes perfect sense. E=mc2 IS CLEARLY F=ma. I now have mathematically unified physics/physical experience. Time DILATION ULTIMATELY proves ON BALANCE that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. INDEED, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 is CLEARLY proven to be F=ma in a BALANCED fashion. Again, BALANCE and completeness go hand in hand. So, I have successfully and consistently used time in order to to CLEARLY PROVE that ELECTROMAGNETISM/energy must be gravity; AS E=mc2 IS necessarily F=ma in what is a consistent and BALANCED FASHION. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Therefore, gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; as E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Great. Again, notice that the DOME of a person's EYE is ALSO visible. So, consider what is balanced BODILY/VISUAL EXPERIENCE. Magnificent. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, as E=mc2 IS F=ma. The Moon is a universal reflection of the Earth/Sun BALANCE, as the MIDDLE DISTANCE in/of SPACE AND the FULL DISTANCE in/of space are linked AND BALANCED; as gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; as E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. The Earth AND the Sun are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Great. Therefore, the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. E=mc2 IS CLEARLY proven to be F=ma !!!! The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. GREAT !!!!! The EARTH and the Sun constitute and comprise the MIDDLE AND THE FULL DISTANCE in/of SPACE (IN BALANCE) in full and BALANCED compliance and conformity with the CLEAR and universal fact that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Great !!!!!! Hence, it is CLEARLY proven, in fact, that the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. Obviously, what is THE MOON is subject to and constitutive of both E=mc2 AND F=ma. E=mc2 IS CLEARLY proven to be F=ma. "Mass"/energy involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. The following constitutes even further proof of the fact that ELECTROMAGNETISM/energy is gravity. Very importantly, in dream experience, BODILY/VISUAL EXPERIENCE is invisible AND VISIBLE IN BALANCE. Dream experience is/involves true/real QUANTUM GRAVITY, as ELECTROMAGNETISM/energy is gravity; as E=mc2 IS F=ma. By Frank DiMeglio
@@Brodda-Syd No not really, the point of the video is that the very complex individual variables and numbers don't matter as much as the mathematical concepts you can use to study the field, concepts which are much easier to understand when you're not looking at large equations and functions.
@@pogtuber5146 I understood the point of the video, what I could not comprehend was her explanation on how she arrived at this conclusion as I am unable to interpret any of the formula's that were presented and so could not follow her steps.
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at 10 seconds she acts like we are scared of mathsymbols and directly proceeds to explain bra ket notation. i think she has a screw loose
This was so concise and a great explanation. Absolutely perfect for someone at my level of understanding, which is that I can do math, I just can't decipher the Wikipedia page.
Hello, I recall trying to read Dirac's Principles Of Quantum Mechanics when I was in 4th year as an undergrad 1974/1975. I recall turning a page and thinking I haven't understood a single word of the page I had just read. Till we understand what the wave function is we understand nothing. Peter Nolan. Ph.D.(physics). Dublin. Ireland.
'wave function' represents the probability of electron being at a place, is it? But why probability comes into picture in the first place? How come the electron behave/move randomly as if it has a mind of its own
@@rgudduu Hello, Even Einstein was upset when he said something along the lines that God does not play dice with the universe. Google for more about that. It was Max Born, as far as I recall, who first said that the square root of the wave function multiplied by its complex conjugate is the probability. I will never accept that the motion of the electron around the proton in the hydrogen atom is described by probabilities. Peter.
Thank you, Sabine. I love it when people teaching science trust us with the math. Sure, my linear algebra is rusty. But I get the basic ideas and am enriched when you explain the mathematics.
I love Dr. Hossenfelder's teaching style. Anyone can understand this generally difficult subject after her lecture. I derived some good ideas for teaching. Thank you
just finished 3b1b‘s video in which I learned that linear algebra is a tool that can fit in any problem satisfies the linearity axiom. so this makes perfect sense
Thank you for this video. I didn't have a great quantum physics professor so he didn't explain Bra Ket notation very well. This video breaks it down so well.
I can't even add up my shopping list correctly, and she says it's not the Quantum Mathematics that's hard. The only way I could leave 3rd grade was to burn the school down.
Adding up the costs on a shopping list requires calculating the dot product between the unit-cost vector and the quantity vector. I suppose you could arbitrarily take one of those to be the row vector and the other the column vector.
@@bozo5632 Things started going down hill when my parole officer told me that I was borne in the alcoholic ward of a mental institution for the criminally insane. That reminds me, I need to get batteries for my calculator.
@@jrbleau I know some intelligent folk that didn't know the very basic credits (like child tax credits) and deductions before I explained it to them. Also, many actual accountants don't even know or understand tax laws completely. If you use an accountant, you really have to keep tabs on them because they are not always up-to-speed on the deductions, exemptions, and credits.
HA! "not so difficult"...You sure fooled me Sabine... ;) You finally lost me at about half of the video...around the fourth minute or so...It just got only worse from then on. For example: I don't understand at all this bit about the value of ONE in these equations. WHAT is the importance/meaning/sense/signification of the value of ONE in these equation. WHY "1"? Thank you for all your efforts. You are one of the best here -nonetheless!
1 = 100%. It is 100% sure, that one of the possible outcomes will be measured, because there is no other possible outcome. So all probabilities summed up have to be 1=100%
a1a1* means the probability of finding the system in state 1; a2a2* means the probability of finding the system in state 2; a3a3* means the probability of finding the system in state 3; ..., akak* means the probability of finding the system in state k; ..., The sum of all these probabilities is 100%. a1a1* + a2a2* + a3a3* + ... + akak* + ... = 1 = 100% That's because when you perform a measurement on a quantum system, you will always find it in one of its possible states. Thus, we say that the probability of finding the system in one of the possible states is 100%.
