@@AndrewDotsonvideos What's exactly means the expect value? The sandwich of the bra vectorand a operator acting over a ket vector it's like a scalar product? Sorry for my bad english
@@tomasmanriquezvalenzuela5909 It's the expected value, or expectation value. This is analogous to the concept in probability theory: en.wikipedia.org/wiki/Expected_value However, I think this requires that you adopt the Copenhagen representation in which states actually collapse and give rise to probabilities, since in the many world interpretation, the wave function never collapses, so there is no randomness and therefore no probabilities.
I'm 2-3 years behind you learning this, but as a self-learner, it's nice to have a human explain the idea behind the path integral in a few minutes. With most textbooks I've seen you have to wade through a lot of text and math to extract anything from it.
I was super lucky that my first exposure to it was from a professor who took a very similar, more pedagogical, approach. I agree that it's really hard to follow in most textbooks. Leave the wiener measure stuff to mathematicians (unless I mention it in these videos, I can't remember).
See Julian Schwinger's derivation of it in his book on ordinary quantum mechanics. It follows naturally from considered from the mutual exclusivity of individual "atomic" measurements in experiments where selective measurements are performed (the idealization and most simplest case of such a measurement being an SG experiment which... see the book) , its basically a law of total probability but for the quantum probability amplitudes rather than th classical probability. Someone elsewhere asks "why the insertion of the identity", it is to conditionalize the probability amplitudes so you get chains of conditional amplitudes (sequential events considered as a composite event's probability amplitudes multiply) which lets you get to the result of interpreting the whole thing as a sum over paths.
Andrew Burger Me watching this video despite being a freshman that only did a semester of first year calculus and advanced physics: mom I’m scared come pick me up.
Andrew! you have no idea how many physicist lives you're saving on the daily. I've been watching your channel since I was an undergrad, and ngl, it's like 40% your contribution to keeping me motivated to keep studying physics! You really deserve all the Olive Garden coupons in the world! GG yo, GG!
Wow, there's a serious lack of videos on this. I'm coming from a comp neuroscience / quant finance background, and videos like this are indispensable! Thank you
You are not afraid of writing down the technical aspects of this. I wish these videos where longer with complete detailed derivations. The material is exquisite and complete. In the internet people talk about the Feynman path integrals but no one dares to get into the nuts and bolts of them. This should be it.
I'm currently taking classical mechanics lessons, so my path into theoretical physics isn't too far by now, but I am absolutely fascinated by it. Just as well as I am fascinated by the topics in these videos! Although I don't understand a lot of it yet, I am sure hoping to do one day, and I am super looking forward to it! Hopefully I'll be able to get my head around these things some time, because otherwise I'd probably be really disappointed by myself. It's just too fascinating!!
Can Sub SCALAR value using the Quadratic forms with the PRIME algorithm and division algorithm in Expansion / looking for unit INTERGRATION /DERIVATION in the Taylor maculin SERIES sub Guass measure with Stiglre INTERGRAL decompose lipintz as a EIGENSTATE STATE Operators into a Symmetric Skewed Non degenerate Matrix using lesbuege measure [1505.04809] The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment ARXVI PHASE THEORY INVARIANCE NON LOCAL FIELD USING PATH INTERGRAL QUANTUM FIELD PERTURBATION
Awesome subject ! Engineer trying to learn QFT on my free time. Not gone yet on feynman path integral. And your lessons are so clear, I am confident I will go through and follow ! Looking forward to see next parts. Big Thanks
Currently doing comp sci and math at uni going into my senior year, watching your videos makes me wish i had more time to also do physics! Good job Andrew
I'm an engineer studying vibration mechanics and resonance, and I found that the math used in quantum mechanics and the one used in vibration analysis (modal analysis) is stupendously alike, but of course it is all about oscillation. Not much in this particular integral though
Can Sub SCALAR value using the Quadratic forms with the PRIME algorithm and division algorithm in Expansion / looking for unit INTERGRATION /DERIVATION in the Taylor maculin SERIES sub Guass measure with Stiglre INTERGRAL decompose lipintz as a EIGENSTATE STATE Operators into a Symmetric Skewed Non degenerate Matrix using lesbuege measure [1505.04809] The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment ARXVI PHASE THEORY INVARIANCE NON LOCAL FIELD USING PATH INTERGRAL QUANTUM FIELD PERTURBATION
Not quite the same! Expansions of orthogonal functions in QM meaning ultimately on the empirical side of things comes from the born rule which translates amplitudes into probabilities. So each term in the expansion corresponds to a different outcome, whereas this can not be said in the mechanics case. You mesure the system (the amplitude or position above the reference value) bc states and measurement are 1-1 correspondence you essentially sample the state at that point drawing on every term in the expansion to yield the displacement above the reference value outcome since it is a classical wave not a quantum mechanical one. So yeah some parallels but I wouldnt go to far with it. A QM wave is not a mechanical / classical wave by any means. There is no obvious mechanical medium (see Schrodinger's failed attempt to interpret Psi as a charge density function) per se in which QM probability waves are "waving".
