Please do another video. How do you go from the Lagrangian to wavefunctions (probability densities)? Schroedinger's equations involves the Hamiltonian. Why does particle physics use the Lagrangian instead? Is there a wave equation in particle physics?
Ok here's what I've learnt so far in my MS Physics course... Lagrangian formulation is almost always the preferred option to study any system. It is done using the Euler-Lagrange equations to find the equations of motion, which are differential equations describing the system. So it turns out that if you have a Lagrangian, you can always get equations of motion from it. The number of equations depend on the degrees of freedom and constraints on the system. Now, you know that the Schrödinger equation is a differential equation which begs the question: Can we find a Lagrangian for it too? The answer is YES! Even cooler fact is that it is not the kind of Lagrangian you may get in, say, a simple pendulum. It is a "Lagrangian density", and if we use the "Euler-Lagrange equations for fields" on it, we will end up with the familiar Schrödinger equation, and its complex conjugate. The wave-functions found in the Schrödinger equation are simply "field variables" in the Lagrangian density, existing in the Hilbert space.
Yes, @@shoaibansari3224. Also, in addition to this, the Lagrangian is highly effective when exploring the internal symmetry properties of a system (which elucidate the general characteristics of the system), and is involved in the standard quantization of field theories (where "fields" are commonly used in particle physics, including the Schrödinger Field). For example, while studying Quantum Field theories myself, the Hamiltonian formalism was hardly explored but occasionally crucial nonetheless.
The legendre transform of an L is an H, but that’s not relevant here. The SM is a relativistic quantum field theory, so processes are computed in the S matrix formulation….basically you calculate cross sections, maybe masses. Schrödinger and wave functions are entirely different…non relativistic quantum mechanics. They might overlap in say, the quark wave function of a J/Psi? But then q qbar bounds states are way more complicated than positronium…so idk.
True, @@DrDeuteron. However, the time-ordering involved in computing the S-matrix elements is obtained from the interaction Hamiltonian. Although Feynman diagrams reduce the computational complexity, the intricacies of Wick's theorem are implicitly incorporated.
@@HunnidTheTrapper02 and that's the problem with most layman QFT questions, by the time you know how to answer them, your would never bother asking them.
The „Dragon“ comment reminds me about something Prof. Gassner said in his series „From Arstotle to String Theory“ (sorry, only in German, on the channel „Urknall, Weltall und das Leben“) when he discussed General Relativity. He wanted to tip-toe around the deep where the Monster lives, and only do a little peek - at the Riemann Tensors (iirc). 😊
Ha! I first read about Lagrangians last night in Sean Carroll's 'Biggest ideas' book. What a nice coincidence to see this video this morning. I think there's a good number of the public who are interested in this type of content but want a bit more than the usual 'lay' descriptions but who aren't physics students. Anything that takes us slightly 'under the hood' albeit with more math is greatly welcomed.
A couple of people have asked about this... if you need to calculate anything more complicated than a "Spherical cow in a vacuum", then using Hamiltonian or Lagrangian mechanics makes the calculation much easier to do than using Newtonian mechanics... assuming that you understand second order ordinary linear differential equations. The Lagrangian and Hamiltonian stuff is usually not taught until your third year physics class in college, because you need to pass a class on differential equations prior to it. The first year physics class uses Newtonian F=ma stuff because you only need to know Algebra... or if you've had a first year calculus class, maybe F=dp/dt=m•d²/dt² and stuff.
I encourage anyone who finds this interesting to dig into the math(s) themselves! As much as you can find lots of great easy-to-follow introductions like this online, the satisfaction of actually _understanding_ how it works is truly transcendental. Personally I found Leonard Susskind's _Quantum Mechanics: The Theoretical Minimum_ very helpful. (It takes some hard work to get through, but I only have a high-school level of formal physics education and was able to learn a lot from it, so chances are you can too!)
Hello Dr Don, I have always appreciated to have you to be my UA-cam-physics mentor .you are awesome! Also in a lucky case that if you saw my comment, my question would be asking about how come the general relativity has incompatibility with quantum mechanics. What are physicists really looking for to unifying these two theories?
@@drdon5205Hello Dr. Don! Thank you for the comment and explanation. However I still don't quite understand why infinite number of infinities would pop out. Maybe it is that the equation of General Relativity was built to explain the intensity of gravitational force ,so it cannot be quantized? Thank you for taking time to read my comment. I still want to ask you some other questions . First ,could gravity be a result of the expansion of space-time, due to the uneven distribution of dark energy? I have watched a fermilab video you made ten months ago. In that video, you have mentioned something called entropic gravity. Can we have more details about this topic in future videos? Second question. Since photon is electromagnetic wave, can space itself waving like photon does? If it could, would this waving property of space cause the universe to have a electric field just like single photon does? And after all,can this be the reason that universe ended up to have more matters than antimatter? Based on my shallow knowledge about universe. I can only assume that different electric-field type may be able to affect the rates of different types of nuclear decay. And I could be so wrong about my idea. Hope to receive some corrections from expert like you. Thank you so much for all the works you have done through these years. Hope see your video soon! take care Dr Don.
I would love for you to dig into the advanced math! Maybe in a separate video. I took a course on the calculus of variations ages ago in college and we studied the langrangian as well, and lately I'm having a midlife crisis about never doing anything with that part of my education. I would love a refresher.
Wow that homework was really a tough one, but after pulling some strings i could find a solution for a 26 dimensional homogenous, isotropic Anti-de Sitter space. Then i failed miserably to figure out to whom or where i should send the homework to.
There is no due date for your homework; you do not have to turn it in; it will not be graded; keep working on it for the rest of your life. You cannot possibly finish it because L = T - V has no physical meaning.
Probably Juan Maldecena, since you’re clearly using his AdS/CFT correspondence. He’s likely to only give partial credit, since you didn’t do the full compactification from 11D M theory, but instead used one of the old purely bosonic string theories (the ones that literally had & required 26 spatial dimensions) 😅
Nitpick: The Lagrangian is usually written with a usual L, hence the equation at 2:45 should simply be L = T - V. The strange version of the L on the shirt actually is the Lagrangian _density_; you have to use energy _densities_ for that, not simply energies.
Bugged the hell out of me that as a physics student, we resolved forces in high school, as undergrads, and it wasn't until THIRD YEAR undergrad, we were finally taught this much easier way of doing things. The Langrangian should be taught in high school.
Not publishing advanced physics on a physics channel is a pretty bad idea... if the editor is reading this, bro let the physicist make the physics content, you don't get it because you are not into physics like that, just focus on bringing stuff to life with editing... you do a really good job of editing it, please let him expand on the physics. I personally would've loved if this video explained everything in more depth.
I don't think it's right to assume that the editor isn't into physics "like that." It could very well be that it's the opposite, and the editor just didn't want to confuse people or turn people away from the video.
So... my $5 Panasonic calculator isn't going to be of much use here, is it? Thank you Dr. Don! This stuff is fascinating to me, even though I still count using my fingers. 😊
He just named some parts, that's not really an explanation. A viewer might think that Ψ here is a number of a number-valued function, and be very far from what it really denotes.
I am a physicist and know what a Lagrangian is. I even recognize this version representing the standard model. But frankly, I never needed to use this approach in my own research. Am I lucky?
If you need 2 sections to fix the previous sections, shouldn’t the other section be rewritten so they are correct? Do we know why the correction is needed?
