The First Thing You'll Learn in a String Theory Class
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- Опубліковано 21 лис 2021
- As a string moves through spacetime, it sweeps out a surface called its worldsheet. The starting point for string theory sets the action equal to the area of this worldsheet. Get the notes for free here: courses.physicswithelliot.com...
Get all the links here: www.physicswithelliot.com/str...
This video is part 4 of the series I've been sharing with you about the principle of least action. The first video was about a particle in Newtonian mechanics, the second was about a particle in special relativity, and the third about a particle in general relativity. In this video, we'll learn about the principle of least action for string theory. It's called the Nambu-Goto action, and it's given by the area of the worldsheet that the string sweeps out as it moves through spacetime.
Part 1 Introduction to the principle of least action: • Explaining the Princip...
Part 2 The action in special relativity: • The Special Relativist...
Part 3 The action in general relativity: • How Einstein Uncovered...
Tutoring inquiries: www.physicswithelliot.com/tut...
If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at / physicswithelliot , or make a one time contribution at www.physicswithelliot.com/sup.... Thank you so much!
About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com. - Наука та технологія
For the first time ever I think I found a channel before it blows up. Good luck and keep at the amazing videos! Your explanations are very good and intuitive!
Thank you!
@@PhysicswithElliot can you do full string theory and quantum physics course
@@PhysicswithElliot teach us everything that is in uni please
Yes please! Don't be afraid to be technical
It will never blow up no matter how good it is, unfortunately. That's just the fate of the type of content he makes
FINALLY someone that does not fear presenting "too much maths" (however that is possible). Most maths/physics youtubers seem to think that they shouldn't include details and instead only focus on the results, explaining them in wishy washy terms. But it is the little details, the insights leading up to the final result that make the result all the more interesting in the first place. Keep up the good work :)
13:51 Well, then you know which video has to come next :D
Glad you liked it!
It's not possible to say too much maths. It's possible to say more than a viewer can understand and incorporate in one go. The key isn't presenting less maths, but to present them using some kind of physical or everyday analogy, so the audience can imagine the mechanics of the math object. If a person were to see a mathematical concept out in the real world, they would surely see it a something they could interact with, or observe over time. Therefore, explanations should provide that kind of information, so a person can relate to new subject matter more easily.
I don't mean to denigrate anyone's perspective, I just feel strongly about this.
Holy grail teaching! Your teaching often gives me GOOSEBUMPS!
I agree with a video on tensors, also a four part series on the big black hole equations!
I love your high quality videos. I also love how you don't shy away from showing all the steps of the mathematics. THIS is the most important part, to show the step by step math and the clear and concise explanation behind it. Keep it up. Its difficult to find high quality graduate level physics content on UA-cam. May I suggest you cover Mathematical Methods and Statistical Mechanics and Thermodynamics? I struggled the most with these subjects. Some more ideas to cover are Classical Electromagnetism, Quantum Field Theory, and more General Relativity. In GR, if you could explain the Alcubierre Metric (Warp Bubble), that would be amazing. This string theory video is great, I want to learn more. Please continue this too.
Thanks Kenneth! Glad to hear it was useful!
Man this is amazing! I'd love if you went in like this on other things like LQG or QFT.
As a Physics Major I don't get to do all the cool courses offered. This is so cool and well explained for a string theory apprentice :)
Glad you liked it Joao!
I watch a lot of these sorts of videos, and I have to say yours are the best presented, most clear I've seen. I especially appreciate your explicit use of units in working problems and equations. This is how I learned physics, but it seems to be lacking in other educational videos I've watched. There's one historical derivation that I've not seen on YT (maybe PBS Spacetime?). Perhaps it's not interesting, but I'm super curious about the derivations of the Kaluza-Klein theory, and where it stands today.
Thank you! Yes I'd thought about whether I could explain Kaluza-Klein in an accessible way to make a video about it
Excellent quality and great discussion !
I hope your videos get the engagement they deserve !
Thank you João!
Sir I am new to this channel and this video is useful for introductory level of string theory
Excellent video Elliot, thanks
Dude I am so subscribed it's ridiculous!
Great job! I feel like I understand some of the initial principles of string theory, at least the very beginning of it thanks to you.
