Breaking Quantum Physics (But Not Really): Mixed States + Density Operators | Parth G

[@domainofscience]

This was brilliant! Perfect explanation.

[@GouthamR013]

Better than you😂😂

[@Arman_Shamlewale]

Whoa 😮 Mr. Walliman is here! I truly like your books. Keep going!

[@sjnscnslsf]

​@@GouthamR013 Wtf? He literally tagged domain of science and said that they have a way better and full mathematical explanation..!?

[@risingredstone5949]

minor error at 2:50 both the arrows in the first two spin states upwards, one has to point downwards

[@sagnikdey828]

I have been so confused with the concepts of pure and mixed states and the density matrix for so long, and watched numerous videos on KZbin. But finally I got it clear after watching your video. Thanks Parth, it was a brilliant explanation!!

[@upsal.nanayakkara2457]

wow man . its not about the mixed states but this is the simplest yet most detailed explanation of density matrix . you can find tons of videos people are trying to explain density metrices yet couldnt make a single sense even with math. Brilliant how you summered an entire 2 hour lecture to a 7 minute video. just brilliant .

[@kyozpsycho]

EXTREMELY USEFUL, starting to see the path.

[@triviumdaniel]

At 2:48 the arrow in the spin down ket is upside down. Great video overall keep it up dude!!

[@gazsibb]

That's peculiar, in my branch of the multiverse the arrow is pointing down... 🤣

[@IragmanI]

Honestly, I don't even know how I exist some days.

[@rsbenari]

Brilliant. An essential and much needed, intuitive intro. Thanks.

[@MusicEngineeer]

thanks for clarifying this. the terminology is really confusing here. i initially thought, a "pure" state is something like "100% up" or "100% down" - as in: no superposition. and "mix" would be kinda synonymous to "superposed". so, what are these "100%" states then called? basis states?

[@ParthGChannel]

You could call them basis states for sure! They're not really too different from any superposed state aside from the fact that they happen to be in a possible experimental result state. :)

[@MusicEngineeer]

@@ParthGChannel i guess they are not something special because the basis is chosen arbitrarily anyway?

[@portugalforme1198]

Terrific explanation....saved me a good few headaches.....thanks very much for posting.

[@shreyaspradhan8546]

Damn that was super intuitive. Perfect explanation. I wish all sources were this clear and intuitive.

[@dasmolduck]

Hi Parth, Thanks for making the video. Have a few questions that I am not quite sure - 1:47 Should it be 1/2 rather than 1 / sqrt (2) - 2:49 Should the middle equation be spin down

[@AdrianBoyko]

A1: No, it is 1/sqrt(2), AKA sqrt(1/2), because that number *squared* gives the probability for the associated state.

[@AdrianBoyko]

A2: Yes! Good catch!

[@DavidAspden]

Great length and good content density.

[@massmanute]

I have been trying to understand density matrices for a long time. Let me ask a question. Is it possible to do physics and chemistry without density matrices? I am not sure I can fully articulate what I mean here, but let me try. Suppose there is a physical system that is in a pure state. I will call it a nonstationary state, simply because that is the terminology I am used to. Now suppose that this nonstationary state is a superposition of the eigenstates, with the absolute values of the coefficients being weighted according to an exponential function of the energies. (Basically, the eigenstates in the nonstationary state are weighted according to Boltzmann statistics. Now let a say that the phase relationships between the eigenstates in this nonstationary state are unknown to us (Perhaps it could be known to an omniscient being, but I am using the word "omniscient" in a kind of metaphorical sense, not a metaphysical sense.) Is there any experiment that can distinguish such a state from a mixed state with the same (Boltzmann) energy distribution? If not then we must consider mixed states to be a convenient but not strictly necessary way to describe nature, or at least that part of nature that relates to statistical mechanics. One could extend this question to other types of nonstationary states, i.e. states that are not Boltzmann-weighted, but for sake of discussion let's limit the discussion to the simple question posed above. Now a related question. I seem to recall reading somewhere that mixed states do not obey time dependent Schroedinger wave equation. Is that correct? If so then how do we interpret the meaning of the Schroedinger equation? In other words, if mixed states are necessary, and they do not obey the Schroedinger equation then Is the Schroedinger equation a valid description of nature or not?