beautiful work, thank you 😁 the balance of execution and reiterating fluency of terms is refreshing (I've forgotten more than I know, and there are too many collisions)
Just clicked your channel and saw you had 66 999 subscribers. Subscribed with my other account and refreshed. Now you have 67 000. Overwhelming satisfaction. Edit: 67000 not 70000 lol
Fun thing to think about, if on each slice you restrict the motion to the light cone (i.e. don't integrate over the whole coordinate, only within cΔt of the previous coordinate), the set of paths possible in this discussion actually converges to a discusable set of paths, i.e. lipshitz continuous functions.
I feel like I should make an annoying comment about the mathematical issues with defining a path integral but then I remembered the whole of QFT has that problem... cries
Me starting this video thinking I could actually follow along: Him: The propagator might be a new term to you. Me: Mhm never heard of it. Him: Oh its just simply the expectation value of the time evolution operator. Me: ....ah...right..
Can Sub SCALAR value using the Quadratic forms with the PRIME algorithm and division algorithm in Expansion / looking for unit INTERGRATION in the Taylor maculin SERIES sub Guass measure with Stiglre INTERGRAL decompose lipintz as a Operators into a Symmetric Skewed Non degenerate Matrix using lesbuege measure [1505.04809] The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment ARXVI PHASE THEORY INVARIANCE NON LOCAL FIELD USING PATH INTERGRAL QUANTUM FIELD PERTURBATION
Awesome!! Thank you so much for the video! Please, continue deriving Feynman`s path integral. Also, it would be pretty cool to see Dirac`s equation and the Schwarzschild metric derivation. Thanks again and congratulations for the wonderful content!
From 8:50 to 10:23 what have you written could you please explain in Layman language as I only did introductory QM and doing reading project on Feynman's path integral. Could you explain it a bit eloquently?
In 11:07 what is the vertical axis and why are we integrating along it? From the integral expression above shouldn't you be integrating along the horizontal axis?
Wow this is very intuitive! I have a question though about the interpretation of the multiple integrals multiplied together at around 10:40 as slits. I see how the x,x' and x_{i}, n=1,...,n-1 correspond to points in space, but i don't get the slit part of the interpretation. Any insight would be helpful! Thanks!!!
Curious, do you cover Fermionic and Bosonic path integrals in your QFT course? Cause Grassman variables are wack and maybe one day you can talk about them.
The cool property of Grassmann variables is that if you have a Grassmann number Ψ, then Ψ²=0. This is cool since before if something squared to zero then it must be zero, now it don’t. I would highly recommend Shankar’s last chapter for a nice discussion of it.
SUM Integral, Andrew? Without even properly defining it first? Does anyone know if there's a protective services department I can call to report notation abuse?
If you start with the double slit experiment you'll get to this. Essentially ask how to calculate the probability amplitude for a given point on a screen B (the screen behind the slits), given our initial emitter's position. The answer is we must sum the paths which get us there from the initial point to the point on screen B. There are two paths (one from emitter through slit 1 to the point on Screen B, and the other through slit 2), where each path has a probability amplitude. You sum the two and you have the probability amplitude of going from emitter to the point on screen B. Now what if we had 3 slits? We sum for the three paths. What about 4? Or 10? Or a million? We sum for the million paths. What if we add so many slits that there is no screen left? Then we sum for the infinite paths that get us there. Since its now a continuous range, we integrate over all the paths. That gives you a general concept. Now formulation wise you have 1) generalize to infinite number of layers of screens with infinite slits 2) generalize to calculating this for events in succession, like going from a to b and then b to c to get a to c That's the very basic form of it. You define a action, define the lagrangian, define the kernel as the integration over the lagrangian in space time over past and future, and you have your formulation. This of course will be a closed system formulation. For open system formulation you have to add in the external potentials (perturbation expansion) and that's it. The main idea that feynman used was the many-worlds theory (yes I said theory, because mathematically you can derive it when you show its equivalency with the Schrodinger equation). I love the formulation in that sense, and one thing I have to say is he is not eliminating operators, you still have operators (reference : feynman and hibbs formulation of short time evolution operator), and you rederive Schrodinger's equation using it. I am not a physicst nor a mathematician, but I do my best to study these in detail. Simply thought it would help to share the experience of how Feynman came up with this. One last thing is Freeman Dyson helped Feynman with the math a bit more, as his approach was more diagramatic, as shown later in Feynman diagrams.
