College Level Quantum Mechanics (Zero Prerequisites)

Поділитися
Вставка
  • Опубліковано 23 лис 2024

КОМЕНТАРІ • 127

  • @LookingGlassUniverse
    @LookingGlassUniverse  9 днів тому +3

    I'm making a live version of this course and the first cohort starts this week- I'm closing signups by this Tuesday (sorry, I know that's very soon!). The lectures will all be free and. available on youtube, so the course is just for those who want to go a bit deeper by doing homework problems, a weekly tutorial, and asking questions. If that sounds interesting to you, there's more information here: looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals

  • @SamAlegria-tg4qu
    @SamAlegria-tg4qu 23 дні тому +50

    Did we just get 3 looking glass videos in a week and 2 of them are about quantum mechanics? I'm beyond excited 😂

  • @adityapotukuchi4043
    @adityapotukuchi4043 23 дні тому +16

    YIKES!! Essentially all I understand in quantum mechanics comes from your videos from some 8-9 years ago. Everything about them, the history, physics, mathematics, art style, colors, and the Alice theme make them (imho) the gold standard in communicating science with a substantial theoretical component. I had just started my PhD (not quantum), and they inspired me more than anything, to maybe try something like this myself. I am absolutely excited for this series. Thank you so much!!!

  • @siddhiagrawal7887
    @siddhiagrawal7887 23 дні тому +7

    Oh my god, i'm in 12th grade rn and like quantum mechanics is not in our syllabus but i've wanted to learn about it since soo long! Aahh i'm soo excited for it!!!

  • @poogitypooheh
    @poogitypooheh 23 дні тому +4

    Great video! Impressive how little maths you used, and what little there was, was 100% explained, even quite basic things! I feel like these videos are going to be a resource I am going to be returning to in the future!

  • @peetiegonzalez1845
    @peetiegonzalez1845 22 дні тому +4

    Oh man, this takes me back. I originally discovered your cute educational videos about QM when I was learning about it almost 10 years ago. ViaScience, whilst very dry, had the most complete yet understandable content back then but you explained some things in a really good way. Quite looking forward to revisiting it with Mithuna and maybe Alice again.

  • @MaximoJoshua
    @MaximoJoshua 23 дні тому +8

    You are such an amazing science educator!

  • @pranavmistry3225
    @pranavmistry3225 17 днів тому +1

    I know next to nothing about QM or physics, I started this video randomly while having dinner, It is so lite and engaging that I am 30 mins in without pausing. Amazing work! I hope you keep this up :)

  • @brucegray8591
    @brucegray8591 11 днів тому

    Very good intuitive explanations! I worked through Lenny Suskind's UA-cam lectures and book a few years ago, and struggled mightily early on to get my mind around the basics. I feel your videos would have made a good introduction and saved a lot of the struggle.

  • @username-password
    @username-password 23 дні тому +2

    Thank you! looking forward to future episodes

  • @ciencialogica7783
    @ciencialogica7783 23 дні тому +1

    Learning is good, but understanding is better. There are things to accept (learning) and there are things to question (understanding)

  • @tcaDNAp
    @tcaDNAp 20 днів тому +1

    0:00 welcome back
    1:00 laser system
    5:25 filter mystery
    8:40 measurement collapse
    12:00 vector measurements
    16:00 superposition
    20:00 more examples
    26:00 dot product probability
    30:17 laser example
    35:00 photon filter
    38:16 recap preview

    • @tcaDNAp
      @tcaDNAp 20 днів тому

      Dr. Yoganathan spaced out the checkpoints so regularly that pressing almost any keyboard number will skip to the start of a section! It helped me get these notes just to show that not everything is a nice round number (but I was tempted to drop the 17 seconds from the 30 minute mark)
      9:49 rule 3 done
      29:48 live courses?
      31:55 Different mic!

    • @LookingGlassUniverse
      @LookingGlassUniverse  20 днів тому +1

      Do you mind if I steal these?