@@SabineHossenfelder So the "1" means that the probability would be 100% that the calculated event would occur? And 0.5 would mean that the chance is 50%?
Bravo! For years i’ve been saying quantum mechanics is not all that difficult, it just uses linear algebra and complex numbers, both studied in high school. A friend accuses me of arrogance saying something like, “Feynman said nobody understands QM, but you do. Are you saying you are smarter than Feynman?” Now I can point him to this video. Please answer the obvious question. What did Feynman mean? BTW, I love your music.
I am sure these ~24 dislikes are from the Physics academicians who first made their students life miserable, and are now unhappy how elegantly, openly and honestly she has explained the secrets of QM. Best regards from Munich.
I took quantum 1 last quarter. This is basically the first half of the class. The way it was explained to me, we learned by using the "Modern Approach," which starts with Dirac Notation on the first day.
There are two principal types of problem in quantum mechanics. In what may be called quantum dynamics we have the time marching problem where we solve for a differential equation by doing a timelike integration. Some of the solutions can have a special character and are called eigen-something solutions or characteristic solutions or stationary solutions. To ascertain these eigensolutions we solve for a problem in quantum statics which normally means determining the eigenvalues of a Hermitian matrix, which is a type of matrix with complex numbers as entries which is nevertheless guaranteed to have real eigenvalues. Even the basics are a little complicated. I did "O" Level German at school. It helps. Most English speakers will talk about an eigensolution or an umlaut rather than a characteristic solution or a dieresis because of the context in which we meet these words.
@@JohnVKaravitis What do you mean? There is nothing wrong with the things said or showed at the time marks you commented. Do I understand something wrong what you said?
Thanks Sabine. Just joined your Brilliant suggestion, hoping to brush up on my own understanding but my stretch goal is the courses are fun enough to attract my 14yo daughter to be interested in STEM
I both understand perfectly and am completely clueless at the same time,I must be the Human version of Schrödinger's cat.
My problem with Quantum Mechanics is always the internal visualization element. I have to be able to visualize in my head what Im working with. How do you visualize 'wave' functions? If the math doesnt mean more than the numbers I have a hard time with it. I have to see what its supposed to look like at the beginning and then work from there. I dont understand how you can do that with most of this stuff.
Aren't you Jaguar?
funny
And instinctively you are able to accurately express the oxymoronic truth that encapsulates the entire process of creation. Being that as we create our Present Now and Past and Future , we totally annihilate the now and replace it with the new now singularity... for example I just did that in a practical action as I had to cut a comment completely and replace it with an updated copy of the same comment... that is what life is. The past now is wiped out and replaced by the present now which came from the future now... constantly refreshing our old past reality with our new present reality which will be replaced by our future reality which was created by our present reality which is the only reality that can ever exist because
the past does not exist anymore 0
The future does not exist yet 0
The Now always exists as the 1
Singularity that keeps changing form
1010101010 satisfying the law of the conservation of energy.
@@thetruthchannel349 > Someone said that as the photon flies along, it contains a little arrow that goes around and around. If the photon splits up and goes by more than one route to a detection site, the little arrow goes around and around along each route, and where they come together, those add up, and so they could cancel. So your detection site could see nothing; it might be in the middle of a dark band of the interference fringe.
Finally something at my level! I'm an engineer. The average "laymans" explaination is too layman. The average specialist explanation assumes you spend all your time doing physics - and have read all these books and papers. Thank you.
Exactly, I got indulged in this video because of the Math that is rarely shown on YT.
On the other hand, articles assume you are well versed in the subject and you are willing to spend hours researching the technical jargon..lol
I think you would like the lessons of Leonard Susskind on the Stanford University Channel on TH-cam as well. He explained this. They do take time, though!
@@ronaldderooij1774 well he is old😅 but nevertheless the quality is still delivered
Yeah - that's just how it is for me too. Have a good day. :-)
Yep, engineer here. This is about the perfect level for me.
It's amazing how linear algebra underpins quantum mechanics, machine learning, digital signal processing, error correcting codes, computer graphics, and so much else. It's a great example of how learning the underlying math allows one to understand so many seemingly different fields of knowledge. Great video.
It is just a tool , it is not the "underlying" thing. Tools are replaceable and certainly all those ideas can be formulated without that math.
@@Ernesto1317How?
I just found amazing that tomorrow i have 2 exams in the same day, quantic mechanics and machine learning and you managed to mention both right in the start ahahah
Just like learning Latin helps you understand so many languages.
I actually have a Master degree in Physics from ETH Zürich ( 25 years ago) , but had my Professor explained me the basis of QM like this
I would have had much less problems and sleepless nights :-) !
( now in the right videos comments)
Her videos plugged a lot of holes I had in my knowledge of QM. It really made me seriously get back to studying.
Wow! Talk about PTSD! You should sue ETH Zurich!
@@l0_0l45 search ViaScience on TH-cam. There is an entire masters-level course in bite-sized pieces.
It's really amazing. I only followed the parts I was interested in, but this channel contains the equivalent of a master's degree for sure.
@@peetiegonzalez1845 Indeed, particularly the QM series from ViaScience is great, imho.
"In quantum mechanics, we only ever observe the shadow of tge wave function" - Woah, Plato was right all along!