That explanation at the end, you could've put it in the beginning. I kinda just had to guess what x' was (I guessed either a different reference frame or the time derivative of x, but it was neither)
Gustav Gade Hebsgaard I said at the beginning it had to do with a probability for propagating from point A to point B which I thought made things pretty clear. I also referred to x’ as a different point in space when I related the wave function psi(x’,T) to the propagation and the original wave function.
Ah, okay. Fair enough. It's just that diagrams usually help a lot, so it's nice when they're at the beginning of the video as a form of foundation for the calculations... But also, I really love your videos, and don't take it as too big of a critique, because you're still the best physics youtuber I know
Deterministically, calculating in "isolation" of the particle presumes you are right from the start Yet when elucidating by measures, requiring at least 2 real particles, you have an interference of propagators that modifies the waveform by interference to a "net" result that is different from either particle's propagator alone. Moreover entropy modifies both the propagators from either particle, and the net propagator, because the "background field" of the environment of the particles absorbs or contributes some of each propagator by impedance match. So, for realism by measure, you must always analyze at least 3 entities at the same time: 2 particles, and a background. Quite Yin Yang, don't you think?
Okay, so I am just scratching the surface of quantum mechanics and I don't have a good background with math, so please forgive me if this question is based on a false assumption or is just stupid. So, from what I think I understand, the path integral is very similar to langrangian mechanics, but instead of the principle of least action dictating the paths of the quantum particles, the most wild possible ways the particle could go are usually cancelled out because the vectors cancel each other out due to destructive interference. My question is this. The many worlds theory states (I think) that in a different universe, the quantum particle did take another path, but we can only observe it taking one path when the wave function collapses. So, according to that interpretation, can particles in other universes take a path where the path in this universe cancels itself out, or does the interpretation only consider paths in which the wave function doesn't cancel itself?
Correct me if I’m wrong , but aren’t you deriving the S-matrix ? Btw great topic and great video itself . I also study QFT and love watching another perspective , besides books. It is very helpful , thank you !
7:20 the complex conjugated term should be the other one I think.
Yeah you're right, sorry about that!
@@AndrewDotsonvideos awesome video and topic, keep them coming.
@@AndrewDotsonvideos What's exactly means the expect value? The sandwich of the bra vectorand a operator acting over a ket vector it's like a scalar product? Sorry for my bad english
@@tomasmanriquezvalenzuela5909 it means if you make an experiment the most probable result you can get is the expectation value....
@@tomasmanriquezvalenzuela5909 It's the expected value, or expectation value. This is analogous to the concept in probability theory: en.wikipedia.org/wiki/Expected_value However, I think this requires that you adopt the Copenhagen representation in which states actually collapse and give rise to probabilities, since in the many world interpretation, the wave function never collapses, so there is no randomness and therefore no probabilities.
I'm 2-3 years behind you learning this, but as a self-learner, it's nice to have a human explain the idea behind the path integral in a few minutes. With most textbooks I've seen you have to wade through a lot of text and math to extract anything from it.
I was super lucky that my first exposure to it was from a professor who took a very similar, more pedagogical, approach. I agree that it's really hard to follow in most textbooks. Leave the wiener measure stuff to mathematicians (unless I mention it in these videos, I can't remember).
and i am trying to learn from you...
You two are great
But i like the wiener measure stuff :(
You're slowly evolving into a hippy professor...
It's not necessarely a bad thing
We need more of those. Professor meme lord is the peak of humanity
@@jibran8410 exactly...