Good on you!
🤘
Wow! That was fantastic! Brilliantly clear explanations.
For the first time, I can intuitively understand physics equation without my brain going blank, all thanks to your wonderful channel. The notes accompanying the videos are very helpful.
My advice for future topics will be to cover basic mathematical tools of Standard Model, General Relativity, Lambda CDM model, and String Theory, just as you gracefully did with your series on Minimal Action principle.
Hoping for more great videos on maths of advanced physics from you. 😇
Thanks Abhishek! Glad it was helpful!
I never experienced formation of a new great channel firsthand, turns out now I will 👍👍
Thanks for the fantastic lecture. I hope you may explain how Minkowski formulated Maxwell equations into the electromagnetic field tensor in the future.
I've never been much of a physics person vs math, but I LOVE your channel! I would love to see more videos about Riemannian geometry and manifolds in physics, because I love seeing the real examples of the things I study in an abstract sense. Thanks and keep up the good work!
Crystal clear explanations, illustrations and summaries. Only a person with a sound and profound understanding of these concepts can help others begin to understand or continue to explore these universal physical phenomena. Elliot has a strong and rigorous background in pure and applied Mathematics to be able to show these relationships and connections. We do live in a Mathematical Universe. Thank you, Elliot!
Could you make an intro to tensors?
I will put that on my list! I definitely want to make some videos focused on mathematical methods for physics
The UA-cam channel eigenchris Tensor Calculus (a series of videos) is real good. I subscribe to his channel too.
Im really enjoying these videos. Very well scripted and interesting, keep up the great work! More string videos would be great :)
Glad you like them!
Great work on pumping out a lot of quality content in only 2 months or so. Look forward to see what else you'll make in the future, your level of quality is more consistent with monthly uploads and you already have 15.
Thank you!
Love your approach. I never studied string theory but this makes it seem so intuitive and accessible. Thank you! :)
I'd love for you to go even deeper into string theory. Learning it seems daunting but you make it sound sort of "intuitive", I'd say. Great video
Thanks Anurag! I'll probably make more videos about string theory in the future!
@@PhysicswithElliot thanks. It's quite a fun and interesting topic
Thank you very much Elliot because I am understanding the mathematic theory about relativity that I didn't on my undergraduation.
Glad to hear!
Thank you for your great work. I'll definitely follow you thru this rabbit hole :)
Thanks for an amazing explanation.
phenomenal, very well done Elliot!
Thanks Nick!
Thank you so much! I am super grateful for the fact that you don't skip over the mathematical details and even more grateful for the fact that you justify the approximations used when deriving the solutions. As a physics enthusiast with a formal math background who works as a programmer, I love your approach!
Thanks Monis!
Dude you are amazing at explaining keep up the good work!
Great video! A video on fermat’s principle of least time would be great!
Loving the videos, thanks
Wow! I can't wait for learning more about String Threory 👍
To watch your videos is to apply the principle of least action to learning modern physics. Very difficult topics can be grasped in just 15 minutes. What a great head start to string theory. Thank you.
Thank you so much Koorosh!
This is a totally amazing channel!!!
Welcome Frank!
That was so cool!! Thank you.
You are a legend mate, top-notch guy. Thank you
What a wonderful introduction to the subject. This is a university standard content. I would like you to teach us the entire string theory at least how far you can take us.
Great video and thank you so much.
Glad it helped Fazil!
A really great video
I would Suggest you should cover "Hidden-Variables theory". Please!!
keep up the great work!
Fantastic video!
Very nicely done. You seem to have a very natural and intuitive sense of what needs to be shown. For example the motivation of using a det , transitioning from full expression under sq rt to more compact form was perfect, completely avoiding the huh , were did that come from mystery
Interesting and worthwhile video. It would be helpful if your linked notes were available as pdf downloads.
Thanks, Elliot this is an amazing presentation, hope you do also for similar ideas like loop quantum gravity and twistor theory if you have free time....
If teachers were like doctors (which I think is an apt comparison as they should be vetted with the same amount of scrutiny) then most teachers I’ve had are like general practitioners from Caribbean medical school, and you’re a neurosurgeon from Mayo Clinic. Everything is so precise and concise yet still substantive and dense. It reminds me of Landau and Lifshitz. I cannot sing your praises enough.