    • @tcaDNAp
      @tcaDNAp 20 днів тому

      @@LookingGlassUniverse I was hoping you would say that! Go ahead and steal them, and you can change those numbers to be even more round too 😛

  • @BenjaminGatti
    @BenjaminGatti 21 день тому

    In the US: Polaroid is a brand, polarized and polarizer describe light states and tools for interacting with light based on polarity.

  • @negativevariance1363
    @negativevariance1363 22 дні тому

    Excellent video and explanation. A humble suggestion I would make is to show explicitly how you get the same result, especially for the counter-intuitive double filter case, using two different orthonormal measurement bases. Also, you could emphasize even more that the superposition states don’t mean that the light is aligned in all directions at once or some similar notion. Rather according to the orthodox interpretation, a superposition means there is no defined polarization before measurement. It would be a type of “category error” to even ask that question. As the physicist/philosopher David Albert put it, it’s like asking what is the “marital status of the number 5.” Of course other interpretations attempt to rectify this problem, but that’s beyond the scope of your basic course…

  • @obviouslyblack
    @obviouslyblack 21 день тому

    My favorite interpretation of dot product is a scalar projection. I like looking at it as such "If one vector is the floor and there's a Sun directly above it, then the dot product is the length of the shadow of the other vector on that floor".

    • @CrazyShores
      @CrazyShores 21 день тому

      The dot product is not a projection, it's a scaled (magnified) projection!

  • @generichuman_
    @generichuman_ 23 дні тому +2

    I've been trying to wrap my head around quantum mechanics for a while, and there's an intuition that's incredibly hard to shake. It's this idea is that, for example, the uncertainty principle shows that we can't measure a particles position and momentum precisely, but surely an exact position and momentum must exist in reality, despite our inability to measure it. I noticed myself having this thought and I started to wonder why?
    It makes sense as an evolved creature to have a heuristic, a modus operandi that applies an intuition to things unseen. My coffee cup in the other room is probably still sitting on the table, despite it not being in my view. Object permanence in this case, is a useful heuristic. I think where we run into trouble, is when we apply these heuristics to the fundamental underpinnings of reality, which have no obligation to be intuitive. We acknowledge the wacky math, and accept that it gives us the right answer, but still we snap back to the idea that underneath that, things must behave the way we think they should.
    A second of reflection shows how unproductive this thinking can be. It feels right to think of particles as billiard balls, for example, but a billiard ball is a collection of about a septillion particles. So we're using a septillion particles to develop an intuition for one particle...
    When we look at things in this way, it begins to make more sense why physicists treat reality as what we can measure. The laymen has this false notion that the world consists of definite objects in definite positions, and these intuitions run through to the base level of existence, when in reality they are an arbitrary convention, a world model built by natural selection to maximize survival of creatures living in a world of medium sized objects travelling at medium speeds. The world is only what we can measure, because beyond that, there's nothing that we can say about it.
    I know this is a little tangential and philosophical, but I thought you'd be a good person to see if my "intuitions" are correct here.

    • @LookingGlassUniverse
      @LookingGlassUniverse  23 дні тому +4

      Yes, you're quite right! We really aren't suited for understanding the reality of things at a quantum level. We just don't operate in the regime where those laws are usually relevant.

    • @brothermine2292
      @brothermine2292 23 дні тому +1

      You should also question the assumption that the tiny things are "particles." Although that term is often used by physicists, it's shorthand for an excitation of a quantum field.
      It's possible that "waves" is a much better description of the excitations. But these couldn't be "classical" waves... they must have a strange Locality-violating property: whenever two waves interact, they interact as if all of the waves' energy is entirely at the interaction location, even though the waves were widely distributed in space a moment earlier. The founders of quantum mechanics were very confident that the Locality axiom always holds, so they favored particle models even though particle models require other strange properties.
      The Locality axiom is: "Nothing can be influenced by anything outside its past lightcone." (Einstein, Podolsky & Rosen named it Separability in their famous 1935 paper known as EPR.) It's related to the idea that the speed of light is the maximum speed of causal influences.