Wow, I love that! Thanks for pointing that out, I'll probably use that image!
In other words, you mean, nothing more than magnetic flux of a magnet against copper, of course, 'scientist'.
Wow, the same thought like mine!
The fact that part of the probability of the wave function that we can't observe is an imaginary number makes the resemblance even more uncanny.
Schrodinger's cat is just Hegel's cat in disguise:-
Thesis is dual to anti-thesis -- the time independent Hegelian dialectic.
Being is dual to non-being creates or synthesizes becoming -- Plato.
Hegel's cat: Alive (thesis, being) is dual to not alive (anti-thesis, non being) -- Schrodinger's cat.
Plato discovered Schrodinger's cat 2500 years ago, he was a smart dude.
All vectors are dual, they are defined by two dual points, the origin and the arrow head.
Vectors are dual to co-vectors (forms).
Dirac notation is based upon inner or dot products.
The inner product is dual to the cross product.
Probability leads to projection, prediction or syntropy.
Syntropy is dual to increasing entropy -- the 4th law of thermodynamics.
"By imagination and reason we turn experience into foresight (prediction)" -- Spinoza.
Syntropy is the convergence or integration of ideas to form predictions or expectation.
Teleological physics (syntropy) is dual to non-teleological physics (entropy).
"Always two there are" -- Yoda.
Symmetry is dual to conservation -- the duality of Noether's theorem.
Sabine, to me you are the best Physicist on TH-cam! The no-nonsense style, concise and clear structure of the episodes and the intellectual rigour and honesty - you’re doing something that, as far as I know, is in very short supply here. Keep up the good work, we need people who have deep understanding and can also explain as clearly as you can!
I love your channel.
Also, I’m not German but I enjoy hearing the correct pronunciation of German names on the Internet.
This has very quickly become one of my favorite youtube channels ever.
Concise explanations of scientific theories without climbing aboard the hype train or spending an hour explaining the double slit experiment for the millionth time. Thank you!
On that note, I would love to get your thoughts on the delayed-choice quantum eraser experiment.
Excellent explanation! As a Science teacher myself, I love when someone can break down seemingly incomprehensible concepts into understandble smaller chunks.
I think it's official now, Sabine's channel is where you go to fully understand what you've been taught in the university. 🔥
It's been almost 40 years since I took Quantum. This is a wonderful refresher. Thank you.
Bro studied QM with Werner Heisenberg himself. 💀
I once took my car to a quantum mechanic. As long as I don't look at the speedometer, I can get where I'm going.
That’s hilarious!
:-D :-D :-D
A good explanation of Heisenberg's uncertainty principle
But if you looked at the speedometer, you could be anywhere.
Great joke.
It’s important to realize that the wave function is not |psi> but is
psi(x)=. |psi> is the state vector, and is independent of x. It depends only on the various quantum numbers of the problem and perhaps on time.
this were 8 minutes which answered a lot of questions which i never dared to even try to find out, because I thought I would never even get a clue of what these brackets mean. Thank you so much!
ON THE ABSOLUTE PHYSICAL EQUIVALENCY AND BALANCING OF E=MC2 AND F=MA:
It is a very great truth in physics that the ability of thought to DESCRIBE OR reconfigure sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (THOUGHTS ARE INVISIBLE.) INDEED, E=mc2 IS DIRECTLY and fundamentally derived from F=ma; AS time dilation proves that electromagnetism/ENERGY IS GRAVITY. Therefore, ultimately and truly, time is possible/potential AND actual IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In fact, INSTANTANEITY is FUNDAMENTAL to the FULL and proper understanding of physics/physical experience; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. GREAT !!! BALANCE AND completeness go hand in hand. It all CLEARLY makes perfect sense. (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Gravity IS ELECTROMAGNETISM/ENERGY.
By Frank DiMeglio
Great introduction, Dr. Bee!. I cannot emphasize the importance of using the Dirac bra-ket notation too much, as it greatly simplifies the mathematics of QM. My favorite elementary text is Sakurai's Modern Quantum Mechanics, whose first three chapters provide everything one needs to know about the notation and its applications.
Ah, yes the Sakurai. I really understood QM only after I read this brilliant book. But only from the library. Buying it was way too expensive.
Hossenfelder is knowingly and deceitfully lying about physics.
@@frankdimeglio8216 Not that I can see.
I was literally taking a break from reading Sakurai's first chapter and watched this video. Excellent explanation. I appreciate the part on the density matrix, I guess that's where things get really exciting.
THANKS A LOT .NOW I HAVE ENOUGH COURAGE TO GO BACK AND PICK UP SAKURAI TO PROCEED FURTHER IN QUANTUM MECHANICS.
@@anupamkumarsinha9384 Do it!! QM is so cool and interesting!!!
Yes, I think the density matrix makes the transition from the very tiny to the classical regimes much clearer.
I’ll need to watch that one again.
The missing part is that for a complex number z, we have zz* = |z|^2 which is a real number, positive or null. It was somewhat implied but it was never written.
And again, and again, ad infinitum.
Bravo! I watched many lectures and taught myself linear algebra to better understand QM. This is by far the best!
This must be the most "not so difficult to understand" difficult to understand video I've ever seen 🤷🏻
If you know linear algebra at least this isn't that bad.
Poorly explained
I am a final year Bsc physics student who was very worried about their understanding of QM, something just didn't click for me. You just summarized everything that needed clearing up for me within 8min, I feel like all the lectures I have witnessed finally made complete sense. I am shocked and honestly a little in love. I never write comments on yt videos but WOW and THANK YOU... THANK YOU SO MUCH.
