Interpretation of the wavefunction

[@federicoragno1921]

I love how he randomly positions the horizontal line in the middle of the word when writing the letter "t"

[@jacobvandijk6525]

Well, you can't say that the man does not have a real passion for explaining this subject. Chapeau!

[@momen8839]

What is your email address?

[@stevegovea1]

Max Born is my new hero.

[@williamolenchenko5772]

Max Born was Olivia Newton John's maternal grandfather.

[@diegoarce6549]

Great professor 👏 👌 👍

[@carmensolissanchez4022]

if i can see 6 videos per day y going to learnd the full course and the other 3 in less than 2 months ,this is so good i really love mit ocw bacause you cant learnd a lot in a single plataform without leave your home and waste time ,even for me it imposible pay a school and 6 videos is like 90 minuts per day

[@abhirambhat9277]

Ocw is just great right?

[@ashvinla]

I have a question on the probabilistic interpretation of the wave function. As a thought experiment, let's take the coulomb potential problem. In this case, the probability decreases as 1/r^2. What this means is that there is non-zero probability (albeit negligible) of the particle being found in Jupiter in the next moment, even though the particle is currently on earth at the present moment. However, that breaks the relativistic mechanics assumption that nothing can travel faster than speed of light. We know for a fact (based on observations), that it is indeed true. However, the probabilistic interpretation of the wave equation seems to indicate that if you do the experiment enough times (depending on how negligible the probability is), you will get a particle that would travel faster than light.

[@materiasacra]

The Schrödinger equation is inconsistent with Special Relativity. This is obvious from its form: it expresses the non-relativistic relation between energy and momentum, E = p^2/2m + V.

[@rohitguptartg]

Anti-particles were initially invented to construct a relativistic version of quantum mechanics. Those efforts led to Quantum Field Theory, which is a framework that combines Quantum Mechanics and Special Relativity. Now, Quantum mechanics + General Relativity ...... good luck! :)

[@handhdhd6522]

Rohit Gupta this is correct, QFT is QM + SR, uniting QM + GR would yield QG. Then, along with QFT, QCD, QED, we would have a complete unified theory of everything. Someone correct me if I’m mistaken.

[@handhdhd6522]

String theory, m theory, quantum loop gravity are all attempts to unite QM and GR, look into those but it’s very hard, you need A LOT of math

[@abhirambhat9277]

If you find the particle on earth now and on jupiter later, that doesn't mean the particle travelled from earth to jupiter.. So it does not violate relativity

[@서지우-q5l]

Subtitles are delayed little bit over the video. Listeners should change subtitle setting from C.C. to auto-provided.

[@not_amanullah]

Thanks ❤️🤍

[@Balbok98]

That's rather a minor problem, but subtitles are little bit delayed (with respect to audio) at around 6:03.

[@lambda2693]

yes

[@ryancroy]

I haven't even taken High Scool physics and I'm here. Why?

[@davidhand9721]

you tunneled in.

[@toygarozel6261]

@@davidhand9721 that's how to be genius

[@jacobvandijk6525]

Because you want to know how physicists think about 'reality' ;-)

[@shaikhaalbedwawi4104]

RUNNNNNNNNNN

[@3rdEarlRussell]

that’s a great sign!

[@harishravishankar]

Great to see 10 boards to explain science while you need only 1 for school..

[@not_amanullah]

This is helpful ❤️🤍

[@zphuo]

Could some guys give me a hand to explain why "knowing the wave function at one time determines the wave function at all time will run into a big problem"? I am not very clearly understand his explanation at last part of lecture from @7:00.

[@rafaelrobsonlinodossantos5220]

Suppose that you know the wavefunction at time t0 (so, it is normalized at this time). Since the Schrödinger equation is first order in time you can know the wavefunction at any time. The question is "Can you assure that it will be normalized at any other time later? ". It would be great for the consistency of probabilistic interpretation. This question is answered in the next lecture.

[@zphuo]

Yes. Thanks very much.