[@stevenschilizzi4104]

Brilliantly crystal clear! Please keep doing these! Many thanks.

[@SomethingImpromptu]

In your example about an electron source you said that it sometimes spits electrons out with spin up, sometimes with spin down, & sometimes a superposition of the two... I thought the way it worked is that the spin state will always be a superposition until observed, & after observation it will always either be spin up or down. Is that incorrect? My impression was that the collapse of the wave-function occurred because when you observe it, you bounce photons off of the wave-particle, which interferes with the wave-function & forces it to settle in a particular state, so you wouldn’t have an electron source that just straight up spits particles out sometimes in a particular state & sometimes in a superposition. At any rate, extremely interesting & well articulated video. I had never heard of these mixed states & quantum theory just gets more mind-blowing with every new thing you learn about it. The nature of our reality is truly just about the strangest & most amazing of all possibilities.

[@AdrianBoyko]

Hi Matthew. Your assumption that an electron is in a spin superposition after being measured is incorrect. Consider this: If an electron is in a superposition of spin states and you measure its spin, it will collapse to to up or down. If you then measure the spin of *the same electron* a second time (in the same direction) you'll *always* get the same answer that you got from the first measurement. This is because the electron is not in a spin superposition going into the second measurement. So, think of the his source like this: Inside, it produces a stream of electrons each of which is in a 50% up / 50% down superposition. The source also has a random number generator that randomly produces "1", "2", or "3" each time you ask for a number. For each electron in the stream it produces, the source will get a random number. If the number is "1", it will let the electron out of the source as it is, in superposition of up and down. If the number is "2" or "3", then the source itself measures the spin of the electron *before emitting it*. This internal measurement forces the measured electrons into state up or state down, with 50% probability for each. As a result, the electrons emerging from the source are 1/3 superposed, 1/3 up, and 1/3 down.

[@bapanbiswas4678]

Sir please one details video on gradient 🙏

[@prashantlale4976]

That was astonishingly great and i like the change in your background.

[@avnishsaravanan7052]

Parth this was a great explanation. I'd just like to add one thing. We do not know if the wavefunction collapses out of superposition into one single reality like you said (Copenhagen interpretation), or if we only see ONE of the many alternate realities (Many Worlds interpretation). BTW I love quantum physics and your videos teach me a lot. Thanks!

[@moondo60]

Parth You are an answer to many prayers, namely that of bridging the gap between those of us who are rudimentary or Ancient calculus Education, but I rather more profound Interest in the subject at hand Thank you kindly and I’m going to patrion

[@bryanreed742]

There's what I think is an important point missing at about the 4 minute mark. There is no possible set of measurements you can do to figure out those pure states and their probabilities. All measurement outcomes can be calculated from the density operator, and there are infinitely many ways to mathematically decompose a mixed state into pure states. Any particular decomposition is just a calculation tool we use to analyze the problem. There's no reason to think that there's an actual fact of the matter as to which decomposition is correct. Additionally, it's not merely difficult to produce a particle in an absolutely pure state. It's actually impossible. It would mean creating a state with exactly zero entropy with finite time, energy, and control. It can't be done. In the real world, everything is entangled with its environment at least a little bit. You can get very very close to preparing a pure state, but you can never achieve it. It's like absolute zero. The surprising implication is: in the real world, particles don't have wave functions. As usual, the short version of the statement is lacking some nuance, but it's still essentially true.

[@nirmalbk9531]

Finally ...i get it ❤the concept of mixed state

[@haha-qj8pw]

Can you do a video on the photovoltaic effect? Which science options did you pick at first year undergrad and can you talk about how they were except the physics option? I am considering a physnatsci application submission and I am wondering what the chemistry and material options are like, compared to alevels.