What is it that is now clear that wasnt before?
How do you visualize QM and the wavefunction now as compared to before?
In this video I understood something which I never understood by watching 100rds of videos!!!
Thankyou so much for this simple and powerful explaination!
It would be amazing if you write a book on quantum mechanics,,,hope to see that soon....!!!
Agreed, rip off the mask and look under the hood. Love it.
same for me with Science Asylum. The method of explanation is SO important. The more clearly someone understands a subject, the more clearly they can explain it. Even better if they use graphics.
Glad I was binge watching a Linear Algebra playlist earlier today. Helped with this discussion.
Just bought your book. Can't wait to dig in.
What's the book's title?
@@yahiakandil4086 Lost in Math. It's pretty good. It's about Sabine's quest to understand why physicists are obsessed with the notion that physics must be beautiful, and her impressions of how that has backfired in modern physics. It's a refreshingly honest take on the shortcomings of modern academia.
@@1ucasvb thanks :)
@@1ucasvb "lost in math" explained, perfect 👌
@@1ucasvb "Beauty is in the eye of the beholder."
Historically speaking, physics has gotten more "beautiful" over the centuries. Part of that is discovering new symmetries (which means we can merge two fields together) and part of it is simply notational improvements.
The real reason physicists chase 'beauty' so much these days is that we don't really have anything else to look for. The LHC confirming the Higgs to be basically what we expected means we don't have any real leads for the next step to take. We know there _is_ a next step because of the fundamental incompatibility between QM and GR, but we're not going to be able to directly probe those energy levels likely in the next few hundred years, if ever. Short of a miracle new collider design or a complete fluke with some astronomical event, we're stuck with just poking around at the energy scales we have available and hoping to prod something out to give us a hint.
In the meantime physicists want to stay employed, and our only real "hint" for what's next is following the history of unification. Maybe the planned LHC upgrades will prod out something new like those elusive SUSY particles we keep expecting, but really there's not much guarantee that anything exists between the Higgs and the energy levels where we expect GUT to occur, and even that is likely a good couple of collider generations (not just upgrades) away still. Which could be a century or more given how long it takes to design, fund and build such immense projects.
This is an amazing video. I am a biologist with a master's in physics: I always had trouble with mathematics but come to realize that it only takes a simple explanation from someone at the correct speed and structure of ideas. Everyone is different. I wished I had seen this video when I started my master's. Thank you, I can't believe how well you explain these concepts!
Nature uses QM frequently in biology, especially in chemical reactions, processing of light, and capturing energy from the Sun. Most non-biologists don't know this.
Whenever I come across a video claiming in its title that "Quantum Mechanics (or any other fancy, popular scientific term) were not so difficult" I find myself thinking about misleading titles and how they are supposed to generate traffic. The explanations in this video, just as in all the other videos on the matter, are neatly arranged versions of standard textbook contents. While I do appreciate the effort that goes into scripting and producing these videos I am always missing an advice of caution. The fact that the mathematical basics of Quantum Mechanics are comparatively simple does not imply anything really, least of all that Quantum Mechanics are not so difficult. The brief glimpses on "vector spaces", "dual spaces", "inner products", etc. provided in this video are merely first steps into a massive subrealm of mathematics. I agree that anyone who is interested in Quantum Mechanics has to work on their mathematical abilities although I highly recommend using these videos as a motivation to acknowledge, rather than to deny, the difficulties of theoretical physics and maths. The net information seldom surpasses party-trick quality standards and that is all well because being too complex to be legitimately summarised in any video (of finite length and information density) is in the nature of things!
Broseph you are incorrect about the value of this presentation. I have multiple degrees including physics (see a comment a cpl days after yours) and what is sorely lacking in many formal instances is SIMPLE CONTEXT. It annoyed me the abstract manner I was "taught" QM (I wasn't taught anything I was "read")
You are correct about the whole other branch of mathematics and solid foundation needed before tackling any of this QM stuff. If you are doing an undergrad physics degree like 2/3rds of it will be maths for the first 2 years, then in years 3-4 you get the pleasure of using said maths. Fourier transforms, separating the variables, deriving and solving Schrodinger's equation, Maxwell's equations, of course general relativity and Lorentian transforms (pretty easy in comparison to the rest).
Then after all that some twat will "read" to you and introduce entirely new notation and processes, talking to you about Laplace this, Dirac that, and asking, "is this Hermetian"? Bitch it would help if you told me what type of Hermit crabs first. Oh you weren't talking about crabs or lap-dancing clubs but some random maths you are reading to me for the very first time in my life. Reading me maths. No don't try and work out what's happening or what any of this stuff is, just copy and paste, the lecturer is paid to "read" not "teach"
Ok
@@Pax_Veritas I'm not entirely sure whether your comment is directed at me since I don't know who Broseph is. However, I'll just go ahead and pretend you were targeting my comment. In that case I feel like you misunderstood my critique - I do agree that simple explanations and teachings are both often missing at university and important for scientists in training. I just don't agree with the way in which many attempts at simlpe explanations seem to downplay stuff in the same breath. In my opinion presenting a smart, intuitive and simple ACCESS to a difficult subject loses its added value when it is sold to be the "real deal".
Also, congratulations on your multiple degrees including physics! Good job! Finally, I'm not sure what happened to you in that last paragraph and it's hard to judge one's emotional state via a TH-cam comment section. Still I sense some measure of frustration - is that right? In that case: Hang in there, mate! Everything's gonna be okay! :-)
@@manjsher3094 is it, though?