  • @jamie9060
    @jamie9060 15 днів тому

    This is one of the best explanations I have seen. I am hoping to be a part of your first cohort!
    I think a large gap in my understanding (and maybe others with a decent background in math/ science outside of QM) is the naming and terminology conventions.
    A particle of light (a boson, a photon), is not in fact a particle. QM uses that term for historical reasons.
    The continuous variable of the angle of a light wave’s oscillation (with a basis in a plane orthogonal to the direction of transverse travel) is called the “state.” Is there a more specific term to describe that angle? I would call it the “angle of oscillation.”
    The term superposition can have a few meanings: the math representation of a single vector by 2 basis vectors. Or the retroactive characterization of a position/ state “angle of oscillation” after light’s non-random interaction with an electron.
    Despite these questions, your channel has motivated me to learn more about QM. The experiments feel reproducible and accessible. The explanations are clear, to the point. The content selection is top choice. What could be more interesting to learn!
    Thank you

    • @LookingGlassUniverse
      @LookingGlassUniverse  11 днів тому

      Great questions!! As far as I know, there’s not a standard way to describe the angle of oscillation. But the “state” in QM always refers to the wavefunction.
      And as you point out, superposition is a hard to define term. The term comes from thinking about waves overlapping, so mostly I think of it as adding (two or more) basis vectors. The thing that you point out though is that every state is a superposition- if you change the basis. For humans though, we’re very attached to certain basis over others because they are the most natural classically. Eg, the position basis or the momentum basis. So we tend to think of superposition states as ones that have multiple positions in it, or multiple speeds. It’s not very principled though!

  • @ytpanda398
    @ytpanda398 23 дні тому +2

    Hey Mithuna! Always enjoy your videos. Can I ask what made you want to make your own lecture series for introductory QM?

    • @LookingGlassUniverse
      @LookingGlassUniverse  23 дні тому +5

      Hey :) I was looking back on my videos a little while back and it frustrated me that I didn't have a series of videos just explaining quantum mechanics from start to finish. I'd made lots of individual topics, but they were quite disjointed, and the basics weren't all covered. So a few months ago I set about making a really really long video explaining everything... and then it broke into an (at least) 10 part series!

  • @oliviasvahn4090
    @oliviasvahn4090 23 дні тому +2

    Thank you so much for this! ❤️

  • @BenjaminGatti
    @BenjaminGatti 21 день тому

    Tldr: filters "coerce" polarity. It's not a "filter" but rather it's an "operator". If by filter we mean that some quanta are excluded whilst other quanta are permitted. But such a polarizing filter would exclude 99.99999999999_% of light (if perfect) because only 0% of light is perfectly aligned with a perfect p filter.
    But it's not a filter, it's an operator. The "filter" captures about 50% of the light and reorients it. Calling it a filter when it isn't allows us to claim "weird results".

  • @Mushrraff
    @Mushrraff 22 дні тому

    really 2 videos in 1 days and both videos are above 30 mins and i mean thankyou ... 💙

  • @generichuman_
    @generichuman_ 23 дні тому +3

    If you continued to add in filters between the existing ones, at half angle increments (assuming no loss), would the intensity of light approach the original intensity as the number of filters approached infinity?

    • @davidcarter5038
      @davidcarter5038 23 дні тому +1

      I think the "assuming no loss" is the problem. Expressing the incoming state in terms of the two new basis vectors, one will have a coefficient of (say) 0.999 and the other 0.001. So the probability of an incoming photon being transmitted will be (0.999)^2 but the probability of it being reflected will be (0.001)^2, or one in a million which is tiny but non-zero. As the number of filters approaches infinity, the losses build up and the intensity of the transmitted beam will tend to zero.