[@AdrienLegendre]

Parth, well done!

[@theartofmusic05]

Good explanation Parth your videos make me love more physics..

[@Draginx]

Parth, you're my favorite youtuber! You make amazing content and you're a great teacher and you motivate me to do better at physics! You make me remember why I love physics and science so much. Bet you won't reply to this...

[@sudeepghosh7723]

Typo at 3.01, the |Phi> in the middle should be down.

[@rajgupta759]

Bhaiya please make a video on fine structure constant.

[@ProCoderIO]

Nice blend between math and concept.

[@ahammadnafiz3705]

your explanation level is ultra ..

[@bragoen]

Somehow it had never occured to me that a mixed state was different from the superposed state. I thought that's what the superposed state was, just a representation that it is unknown and behave as both. The more you know

[@MysteriousSlip]

I am giving 'thumb's up' to every video of yours that I find well presented and useful. So far I am just spamming upthumbs to you. I wish the best for your channel because I truly believe you deserve it.

[@daphenomenalz4100]

Thank you I have a question(sry it's a stupid question 😅) Does Parth G like Parle G?

[@shreyanshsrivastava5888]

please upload video on stern gerlach experiment if possible , I had not get any good explanation of it in youtube

[@rc5989]

Mind. Blown.

[@malcolmscott4595]

Hi there knowing nothing about physics I'm sure that I am wrong but as you say the 'superposition' state proceeds measurement. Thus an electron in our system is either spin up, spin down or unknown. Unknown is describes as a superposition but is it really in both states at once or is it that we just don't know its state. I guess this gets back to what does the wave function actually represent. Is it just a Mathematical tool for calculating probabilities or does it have something that corresponds to it in reality.

[@Jehannum2000]

The evidence suggests that the superposition really is an undefined state and not merely a reflection of our ignorance of its true state.

[@devashishshah9021]

Awesome videos... pls make a full course on QM.

[@ayushscientistphysicst2726]

Please give the information of physics papers published

[@arjyadebsengupta8159]

Thank you sir for these wonderful videos

[@TeluguAstronomer]

Sir can please answer why gravity is towards center?🙏🙏🙏

[@Jehannum2000]

If you add up all of the little attractions between atoms, the resultant force acts towards the centre of Earth.

[@antonhibl4083]

Amazing explanations, Thanks so much!

[@ill_eye]

How can we distinguish up or down vs superposition of two by measurement? We are measuring only up or down, right? So how can it be 1/3 up, 1/3 down, 1/3 superposition of two? Ah, this is confusing...

[@ill_eye]

Nevermind, watched Professor's M video, can't say I got all of it, but I can kinda see now how these are different.

[@ChiDraconis]

@@ill_eye The Muon g-2 → What I studied came up with a minus sign and a zero on the Bottom Quark and did not bother to try for the up quark as it seems to be quite a zoo ○ Current effort is to determine if Stern-Gerlach up/down has anything to do with the observation being in a gravity well → In other words if Top Quark / Bottom Quark is affected by a resonance with gravity

[@avnishsaravanan7052]

Awesome explanation. Just one question: why is each state in the superposition given 1/sq rt. 2 rather than just 1/2 ?

[@pranavk9685]

That's because the probability is given by the square of the absolute value of the wave function, i.e, |ψ|^2, so since the probability of each of those states is 1/2, the coefficients in the wave function have to be 1/√2

[@avnishsaravanan7052]

@@pranavk9685 ohhhhh now I get it. Thanks.

[@khaithatton9266]

Really awesome explanation! Keep up that work!

[@IWKFF]

Can you start quantum physics how to make equation series just like you have made an equation of black hole

[@chqaisar4381]

Make a video on pauli matrices

[@juantkastellar2655]

Sencillamente fenomenal. Gracias.

[@aryanbhatia6992]

thx for the super clear explanation

[@birendrachhotaray2263]

Hi, it's a nice video! Could you please explain why density operators for the mixed states are added(not multiplied)?