@@user-yv8bw3zf6n it is very ok.
The way Sabine Hossenfelder presents information is comfortable to view. I perceive the nonverbal hand gestures as offering knowledge.
Thank you for sharing
“The math is not as hard as it looks”. Yes, it is🙂. Love these videos.
Yes it is... What? It is hard.
@@ericreiter1 It is certainly hard if you can't understand the notations that are used.
In this theory the mathematics of quantum mechanics represents geometry, the Planck Constant ħ=h/2π is linked to 2π circular geometry representing a two dimensional aspect of 4π spherical three-dimensional geometry. We have to square the wave function Ψ² representing the radius being squared r² because the process is relative to the two-dimensional spherical 4π surface. We then see 4π in Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π representing our probabilistic temporal three dimensions life. The charge of the electron e² and the speed of light c² are both squared for the same geometrical reason. We have this concept because the electromagnetic force forms a continuous exchange of energy forming what we experience as time. The spontaneous absorption and emission of light photon ∆E=hf energy is forming potential photon energy into the kinetic energy of electrons. Kinetic Eₖ=½mv² energy is the energy of what is actually happening. An uncertain probabilistic future is continuously coming into existence with the exchange of photon energy.
Well, if there had ever been any doubt, I didn't miss my calling in quantum mechanics Thx
Thank you. This video really emphasized what I already knew; to go beyond the high level videos on quantum mechanics I have to commit to honing my math skills. Otherwise it's like trying to learn a topic without having a good grasp on the language it's being taught in. And math is essentially a language.
I've always wonderd how even janitors in star trek have a firm grasp on quantum physics.
I do not wonder anymore, your vidieos are pointing us into a future where this is possible (Maybe not Star Trek, but the 'Janitor builds a particle accelerator for funsies at home future').
And for that i am grateful. Not just for me, but to see that knowledge is finaly spreading to those that want to know regardless of birth of wealth.
Just... THANK YOU
Sorry the future was many years ago - Michio Kaku built one as a high school science fair project -
Very nice video. I really really very much appreciate the lesson and also how & where to go to find more about it in Brilliant. I'm glad that you don't assume your audience is Physics PhDs only. You are Great lady and teacher.
This was so good, it's useful to see this video years after I learned these concepts in separate subjects.
Now that was a high density information transfer - not a word wasted, yet completely clear, at least if you already know about linear algebra and complex numbers. Thank you.
Great Video Sabine!
You maam, are brilliant. Unlike so many other 'orthodox' scientists you mostly qualify your statements. Other scientists lack humility, stating ' conventional models of phenomena' as undisputed fact. Thanks for all you do in this respect.
Thank you so much for your beautiful explanation you are my hero
I could spend every second of my life with you Madam Sabine and never get bored... Thank you so much for the videos . I've learnt a lot, a bit too complex such that I have to watch the videos twice to get it. But worth it. 😁 and I appreciate the time you take to share your knowledge with us...
Watching from Lusaka, Zambia.
I think one should make a distinction between the state and the wavefunction. The state is an abstract mathematical object whereas the wavefunction is a complex function of spacial coordinates. If you want to obtain the wavefunction from the state you project it onto your spacial basis.
Damn, the clarity that comes with deeply internalizing a concept - she is the embodiment of sheer genius in simplicity !
I love ho Sabrine explains a lot of linear algebra concepts in the context of QM
You have a gift for communicating the seemingly complex in a straightforward and clear style. Absolutely wonderful discussion. Thank you for taking the time and making the effort to do these. Very much appreciated!!!
There is nothing complicated here. This is high school math in slightly different notation with zero physics in it.
I love when things become more technical, thank you Sabine to make them so simple, but not dumb. Btw, did you know that Max Born was the grandfather of Olivia Newton John?
Yes!
I really didn't! But this fact confirms that Born was a genius.
@@hernando-d We all are related.
Wow !
'Let's get physical'!
6:27-6:33 This is THE prerequisite for understanding this vedio. In summary, this Lecture is a excellent reminder of how the basis vectors are reprsntd and works, if one hasnt been through transforming position-space rep to momentum-space rep then it will be hard to understand. We choose particular basis for diagonalizing our particular choice of Hamiltonian,for example.
How I wish I had a physics lecturer in uni that could have explained things as you just did in this video.
Well, the real mental challenge arises from entanglement and/or second quantization (quantum field theory QFT) later. As in a superposition of a (possibly infinite) number of quantum states. For example, how many (non-physicist) people do know and can grasp that a laser state has a definite (electromagnetic) phase, but is actually a superposition of an indefinite number of (photon) quanta?
Thus, even such a simple thing as a laser pointer already exceeds ordinary human intuition and understanding by far. Yes, we can describe such physical states mathematically in terms of Hilbert vectors, but one can easily put a question mark on what do we people understand about the nature of reality from that.
Doctor Feynman once said
"If you think you understand quantum mechanics, then you don't understand quantum mechanics
I Agree
Reminds me of the first line in the Tao: "The real Tao is not the Tao that can be spoken about nor understood" or in your words "If you think you can understand the Tao, then you do not understand the Tao"
yeah well that was valid back then in the beginning days of QM, today more and more is understood as is also explained in vids like this. 500 yrs ago electricity was also something that one could think to understand but dont understand it at all... same goes for all new discovered natures features. of Einsteins theories it was close to the same....and now every simple soul can understand it simply. So Feynmans statement wears off over time. Thing is one needs to start thinking in different ways then one was used to and then it becomes more easy over time.