Why are weyl fermions not on the standard model or a nonstandard model? Since they naturally occur sometimes but granted they are kind of rare compared to most other particles. Why not include Majorana fermions, and other quasi particles?? Can you do a video on that? Please and thank you in advance!
Personally, I not only welcome deep dives and math but encourage them thoroughly! Still a good very base level intro to topic, but I fear I may need to return to university to advance as UA-cam vids seem to be far too shallow on advanced topics as of late (or just go back to watching lectures on here, like Leo Susskind and others)
Dr. Don, Great video! It sparked another question: Could black holes be where antimatter collected? I.e., could antimatter from the early universe disproportionately collecting in black holes explain the antimatter paradox?
Dr. Don, Great video! It sparked a question: What happens when antimatter falls into a black hole? My understanding is that black holes can have net charge, but it seems that positrons and antiprotons could equally contribute. It seems that black holes must contain antiparticles (rather than exploding from the annihilation energy). Could black holes be where the antimatter collected? (I.e., does this explain the antimatter paradox?) If there is an “anti-black hole”, what would happen if it collided with a standard black hole?
I love how Dr. Don can take the scariest possible equations, and make them at least slightly comprehensible to us lay persons who only took high school physics and chemistry classes, and those were 50 years ago for me.
THANK YOU... PROF. DR. LINCOLN...!!! Theoretically interesting to look at it... but mathematically don't even think to be close to that equation except: L = Kinetic Energy - Potential Energy. THANKS AGAIN ...!!!
what's the chance that dark matter or dark energy can be detected or disproved? would a vat of Bose Einstein condensate in outer space have a better chance of detecting it? do you guys use materials with negative absolute temperatures for anything?
There's a funky popularization article by Woithe et al. (2017), that invites you to have one or more (hot) coffees "h.c." with the Standard Model of particle physics. ☕ I've been drinking my coffee from the famous mug (the one with the Lagrangian written in white on a black background, that I bought at CERN) for 4 or 5 years now. Although I work in a completely different professional field, the desire to understand this equation has given me the urge to study physics (and therefore maths ! ), just for the fun of it ! So thank you, Don, (and the whole team) for this video! >> And don't forget - especially if you're going to Switzerland and visiting CERN - if you're worried that too much "h.c." (hot coffee) is bad for you, you can also fill your "Standard Modell mug" with Hot Chocolate ! 😋
I *_think_* the preliminary results from Fermilab are that their measurements of Muon G-2 *are* in agreement with the value predicted by the Standard Model. I can't quite find the results with Google at the moment, but Google Search sucks now, and I thought I heard some Muon G-2 news recently about these results.
Quite possibly though there is also a good possibility that this is a consequence of phsyicsits using complex numbers rather than the more accurate quaternion mathematics. Looking this up these terms of ghost particles appear to be related to conserving gauge invariance within the path integral formulation. They are ghosts or virtual particles because these terms themselves are not directly observable and there is a corresponding term associated with each gauge field. Apparently if you try and solve the equations without them the matrices become singular and these terms are basically a way to get around that. Now quaternions are the correct way to represent mathematics of symmetry groups in that other approaches are more or less approximations which have the potential to break down. This has an interesting classical parallel problem in the form of another types of matrix math operations in physics rotation matrices which can be eliminated by utilizing quaternions instead of complex numbers where there is now effectively 3 different kinds of imaginary numbers. As the operations these ghosts are used to get around in the standard model here are all symmetry group relations we thus are guaranteed singularity if we don't correctly use quaternion operations which is particularly a problem with distributed quantum fields where you can't just ignore the singular domain of matrices in 3D+time space. Notably these ghost terms share most of the properties of anticommutation seen in quaternions so in all likelihood there exists a formulation of the standard model with quaternions rather than simple complex numbers. It is just either undiscovered or physicists are uninterested in formulating the equations this way. Quaternions originally were formulated/discovered by Sir William Rowan Hamilton and his reformulation of Newtonian and Lagrange Mechanics into Hamiltonian mechanics. This invention proved critical in allowing Maxwell to formulate Maxwell's equations which were defined in terms of quaternion operations. Modern physicists have for some reason or another likely the inherit complexity of managing quaternion operations developed a way of approximating them using matrices. We don't really have any intuition working with quaternion mathematics so they are cumbersome to us. Notably however the mathematics of spinors also relies on quaternions and is one of the few context where physicists still begrudgingly use them though only in the form of Pauli matrices. Quaternions have become important in computer science particularly in the case of handling graphics since the little tricks physicists use to get around quaternions are computationally more expensive than just solving the quaternions. Computers unlike humans have no qualms or difficulties solving quaternions. Heck the brains of some animals like dragonflies are able to perform maneuvers which in aerospace/machines require quaternions to achieve without critical failure so it really looks to be an "us" problem we will at some point have to grow out of as a species.
The total energy, T + V, kinetic energy plus potential energy has real meaning. However, the Lagrangian L = T - V has no real physical meaning. Are we missing something?
The total energy T + V is the Hamiltonian. It's a bit easier to use since it's multiple first order linear differential equations, rather than the Lagrangian which is a second order linear differential equation. You need to setup the Hamiltonian in an abstract phase space, depending on the particular degrees of freedom in the system that you are modeling. Like... should I go on about how to derive the Action, and how to convert from Newtonian force vectors into potential energy, and stuff? (And Nöther's Theorem?) Basically, if it's the 1800's and you need to analyze the movements of a complicated mechanical device, then Lagrangian or Hamiltonian mechanics is much much easier to calculate than Newtonian mechanics (if you know differential equations). (They don't actually teach this stuff until the third year physics classes in college, because students must know differential equations first.) Like, if you want to calculate the motion of a small mass, that is spinning around on a vertical wire hoop, that is bouncing up and down on a spring, that has the other end attached to the floor of a rotating Merry-go-round, etc. etc. with air resistance and friction accounted for... this is written as just one simple to solve Lagrangian equation. Doing this same calculation with Newtonian mechanics is a tedious pain in the ass, filling several sheets of paper to get the same answer.
Electrons _are_ leptons. The other leptons are muons and tau particles, which are basically heavier electrons. Unfortunately they aren't stable, so you can't really do anything with them. Then there are the neutrinos, which you really can't do anything at all with.
@@narfwhals7843 Oh wow. It’s sad the Millennium Project cited them as a future tech. I know neutrinos don’t interact with anything but Isaac Arthur (futurist) believes they can be used for power generation and propulsion.
@@Italianjedi7 I mean, if you want to talk _extremely_ theoretical *far* future applications, then yes. It is possible that neutrinos may be used for propulsion and power generation. They don't "not interact at all" they interact very weakly. But if you have enough of them they can sustain a star from collapse. But the process to get enough of them is a super nova. So that might give you a sense of scale. You don't need a super nova to move a rocket. But you need a sustained fusion reaction far above what we are even remotely considering for the neutrinos to be an appreciable part of the energy output.
Thanks Dr. Don. I love the concept, "What does that equation mean?" to make complex ideas more intuitive. How about doing, "What does that diagram mean?" I have been enthralled by the beauty of the Feynman Diagram for electron positron annihilation, with the positron and anti-quark moving backward in time. And what does that really mean for the concept of causality?