    • @generichuman_
      @generichuman_ 23 дні тому

      @@davidcarter5038 I don't think the lossless assumption is an issue, after all, this is just a thought experiment, like a frictionless plane. I wrote a little python script to try and simulate this. I iterated from 2 filters (horizontal and vertical) up to about 500, here's the intensity values
      0.2500000000000001
      0.4218750000000001
      0.6054290497131062
      0.7591476665785687
      0.8647211086017267
      0.9279309258713426
      0.9627478761832712
      0.9810541589877853
      0.9904450986764215
      0.9952017921060033
      Looks like it's converging to an intensity of one.

    • @generichuman_
      @generichuman_ 23 дні тому

      @@davidcarter5038 Here's the code
      import numpy as np
      def normalize(arr):
      length = np.sqrt(np.sum(arr ** 2))
      return arr[0] / length, arr[1] / length
      def calculate_angles(num_divisions):
      num_f = (2 ** num_divisions) + 1
      angles = [(i/num_f)* (np.pi/2) for i in range(num_f + 1)]
      return angles
      def malus_law(theta):
      return np.cos(theta) ** 2
      def calculate_intensity():
      for i in range(10):
      angles = calculate_angles(i)
      print(len(angles))
      intensity = 1
      for i in range(1, len(angles)):
      intensity *= malus_law(angles[i] - angles[i - 1])
      print(intensity)

      calculate_intensity()

    • @generichuman_
      @generichuman_ 23 дні тому

      @@davidcarter5038 weird... my comments keep disappearing. I pasted some python code, maybe that's not allowed. I coded a simulation of this to verify and it looks to me like the intensity converges to 1 or full intensity.

    • @Miguel_Noether
      @Miguel_Noether 18 днів тому

      If a filter does not block anything then what's is it doing?

  • @VincentGroenewold
    @VincentGroenewold 23 дні тому +2

    Ohhh awesome! Thanks for making it!

  • @sanjuansteve
    @sanjuansteve 8 днів тому

    The most intuitive way to explain how or why a particle like a photon (or electron) might behave as an uncertain location particle while also like a polarizable axial or helical wave ''packet'', given that everything in the universe from electrons to solar systems are in orbit with something else pulling them into polarizable axial or helical apparent waves depending on the orientation of their orbits as they travel thru space, is that they’re in orbit with an undetectable dark matter particle pulling them into polarizable axial or helical apparent waves as they travel.
    And given that we know we’re in a sea of undetectable dark matter but don’t know where it’s disbursed, we can imagine that they’re in orbit with an undetectable dark matter particle pulling them into polarizable axial or helical apparent waves as they travel where the speed of their orbit determines the wavelength and the diameter is the amplitude which would explain the double slit, uncertainty, etc. No?
    I think Einstein's wrong, that time is constant and that dark matter is the limiting factor to the speed of light. I think it’s not 'space-time' bending but rather gravitational and dark matter density variations.
    #DipoleElectronFloodTheory #WaveParticleDuality #TheoryOfEverything

  • @jimparsons6803
    @jimparsons6803 8 днів тому

    Enjoyed the presentation. Thanks.

  • @BenjaminGatti
    @BenjaminGatti 21 день тому

    The "not perfect" claim is an important jump because it obfuscates a potential bells loophole. Instead stick to either "the data" or "pure imagination".

  • @alandrury9955
    @alandrury9955 21 день тому

    Now you've got me wondering what kind of states require complex numbers to define them. Hopefully you'll be able to come back to this at some point

  • @BenjaminGatti
    @BenjaminGatti 21 день тому

    Looking forward to your comments on Entanglement

  • @eckligt
    @eckligt 23 дні тому +2

    Dear Mithuna, I actually stumbled into that experiment where a "filter" causes more instead of less light to pass through, back when I was just messing about with some polarized sunglasses and a computer monitor. But I have one question about this phenomenon that I've been wondering for years:
    Is there any exchange of angular momentum between the light and the polarized filter? And if so, has someone measured any kind of rotational force excerted on the filter?