I think I don't understand quantum mechanics, then now I am sure I understand quantum mechanics.
@Bertrand de Born are you always so unpolite by calling people idiots before you even know them ?????
well you know what they say......... it takes one ...... to know one
Here Sabine as always gives most precise and honest prelude on mathematics in QM. Many thanks!
She: ‘It’s really not that difficult’
Me: 3 minutes in....fast asleep, brain cooling down......
😂 me rn
I’m off to conjugate my basis vectors and stick them up my variable coefficient. Wave functioning goodbye...
I often worry about the situation where professional scientists go out of their way to explain what seem like complex concepts and do their best to clear up common misconceptions and some comments suggest science is wrong seem to me to come from these misconceptions and even worse it feels as if the time hasn't been taken to understand what had been said. I have taken a lot of time to deepen my understanding of physics over the last few years and it is thanks to this an many other channels that I have learnt much and realize that I still have even more to learn and I appreciate the work done here especially as I am a science teacher.
“physicists have debated this back and forth for 100 years.” I am glad that I am not the only confused soul!
Haha. My linear algebra professor was a mathematician. Now I have to crack the old book from a different point of view. Thanks Sabine for a clear and concise reduction of a subject shrouded in mystery. Thanks I signed up for Brilliance. Hopefully it will will make it clear also. Not holding my breath.
great stuff! please do more of that kind - with equations. i've heard some popular science authors say that they avoid equations because it supposedly scares away readers. not so for me. i want to see the equations. there's way too little physics content out there at the math level of an engineer or scientist. it's mostly either full blown professional physicist level or level zero - and very rarely something in between. i also especially like the "theoretical minimum" books by leonard susskind (eagerly waiting for the next volume to come out). i really like to see more content at this level! (edit: and higher - maybe tensors at some point? :-))
Most enlightening! Concise & comprehensible. 🌟🌟🌟🌟🌟
Very direct, no nonsense style of presentation.
Two things: One, your explanation of the braket was quite helpful; two, hearing you pronounce your name was beautiful!
Very concise math intro. I will pass this along to my young students.
“Keep in mind the density matrix.” Easier said than done 😅. Awesome video!
Keanu Reeves was great in that movie.
I concur based on what I barely know about linear algebra so good work. I follow but struggle to correlate it to anything quantum but I understand it implicitly when it comes to complex ac circuit analysis. So I need more. Thanks.
'Trust me, it's simple'.
Sabine proceeds to melt my brain.
Not even at watching half the video yet and Ive already had so many questions answered. Thank you, Dr. Hossenfelder.
I loved physics. Sir Ernest Rutherford and Fermi were my heroes. I built my own cloud chamber. I understand the concepts but I never got the math.
I just took Quantum last quarter. For the most part, the math for Quantum 1 is pretty easy. There are no long differential equations. Most of my solutions were less than a page long. If you understand basic linear algebra, given enough time, you can get a basic understanding of it. You have to remember that it's very abstract, so it is hard to model in your brain if you don't understand that math,;and that is mostly due to using Hilbert Space, which isn't really a space like you are used to.
You are Michael Faraday and I claim my £5.
I am finishing my quantum mechanics course this week and I am so disappointed to just find your channel now. I appreciate how clearly you explain concepts. Thank you, I look forward to your Brilliant instruction.
I wish you had been my teacher in my first course of quantum mechanics.
Nice lecture! During the covid shutdown, I revisited QM to re-acquaint myself since university some decades ago. I struggled with it back then, being overwhelmed in electrical engineering coursework. But - Dirac was a genius and using Bra-Ket notation really makes this a lot easier.
I thank Sabine Hossenfelder and Leonard Suskind have inspired me to study QM. I don't think I would ever get interested in the subject, and start doing the math rather than just reading theory.
Did you read Susskinds the theoretical minimum? That’s what first inspired me!
Now what about the tensor concept which is a genrealization of the vectot concept. Some visualization pictures or stories will be useful.
This is extraordinarily good. I´m "out of the game" since some years, but with this I´m quickly back in track. And IT. FEELS. GOOD!!!
Well, Im certainly glad that’s all cleared up🤤🥴
NOT!
You should be. It is, as the 'story so far.' Later episodes get us farther. Just wait!
She could have gone a bit faster.