[@joeeeee8738]

Because the probability must add to 1

[@matt_hart]

don't worry about the quantum stuff, just think about it as normal probabilities: if you have a 0.5 probability of one outcome, and 0.5 of another, you want to add them to get the total probability of being either outcome as 1. if you have a 1 probability of one outcome and 0 of another, you add them to get a total probability of 1 multiplying gives you the probability of getting both (probability of getting heads AND tails in two tosses is 0.5 x 0.5 = 0.25)

[@himanshumishra7718]

How do u make ur video? Please make a video about it.

[@Jop_pop]

At 2:55 the second state is the same as the first - just FYI!

[@badlydrawnturtle8484]

It would seem there's a conceptual problem, here: How would you tell the difference, experimentally, between an emitter that produces some spin up electrons and some spin down electrons versus an emitter that produces electrons with superposition of spin up and spin down? Wouldn't you get the same measurements either way? What experimental evidence can there be in support of the conceptual separation of these mixed states from "true" superposition states?

[@schmetterling4477]

Stern-Gerlach is your friend.

[@badlydrawnturtle8484]

@@schmetterling4477 The Stern-Gerlach experiment doesn't appear to have anything to do with superposition, so I'm not sure how it could answer my question.

[@kamalay.c.9734]

Excellent. Well explained...

[@android01978]

One thing I’ve always wondered is; if a superposition always collapses into one state or another when measured, how do you know it wasn’t in that state already? (Hidden variable?) isn’t the superposition just the representation of the probabilities before measuring?

[@drdca8263]

Well, for one thing, with entanglement, the ways that outcomes can be correlated are more varied than they could be with just a hidden variable. But, not even getting into entanglement, if you have e.g. a sequence of electrons where someone claims that all of them are in the state (|up> + |down>)/sqrt(2) , if their claim is true, if you measure the spin of each along a specific different axis (not the up/down axis, but one perpendicular to that) you will get the same result each time, If instead the 1st, 3rd, 5th etc electrons were all in state (|up> + |down>)/sqrt(2) , while the 2nd, 4th, 6th etc were all in the state (|up> - |down>)/sqrt(2), if you measured each along this particular axis, the 1st, 3rd, 5th etc. would have one result, while the 2nd, 4th, 6th etc would have the opposite result. Meanwhile, if you measured any in the up/down direction, you would get a result of up half the time and down the other half of the time. Splitting things into the up part and the down part is just one choice of basis, and one can choose any 2 opposite directions for the basis to express things in.

[@neoleosoul]

Correspondence (6:21) "Georg Cantor"

[@fuzzylumpkin8030]

Thank you always

[@semmering1]

I live in the city where Schrödinger lived, and Boltzman, and Pauli..... This is the first time I really understood this... Thanks Parth!

[@matt_hart]

just like how we need vectors to represent superpositions of possible measurement values, we need matrices to represent these "superpositions" of possible vectors

[@snehasismaiti342]

2:47 Please rectify the spin down notation.

[@TarekAbdelmoniem--]

Thank you

[@WhitefirePL]

I don't accept the logic of not knowing (mixed state) being different from not measuring (superposition state). Yes I imagine this can lead to all sorts of further problems. If you go this way, you could add 5th state: up, down, superposition, mixed and "I don't know but I also don't want to know" :)

[@drdca8263]

“Superposition” isn’t a single state, it is a description of a state in terms of other states. You can describe a state as being a superposition of up and down, for example, you could describe spin left as a superposition of spin up and spin down. But you can also describe spin up as a superposition of spin left and spin right. For a single particle, you can basically* describe the spin state with a direction (like, any direction, not just the main coordinate directions), and this is equivalent to specifying it as a particular superposition of spin up and spin down. *small caveat : this throws away the information of the overall phase, but for a single particle, this is not observable, and so basically doesn’t matter. Alternatively one could use a direction along with an angle around that axis/direction.

[@WhitefirePL]

@@drdca8263 I appreciate the explanation. It corrects my (apparently) lousy use of word 'state'. But the logic of unknown vs. unmeasured still seems like just a semantics trick rather than a thing of reality.