    • @LookingGlassUniverse
      @LookingGlassUniverse  23 дні тому +3

      Great question! Can I ask a follow up though? Why do you think there'd be an angular momentum exchange? I thought only circularly polarised light has angular momentum. In the case of that sort of light being measured... I guess there must be an angular momentum exchange to keep the conservation law true! That's really interesting.

    • @eckligt
      @eckligt 23 дні тому

      @@LookingGlassUniverse I fully concede I am using classical intuitions here, and they may or may not apply for proper quantum mechanics (which I have not studied). But here goes: I think of the light packets as wiggling along in a plane, and as they meet a polarizing filter, which acts as a kind of grate, the structure of the filter interacts with the light packets to nudge their wiggle-planes so that they align with the crystalline structure of the filter.
      If the angle between the polarization of the incoming light and the crystalline structure is "more orthogonal", the nudge is mostly ineffective and most of the energy is just absorbed by the filter, and there's little exchange of angular momentum.
      If the polarization of the incoming light and the crystalline structure are already aligned, the light just passes through, and also there is no exchange of angular momentum.
      But if the two directions have an in-between angle, let's say 30 degrees, the energy loss is relatively small, and the light that is let through the filter has its direction of polarization rotated by those 30 degrees, and I imagine this exerts a counter-force on the material of the filter itself.
      Note that all of the above assumes the incoming light is already polarized. If it's a unpolarized, I imagine any such effect to be cancelled out due to the incoming light having an equal probability of exchanging angular momentum clockwise and anticlockwise.
      Again, this is all unfounded supposition. I'd be very curious to hear what a proper scientist such as yourself thinks about it.

    • @eckligt
      @eckligt 23 дні тому

      Replying to myself to add an analogy: Think of propellers. You can have a very poorly designed propeller where the blades are fully aligned with the direction of motion. They wouldn't nudge the water at all, at least not in a coordinated way that would yield a net force. Then imagine the other extreme, the blades are at a right-angle to the direction of motion. They'd cause a heck of a lot of energy to be deposited in the water by churning it up, but again wouldn't result in a resultant force since the interaction with the water would be very uncoordinated. Lastly, imagine the types of propellers that we have in reality, where the blades are at an in-between angle. As the blade moves through the water, the interaction is such that the blade can push on the water, but the water also pushes back.

  • @mikebermea9366
    @mikebermea9366 15 днів тому

    It is interesting that these quantum rules are similar to the rules that one must implement to visualize a 4th spatial dimension.

  • @randbo40
    @randbo40 23 дні тому

    Great video. Why did you use (1/(sqrt2 squared)) for the vector lengths in the first example?

  • @hitoshiyamauchi
    @hitoshiyamauchi 14 днів тому

    This sounds a great series. I am looking forward to.
    23:17 do we always need orthogonal basis? A skewed is not allowed or it is because convenience?
    Thanks for the video! 😀

    • @LookingGlassUniverse
      @LookingGlassUniverse  11 днів тому +1

      Thank you so much!!
      Great question. So the answer is that we need the basis vectors to be 90 degrees apart for a “measurement basis”. That’s because in QM two outcomes can only me mutually exclusive if they are 90 degrees apart. Eg, when you measure something, you can’t get both horizontal and vertical. It’s one or the other. That’s why those two “options” are 90 degrees apart

    • @hitoshiyamauchi
      @hitoshiyamauchi 10 днів тому

      @@LookingGlassUniverse Thanks a lot!
      (I'll see you in the course.😀)

  • @live_free_or_perish
    @live_free_or_perish 21 день тому

    I would definitely watch a video about complex numbers. You always have a novel approach to math and physics topics.

  • @jaykawala3270
    @jaykawala3270 23 дні тому +1

    I'm not familiar with QM, so this question may be silly - but, I'm wondering as far as the model at about 10 minutes into the video goes... if the polarization and intensity of the light can be modelled as a vector, then would the light filtered at 45 degrees be 1/root 2 of the original intensity rather than 1/2? Maybe I'm taking the model too far. Why are we expecting 1/2 the intensity?