@@meowwwww6350 i hope I can be one too, I also recently finished my masters in physics xD
@@ALPlays congrats dude!!! wait No, congrats Dr!!!
I'm a simple man; I see Feynman in a video title, I click.
me too
Welcome to Matrix 👻
"The completeness relationship, which I hope you all know ..."
Me: wut
See Julian Schwinger's derivation of it in his book on ordinary quantum mechanics. It follows naturally from considered from the mutual exclusivity of individual "atomic" measurements in experiments where selective measurements are performed (the idealization and most simplest case of such a measurement being an SG experiment which... see the book) , its basically a law of total probability but for the quantum probability amplitudes rather than th classical probability. Someone elsewhere asks "why the insertion of the identity", it is to conditionalize the probability amplitudes so you get chains of conditional amplitudes (sequential events considered as a composite event's probability amplitudes multiply) which lets you get to the result of interpreting the whole thing as a sum over paths.
Me watching the video despite being a high school senior with basic calculus knowledge: 10:21
At least I’m learning from osmosis
Same
Andrew Burger Me watching this video despite being a freshman that only did a semester of first year calculus and advanced physics: mom I’m scared come pick me up.
Well I have 14 years old and I know differential geometry
@@tomasmanriquezvalenzuela5909 ok
I think the best part about your videos is being able not only to learn with you, but to also grow and mature together
Andrew! you have no idea how many physicist lives you're saving on the daily. I've been watching your channel since I was an undergrad, and ngl, it's like 40% your contribution to keeping me motivated to keep studying physics! You really deserve all the Olive Garden coupons in the world! GG yo, GG!
Thank you!
Wow, there's a serious lack of videos on this. I'm coming from a comp neuroscience / quant finance background, and videos like this are indispensable! Thank you
You are not afraid of writing down the technical aspects of this. I wish these videos where longer with complete detailed derivations. The material is exquisite and complete. In the internet people talk about the Feynman path integrals but no one dares to get into the nuts and bolts of them.
This should be it.
A: Sir, what is the propagator?
B: well, its simply the Green's function
A: ah, then I get it...
I'm currently taking classical mechanics lessons, so my path into theoretical physics isn't too far by now, but I am absolutely fascinated by it. Just as well as I am fascinated by the topics in these videos! Although I don't understand a lot of it yet, I am sure hoping to do one day, and I am super looking forward to it! Hopefully I'll be able to get my head around these things some time, because otherwise I'd probably be really disappointed by myself. It's just too fascinating!!
Enjoyed your presentation of the path integral very much thank you
I have 5 years old and I am watching this
me 2
This series is gonna be a fun lil side project over the summer for me. Thanks for them, Andrew :)
Your videos are so helpful Andrew! Love the hat btw lolol
Andrew if you ever have become a profesor can I be invited to your first official lecture?
yuh
Thank you for listening to us and making us happy, A. D.!
That normalized unit hat is a gd flex and a half my guy! Sick vid ty bröther
thanks!
Can Sub SCALAR value using the Quadratic forms with the PRIME algorithm and division algorithm in Expansion / looking for unit INTERGRATION /DERIVATION in the Taylor maculin SERIES sub Guass measure with Stiglre INTERGRAL decompose lipintz as a EIGENSTATE STATE Operators into a Symmetric Skewed Non degenerate Matrix using lesbuege measure
[1505.04809] The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment ARXVI PHASE THEORY INVARIANCE NON LOCAL FIELD USING PATH INTERGRAL QUANTUM FIELD PERTURBATION
The mathematician in me is cringing at that integral/summation notation. Great video, y’all physics people are wildin’
Lol me too, when he wrote it I was like "how the fuck can you even define that?" Video was very interesting though
@@andyshreds573 By defining a proper measure on spectrum of the self adjoint maps. Then defining an appropriate integral wrt that measure.
You know 'that smart kid' who is not actually smart or even knowledgeable. Those people should watch this video.
Awesome subject ! Engineer trying to learn QFT on my free time. Not gone yet on feynman path integral. And your lessons are so clear, I am confident I will go through and follow ! Looking forward to see next parts. Big Thanks
Thanks a lot!
Why am I watching this while I'm just on my first undergraduate year..
Why am i watching this... im 16
@@Ridwan-wm3is you certainly are Schrodinger
Man, I'm in my first year of high school
@@HenriqueMarquesCruz lol
@@Ridwan-wm3is same lol. im learning calc 1, 2, and 3 via self studying. what maths are you up to?