[@drdca8263]

@@WhitefirePL you might want to look into the EPR paradox and Bell tests. There have been experiments which provide strong evidence against what is called “local realism” (“realism” is, if I understand your position correctly, basically your position. “Local” refers to there being no faster than light influences in a certain sense.). Basically the only loophole remaining to allow for local realism is “superdeterminism”, which would essentially mean that the experimenter can’t actually choose parameters for the experiment freely or randomly, and would essentially imply that the whole universe is “conspiring” to force what things we “choose” to measure be the ones which would result in outcomes which match the theory. This hypothesis seems like it would undermine the possibility of doing science if it were true? I think we should reject superdeterminism. Therefore, there are really only 2 options: reject locality, or reject realism. I think rejecting realism is the right interpretation.

[@schmetterling4477]

The math simply describes the fact that measurements are not repeatable. Unless a system is in a pure state, already, a measurement of that state will give random outcomes. This is an easy experimental fact and you can't get around it. All you can do is to describe it and that's what the formalism does.

[@pranavk9685]

In the example of the electron source you mentioned, how can we find the density matrix? Say we measure the spin for lots of electrons, which gives us the total number of spin up and spin down. How can this be used to calculate the density matrix? Love your videos btw

[@DanielaAngulo]

Hi! Try to look for something called quantum state tomography. What you're asking for is an inverse problem ie reconstructing the state from a given set of measurements. It's a very interesting question :) take a look at that subject.

[@nileshkulkarni6196]

Hey parth will you please make a video on how there is supposed breaking of newtons third law when two charges are moving perpendicularly like ⬅️⬇️ and why the electric fields and hence forces are not equal and opposite........also tell the relationship between this and special theory of relativity.....it’s a request from a huge fan

[@psiwavee]

Great video

[@namanjain989]

OK but how can we use the density matrix for the meixed state and I actually want to ask what does the densirty matrix tell us

[@vivekc8563]

so i understand you getting the probability as something like this: the 1st 2 times you get to know whether its +1/2 or -1/2 and you don't know what spin the third electron would have?is it right? if I am wrong, pls do feel free to correct me.

[@schmetterling4477]

A mixed state is not a description of two electrons. It describes what we can know about an infinite number of repetitions of the same experiment.

[@amshumansharma6967]

love from India bro

[@siddharthmishra7504]

Sir please make video on“ GODEL'S INCOMPLETE THEOREM” PLEASE SIR

[@JohnVKaravitis]

COOL!

[@ruddyxmax]

Easy and exact

[@Frank-si2jd]

How can you measure a superposition (spin up or spin down) of the electron if the moment of measuring collapses the ‘super position’ state immediately to one of the states - spin up or spin down?

[@Jehannum2000]

You measure lots of identical states and see the distribution of probabilities.

[@drdca8263]

You can measure along a different axis! If the spin up state refers to the state after you measure it to be up when measuring in the z direction, the various superpositions of the up and down states are such that there is a particular direction where if you measure it along that direction, you always get the same result. So like , (|up> + |down>)/sqrt(2) could be the same as |positive x direction> (and then (|up> - |down>)/sqrt(2) would be |negative x direction> ) The idea of the Bloch sphere is closely related.

[@frankwitsel9326]

@@drdca8263 dear drdca, thanks for responding to my question. I was and - unfortunately - still am struggling with this difficult physics subject. To my idea "measuring" a superposition must be based on theory and derived (indirect) measures/outcomes, like is done in using a quantum computer, but cannot be "measured" directly. If I'm wrong, I hope to hear about it from you. Kind regards, Frank

[@amaanabbasi9443]

Cell and subcells are confusing me does a cell have same energy for all particles or subcell ???

[@jayfordbersamin6042]

well said

[@joeboxter3635]

This is a GR question. Is GR generally lorentz transform invariant?

[@dhritimanroyghatak2408]

Only under weak field approximations

[@colepenick5238]

Good shit G

[@aclearlight]

Great work!