    • @LookingGlassUniverse
      @LookingGlassUniverse  23 дні тому +1

      Great question! To answer this, we need to know what fraction of the light would get through the 45 degree filter. It's natural to think it's 1/sqrt(2) because of that factor in the equation. But actually the answer is to look at the probability- since that's the fraction of the light that goes through. To get the probability, you need to square the factor. That gives you 1/2, which is what we expect from the experiments.

  • @lightlegion_
    @lightlegion_ 21 день тому

    Hi! Cecilia here. Wonderful to meet you!

  • @tbur8901
    @tbur8901 22 дні тому

    What happens to the filtered out light, does it turn into heat or a different quantum state or is heat itself a quantum state ?
    Aren't you just filtering out part of the wavelength of a continuous stream of photons ?

  • @Lucidthinking
    @Lucidthinking 23 дні тому +3

    I haven't finished watching yet, but I don't agree with the explanation given at 9:33 that "the measurement changed the light's polarization." I believe it is actually the polarizer's interaction with the laser light that alters the light's polarization. If we had attempted to "measure" this effect using normal glass, it would not have occurred. Therefore, it is not our attempt to measure something that causes this effect; rather, it is a specific interaction between light and matter that leads to the change in polarization.
    We should remember, especially from your excellent videos on electromagnetic waves, that light does not simply pass through transparent materials. Electromagnetic waves interact with the electrons in these materials, causing them to vibrate, which in turn produces "new" electromagnetic waves. The specific superposition of the incoming light and the newly generated light determines whether the light appears to pass through the material, be absorbed, slow down, or change polarization.

    • @peetiegonzalez1845
      @peetiegonzalez1845 22 дні тому

      At some point down the rabbit hole you figure out that any interaction is effectively a measurement. (but also you can measure without interaction, by implication... it's complicated...) Schrodinger's Cat was supposed to be an obviously ridiculous example to stop people using the word "observe" thinking it meant to actually consciously look at. A particle which interacts with a quantum superposition does enter its own superposition and particles interacting with that again enter their own... but the range of possible states shrinks very very quickly as you increase the size or number of interactions, to the point where it would be impossible to differentiate any quantum effects anyway and is essentially "collapsed" for all intents and purposes. Penrose has proposed experiments designed to test and measure this effect, to see just how "macro" we could maintain a "non-collapsed" state which would show quantum effects. Sorry no citations it's been a very long time but you can still find Penrose lectures with his adorable OHP sketches on acetate.

  • @Maths_Physics_Mathematics
    @Maths_Physics_Mathematics 20 днів тому +1

    Very good work 👍

  • @TheOldBlackCrow
    @TheOldBlackCrow 23 дні тому

    This Is quite helpful! Thank you soooo much!
    Question - is this how the Feynman diagram was derived?

  • @PhilMoskowitz
    @PhilMoskowitz 21 день тому

    Can you do an episode on Heisenberg's development of Matrix Mechanics? I think it's a fascinating subject as it was the first formulation of Quantum Mechanics and brought the concept of probabilities into physics. Yet Matrix Mechanics is rarely ever talked about.

    • @Miguel_Noether
      @Miguel_Noether 18 днів тому

      Every UA-cam video on quantum computing is using that, I guess you're not paying attention

  • @lambda4931
    @lambda4931 21 день тому

    Great teacher! Thank you!

  • @drmoccy
    @drmoccy 21 день тому

    I tried and tried to understand this via S. Hossenfelder course, but somehow I dont get it fully. Gonna try again.

  • @ryanwaldt1710
    @ryanwaldt1710 20 днів тому

    Why do people say quantum mechanics is not geometric, when we use geometry to model it? What am I missing?