If quarks have not been isolated and gluons have not been isolated, how do we know they are not parts of the same thing? The tentacles of an octopus and the body of an octopus are parts of the same creature. 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. ===================== 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.
Hmm I do think building off Kaluza-Klein Theory probably an extension using quaternions which are the most exact mathematic operations for symmetry groups and rotations. As a conventional theory I don't think neutrinos can account for dark matter though its possible they could become relevant in the context of extended indirect effects such as the implied handedness which appears within the generalized unconstrained Einstein field equations so long as one does not artificially/forcibly constrain its behavior to symmetric solutions (and thus universally violating conservation of information with regards to the initial conditions). Specifically the interactions of anisotropies and inhomogenities propagate into the rate of expansion locally based on the past history lightcone. Following the implications of the proof by self contradiction within Inhomogeneous and anisotropic cosmology by Matthew Kleban Leonardo Senatore 2016,(which the authors barely touched on) the conditions for the Einstein field equations to be internally self consistent is that off diagonal elements of the metric must always have an irreducible nonzero asymmetric contribution imprinted in the rate of expansion of space. Looking into this further this just so happens to eliminate any and all need for "dark energy" the latter becoming a pure consequence of gravity in a nontrivial universe, while also implying all possible quantized elements of spacetime should they exist must have a uniquely defined state for each and every possible element of the metric that is to say that if a summation form of the Einstein field equations exists all these base elements of spacetime must anticommute or be what are known as Dirac sponsors which obey the property known in quantum mechanics as the Pauli exclusion principal. In essence the full irreducibly nonlinear(chaotic) domain of the unconstrained Einstein field equations is casually forbidden from having a boson based quantization of space and or gravity. Only Fermions are allowed to exist as a force carrier and gravity is likely fundamentally involved in spin flip transitions. The type of frame work you have proposed here seems to be consistent with that though the caveat is that any theory to be consistent with the above must be "nonlocal" if we do not properly account for perturbations on the rate of expansion in the metric carrying information on the past history of that region of spacetime. I should note that from a limit analysis if as implied from the simplest model I can think of for the above the exitance of a nonzero minimum contribution to gravity for every element of the metric would in general lead to a transition from the local 1/r^2 dependence towards a cosmological baseline minimum. In essence everything might be expected to feel extra gravity from everything else in the universe which for an isolated galaxy in the limit where everything else is sufficiently far away you would likely recover the formalism of MOND (Modified Newtonian Dynamics). In essence both "dark energy" and "dark matter" might simply be consequences of the quantization of gravity in separate distinct and seemingly absurd and surprising ways. Neutrinos actually have been suggested to be a possible candidate for this gravity force carrier. I think I remember reading something from a Russian physicist by the name Boris V. Vasiliev. Also one important implication at least for testability of theories with this kind of asymmetric framework within the general formulism for the unconstrained Einstein field equations having a Fermionic character is that true black holes with an event horizon do not exist except as an abstract limit where the resulting gravitational redshift of a bodies black body spectrum will asymptotically approach the hawking limit. For a supermassive black hole there might as well not be a difference other than the possibility for such a SMBH to have an intrinsic magnetic field (which could explain some odd properties of AGN currently assumed to be somehow generated by the accretion disk through some poorly understood mechanism) instead we might expect a gradual transition from neutron star to black hole where the escape velocity asymptotically approaches the speed of light(or rather causality or information) as the mass of a compact body approaches infinity. This possibly provides a testable prediction in the form that we might expect highly redshifted luminous outbursts such as the recently discovered fast radio bursts to be able to originate from massive bodies which are above the Tolman-Oppenheimer-Volkoff limit.
@@wj9494 If you watch some of the animations/simulations on UA-cam of 1/2 spin, some of them appear to be modeling twist in my humble opinion. The Hopf Fibration seems to be showing the same concept. What is the simplest explanation for a basic unit of geometry which could produce a "Quantum" cycle proportional to Planck's Constant?
The Lagrangian is not an equation but a definition that is used to derive a real field equation (Euler-Lagrange) via calculus of variations. Other than that, a great breakdown 👍
so whenever i see things in physics videos / articles that say 'dont worry about this, its only here to fix some unwanted predictions of the equation'... it always feels to me like theyre just hand-waving away things they dont like so they can make the math work out the way they want it. i realize that, as a lay-person, i dont have the knowledge or background to really understand the 'why' of this hand-waving... but it sure does feel like a dodge to me, all these things that go into equations simply to 'make them work' without messy consequences. isnt it possible those unwanted things might actually be legitimate?
What happens when some sub-atomic particle wasn't paying attention in class during this Lagrangian lecture and decides to misbehave? What happens if all the electrons you see are actually just that one electron?
Dr Don , please show us pure Mathematical sides of the formulation of equations to do justice to this channel and to do justice to us (viewers) as well. Let the normal viewers skip it and we all advanced Physics + Maths students will watch it whole heartedly 🔥💥
Your editor might be wrong. On another channel a chap derived the neutron diffusion equation from scratch. He also calculated a first approximation to the mass required for an atomic bomb. 55kg if case you were wondering. You can get this mass down with some clever physics but thats another story. Rather than putting off viewers his numbers went exponential. Shares etc also went nuts. High quality tutorials rather than hand waving seems to have a audience on youtube
Look at it this way, and see if you agree: gravity and electromagnetism are both distance-oriented forces. If the "weak force" was a magnification with time, then it would build up. But decays by the weak force are infrequent but regular. The nucleus has too many degrees of freedom to "build up" easily; it is always leaking out retention energy to the orbitals. So, what if instead the "weak force" was a configuration-oriented force? That would make it statistically probabilistic. In other words, you might as well call it a resonance that quenches itself, in which case why bother calling it a "force"?
OK so here's a question from a non-scientist. If you need ghost particles to maintain the integrity of the equation doesn't that indicate a problem with the equation that may mean the equation is wrong? (Please note, I"m not pointing any fingers, I"m just trying to understand.)
If I understand correctly(sort of big IF), Ghosts are a type of "regularization". Which is a procedure that introduces a correction term as a placeholder for "new physics". Since we know that the standard model is incomplete, these ghosts tell us "hey, the rest is pretty well understood, but here is where your new theory could do work!" An example for this is _defining_ the electron to have a non-zero radius in classical mechanics so we don't have to deal with the potential at r=0. en.wikipedia.org/wiki/Regularization_(physics) en.wikipedia.org/wiki/Ghost_(physics) So yes, the equation is "wrong", but we know that the standard model isn't the final answer already. So this wrongness is there to keep the rest in line with observation.
it takes hundreds of hours to actually explain the underlying notions and math. It's a long path from school arithmetic this channel allows to show, to QFT's "oh we take e to the power of integral over spacetime of a field of quantum operators acting on state vectors in infinite dimensional Fock space to get an element of the scattering matrix that would give a probability amplitude of getting from one state to another, and by representing the exponent as a series we get a Feynman diagram for every piece of it... what, D? that's just the covariant derivative that takes into account effects of local gauge symmetry by including a term that couples a gauge field to the original one, easy!" You can't imagine how much you ask from Don. :)
Not being a physicist, I've never understood what these equations actually do. As in, how are they used? I get that they describe nature, but what are the practical applications?
They describe our models of how the universe works, so things like computers and nuclear reactors need this in design. Others detail how fluids and gasses flow and reactions take place. Useful in engine and aircraft design. This is just a compact way of describing how particles interact.