Loooooooooooooool
WHY THE MOON CONSTITUTES A CLEARLY BALANCED QUANTUM GRAVITATIONAL FORM IN ACCORDANCE WITH E=MC2 AS F=MA:
What is the THE MOON is necessarily invariant AND terrestrial (a LAND relation) in accordance with the fundamental fact that E=mc2 IS F=ma, as ELECTROMAGNETISM/energy is gravity. So, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE. Therefore, the rotation of WHAT IS THE MOON matches it's revolution. Therefore, the Moon is moving AND not moving IN BALANCE in conjunction with invisible AND VISIBLE SPACE in fundamental equilibrium AND BALANCE; AS E=mc2 IS then F=ma. THE MOON is ALSO manifest or shaped in balance WITH THE EYE. The Moon IS THEN manifest ON BALANCE as what is ALMOST invisible in RELATION to/with the BLUE SKY, AS the dome of a person's EYE is ALSO visible on BALANCE. Magnificent. Notice that the shape or curvature of what is the Moon matches that of what is the EARTH/ground (given what is a clear horizon, of course). SO, the ORANGE SUN is CLEARLY proven to be FUNDAMENTALLY in accordance WITH the setting, WHITENED, AND fully illuminated Moon; AS the INVARIANT form of what is the TERRESTRIAL or LAND BASED Moon is then clearly proven ON BALANCE. It is CLEARLY predictable that there will then also be the experience of less gravity in relation to what is the Moon. Importantly, BALANCE AND completeness go hand in hand. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. So, it is also CLEARLY explained why objects fall at the SAME RATE (neglecting air resistance, of course), AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. Great !!! It ALL CLEARLY makes perfect sense. Notice that the Earth is also BLUE (as water), AND the Earth is also ORANGE (as lava). The composition of lunar rocks is, in fact, practically identical to that of Earth rocks. Notice the black space of what is THE EYE. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. GREAT !!! (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) SO, it ALL CLEARLY makes perfect sense. E=mc2 IS CLEARLY F=ma. I now have mathematically unified physics/physical experience. Time DILATION ULTIMATELY proves ON BALANCE that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. INDEED, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 is CLEARLY proven to be F=ma in a BALANCED fashion. Again, BALANCE and completeness go hand in hand. So, I have successfully and consistently used time in order to to CLEARLY PROVE that ELECTROMAGNETISM/energy must be gravity; AS E=mc2 IS necessarily F=ma in what is a consistent and BALANCED FASHION. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Therefore, gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; as E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Great. Again, notice that the DOME of a person's EYE is ALSO visible. So, consider what is balanced BODILY/VISUAL EXPERIENCE. Magnificent. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, as E=mc2 IS F=ma.
The Moon is a universal reflection of the Earth/Sun BALANCE, as the MIDDLE DISTANCE in/of SPACE AND the FULL DISTANCE in/of space are linked AND BALANCED; as gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; as E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY.
E=mc2 IS F=ma. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. The Earth AND the Sun are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Great. Therefore, the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. E=mc2 IS CLEARLY proven to be F=ma !!!! The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. GREAT !!!!! The EARTH and the Sun constitute and comprise the MIDDLE AND THE FULL DISTANCE in/of SPACE (IN BALANCE) in full and BALANCED compliance and conformity with the CLEAR and universal fact that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Great !!!!!! Hence, it is CLEARLY proven, in fact, that the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. Obviously, what is THE MOON is subject to and constitutive of both E=mc2 AND F=ma. E=mc2 IS CLEARLY proven to be F=ma. "Mass"/energy involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma.
The following constitutes even further proof of the fact that ELECTROMAGNETISM/energy is gravity. Very importantly, in dream experience, BODILY/VISUAL EXPERIENCE is invisible AND VISIBLE IN BALANCE. Dream experience is/involves true/real QUANTUM GRAVITY, as ELECTROMAGNETISM/energy is gravity; as E=mc2 IS F=ma.
By Frank DiMeglio
I'm trying to grasp this, but my brain packed it's bags and left about a minute in
Me too. I guess it takes 10 years of studying to get up to that level of understand
@@Brodda-Syd No not really, the point of the video is that the very complex individual variables and numbers don't matter as much as the mathematical concepts you can use to study the field, concepts which are much easier to understand when you're not looking at large equations and functions.
@@pogtuber5146 I understood the point of the video, what I could not comprehend was her explanation on how she arrived at this conclusion as I am unable to interpret any of the formula's that were presented and so could not follow her steps.
at 10 seconds she acts like we are scared of mathsymbols and directly proceeds to explain bra ket notation. i think she has a screw loose
This was so concise and a great explanation. Absolutely perfect for someone at my level of understanding, which is that I can do math, I just can't decipher the Wikipedia page.
"funny brackets" i love her way of teaching
Best explanation I have yet seen about the Bra-Ket notation!
Hello,
I recall trying to read Dirac's Principles Of Quantum Mechanics when I was in 4th year as an undergrad 1974/1975. I recall turning a page and thinking I haven't understood a single word of the page I had just read. Till we understand what the wave function is we understand nothing.
Peter Nolan. Ph.D.(physics). Dublin. Ireland.
'wave function' represents the probability of electron being at a place, is it? But why probability comes into picture in the first place? How come the electron behave/move randomly as if it has a mind of its own
@@rgudduu
Hello,
Even Einstein was upset when he said something along the lines that God does not play dice with the universe. Google for more about that. It was Max Born, as far as I recall, who first said that the square root of the wave function multiplied by its complex conjugate is the probability. I will never accept that the motion of the electron around the proton in the hydrogen atom is described by probabilities.
Peter.
Thank you, Sabine. I love it when people teaching science trust us with the math. Sure, my linear algebra is rusty. But I get the basic ideas and am enriched when you explain the mathematics.
6:44 feeling called out right now
I love Dr. Hossenfelder's teaching style. Anyone can understand this generally difficult subject after her lecture. I derived some good ideas for teaching. Thank you
Simple: if you unhook the bra, you have to conjugate the cat, and cast imaginary shadows on all your bases (which are belong to Sabine)
More bra than we´re used to...
just finished 3b1b‘s video in which I learned that linear algebra is a tool that can fit in any problem satisfies the linearity axiom. so this makes perfect sense
“What that weird bracket?” I think you mean bra-ket 😎
Thank you for this video. I didn't have a great quantum physics professor so he didn't explain Bra Ket notation very well. This video breaks it down so well.
I can't even add up my shopping list correctly, and she says it's not the Quantum Mathematics that's hard.
The only way I could leave 3rd grade was to burn the school down.
