I have about 10 videos planned out for this series. The plan is to teach you want the curriculum I would teach if I was the lecturer for a quantum mechanics 101 class. The lectures themselves are all going to be free here on UA-cam. But if you're interested in doing this course more intensively over 4-6 weeks with a cohort and live tutorials etc, here's some more information about that: forms.gle/KfQEwkh2XcKwBERm6 Either way, thanks for your support! I've missed teaching a lot, and it's been very fun making this course.
I've really been dabbling in the idea of getting some formal education in quantum physics, but I'm weary about the level of time and effort I would need to put into learning and understanding the maths aspect of it. Calculus alone seems daunting, let alone linear algebra and differential equations.
I would totally pay for this if I could currently afford to. I would happily pay a much smaller amount for access to the HWs and recordings of the tutorials without the live support and accountability elements of it. I totally understand if having that option wouldn't work for you, just indicating interest.
Awesome! I have a background in maths and I am quite familiar with linear algebra, calculus, differential equations, Lie algebras etc. Sometimes the discussion on the math is the only part I really understand in physics videos :) do you think it still efficient for me to take your course? Also, do you have a textbook you can recommend as a companion to your course? Thanks for doing this!
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!!!
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!
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.
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!!!
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…
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.
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.
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.
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?
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.
@@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.
@@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.
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.
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.
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?
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.
@@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.
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.
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!
Unification of classical mechanics and quantum mechanics suggests classical and quantum are two sides of the same coin rather than two different theories.
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?
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.
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)
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
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.
I have about 10 videos planned out for this series. The plan is to teach you want the curriculum I would teach if I was the lecturer for a quantum mechanics 101 class. The lectures themselves are all going to be free here on UA-cam. But if you're interested in doing this course more intensively over 4-6 weeks with a cohort and live tutorials etc, here's some more information about that: forms.gle/KfQEwkh2XcKwBERm6
Either way, thanks for your support! I've missed teaching a lot, and it's been very fun making this course.
I've really been dabbling in the idea of getting some formal education in quantum physics, but I'm weary about the level of time and effort I would need to put into learning and understanding the maths aspect of it. Calculus alone seems daunting, let alone linear algebra and differential equations.
Nice try but I already solved all the quantum mechanics😂...all of it
I would totally pay for this if I could currently afford to. I would happily pay a much smaller amount for access to the HWs and recordings of the tutorials without the live support and accountability elements of it. I totally understand if having that option wouldn't work for you, just indicating interest.
Awesome! I have a background in maths and I am quite familiar with linear algebra, calculus, differential equations, Lie algebras etc. Sometimes the discussion on the math is the only part I really understand in physics videos :) do you think it still efficient for me to take your course?
Also, do you have a textbook you can recommend as a companion to your course? Thanks for doing this!
Did we just get 3 looking glass videos in a week and 2 of them are about quantum mechanics? I'm beyond excited 😂
I'm sorry to have kept you waiting for so long!
@@LookingGlassUniverse Well worth the wait.
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!!!
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!
You are such an amazing science educator!
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.
Thank you! looking forward to future episodes
Thank you so much for this! ❤️
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!!!
Exactly buddy ;)
Ohhh awesome! Thanks for making it!
Learning is good, but understanding is better. There are things to accept (learning) and there are things to question (understanding)
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…
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.
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.
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.
really 2 videos in 1 days and both videos are above 30 mins and i mean thankyou ... 💙
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?
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.
@@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.
@@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()
@@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.
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.
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.
Great video. Why did you use (1/(sqrt2 squared)) for the vector lengths in the first example?
If you understand fluid dynamics you understand quantum physics. It’s all water
This is the most casually insane comment I have seen today! Cheers!
Thank god, I thought I was eating too many pizzas!
Oooooh! love all the rules except the last, which strikes mortal terror in me. 🙀 -An undecided cat
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?
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.
@@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.
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.
Hey Mithuna! Always enjoy your videos. Can I ask what made you want to make your own lecture series for introductory QM?
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!
This Is quite helpful! Thank you soooo much!
Question - is this how the Feynman diagram was derived?
Unification of classical mechanics and quantum mechanics suggests classical and quantum are two sides of the same coin rather than two different theories.
Wouldn’t it make more sense to see the film as something that forces the light into a certain polirization direction?
You're gonna give a whole course?! 🤩
Scientists have an interesting task: They should always doubt themselves to be really good
Just because you can doesn't mean that you should.
Very cool.
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?
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.
May I suggest that you get a Patreon on similar account, so that your many fans can financially support you?
How does the universe convert the probability distribution to actual result? Computers use Math.random, what does the universe use?
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"
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)
No, because the vector at -45 degrees is not one of your basis vectors.
Great question! And the emojis are quite useful! You're right too! Did I get that the wrong way around in the video?
OK, I just bought a set of 3 cat lasers and now can't see the cat. 😮
dont look into the lasers haha
@smilesmile1237 I taped polarizer all over the cat. 🌈
❤️❤️❤️❤️
.
Thank you so much!
@@LookingGlassUniverse You deserve more. Sorry I never noticed the thanks button before.
@@michaelsommers2356 No this is really generous of you!
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
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.
I think you meant Polarised film, Polaroid was a company lol. Great video though 👌