[@kaushaljain5999]

1:05 to 1:33 Explain

[@jacobvandijk6525]

If you know what the Coulomb-force is (between proton and electron), then you should know how to derive the potential ;-) Here it is: Epot = - k . Q / r

[@naimulhaq9626]

Copenhagen will become complete only when a complete formulation of a complete 'quantum system', like a stable hydrogen atom or a black hole. When a complete understanding of 'state vectors'/hidden variable (which is possible, I don't know how).

[@demr04]

This is the part when you see the math fall apart. It's not bad, but very misterious

[@DagonFF]

The probability interpretation is not "right" like he says in the video. It is the interpretation we use in order have an insight about observable when operating on the wave function. There are other interpretations around, and many physicists, such us Roger Penrose claim the the theory is incomplete and inconsistent. To say that the Copenhagen Interpretation is right is antiscientific and I am truly shocked that this guy said this in a video lecture from MIT

[@lepidoptera9337]

The Copenhagen interpretation tells you exactly what happens in experiments. None of the other interpretations do. In that sense it is the one and only "realistic" interpretation. It's also the only one that you can actually use in the laboratory.

[@DagonFF]

@ that is absolutely false. The Copenaghen interpretation doesn’t tell you anything. So any interpretation will describe the outcome of an experiment mathematically in the same way.

[@lepidoptera9337]

@@DagonFF Dude, I understand that you never spent a single thought on Copenhagen. So what? So nothing. Hint: What does the projection operator in the Born rule do and why do you need it? If you don't understand that, then you don't understand anything. ;-)

[@DagonFF]

@ and what has all this to do with the fact that “Copenaghen is right”? If if was right we would’t have debates about locality, many worlds or non local theories such us pilot Waves or others. Also, what you mean by “right”? That is the correct theory? No such a thing in science lol are you a retard?

[@lepidoptera9337]

@@DagonFF "We" don't have debates about locality. Only people who don't understand physics have these idiotic debates. Quantum mechanics is fully local because if it were non-local then your iPhone would have and ansible, but the universe would also not exist, so it's a wash. :-) Some wave functions are not separable. So what? Wave functions are not real and separability is therefor not a physical property of systems. Quantum mechanics is a system theory that applies to certain systems but not to others. It is absolutely correct (just like thermodynamics) because it is entirely based on mathematics. If a physical system approximates those assumptions sufficiently, then quantum mechanics applies to it necessarily. There are no loopholes. The main assumptions are independence, unitarity and Poincare symmetry. In my opinion both independence and unitarity follow from Poincare symmetry, so at the end quantum mechanics follows directly from Poincare symmetry, which in turn is nothing more than the modern way to talk about Galileo's relativity principle. Seriously, Dude, you are giving the best example of Dunning-Kruger on the internet today. ;-)

[@Schrodinger2218]

Why we use complex function to represent a wave function ? If we used imaginary think to represent a wave function then why we study about quantum mechanics if its wave function have no physical significance😢

[@lepidoptera9337]

Because they are a solution to Kolmogorov's axioms about statistically independent experiments. There are at least two significantly different solutions to these axioms. One is probability theory, the other one is quantum mechanics. Even that is a slightly misleading way of looking at it because in reality the most general such experiments are being described by a formalism that is called "the density matrix", which combines both quantum mechanics and probability theory into a single entity. Many important quantum systems (like those at T>0) require that formalism, so we should really say that nature implements the most general form of Kolmogorov and we just happen to have separated it into two independently taught special cases for historical reasons.

[@purvathakre5625]

This lecture is out of order in the playlist.

[@mitocw]

Thanks for the note! Fixed. We'll take another look and see if there are any more that need fixing.

[@clasicus]

@@mitocw Hello! Thank you very much for video! But I want to say that subtitiles little bit not synchronized with video. Thank you!

[@vs6x3]

3:40 board😆🎆

[@priyanshu7206]

जयबाबाकी❤

[@Jo-ti6vz]

Ohhhhh

[@arlennedlr]

This is not a very good explanation. Also, he made a mistake: psi(x, t) is not the probability as he wrote on the board, but |psi|^2 is.