Currently doing comp sci and math at uni going into my senior year, watching your videos makes me wish i had more time to also do physics! Good job Andrew
rampage14x13 thanks a lot!
I'm also studying comp sci and maths, and I'm planning on focusing on applied maths/(hopefully) mathematical physics in later years :))
It is so infuriating that you are not using ħ = 1 when it's LITERALLY ON YOUR HAT
"Which is usually 1, but whatever." Maybe listen to the video?
I'm an engineer studying vibration mechanics and resonance, and I found that the math used in quantum mechanics and the one used in vibration analysis (modal analysis) is stupendously alike, but of course it is all about oscillation.
Not much in this particular integral though
Can Sub SCALAR value using the Quadratic forms with the PRIME algorithm and division algorithm in Expansion / looking for unit INTERGRATION /DERIVATION in the Taylor maculin SERIES sub Guass measure with Stiglre INTERGRAL decompose lipintz as a EIGENSTATE STATE Operators into a Symmetric Skewed Non degenerate Matrix using lesbuege measure
[1505.04809] The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment ARXVI PHASE THEORY INVARIANCE NON LOCAL FIELD USING PATH INTERGRAL QUANTUM FIELD PERTURBATION
Not quite the same! Expansions of orthogonal functions in QM meaning ultimately on the empirical side of things comes from the born rule which translates amplitudes into probabilities. So each term in the expansion corresponds to a different outcome, whereas this can not be said in the mechanics case. You mesure the system (the amplitude or position above the reference value) bc states and measurement are 1-1 correspondence you essentially sample the state at that point drawing on every term in the expansion to yield the displacement above the reference value outcome since it is a classical wave not a quantum mechanical one. So yeah some parallels but I wouldnt go to far with it. A QM wave is not a mechanical / classical wave by any means. There is no obvious mechanical medium (see Schrodinger's failed attempt to interpret Psi as a charge density function) per se in which QM probability waves are "waving".
lmao i just learned integration a few days ago and now im watching this having no idea whats going on
beautiful work, thank you 😁
the balance of execution and reiterating fluency of terms is refreshing (I've forgotten more than I know, and there are too many collisions)
Yeah, that's a no for me dawg
I’m a Statistics major and have no idea what’s going on here but it looks fantastic.
Maybe you'd like statistical mechanics instead😅
Just clicked your channel and saw you had 66 999 subscribers. Subscribed with my other account and refreshed. Now you have 67 000. Overwhelming satisfaction.
Edit: 67000 not 70000 lol
SGRendel thanks you for your service
But I think you mean 67,000
@@AndrewDotsonvideos Damn It's just like tests, as soon as I get to the numbers I screw up.
dont mind me 16 year kid trying to learn uni physics. love ur channel helps me show of a lot
How can you:
-Be good at physics,
-edit great videos,
-and maintain that beautiful hair?
Fun thing to think about, if on each slice you restrict the motion to the light cone (i.e. don't integrate over the whole coordinate, only within cΔt of the previous coordinate), the set of paths possible in this discussion actually converges to a discusable set of paths, i.e. lipshitz continuous functions.
hmmm
@@AndrewDotsonvideos dm me if you want more esoteric ramblings on path integrals
Awesome.
You put Feynman in a poll and it'll win. It's pretty much a buzz word.
I feel like I should make an annoying comment about the mathematical issues with defining a path integral but then I remembered the whole of QFT has that problem... cries
You know it's a good integral when it takes multiple videos just to derive it.
This boiiiii actually listened to my plea.
Love you bro😁
2:47 Should be "outer product", rather than "inner product". Sum of outer products would be even better. :)
yup, don't know why I said inner product
These videos get me so pumped to start grad school
This was good, pls keep them coming!! Thanx for the video.. Actually a video about 2nd quantization would be very nice..
Reflecting on the mindless mass of mathematical spaghetti at the end of the video, I've come up with a motto:
"Whatever you say, Prof."
I love that hat so much
Me starting this video thinking I could actually follow along:
Him: The propagator might be a new term to you.
Me: Mhm never heard of it.
Him: Oh its just simply the expectation value of the time evolution operator.
Me: ....ah...right..