GPS satellites are the greatest example of how einstein's relativity is extremely useful.. satellites in orbit, travel, just a little bit faster in kph terms, but in terms of getting towards the speed of light, their clocks move slightly slower than the ones on earth do.... they're difficult concepts, but with some research they become easier to understand. basically your mobile phone wouldn't work without certain equations. and that's just for starters.
So i studied Computer Science on a recommended University. I would handle the math and there are really many people who are educated in math and want to learn more about that. I understand that most viewers are not interested in it, however, there are also a lot of viewer who are only interested in such a topic. There is no one providing a really deep step into the real complicated math level.
Argh, pronouncing Hermitian! I've been diving into the matrix representation of quantum mechanics and I can't find a consistent pronunciation of "hermitian" First I thought the 't' was said like a 'sh' like Dr. Don says here, then I saw other sources saying it with a hard 't' like "hermit" -- maybe there's a grand unified pronunciation?
All the open space between the writing seems to be a spiral path around a vortices maybe one must focus on the absence of what they thought should be there
Nice video DrDon, thanks, here's an additional excerpt from our latest conversations, hope you don't mind ;-) ... So we use kinetic mass to describe space, but the tensors themselves have no aperture so why do these vector tensors persist ?? Why does space abhor a vacuum and how does that tensor express in the Higgs field considering there is no flow space for the Kinetic drive ?? Furthermore, how the hell does a Gravity wave persist through space as it has no flow space aperture only density ?? This implies a whole new layer of space that we need to describe. **EINSTEIN**
This was a bit too shallow... not that i'm am expert but i preferred It to go a bit deeper and explain why and how this equation predicts anything... like why minus and plus signs and all. To make connection between mathematical equation and physical concepts
Entropy comes out of the equation... so to speak. The Lagrangian only describes the mechanics, that is *how* things interact, but not _what_ combination specific things you happen to have in the system you are modeling... Classical mechanics will tell you the position and momentum of the billard balls on a pool table, and how the balls will interact with each other in the collisions... but Classical mechanics isn't a theory about billard balls... Anyway, the entropy of the billard balls on the pool table... depends on how many balls you have, how fast they are moving, and how big your pool table is... and Classical mechanics only tells you how the parts interact with each other... from all of those interactions, you can then calculate the entropy. Quantum Field Theory is basically like this except rather than billard balls, it's describing probabilities of having more than zero ±h energy at every location in spacetime which is coupled to every other location in spacetime (which describes a wave)... and then you have a bunch of these probability fields that have a different probability of interacting with each other. The φ and ψ parts of the equation in this video are themselves another big differential equation for a bunch of waves of probability propagating through space and time.
What would have been interesting is seeing the relationship between the parts of the compact expression of the standard model Lagrangian and the T and V parts….
All of that is the "T" part, except for the -V(Φ) at the end, which is where you stick in the details of whatever your experimental setup or the arrangement of the parts of your system that you want to calculate. (Like say, a bound electron in a hydrogen atom or the collision of two protons for example.)
... in Classical Mechanics. Is it too much to ask. What is the physical reasoning behind the Classical Mechanics Lagrangian? Don't use F = ma. Again: don't describe. Explain. Thanks.
Yeah, but solving a Lagrangian requires solving a PDE, whereas solving Newtonians requires solving ODEs, although you have to solve a system fo ODEs: 3N for N particles, and the Lagrangian PDE is linear.
Thanks for the shout out! Great overview and fun to see an exercise I did 25 years ago still has some value to the community.
Thanks for the link Thomas !
You need to put "This fourth section is kind of technical" on a t-shirt next to the expanded equation! Lmao
We are blessed to having you to explain us these things, Dr. Don.... we love you!!!
"The solution is left as an exercise for the student" OMG! It's been 30 years out of college and I remember this!
And I still hate it.
I bet it is one of the longest running jokes in universities.
Oh, yes!
It's as bad as "the result is immediately obvious to the casual observer".
@@soaringvulture Worse, if you hear that while you're still nursing that hangover on Monday from the Friday night frat party.
Great stuff. “I leave the details as an exercise” made me laugh. I remember those days. 😂
The Science Asylum made a great video on Lagrangian Mechanics a couple of years ago. It's well worth checking out.
also pbs space time did a slightly more detailed video on the components of the equation.
watch?v=PHiyQID7SBs
That sounds crazy! Well, maybe only a little crazy. I guess that's okay.
Eugene Khutoryansky as well.
"This fourth section is kinda technical" hilarious 😅
That is Don's version of a physics flex! :)
Yup, made me laugh too
Came here to say that. I almost spit out my tea 😂
As a collection of fundamental particles, I can confirm this is how we calculate our Lagrangian.
You collect them too?😮 Want to trade some muons for some neutrinos?🤨😜
Muon decay makes two neutrinos. That is a terrible deal.
As I always say "just because I don't understand it doesn't make it false." I'm really glad somebody does so I don't have to think about it (much).
Or as Neil deGrasse Tyson uses to say: The Universe is under no obligation to make sense to you.
@@SiqueScarface this quote is a great thought to keep in the back of your mind as you encounter strange things and people throughout your life!
Please do another video. How do you go from the Lagrangian to wavefunctions (probability densities)? Schroedinger's equations involves the Hamiltonian. Why does particle physics use the Lagrangian instead? Is there a wave equation in particle physics?
Ok here's what I've learnt so far in my MS Physics course...
Lagrangian formulation is almost always the preferred option to study any system. It is done using the Euler-Lagrange equations to find the equations of motion, which are differential equations describing the system. So it turns out that if you have a Lagrangian, you can always get equations of motion from it. The number of equations depend on the degrees of freedom and constraints on the system.
Now, you know that the Schrödinger equation is a differential equation which begs the question: Can we find a Lagrangian for it too? The answer is YES! Even cooler fact is that it is not the kind of Lagrangian you may get in, say, a simple pendulum. It is a "Lagrangian density", and if we use the "Euler-Lagrange equations for fields" on it, we will end up with the familiar Schrödinger equation, and its complex conjugate. The wave-functions found in the Schrödinger equation are simply "field variables" in the Lagrangian density, existing in the Hilbert space.
Yes, @@shoaibansari3224. Also, in addition to this, the Lagrangian is highly effective when exploring the internal symmetry properties of a system (which elucidate the general characteristics of the system), and is involved in the standard quantization of field theories (where "fields" are commonly used in particle physics, including the Schrödinger Field). For example, while studying Quantum Field theories myself, the Hamiltonian formalism was hardly explored but occasionally crucial nonetheless.
The legendre transform of an L is an H, but that’s not relevant here. The SM is a relativistic quantum field theory, so processes are computed in the S matrix formulation….basically you calculate cross sections, maybe masses.
Schrödinger and wave functions are entirely different…non relativistic quantum mechanics.
They might overlap in say, the quark wave function of a J/Psi? But then q qbar bounds states are way more complicated than positronium…so idk.
True, @@DrDeuteron. However, the time-ordering involved in computing the S-matrix elements is obtained from the interaction Hamiltonian. Although Feynman diagrams reduce the computational complexity, the intricacies of Wick's theorem are implicitly incorporated.
@@HunnidTheTrapper02 and that's the problem with most layman QFT questions, by the time you know how to answer them, your would never bother asking them.