[@shreyasgkamath5520]

Parth Congratulations, your video has been added to MIT open Courser ware along with Walter Lewin lectures

[@ayushscientistphysicst2726]

Sir how to publish physics papers

[@DanyalShabirr]

Publish😂😂😂

[@DanyalShabirr]

abhi tujhe bahut padhna hai

[@dhritimanroyghatak2408]

Well it's really simple write a paper with correct format which is accepted for a research journal (you can get all the required information online from various Physics journals and other Research paper for reference). Then they will check for plagiarism (whether it's your original work or bluntly copied, you can take references but need your original idea) then finally you will probably have to explain your idea through presentation in a conference (which most probably the journal will organise for you). Now if everything works in the end then your paper gets excepted and then finally published. But yeah you will face a lot of difficulty if you are not associated to a reputed institution or research group. Else you can always pay editors to let your stuff get published (Lots of less known journals do so to make revenew but if you are looking for a reputed journal then it would not be possible). Hope this helps. But really all the information is present online.

[@upsal.nanayakkara2457]

should be outer product of two vectors

[@pratichipattnaik1260]

Awesome

[@nsfeliz7825]

i like the way u minimize the math, but not eliminate it totally. just enuf math to get a foothold.

[@pritivarshney2128]

Amazing video!

[@tanvirfarhan5585]

zero point energy ?

[@ishtvibhu]

Great

[@1jj598]

Q SER ILUMINADO DE DEUS OBRIGADO AJUDOU IMENSAMENTE

[@bibeshbasnet2568]

Solutions of einstein field eqns!!

[@BorisNVM]

I FUCKING LOVE U

[@thelocalsage]

great video I learned a lot !((:

[@alphalunamare]

Are not the 33% just artificial numbers to make the video flow easily?

[@AdrianBoyko]

The probabilities for the pure states could presumably have been any three percentages that add to 100%. It probably would have been better for viewers to see three different values - it wouldn’t have complicated the math.

[@PaulMarostica]

Parth: Your explanations of quantum mechanics theory are clearer than those of many others. But since quantum mechanics theorists have no idea what a particle’s spin state really is physically, you are limited, here, to demonstrating how probabilities of spin states are represented mathematically in quantum mechanics theory. You are not actually able to logically explain to your viewers the physics represented by the math. I think this is because, unfortunately, many physically illogical quantum theory assumptions were invented, in whole or in part, to try to explain the surprising results of various particle 2 slit experiments. For a new, unique, logical, wavelike field theory explanation of those results, using assumptions which completely contradict, and eliminate any need for, all those physically illogical quantum theory assumptions, you can view my KZbin video, "Particle 2 Slit Experiments Explained By Paul Marostica". I'm curious to learn what you think of it.

[@schmetterling4477]

You need to read up on quantum field theory.

[@lucientjinasjoe1578]

Call the beast by his name in what environment you meant reality

[@grajalessuarez8272]

this topic is very interesting, please can you place subs in spanish? pleaseeee

[@sahebkhan5395]

Bro my question has no importance please check my question

[@manasandmohit]

What about a day in the life video, it's been three years now

[@stevesastrohowardkings2245]

Study this stuff a while. ago for fun seen another System design by spacing stuff In my notes forgot the guy Name for atoms system i think can come up with another system to do with another unknown factor no has thought of It kind fun to fry the brain I believe a good point by everyone I don't doubt theirs rights and wrongs I except i don't have use this stuff to make a living i don't think all scientist Are always on path together to do with Time it takes to study everything And reject before completely thinking Using a piece of all of it thank

[@CHURINDOK]

Lucky guess, Parth.

[@ppa011]

I have a degree in physics. I would like to know what jobs I can get with a degree in physics.please answer me,thank

[@ayushscientistphysicst2726]

Please reply me

[@ankittiwari1647]

don't mind the dislike I just envy you.

[@physicsmathsandbasketball]

plsssssssss give me a shoutout plzzzzzzzzz