This guy !😂 Uses they Feynman technique to explain the Feynman path intergral
Before consider anything I do, Andrew just know I'm an Engineering student 😂
Can Sub SCALAR value using the Quadratic forms with the PRIME algorithm and division algorithm in Expansion / looking for unit INTERGRATION in the Taylor maculin SERIES sub Guass measure with Stiglre INTERGRAL decompose lipintz as a Operators into a Symmetric Skewed Non degenerate Matrix using lesbuege measure
[1505.04809] The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment ARXVI PHASE THEORY INVARIANCE NON LOCAL FIELD USING PATH INTERGRAL QUANTUM FIELD PERTURBATION
2:45 Either you die a hero or live long enough to see yourself become the villain
I was going to say K looks like an integral kernel, which I think is the same thing (or close to) a Green's function
Deepto Chatterjee it actually is a greens function. Psi(final)=integral(K*psi(initial))
Hope the 2nd video comes soon. It will be cool if you can cover curved space time too 😅
I'm gonna need some time to process this, but I'm listening. 🙂
Love wathing your videos, even though I'm an art student.
@sellbotvpmaster99oh, right, sorry xD my fault...
Saw Feynman and automatically liked the video before watching it
Awesome!! Thank you so much for the video! Please, continue deriving Feynman`s path integral. Also, it would be pretty cool to see Dirac`s equation and the Schwarzschild metric derivation. Thanks again and congratulations for the wonderful content!
Love the cap!
:)
love it! cant wait for the next one!!
Could you cite some references that you have been using for the path integral formalism video?
It would be extremely beneficial if you could do that.
Well I mainly used my own lecture notes, but the course used Van Baal QFT for the most part. So I'm using that with a little peskin and schroder.
Thanks for making this
Damn, this is the good stuff!
th-cam.com/video/vFDMaHQ4kW8/w-d-xo.html 💐
Well 5 min in and I’m already officially close to a “nerd climax”.
Nice hat ;)
Thank you, interesting & easy to understand. Dan B USA
From 8:50 to 10:23 what have you written could you please explain in Layman language as I only did introductory QM and doing reading project on Feynman's path integral. Could you explain it a bit eloquently?
In 11:07 what is the vertical axis and why are we integrating along it? From the integral expression above shouldn't you be integrating along the horizontal axis?
man i love this
Wow this is very intuitive! I have a question though about the interpretation of the multiple integrals multiplied together at around 10:40 as slits. I see how the x,x' and x_{i}, n=1,...,n-1 correspond to points in space, but i don't get the slit part of the interpretation. Any insight would be helpful! Thanks!!!
Helpfull video, thanks!
th-cam.com/video/vFDMaHQ4kW8/w-d-xo.html 💐
Curious, do you cover Fermionic and Bosonic path integrals in your QFT course? Cause Grassman variables are wack and maybe one day you can talk about them.
What are Grassmann variables?
The cool property of Grassmann variables is that if you have a Grassmann number Ψ, then Ψ²=0. This is cool since before if something squared to zero then it must be zero, now it don’t. I would highly recommend Shankar’s last chapter for a nice discussion of it.
Lukas Juhrich Hopefully that makes sense too.
Can you solve or talk about the paradox of schirödinger's cat??
Can you make an introduction to Green’s functions video?
I LOVE your hat
Thanks! There's a link where to get it in the description
Feels like: Deriving one bag of tricks from another. To me.
Physics looks cool, idk if I should go for that or software engineering.
ily
2:58 notation is fun
Hey Andrew, have you seen Carl Bender's lectures on asymptotics? They're really cool. He talks about using divergent series in perturbation stuff.
Duncan W no but that sounds interesting
how I can get back to the video on ordered pairs?
Good shit bro, keep it up💪
A man that can teach and make my dumb ass understand 😍
Me at 10 years old.... duck
I've got my exam tomorrow, I'm in high school,
Too hard men
Could you please derive the Rutherford scattering equation
Please make a video on gauge theory in qft
th-cam.com/video/vFDMaHQ4kW8/w-d-xo.html 💐
It took me 9 minutes before I realized your ħ = 1 hat
SUM Integral, Andrew? Without even properly defining it first?
Does anyone know if there's a protective services department I can call to report notation abuse?
For a physicist, you seem to spend a lot of time thinking about maths techniques than about physics.
Well I'm definitely more inclined in the theoretical physics side which explains it!
where i can buy that hat? Btw, thanks i carefully understand this concept!!