The „Dragon“ comment reminds me about something Prof. Gassner said in his series „From Arstotle to String Theory“ (sorry, only in German, on the channel „Urknall, Weltall und das Leben“) when he discussed General Relativity. He wanted to tip-toe around the deep where the Monster lives, and only do a little peek - at the Riemann Tensors (iirc).
😊
Ha! I first read about Lagrangians last night in Sean Carroll's 'Biggest ideas' book. What a nice coincidence to see this video this morning.
I think there's a good number of the public who are interested in this type of content but want a bit more than the usual 'lay' descriptions but who aren't physics students. Anything that takes us slightly 'under the hood' albeit with more math is greatly welcomed.
A couple of people have asked about this... if you need to calculate anything more complicated than a "Spherical cow in a vacuum", then using Hamiltonian or Lagrangian mechanics makes the calculation much easier to do than using Newtonian mechanics... assuming that you understand second order ordinary linear differential equations.
The Lagrangian and Hamiltonian stuff is usually not taught until your third year physics class in college, because you need to pass a class on differential equations prior to it.
The first year physics class uses Newtonian F=ma stuff because you only need to know Algebra... or if you've had a first year calculus class, maybe F=dp/dt=m•d²/dt² and stuff.
“…and stuff.” being the operative phrase here.
IIRC you told us a while back that you were making a video to explain that equation! I am happy we finally get that answer!
I encourage anyone who finds this interesting to dig into the math(s) themselves! As much as you can find lots of great easy-to-follow introductions like this online, the satisfaction of actually _understanding_ how it works is truly transcendental. Personally I found Leonard Susskind's _Quantum Mechanics: The Theoretical Minimum_ very helpful. (It takes some hard work to get through, but I only have a high-school level of formal physics education and was able to learn a lot from it, so chances are you can too!)
Just commented the same! Susskind's great for this kind of thing, well worth checking out his lectures here on YT.
Yep, and not just QM, his Standard Model lectures on Theoretical Minimum are great to watch too.
Dr. Lincoln is the best physics teacher!
Hello Dr Don, I have always appreciated to have you to be my UA-cam-physics mentor .you are awesome! Also in a lucky case that if you saw my comment, my question would be asking about how come the general relativity has incompatibility with quantum mechanics. What are physicists really looking for to unifying these two theories?
Gravity and quantum mechanics. Unfortunately, when the theories are combined, an infinite number of infinities pop out.
@@drdon5205Hello Dr. Don! Thank you for the comment and explanation.
However I still don't quite understand why infinite number of infinities would pop out. Maybe it is that the equation of General Relativity was built to explain the intensity of gravitational force ,so it cannot be quantized?
Thank you for taking time to read my comment. I still want to ask you some other questions .
First ,could gravity be a result of the expansion of space-time, due to the uneven distribution of dark energy? I have watched a fermilab video you made ten months ago. In that video, you have mentioned something called entropic gravity. Can we have more details about this topic in future videos?
Second question. Since photon is electromagnetic wave, can space itself waving like photon does? If it could, would this waving property of space cause the universe to have a electric field just like single photon does? And after all,can this be the reason that universe ended up to have more matters than antimatter?
Based on my shallow knowledge about universe. I can only assume that different electric-field type may be able to affect the rates of different types of nuclear decay. And I could be so wrong about my idea. Hope to receive some corrections from expert like you.
Thank you so much for all the works you have done through these years. Hope see your video soon! take care Dr Don.
I would love for you to dig into the advanced math! Maybe in a separate video. I took a course on the calculus of variations ages ago in college and we studied the langrangian as well, and lately I'm having a midlife crisis about never doing anything with that part of my education. I would love a refresher.
Wow that homework was really a tough one, but after pulling some strings i could find a solution for a 26 dimensional homogenous, isotropic Anti-de Sitter space. Then i failed miserably to figure out to whom or where i should send the homework to.
There is no due date for your homework; you do not have to turn it in; it will not be graded; keep working on it for the rest of your life. You cannot possibly finish it because L = T - V has no physical meaning.
Probably Juan Maldecena, since you’re clearly using his AdS/CFT correspondence.
He’s likely to only give partial credit, since you didn’t do the full compactification from 11D M theory, but instead used one of the old purely bosonic string theories (the ones that literally had & required 26 spatial dimensions) 😅
Do the sub and super scripts indicate that there are Tensors involved in the equation?
Yes, but simple ones
Is there a video that is a little more detailed on that ghost particle concept?
Give up the 👻, really. It’s an iykyk type situation.
Nitpick: The Lagrangian is usually written with a usual L, hence the equation at 2:45 should simply be L = T - V. The strange version of the L on the shirt actually is the Lagrangian _density_; you have to use energy _densities_ for that, not simply energies.
Bugged the hell out of me that as a physics student, we resolved forces in high school, as undergrads, and it wasn't until THIRD YEAR undergrad, we were finally taught this much easier way of doing things. The Langrangian should be taught in high school.
Not publishing advanced physics on a physics channel is a pretty bad idea... if the editor is reading this, bro let the physicist make the physics content, you don't get it because you are not into physics like that, just focus on bringing stuff to life with editing... you do a really good job of editing it, please let him expand on the physics. I personally would've loved if this video explained everything in more depth.
So glad you wrote this!
Agree 100%
FR!
I absolutely agree with this. Or otherwise, just publish another video for the deep dive.
I don't think it's right to assume that the editor isn't into physics "like that." It could very well be that it's the opposite, and the editor just didn't want to confuse people or turn people away from the video.
So... my $5 Panasonic calculator isn't going to be of much use here, is it? Thank you Dr. Don! This stuff is fascinating to me, even though I still count using my fingers. 😊
Wow, he really did just explain the equation describing the entire standard model of particle physics in 9 minutes and 45 seconds
He just named some parts, that's not really an explanation. A viewer might think that Ψ here is a number of a number-valued function, and be very far from what it really denotes.
I am a physicist and know what a Lagrangian is. I even recognize this version representing the standard model. But frankly, I never needed to use this approach in my own research. Am I lucky?
You just need to be able to recognize it and understand how it fits into the larger picture. Just like any other physical principle application.
@@hugegamer5988it is the larger picture. No single measurements uses more than a slice of that thing.
@@DrDeuteron it is not. It’s the particle energy portion, but lacks geometry. There are multiple approaches to forming it as well.
Can you make a follow up video of the relation with the Lagrange points in space. Which also James Web is using?
Question from a non-physicist: Is the section about "ghost particles" and "cleanup" just a fudge factor? If not, why not?
If you need 2 sections to fix the previous sections, shouldn’t the other section be rewritten so they are correct? Do we know why the correction is needed?
Any book suggestions where I can learn about the derivation of this equation in depth? Note: I am not a beginner physics student.
Michael E. Peskin, Daniel V. Schroeder - An Introduction to Quantum Field Theory; Walter Greiner, Joachim Reinhardt - Field Quantization
Well, you just brought 2 things together that I've been studing months. Thank you.
At 4:59 which one is the psi? Or is it phi? It doesn't look like it...
Ψ = PSI
Φ = PHI
Why are weyl fermions not on the standard model or a nonstandard model? Since they naturally occur sometimes but granted they are kind of rare compared to most other particles. Why not include Majorana fermions, and other quasi particles?? Can you do a video on that? Please and thank you in advance!