I saw this video appear in the r/physics subreddit. Thanks for the video, it was very interesting. Will keep an eye on your future videos. I especially enjoyed the smooth notes! What software do you use for that?
Elliot, You are Superb👍👍👍👍👍
Beautiful. Would love to see you explain about the symmetric groups of the standard model. Specifically the SU(3)XSU(2)XU(1), in a future video
this is awesome!
Hi Elliot.Thanks for the great job in String.We expect more material.I volunteer as a collaborator.
God! Just find this great Physics channel! The level is just right for physics lovers! Thanks Elliot! In adition to those attractive physics topics, I would like to see topics related to other areas like physics of stock market, physics related to neural network and biophysics etc.
Excellent
Very good
This video is helpful for me. Please a video on higgs mechanism
Thank you very much, that was amazing. I would love it if you can give us examples that show the equations of motion of these actions.
Came from the hamiltonian video, awesome channel!!
Thanks and welcome!
Excellent work. Thank you,
Could you please explain the use of string theory
I may make additional videos about string theory in the future if there's interest! It's a theory of quantum gravity, meaning that it combines Einstein's classical theory of gravity and quantum mechanics in a consistent way. We don't know if it contains the correct quantum gravity theory that describes our universe, but studying it has taught us a huge amount about reconciling gravity and quantum mechanics.
Outstanding
Explains what strings are, great. Doesn’t explain why they’re useful - but - still so much better than the other videos, so thank you
There are a lot of good math channels but until you came along not really any good physics channels. Your presentations are top shelf I absolutely love it. I'd be interested in any video you put together but if I had to pick one topic I think it would be great to learn about proton decay from you. Thanks.
Thanks James!
Please make video series on University physics 🙏🙏
That was fantastic, thanks. Do you have any thoughts on Lagrangian versus Hamiltonian formulations? It seems like Hamiltonian is more natural in quantum physics, but your video suggests action principles are the core of string theory. These are dual in some sense, so maybe neither is more fundamental, just easier for certain applications?
Thanks Greg! Yes both the Lagrangian and Hamiltonian formulations are used in quantum physics. The Hamiltonian formulation is usually taught first in quantum mechanics courses. It's what was understood first historically, and Feynman later discovered the Lagrangian formulation of quantum mechanics, called the path integral formulation. Both provide different insights, and one or the other might be more convenient depending on the problem
Another brilliant job.
Know anything about quantum information?
What about the vibration of the string? Do you discuss this in subsequent videos? Very fascinating
More cool things on string theory
Also. I heard from a video that the Ramanujan summation of -1/12 was crucial to the 11 dimensions of string theory. Is there any material you have covering that?
can't you just use the jacobian to find dA?
is there any difference in what you did and the jacobian, or will the answers you get be equivalent?
I'm not certain what you mean, but in general areas and volumes and so on can be computed by integrating the square root of the determinant of the metric. If you have something like a surface with coordinates y^a embedded inside a bigger space with coordinates x^i, then the metric ds^2 = g_{ij} dx^i dx^j of the bigger space "induces" a metric g_{ij} dx^i/dy^a dx^j/dy^b dy^a dy^b on the surface. Then the thing to integrate is the square root of the determinant of h_{ab} = g_{ij} dx^i/dy^a dx^j/dy^b
Can you provide more mathematics of string theory??
I need more notes.
Action principles for field theories please.
Yes that's on the roadmap!
Very well done, but why start with a string instead of a particle? What is the motivation?
Hi Elliot, do you know our current ideas on the cases of the infinitesimal worldline particle rather being (a) the vibrating loop, (b) a vibrating 3d sphere (?) (filled? empty?) (c) some more complex donutopology? :)
…and, also, does gpt know? ^^
Please make videos on renormalization in QFT
Maybe someday! Will definitely be making field theory videos
Please I want to ask you does graph theory of math has any application in quantum physics or not? and thank you
I don't have any personal experience with applications of graph theory in quantum mechanics, but I don't doubt that they exist!
I hope more people could find your channel..as pop science is getting wildly popular instead of actual science leading to misinterpretations and bunch of wannabes too..
thanks for providing such wonderful content ..keep going bro!