Lol shopping List math is the hard stuff. It must be a branch of bistromatics.
Adding up the costs on a shopping list requires calculating the dot product between the unit-cost vector and the quantity vector. I suppose you could arbitrarily take one of those to be the row vector and the other the column vector.
@@bozo5632 Things started going down hill when my parole officer told me that I was borne in the alcoholic ward of a mental institution for the criminally insane.
That reminds me, I need to get batteries for my calculator.
Actually, I know a top-flight mathematician who can't do his taxes.
@@jrbleau I know some intelligent folk that didn't know the very basic credits (like child tax credits) and deductions before I explained it to them. Also, many actual accountants don't even know or understand tax laws completely. If you use an accountant, you really have to keep tabs on them because they are not always up-to-speed on the deductions, exemptions, and credits.
Thank you so much! So simple... yet it looks so complicated.
You're God-sent.
It's not complicated at all. This part, at least, isn't. QFT, that is complicated.
"We only observe the shadows of the wave function."
Here's a fun cartoon for you: th-cam.com/video/qs26qv6C-38/w-d-xo.html
I've been trying to understand Quantum Mechanics for Nuclear Magnetic Resonance applications . Your videos are a big help.
I am trying to understand this and eat chips at the same time.
Very satisfying to understand the basic concept of the mathematics behind the wave functions. Pleas keep on explaining. Thank you so much.
HA! "not so difficult"...You sure fooled me Sabine... ;)
You finally lost me at about half of the video...around the fourth minute or so...It just got only worse from then on. For example: I don't understand at all this bit about the value of ONE in these equations. WHAT is the importance/meaning/sense/signification of the value of ONE in these equation. WHY "1"?
Thank you for all your efforts. You are one of the best here -nonetheless!
Because probabilities have to sum up to 1.
1 = 100%. It is 100% sure, that one of the possible outcomes will be measured, because there is no other possible outcome. So all probabilities summed up have to be 1=100%
a1a1* means the probability of finding the system in state 1;
a2a2* means the probability of finding the system in state 2;
a3a3* means the probability of finding the system in state 3;
...,
akak* means the probability of finding the system in state k;
...,
The sum of all these probabilities is 100%.
a1a1* + a2a2* + a3a3* + ... + akak* + ... = 1 = 100%
That's because when you perform a measurement on a quantum system, you will always find it in one of its possible states. Thus, we say that the probability of finding the system in one of the possible states is 100%.
@@SabineHossenfelder So the "1" means that the probability would be 100% that the calculated event would occur? And 0.5 would mean that the chance is 50%?
@@MauriceApophis Yes
Bravo! For years i’ve been saying quantum mechanics is not all that difficult, it just uses linear algebra and complex numbers, both studied in high school. A friend accuses me of arrogance saying something like, “Feynman said nobody understands QM, but you do. Are you saying you are smarter than Feynman?” Now I can point him to this video. Please answer the obvious question. What did Feynman mean? BTW, I love your music.
OK...although you made it "simpler" my head still hurts...like hell too.
Sorry, lol.
@@SabineHossenfelder Are you _really?_
Fantastic explanation! I've looking for a concise description of Dirac notation for a week now, then TH-cam recommends this vid! what a find, thanks!
I am sure these ~24 dislikes are from the Physics academicians who first made their students life miserable, and are now unhappy how elegantly, openly and honestly she has explained the secrets of QM.
Best regards from Munich.
I took quantum 1 last quarter. This is basically the first half of the class. The way it was explained to me, we learned by using the "Modern Approach," which starts with Dirac Notation on the first day.
My wave function currently has a vector pointing toward my office chair. 😛
Very funny and awesome comment
On a Saturday afternoon?
Damn, Quantum mechanics sucks.
The probability of a nap is approaching 1.
@@obsidianjane2267 - Yes it is!
This is a fantastic explanation. I majored in physics but never got an explanation that was so concise and clear.
according to Prof Feynman: ""If you think you understand quantum mechanics, you don't understand quantum mechanics."
As said, the problem does not lie with the math. It is the interpretation.
There are two principal types of problem in quantum mechanics. In what may be called quantum dynamics we have the time marching problem where we solve for a differential equation by doing a timelike integration. Some of the solutions can have a special character and are called eigen-something solutions or characteristic solutions or stationary solutions. To ascertain these eigensolutions we solve for a problem in quantum statics which normally means determining the eigenvalues of a Hermitian matrix, which is a type of matrix with complex numbers as entries which is nevertheless guaranteed to have real eigenvalues. Even the basics are a little complicated. I did "O" Level German at school. It helps. Most English speakers will talk about an eigensolution or an umlaut rather than a characteristic solution or a dieresis because of the context in which we meet these words.
Just woke from a drunken stupor. Why am I trying to understand this right now?
Great explanation, never saw it like that! Thanks!
3:00 You got your row and column reversed, based on your display.
3:57 Your bra is incorrect.
1: no 2: no , there isn't anything wrong, what did you mean in particular?
@@bekoe2992 Reading comprehension issues?
@@JohnVKaravitis What do you mean? There is nothing wrong with the things said or showed at the time marks you commented. Do I understand something wrong what you said?
Hm... I think you're the one reversed. Just saying.
@@IkikaeruRaimei Good luck on losing your virginity!
Thanks Sabine. Just joined your Brilliant suggestion, hoping to brush up on my own understanding but my stretch goal is the courses are fun enough to attract my 14yo daughter to be interested in STEM
3:35 - this screen made me understand important things!