Personally, I not only welcome deep dives and math but encourage them thoroughly! Still a good very base level intro to topic, but I fear I may need to return to university to advance as UA-cam vids seem to be far too shallow on advanced topics as of late (or just go back to watching lectures on here, like Leo Susskind and others)
Dr. Don, Great video! It sparked another question: Could black holes be where antimatter collected? I.e., could antimatter from the early universe disproportionately collecting in black holes explain the antimatter paradox?
Dr. Don, Great video! It sparked a question: What happens when antimatter falls into a black hole? My understanding is that black holes can have net charge, but it seems that positrons and antiprotons could equally contribute.
It seems that black holes must contain antiparticles (rather than exploding from the annihilation energy). Could black holes be where the antimatter collected? (I.e., does this explain the antimatter paradox?)
If there is an “anti-black hole”, what would happen if it collided with a standard black hole?
If antimatter enters a black hole, it has the same effect as matter entering. If that antimatter has net charge, it will change the way you suggest.
I love how Dr. Don can take the scariest possible equations, and make them at least slightly comprehensible to us lay persons who only took high school physics and chemistry classes, and those were 50 years ago for me.
THANK YOU...
PROF. DR. LINCOLN...!!!
Theoretically interesting to look at it... but mathematically don't even think to be close to that equation except:
L = Kinetic Energy - Potential Energy.
THANKS AGAIN ...!!!
After covering about 100 variables on 12 lines of text: "This next part is kinda technical..." 😮
what's the chance that dark matter or dark energy can be detected or disproved? would a vat of Bose Einstein condensate in outer space have a better chance of detecting it? do you guys use materials with negative absolute temperatures for anything?
"This fourth section is kind of technical." Master of understatement there, Don.
There's a funky popularization article by Woithe et al. (2017), that invites you to have one or more (hot) coffees "h.c." with the Standard Model of particle physics. ☕
I've been drinking my coffee from the famous mug (the one with the Lagrangian written in white on a black background, that I bought at CERN) for 4 or 5 years now. Although I work in a completely different professional field, the desire to understand this equation has given me the urge to study physics (and therefore maths ! ), just for the fun of it ! So thank you, Don, (and the whole team) for this video!
>> And don't forget - especially if you're going to Switzerland and visiting CERN - if you're worried that too much "h.c." (hot coffee) is bad for you, you can also fill your "Standard Modell mug" with Hot Chocolate ! 😋
Does the recent Muon g-2 experiment results call for a modification of this equation?
I *_think_* the preliminary results from Fermilab are that their measurements of Muon G-2 *are* in agreement with the value predicted by the Standard Model.
I can't quite find the results with Google at the moment, but Google Search sucks now, and I thought I heard some Muon G-2 news recently about these results.
Wait how does it change with electroweak theory? Does it become simpler?
Aren't the "ghost fixes" basically an indication, that there is an incoming paradigm shift to replace the Standard Model?
I just figured that they were fudge factors added to make the math come out right, meaning that the math is wrong.
Quite possibly though there is also a good possibility that this is a consequence of phsyicsits using complex numbers rather than the more accurate quaternion mathematics.
Looking this up these terms of ghost particles appear to be related to conserving gauge invariance within the path integral formulation. They are ghosts or virtual particles because these terms themselves are not directly observable and there is a corresponding term associated with each gauge field. Apparently if you try and solve the equations without them the matrices become singular and these terms are basically a way to get around that. Now quaternions are the correct way to represent mathematics of symmetry groups in that other approaches are more or less approximations which have the potential to break down.
This has an interesting classical parallel problem in the form of another types of matrix math operations in physics rotation matrices which can be eliminated by utilizing quaternions instead of complex numbers where there is now effectively 3 different kinds of imaginary numbers. As the operations these ghosts are used to get around in the standard model here are all symmetry group relations we thus are guaranteed singularity if we don't correctly use quaternion operations which is particularly a problem with distributed quantum fields where you can't just ignore the singular domain of matrices in 3D+time space.
Notably these ghost terms share most of the properties of anticommutation seen in quaternions so in all likelihood there exists a formulation of the standard model with quaternions rather than simple complex numbers. It is just either undiscovered or physicists are uninterested in formulating the equations this way.
Quaternions originally were formulated/discovered by Sir William Rowan Hamilton and his reformulation of Newtonian and Lagrange Mechanics into Hamiltonian mechanics. This invention proved critical in allowing Maxwell to formulate Maxwell's equations which were defined in terms of quaternion operations. Modern physicists have for some reason or another likely the inherit complexity of managing quaternion operations developed a way of approximating them using matrices. We don't really have any intuition working with quaternion mathematics so they are cumbersome to us.
Notably however the mathematics of spinors also relies on quaternions and is one of the few context where physicists still begrudgingly use them though only in the form of Pauli matrices.
Quaternions have become important in computer science particularly in the case of handling graphics since the little tricks physicists use to get around quaternions are computationally more expensive than just solving the quaternions. Computers unlike humans have no qualms or difficulties solving quaternions.
Heck the brains of some animals like dragonflies are able to perform maneuvers which in aerospace/machines require quaternions to achieve without critical failure so it really looks to be an "us" problem we will at some point have to grow out of as a species.
What I draw from all Dr Don’s videos is that a big bloke can also have a big brain, both literally and figuratively! 😊
The total energy, T + V, kinetic energy plus potential energy has real meaning. However, the Lagrangian L = T - V has no real physical meaning. Are we missing something?
The total energy T + V is the Hamiltonian. It's a bit easier to use since it's multiple first order linear differential equations, rather than the Lagrangian which is a second order linear differential equation. You need to setup the Hamiltonian in an abstract phase space, depending on the particular degrees of freedom in the system that you are modeling.
Like... should I go on about how to derive the Action, and how to convert from Newtonian force vectors into potential energy, and stuff? (And Nöther's Theorem?)
Basically, if it's the 1800's and you need to analyze the movements of a complicated mechanical device, then Lagrangian or Hamiltonian mechanics is much much easier to calculate than Newtonian mechanics (if you know differential equations). (They don't actually teach this stuff until the third year physics classes in college, because students must know differential equations first.)
Like, if you want to calculate the motion of a small mass, that is spinning around on a vertical wire hoop, that is bouncing up and down on a spring, that has the other end attached to the floor of a rotating Merry-go-round, etc. etc. with air resistance and friction accounted for... this is written as just one simple to solve Lagrangian equation. Doing this same calculation with Newtonian mechanics is a tedious pain in the ass, filling several sheets of paper to get the same answer.
One way to give it meaning is looking at en.wikipedia.org/wiki/Path_integral_formulation
@@thedeemon Feynman used the L = T - V approach in his path integral formulation. If you look closely at it, it has very little meaning.
Hey , Dr Don, unrelated question. Can leptons be used instead of electrons to power our devices. Leptronics?
Electrons _are_ leptons. The other leptons are muons and tau particles, which are basically heavier electrons. Unfortunately they aren't stable, so you can't really do anything with them.
Then there are the neutrinos, which you really can't do anything at all with.
@@narfwhals7843 Oh wow. It’s sad the Millennium Project cited them as a future tech. I know neutrinos don’t interact with anything but Isaac Arthur (futurist) believes they can be used for power generation and propulsion.