[@lepidoptera9337]

Your formula isn't it, either. That's a common mistake in most QM textbooks. In reality we need to use the Born rule. It just happens that the spatial projection operator reduces to unity in case of the wave function in a spatial basis. If you go away from that basis, then it doesn't. The Fourier transformation of 1 is a delta function, i.e. if you were to use the k-space representation of psi, then there would have to be a different measurement operator in there somewhere. I don't know why the theorists are getting this so wrong. You could not possibly get away with this nonsense in textbooks on linear algebra, differential geometry or general relativity. Heck, it probably won't even fly during a discussion of coordinate system transformations in Hamiltonian mechanics. It's only in introductory quantum mechanics that everybody and their grandmother keeps repeating such an egregious mistake (and have been for like a century now).

[@davidhand9721]

There is no way to prove that a process is indeterminate and probabilistic. It's mathematically equivalent to introducing a hidden variable, between 0 and 1, which fluctuates in a way that we do not yet understand, but it selects a percentile along the probability curve. There is no logical difference, except that accepting probability precludes any further endeavor to understand the laws of nature. It tells generations of physicists "don't even try to understand it, we decided a century ago that we know everything that can be known, therefore this cannot be known. So if you feel like asking questions, shut up and calculate instead". More evidence that these Copenhagen folks had their heads inflated a bit comes as soon as we talk about renormalization. If your theory tells you that an electron has infinite mass, then your theory is simply wrong. But in quantum physics, we let that one slide and pretend it was right for further calculations. There is still no good reason, according to QM or QFT, that an electron has finite mass, but we obviously can't know anyway. Any other model that creates ridiculous infinities all over the place would have been rejected a thousand times. Quantum physics seems to be more a religion than physics. It tells you what to value, what to discard. It shuts dissenters up and punishes them. It asks us to believe something that is bizarre and alien. It even has sects. And when we find an inconsistency, we categorically deny it or forgive it instead of looking for something deeper. /rant from someone not remotely an expert but who has searched exhaustively for answers.

[@Stoikpilled]

quantum physics is more engineering than science

[@shenanigans1231]

I feel so bad, I spent the last 30 minutes crafting a response to your comment because I believe we've had similar perspectives on the issue but alas my computer bugged out. To make a long story short, most cutting edge research borders on mystical. I have no doubt that that which is accepted by the scientific community in the future will be added to the pool of common knowledge and that which is rejected will be damned to the realm of the esoteric. That being said, it is entirely possible that materialism is not a correct depiction of reality. I think if you ask mathematicians you'll find that while some believe they understand the nature of reality, most do not. Math like many thing is open to interpretation. When you really get down to the essence of math, the properties assigned to numbers and the axioms which govern the mathematic realm, I think you find that there are many biases, math is not as pure as people would like to believe. I think you want there to be a hidden variable and for materialism to remain consistent(I definitely did), but I think it's important to keep an open mind. Good luck finding an answer.

[@jacobvandijk6525]

In religion there is nothing to prove. In QM there is. Science is all about testing theories! That's why I don't like word theory in String 'Theory'.

[@jorriffhdhtrsegg]

-Quantum idealism! -Parallel worlds! -totally random, man! And here's me constantly wondering whether there is some codification of an epistemic effect in quantum physics. This would involve description of what the subject knows, and inherently describe a subjective effect. So "looks like consciousness but not in the way you think it does" They don't usually adress that effect and yet our epistemiological assumptions should be addressed prior to ontological ones. Maybe someone can help me there. I've seen some deweirding descriptions about quantum eraser so i don't see why its not a major possibility, even if we cannot specifically describe it theoretically still

[@HumbertLaxness]

@@shenanigans1231 Well put

[@thedouglasw.lippchannel5546]

Sigh...

[@kumar-qk2pr]

Kya bol rhe ho uncle😁😂😂😂😂😁😁😂

[@ashishkumarsharma1323]

thodi respect dikha, professor hain vo!