Is it possible to write a Lagrangian and an action for a massless particle?
what resources would you recommend for getting a grasp of linear algebra from? I think a lot of the maths here will be covered next year in my school but i wanna look at this stuff right now and i don't really know where to start
not sure if partial diff is on the modules my class is taking, but we have the textbook for every module so i can use that, the linear algebra stuff i dont think goes into too much detail like whats needed for this, but i have the stuff for most of the calc on here
Can you cover the polykav action?
Potentially!
Is it possible for a string to be a massless string, or does the tension always imply mass?
Quick question; what happens if the string is spinning? Won’t it ‘cut off’ the sheet like a bubble wand cuts of bubbles? Or is it because it’s 4d this doesn’t happen?
Yes you could consider a worldsheet that pinches off into two pieces!
Conservation of Spatial Curvature:
Both Matter and Energy described as "Quanta" of Spatial Curvature. (A string is revealed to be a twisted cord when viewed up close.)
Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree.
String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring?
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine.
Quantum Entangled Twisted Tubules:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr
(lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958)
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change.
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Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase.
Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length )
The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge.
Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms.
In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
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Spin networks and notions of causality that describe an emergent space-time
Please make videos on tensors, topology.....
Will think about it!
nice
Amazing explanation!!.... your channel is amazing Sir 👍🙂
Thanks a ton!
please do black hole theorys please
I am your 682 subscriber
Thanks Akshay!
Q. Why do wave travel live a wave like those up and down motion what make them go up and then also pull them back
Please can you make a explanation on it
I will add an introduction to waves to my potential topics list!
thanks a lot
0:55 how is action=length possible? J.s=m?
Proportionality constant of 'mc'
S = mc(S.I.)
Where S.I. is space time interval
Plz make a video on lagrangian mechanics applied to "two block spring system" in order to find the time period. It will be of great help🙂. Plz I request you
And the following videos? My doubt always with string theory is its relationship with quantum field theory. Since in this fields are defined that fill all space and the particles are disturbances of it. And where if the particle is real, the energy and momentum of the particle will be quantized, their operators being non-commutable. But what about the rope? If the particle is a string, where are the fields that fill the space? Can we interpret the string as a non-point disturbance of a field?
The Ricci tensor is lopsided temporally.
".. to keep it simple.". O-K. This video is a bit tough for ordinary folk, but I'm going to rewatch on string - I mean loop.
So the world sheet is a minimal surface like a soap film?
Yes similar!
2:45 😏
Okay.
Hey man, love your videos, I was wondering if you could comment on Eric Weinstein's Geometric Unity. I think it was fascinating but do not have the math required to take away the major points.
Thanks! I'm not familiar with that unfortunately
Until he publishes a paper with regard to his theory and concretizes his rambling and napkin math, that theory can be considered fraudulent or non-serious
Now I see he's apparently published a widely criticized "draft" earlier this year. But I can't download since I need to add my email address to his mailing list -_-
@@TranscendentPhoenix thats not true at all, he gave a brilliant intro lecture to it
@@TranscendentPhoenix i can see your clearly against it which is fine, but you sound like you've taken the position that I am some big fan of it. Its an interesting idea, and just like when string theory was first introduced, it was heavily criticized.
Surely geometric algebra would make this easier? 🤔🤔🤔🤔
Who's here from NWH?
Im glad spiderman brought you here
Physics is easy. Dating is where I FAIL!
Lol is anyone else really curious wtf those red things in the corner of his room are?
Ok (your presentation) but it confirms my suspicion that this Theory is just a....computer game! How can you justify (in modeling) the jumping from x (lambda- a parameter) to x(lambda, gamma - two parameters). What's the reason? The concept of the distance in 4-D (time-space) analogical to 3-Dimension has a sense (logical one). Well, the effect of this theory as we know until today is...none! Plus: in (physical) experiments one must make a measure something: time, (or) distance- one or the other despite mathematical assumption than one can. measure both (ok in the ordinary everyday experience but in astronomy of QM! Hence, it is obvious that only we have ONE independent parameter (lambda), time (on a precise clock in an isolated system according to a Theory)- well this IT is not at all explained in textbooks (why?)