@@Italianjedi7 I mean, if you want to talk _extremely_ theoretical *far* future applications, then yes. It is possible that neutrinos may be used for propulsion and power generation. They don't "not interact at all" they interact very weakly. But if you have enough of them they can sustain a star from collapse. But the process to get enough of them is a super nova. So that might give you a sense of scale.
You don't need a super nova to move a rocket. But you need a sustained fusion reaction far above what we are even remotely considering for the neutrinos to be an appreciable part of the energy output.
@@narfwhals7843 Wow. Yeah I think Isaac said it was Clarketech. Thanks for the response!
Thanks Dr. Don. I love the concept, "What does that equation mean?" to make complex ideas more intuitive. How about doing, "What does that diagram mean?" I have been enthralled by the beauty of the Feynman Diagram for electron positron annihilation, with the positron and anti-quark moving backward in time. And what does that really mean for the concept of causality?
I love the way that Dr Don says “this fourth part is a bit technical”. By the fourth part both my neurons were spaced out anyway!
To paraphrase Monty Python....this is not an equation for reading; this is an equation for laying down and avoiding
If quarks have not been isolated and gluons have not been isolated, how do we know they are not parts of the same thing? The tentacles of an octopus and the body of an octopus are parts of the same creature.
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.
=====================
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.
Wowww now this is what i can call a Flex!!😅😅
This comment put such a strain on my brain that i have to go and put my head in the freezer to help shrink it down 😂😂😂
You've covered a lot of ground here, but I ask, is there any way to prove/disprove the idea of a twisted tube?
Hmm I do think building off Kaluza-Klein Theory probably an extension using quaternions which are the most exact mathematic operations for symmetry groups and rotations.
As a conventional theory I don't think neutrinos can account for dark matter though its possible they could become relevant in the context of extended indirect effects such as the implied handedness which appears within the generalized unconstrained Einstein field equations so long as one does not artificially/forcibly constrain its behavior to symmetric solutions (and thus universally violating conservation of information with regards to the initial conditions).
Specifically the interactions of anisotropies and inhomogenities propagate into the rate of expansion locally based on the past history lightcone. Following the implications of the proof by self contradiction within Inhomogeneous and anisotropic cosmology by Matthew Kleban Leonardo Senatore 2016,(which the authors barely touched on) the conditions for the Einstein field equations to be internally self consistent is that off diagonal elements of the metric must always have an irreducible nonzero asymmetric contribution imprinted in the rate of expansion of space. Looking into this further this just so happens to eliminate any and all need for "dark energy" the latter becoming a pure consequence of gravity in a nontrivial universe, while also implying all possible quantized elements of spacetime should they exist must have a uniquely defined state for each and every possible element of the metric that is to say that if a summation form of the Einstein field equations exists all these base elements of spacetime must anticommute or be what are known as Dirac sponsors which obey the property known in quantum mechanics as the Pauli exclusion principal. In essence the full irreducibly nonlinear(chaotic) domain of the unconstrained Einstein field equations is casually forbidden from having a boson based quantization of space and or gravity. Only Fermions are allowed to exist as a force carrier and gravity is likely fundamentally involved in spin flip transitions. The type of frame work you have proposed here seems to be consistent with that though the caveat is that any theory to be consistent with the above must be "nonlocal" if we do not properly account for perturbations on the rate of expansion in the metric carrying information on the past history of that region of spacetime.
I should note that from a limit analysis if as implied from the simplest model I can think of for the above the exitance of a nonzero minimum contribution to gravity for every element of the metric would in general lead to a transition from the local 1/r^2 dependence towards a cosmological baseline minimum. In essence everything might be expected to feel extra gravity from everything else in the universe which for an isolated galaxy in the limit where everything else is sufficiently far away you would likely recover the formalism of MOND (Modified Newtonian Dynamics). In essence both "dark energy" and "dark matter" might simply be consequences of the quantization of gravity in separate distinct and seemingly absurd and surprising ways.
Neutrinos actually have been suggested to be a possible candidate for this gravity force carrier. I think I remember reading something from a Russian physicist by the name Boris V. Vasiliev.
Also one important implication at least for testability of theories with this kind of asymmetric framework within the general formulism for the unconstrained Einstein field equations having a Fermionic character is that true black holes with an event horizon do not exist except as an abstract limit where the resulting gravitational redshift of a bodies black body spectrum will asymptotically approach the hawking limit.
For a supermassive black hole there might as well not be a difference other than the possibility for such a SMBH to have an intrinsic magnetic field (which could explain some odd properties of AGN currently assumed to be somehow generated by the accretion disk through some poorly understood mechanism) instead we might expect a gradual transition from neutron star to black hole where the escape velocity asymptotically approaches the speed of light(or rather causality or information) as the mass of a compact body approaches infinity. This possibly provides a testable prediction in the form that we might expect highly redshifted luminous outbursts such as the recently discovered fast radio bursts to be able to originate from massive bodies which are above the Tolman-Oppenheimer-Volkoff limit.
@@wj9494 If you watch some of the animations/simulations on UA-cam of 1/2 spin, some of them appear to be modeling twist in my humble opinion. The Hopf Fibration seems to be showing the same concept. What is the simplest explanation for a basic unit of geometry which could produce a "Quantum" cycle proportional to Planck's Constant?
The Lagrangian is not an equation but a definition that is used to derive a real field equation (Euler-Lagrange) via calculus of variations. Other than that, a great breakdown 👍
@@RockBrentwoodnope
@@RockBrentwoodright sure but on it’s own it doesn’t mean anything. it’s just an expression that lists things and L is the name of that expression.
so whenever i see things in physics videos / articles that say 'dont worry about this, its only here to fix some unwanted predictions of the equation'... it always feels to me like theyre just hand-waving away things they dont like so they can make the math work out the way they want it. i realize that, as a lay-person, i dont have the knowledge or background to really understand the 'why' of this hand-waving... but it sure does feel like a dodge to me, all these things that go into equations simply to 'make them work' without messy consequences. isnt it possible those unwanted things might actually be legitimate?
Epic opening cards, explanation, and closing cards -- and not necessarily in that order!
What happens when some sub-atomic particle wasn't paying attention in class during this Lagrangian lecture and decides to misbehave? What happens if all the electrons you see are actually just that one electron?
Dr Don , please show us pure Mathematical sides of the formulation of equations to do justice to this channel and to do justice to us (viewers) as well. Let the normal viewers skip it and we all advanced Physics + Maths students will watch it whole heartedly 🔥💥
Great. Now explain all the formules on the black board behind you...
So well explained! Thanks!!
Your editor might be wrong. On another channel a chap derived the neutron diffusion equation from scratch. He also calculated a first approximation to the mass required for an atomic bomb. 55kg if case you were wondering. You can get this mass down with some clever physics but thats another story.
Rather than putting off viewers his numbers went exponential. Shares etc also went nuts.
High quality tutorials rather than hand waving seems to have a audience on youtube
"The solution is left as an exercise to the student."
Haha oh man I felt that one!
Look at it this way, and see if you agree: gravity and electromagnetism are both distance-oriented forces. If the "weak force" was a magnification with time, then it would build up. But decays by the weak force are infrequent but regular. The nucleus has too many degrees of freedom to "build up" easily; it is always leaking out retention energy to the orbitals. So, what if instead the "weak force" was a configuration-oriented force? That would make it statistically probabilistic. In other words, you might as well call it a resonance that quenches itself, in which case why bother calling it a "force"?