  • @davidrandell2224
    @davidrandell2224 7 днів тому

    QM classicalized in 2010. Forgotten Physics website uncovers the hidden variables and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie, Planck, Bohr etc.

  • @emperor3744
    @emperor3744 22 дні тому

    Wouldn’t it make more sense to see the film as something that forces the light into a certain polirization direction?

  • @ChalkyWhiteChalkyWhite
    @ChalkyWhiteChalkyWhite 20 днів тому

    Why doesn’t it quantum tunnel through the polar filter

  • @cademosley4886
    @cademosley4886 23 дні тому

    You're gonna give a whole course?! 🤩

  • @bigrigexperience9294
    @bigrigexperience9294 21 день тому

    How did we scrambled vector analysis into optics into quantum mechanics?
    As for Schrodinger's Equation, my basic math education tells me that not all equations could be soluble.
    One could brag about writing the best equation for a problem yet to discover that the equation is pure nonsense.
    After you solve Schrodinger's Equation for the Hydrogen atom, for example, you get few quantum numbers attributed to the spherical harmonics, not of which has any thing to do with the quantum value h.
    I do not think that those who study or master quantum mechanics really know what they are doing.

  • @classicalmechanic8914
    @classicalmechanic8914 23 дні тому

    Unification of classical mechanics and quantum mechanics suggests classical and quantum are two sides of the same coin rather than two different theories.

  • @YinYang-9907
    @YinYang-9907 10 днів тому

    I spent many months learning superficial quantum mechanics. Always looking for videos like this for the layman. I was working at the factory and stumbled upon an emergent gravity theory, i then spent many more months putting it all into a theory of everything. Its on my channel! Id be honored if you looked at my theory and gave me some feedback!

  • @TheAntManMan
    @TheAntManMan 7 днів тому

    Jeez you are awesome.. i wish you the best life

  • @pauldirac6243
    @pauldirac6243 20 днів тому

    Welcome back 🙂

  • @Frahamen
    @Frahamen 23 дні тому

    if the state is |➡>, would it be more logical to write that |➡> = 1/sqrt(2)|↗>+1/sqrt(2)|↘> rather than |➡> = 1/sqrt(2)|↗>-1/sqrt(2)|↖>? or are both equations equal?
    (I can't believe I have to write equations using emojis but it works out)

    • @michaelsommers2356
      @michaelsommers2356 23 дні тому

      No, because the vector at -45 degrees is not one of your basis vectors.

    • @LookingGlassUniverse
      @LookingGlassUniverse  22 дні тому +1

      Great question! And the emojis are quite useful! You're right too! Did I get that the wrong way around in the video?

  • @KarlLew
    @KarlLew 22 дні тому

    Oooooh! love all the rules except the last, which strikes mortal terror in me. 🙀 -An undecided cat

  • @michaelsommers2356
    @michaelsommers2356 23 дні тому

    May I suggest that you get a Patreon on similar account, so that your many fans can financially support you?

  • @TheFman2010
    @TheFman2010 14 днів тому

    Thank you.

  • @شعرکوتاه-ع7ظ
    @شعرکوتاه-ع7ظ 10 днів тому

    Very good miss

  • @tallmatch5866
    @tallmatch5866 10 днів тому

    Too many ads😢

  • @niloymondal
    @niloymondal 23 дні тому +1

    How does the universe convert the probability distribution to actual result? Computers use Math.random, what does the universe use?

    • @amirzaidi
      @amirzaidi 23 дні тому +1

      This is one of the big open questions in physics. The Copenhagen principle says that the universe also uses Math.random when something is "measured"

  • @garyha2650
    @garyha2650 22 дні тому

    Scientists have an interesting task: They should always doubt themselves to be really good

  • @shunpillay
    @shunpillay 22 дні тому

    Very cool.