JMath Channel right in the description:)
@@AndrewDotsonvideos Thanks!
I heard oscillator and thought a=-omega x^2, that is my extent of physics knowledge
I had studied this before and still have no idea how Feynman came up with this.
I definitely wouldn't have
If you start with the double slit experiment you'll get to this. Essentially ask how to calculate the probability amplitude for a given point on a screen B (the screen behind the slits), given our initial emitter's position. The answer is we must sum the paths which get us there from the initial point to the point on screen B. There are two paths (one from emitter through slit 1 to the point on Screen B, and the other through slit 2), where each path has a probability amplitude. You sum the two and you have the probability amplitude of going from emitter to the point on screen B.
Now what if we had 3 slits? We sum for the three paths. What about 4? Or 10? Or a million? We sum for the million paths. What if we add so many slits that there is no screen left? Then we sum for the infinite paths that get us there. Since its now a continuous range, we integrate over all the paths. That gives you a general concept. Now formulation wise you have
1) generalize to infinite number of layers of screens with infinite slits
2) generalize to calculating this for events in succession, like going from a to b and then b to c to get a to c
That's the very basic form of it. You define a action, define the lagrangian, define the kernel as the integration over the lagrangian in space time over past and future, and you have your formulation. This of course will be a closed system formulation. For open system formulation you have to add in the external potentials (perturbation expansion) and that's it.
The main idea that feynman used was the many-worlds theory (yes I said theory, because mathematically you can derive it when you show its equivalency with the Schrodinger equation). I love the formulation in that sense, and one thing I have to say is he is not eliminating operators, you still have operators (reference : feynman and hibbs formulation of short time evolution operator), and you rederive Schrodinger's equation using it.
I am not a physicst nor a mathematician, but I do my best to study these in detail. Simply thought it would help to share the experience of how Feynman came up with this. One last thing is Freeman Dyson helped Feynman with the math a bit more, as his approach was more diagramatic, as shown later in Feynman diagrams.
That explanation at the end, you could've put it in the beginning. I kinda just had to guess what x' was (I guessed either a different reference frame or the time derivative of x, but it was neither)
Gustav Gade Hebsgaard I said at the beginning it had to do with a probability for propagating from point A to point B which I thought made things pretty clear. I also referred to x’ as a different point in space when I related the wave function psi(x’,T) to the propagation and the original wave function.
Ah, okay. Fair enough. It's just that diagrams usually help a lot, so it's nice when they're at the beginning of the video as a form of foundation for the calculations...
But also, I really love your videos, and don't take it as too big of a critique, because you're still the best physics youtuber I know
Bring on the group theory soon please!
Isn't that one of the things that started quantum mechanics in the first place? 10:30
Deterministically, calculating in "isolation" of the particle presumes you are right from the start Yet when elucidating by measures, requiring at least 2 real particles, you have an interference of propagators that modifies the waveform by interference to a "net" result that is different from either particle's propagator alone. Moreover entropy modifies both the propagators from either particle, and the net propagator, because the "background field" of the environment of the particles absorbs or contributes some of each propagator by impedance match. So, for realism by measure, you must always analyze at least 3 entities at the same time: 2 particles, and a background. Quite Yin Yang, don't you think?
No physicist has ever grown a better beard than this guy ,in the history of physics. 😉
Where did you get your hat?
I made it, check the link in the description:)
so basically, dis very cool.
Not really physics related, but you've said that you're a pretty big runescape nerd and I was wondering if you watch Swampletics
Okay, so I am just scratching the surface of quantum mechanics and I don't have a good background with math, so please forgive me if this question is based on a false assumption or is just stupid. So, from what I think I understand, the path integral is very similar to langrangian mechanics, but instead of the principle of least action dictating the paths of the quantum particles, the most wild possible ways the particle could go are usually cancelled out because the vectors cancel each other out due to destructive interference. My question is this. The many worlds theory states (I think) that in a different universe, the quantum particle did take another path, but we can only observe it taking one path when the wave function collapses. So, according to that interpretation, can particles in other universes take a path where the path in this universe cancels itself out, or does the interpretation only consider paths in which the wave function doesn't cancel itself?
Yay! 😁
Correct me if I’m wrong , but aren’t you deriving the S-matrix ?
Btw great topic and great video itself . I also study QFT and love watching another perspective , besides books. It is very helpful , thank you !
I want that hbar=1 hat!
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