Dr. Don who is your tailor? Where is your T-shirts and merchandise?
Do particle physicists actually use these very long equations in their day to day work?
OK so here's a question from a non-scientist. If you need ghost particles to maintain the integrity of the equation doesn't that indicate a problem with the equation that may mean the equation is wrong? (Please note, I"m not pointing any fingers, I"m just trying to understand.)
If I understand correctly(sort of big IF), Ghosts are a type of "regularization". Which is a procedure that introduces a correction term as a placeholder for "new physics". Since we know that the standard model is incomplete, these ghosts tell us "hey, the rest is pretty well understood, but here is where your new theory could do work!"
An example for this is _defining_ the electron to have a non-zero radius in classical mechanics so we don't have to deal with the potential at r=0.
en.wikipedia.org/wiki/Regularization_(physics)
en.wikipedia.org/wiki/Ghost_(physics)
So yes, the equation is "wrong", but we know that the standard model isn't the final answer already. So this wrongness is there to keep the rest in line with observation.
Okay so like where do I get the shirt now though
Sir, please create and publish the math video. I would appreciate it very much.
it takes hundreds of hours to actually explain the underlying notions and math. It's a long path from school arithmetic this channel allows to show, to QFT's "oh we take e to the power of integral over spacetime of a field of quantum operators acting on state vectors in infinite dimensional Fock space to get an element of the scattering matrix that would give a probability amplitude of getting from one state to another, and by representing the exponent as a series we get a Feynman diagram for every piece of it... what, D? that's just the covariant derivative that takes into account effects of local gauge symmetry by including a term that couples a gauge field to the original one, easy!"
You can't imagine how much you ask from Don. :)
🥺 That thumbnail of this video, doctor, it's the beautiful Lagrangiano del modelo estándar de partículas 🥺.. beautiful 🥺
you shloud do clip for hologram quantum gravity
Are you missing a term here? Where's the kinetic energy of the fermions?
Can you explain how light can travel in vacuum?
I entered that equation into the Calculator App on my phone and the darnedest thing happened. The display read: "You're joking, right?"
(😂)
Where can I buy this shirt?
All you need is a black shirt and a white marker.
@@unduloid And good handwriting.
That's great , thanks. I finally know what that equation is on my CERN T-shirt !
Goldstein's "Classical Mechanics" concludes with relativistic field theory.
Too bad it never get covered in class.
Not being a physicist, I've never understood what these equations actually do. As in, how are they used? I get that they describe nature, but what are the practical applications?
Well, they can be put on t-shirts.
They describe our models of how the universe works, so things like computers and nuclear reactors need this in design.
Others detail how fluids and gasses flow and reactions take place. Useful in engine and aircraft design.
This is just a compact way of describing how particles interact.
Predicting how particles interact with each other. You may doubt that this is a practical application. But there are people for whom it is.
@@arctic_haze I have no doubt that there are practical applications. I just don't understand how they're used.
GPS satellites are the greatest example of how einstein's relativity is extremely useful.. satellites in orbit, travel, just a little bit faster in kph terms, but in terms of getting towards the speed of light, their clocks move slightly slower than the ones on earth do.... they're difficult concepts, but with some research they become easier to understand. basically your mobile phone wouldn't work without certain equations. and that's just for starters.
So i studied Computer Science on a recommended University. I would handle the math and there are really many people who are educated in math and want to learn more about that.
I understand that most viewers are not interested in it, however, there are also a lot of viewer who are only interested in such a topic. There is no one providing a really deep step into the real complicated math level.
Love it
Saw it at cern on t-shirt but thought it was the lamda cdm calcs
I wonder why the Higgs part of that equation isn't written in a more compact way
You probably could, at the expense of making the other parts more complicated.
Argh, pronouncing Hermitian! I've been diving into the matrix representation of quantum mechanics and I can't find a consistent pronunciation of "hermitian"
First I thought the 't' was said like a 'sh' like Dr. Don says here, then I saw other sources saying it with a hard 't' like "hermit" -- maybe there's a grand unified pronunciation?
All the open space between the writing seems to be a spiral path around a vortices maybe one must focus on the absence of what they thought should be there
My favorite moment is at 8:07 - "This fourth section is kind of technical.". Yep. Sure.
Are phisasis to have member all that ?
:D I don't always sound stupid
Nice video DrDon, thanks, here's an additional excerpt from our latest conversations, hope you don't mind ;-) ...
So we use kinetic mass to describe space, but the tensors themselves have no aperture so why do these vector tensors persist ??
Why does space abhor a vacuum and how does that tensor express in the Higgs field considering there is no flow space for the Kinetic drive ??
Furthermore, how the hell does a Gravity wave persist through space as it has no flow space aperture only density ??
This implies a whole new layer of space that we need to describe.
**EINSTEIN**
would love to see the more advanced cut
Don at 8:10 "This section is a bit technical". Yes, Don, that's the technical part 😂
I love this channel is a secret vote for our country
Where's the bit describing dark matter and dark energy?
Thank you for the video.
This was a bit too shallow... not that i'm am expert but i preferred It to go a bit deeper and explain why and how this equation predicts anything... like why minus and plus signs and all. To make connection between mathematical equation and physical concepts
Nobody could do that whole standard model Lagrangian by hand! Good thing we have supercomputers to calculate for us… 😁
Ok... but where does Entropy go in that equation?
Entropy comes out of the equation... so to speak. The Lagrangian only describes the mechanics, that is *how* things interact, but not _what_ combination specific things you happen to have in the system you are modeling... Classical mechanics will tell you the position and momentum of the billard balls on a pool table, and how the balls will interact with each other in the collisions... but Classical mechanics isn't a theory about billard balls... Anyway, the entropy of the billard balls on the pool table... depends on how many balls you have, how fast they are moving, and how big your pool table is... and Classical mechanics only tells you how the parts interact with each other... from all of those interactions, you can then calculate the entropy.
Quantum Field Theory is basically like this except rather than billard balls, it's describing probabilities of having more than zero ±h energy at every location in spacetime which is coupled to every other location in spacetime (which describes a wave)... and then you have a bunch of these probability fields that have a different probability of interacting with each other. The φ and ψ parts of the equation in this video are themselves another big differential equation for a bunch of waves of probability propagating through space and time.
Just found this vid. My brain said to me: "thank you for studying philosophy."
My old engineering mentor was always leaving something as an exercise for the student. In time I became a very fit engineer.
What would have been interesting is seeing the relationship between the parts of the compact expression of the standard model Lagrangian and the T and V parts….
All of that is the "T" part, except for the -V(Φ) at the end, which is where you stick in the details of whatever your experimental setup or the arrangement of the parts of your system that you want to calculate. (Like say, a bound electron in a hydrogen atom or the collision of two protons for example.)
... in Classical Mechanics. Is it too much to ask. What is the physical reasoning behind the Classical Mechanics Lagrangian? Don't use F = ma. Again: don't describe. Explain. Thanks.
Yeah, but solving a Lagrangian requires solving a PDE, whereas solving Newtonians requires solving ODEs, although you have to solve a system fo ODEs: 3N for N particles, and the Lagrangian PDE is linear.
8:06 "...kind of technical.." . And the rest wasnt? - Said us with high school math degree 😂
Does it equate to 42? 😅