  • @kricketflyd111
    @kricketflyd111 23 дні тому

    OK, I just bought a set of 3 cat lasers and now can't see the cat. 😮

    • @smilesmile1237
      @smilesmile1237 22 дні тому +1

      dont look into the lasers haha

    • @kricketflyd111
      @kricketflyd111 22 дні тому

      @smilesmile1237 I taped polarizer all over the cat. 🌈

  • @kahdargo7
    @kahdargo7 16 днів тому

    Do the complex number video! If you don't, it will just remain...imaginary! 🤣

  • @abagoffrozenspinach
    @abagoffrozenspinach 23 дні тому

    ❤️❤️❤️❤️

  • @Miguel_Noether
    @Miguel_Noether 18 днів тому

    What's the motivation behind this course??

  • @michaelsommers2356
    @michaelsommers2356 23 дні тому +3

    .

  • @hcm9999
    @hcm9999 22 дні тому

    Just because you can doesn't mean that you should.

  • @brynwhitehead1731
    @brynwhitehead1731 23 дні тому +2

    If you understand fluid dynamics you understand quantum physics. It’s all water

    • @poogitypooheh
      @poogitypooheh 23 дні тому +3

      This is the most casually insane comment I have seen today! Cheers!

    • @theorixlux
      @theorixlux 23 дні тому +2

      Thank god, I thought I was eating too many pizzas!

  • @eduardoo31
    @eduardoo31 22 дні тому +1

    I mean, you do actually need to know calculus, linear algebra, and classical mechanics (at the very least) to even begin to understand quantum mechanics. But ok lol

    • @robo0428
      @robo0428 21 день тому +1

      I mean... if you know calculus, you essentially get (the relevant bits of) classical mechanics for free. And from there I don't feel like it would be hard to learn linear and quantum in parallel. But ok lol

    • @kingplunger1
      @kingplunger1 21 день тому +1

      @@robo0428 I think we have very different ideas about what is relevant in classical mechanics or what a standard calculus course is about, because I can hardly imagine it being enough.

    • @robo0428
      @robo0428 20 днів тому

      ​@@kingplunger1 I mean "relevant" as in relevant to introductory quantum mechanics content such as this. And if I use the free and open source OpenStax Calculus Volumes 1-3 as an example of a "standard' calc course then I'm not sure what relevant info you feel is missing. Looks like that particular course gives you more than enough linear to work with as well.
      What more do you feel is necessary before one is "allowed" to start studying quantum lol

    • @eduardoo31
      @eduardoo31 18 днів тому

      @@robo0428 so you agree. there are prerequisites (or at the very least corequisites)

    • @robo0428
      @robo0428 18 днів тому

      @@eduardoo31 Sorry, let me be clear. I definitely do not agree with you or your prerequisites.

  • @VirtuousSaint
    @VirtuousSaint 21 день тому

    heyyy someone got married it seems, congrats if that's the case

  • @shobhitkhajuria3120
    @shobhitkhajuria3120 22 дні тому

    Took sakurai chapter 1 too seriously

  • @ForNika
    @ForNika 21 день тому +1

    That Laser is not a Cat toy it's what Can damage their eyes.

  • @ZeroInDaHouse
    @ZeroInDaHouse 22 дні тому

    Waves go brr, electrons behave like standing waves around protons, standing waves emit 'quantized' packet of energy because they are standing waves duh. Why make things complicated if they are simple? The end.

  • @ForNika
    @ForNika День тому

    Anyone who wants to learn! Most people don't even want to learn basic Math and Science.

  • @dazzassti
    @dazzassti 22 дні тому

    I think you meant Polarised film, Polaroid was a company lol. Great video though 👌

    • @WanJae42
      @WanJae42 14 днів тому

      Polaroid (the company) got its name from Polaroid (the product), which was a polarizing film, and in many places, polarizing film generically is called Polaroid, in the same way that in some locales, tissue paper is called Kleenex, photocopiers are called Xerox machines, vacuums are Hoovers, and cola is called Coke. Some flight literature calls polarizing sunglasses "Polaroid lenses". It can be really common in some domains.