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.

@jmfwhittle

12 күн бұрын

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

"The solution is left as an exercise for the student" OMG! It's been 30 years out of college and I remember this!

@maythesciencebewithyou

3 ай бұрын

And I still hate it.

@jimmyzhao2673

3 ай бұрын

I bet it is one of the longest running jokes in universities.

@XB10001

3 ай бұрын

Oh, yes!

@soaringvulture

3 ай бұрын

It's as bad as "the result is immediately obvious to the casual observer".

@davestorm6718

3 ай бұрын

@@soaringvulture Worse, if you hear that while you're still nursing that hangover on Monday from the Friday night frat party.

"This fourth section is kinda technical" hilarious 😅

@backwashjoe7864

3 ай бұрын

That is Don's version of a physics flex! :)

@MrKrupp42

3 ай бұрын

Yup, made me laugh too

@huette

3 ай бұрын

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.

@Bob-of-Zoid

3 ай бұрын

You collect them too?😮 Want to trade some muons for some neutrinos?🤨😜

@DrDeuteron

3 ай бұрын

Muon decay makes two neutrinos. That is a terrible deal.

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.

@sheepwshotguns42

3 ай бұрын

also pbs space time did a slightly more detailed video on the components of the equation. watch?v=PHiyQID7SBs

@tomkerruish2982

3 ай бұрын

That sounds crazy! Well, maybe only a little crazy. I guess that's okay.

@minhdang1775

3 ай бұрын

Eugene Khutoryansky as well.

We are blessed to having you to explain us these things, Dr. Don.... we love you!!!

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).

@SiqueScarface

3 ай бұрын

Or as Neil deGrasse Tyson uses to say: The Universe is under no obligation to make sense to you.

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!)

@KSignalEingang

3 ай бұрын

Just commented the same! Susskind's great for this kind of thing, well worth checking out his lectures here on YT.

@thedeemon

3 ай бұрын

Yep, and not just QM, his Standard Model lectures on Theoretical Minimum are great to watch too.

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). 😊

Wow, he really did just explain the equation describing the entire standard model of particle physics in 9 minutes and 45 seconds

@thedeemon

3 ай бұрын

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.

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!

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.

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?

@shoaibansari3224

3 ай бұрын

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.

@HunnidTheTrapper02

3 ай бұрын

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.

@DrDeuteron

3 ай бұрын

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.

@HunnidTheTrapper02

3 ай бұрын

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.

@DrDeuteron

3 ай бұрын

@@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.

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.

@Vatsek

3 ай бұрын

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.

@zackyezek3760

3 ай бұрын

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) 😅

Dr. Lincoln is the best physics teacher!

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.

Epic opening cards, explanation, and closing cards -- and not necessarily in that order!

Thank you for your videos. You are my physics guy! ❤

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. 😊

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.

@paulrapp613

2 ай бұрын

“…and stuff.” being the operative phrase here.

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.

After covering about 100 variables on 12 lines of text: "This next part is kinda technical..." 😮

Fascinating!

Thank you for the video.

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.

"This fourth section is kind of technical." Master of understatement there, Don.

To paraphrase Monty Python....this is not an equation for reading; this is an equation for laying down and avoiding

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 ! 😋

Great videos!

Love it Saw it at cern on t-shirt but thought it was the lamda cdm calcs

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 🔥💥

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 KZread 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)

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?

@hugegamer5988

3 ай бұрын

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.

@DrDeuteron

3 ай бұрын

@@hugegamer5988it is the larger picture. No single measurements uses more than a slice of that thing.

@hugegamer5988

3 ай бұрын

@@DrDeuteron it is not. It’s the particle energy portion, but lacks geometry. There are multiple approaches to forming it as well.

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 ...!!!

That's great , thanks. I finally know what that equation is on my CERN T-shirt !

What I draw from all Dr Don’s videos is that a big bloke can also have a big brain, both literally and figuratively! 😊

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!

🥺 That thumbnail of this video, doctor, it's the beautiful Lagrangiano del modelo estándar de partículas 🥺.. beautiful 🥺

Hello Dr Don, I have always appreciated to have you to be my KZread-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?

@drdon5205

2 ай бұрын

Gravity and quantum mechanics. Unfortunately, when the theories are combined, an infinite number of infinities pop out.

@user-fw1bu6fd2i

Ай бұрын

​@@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.

Very good!

I entered that equation into the Calculator App on my phone and the darnedest thing happened. The display read: "You're joking, right?" (😂)

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?

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?

Awesome!

Loved the math!

Ah, this IS the good stuff!!!

Good job...

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.

"The solution is left as an exercise to the student." Haha oh man I felt that one!

Is there a video that is a little more detailed on that ghost particle concept?

@DrDeuteron

3 ай бұрын

Give up the 👻, really. It’s an iykyk type situation.

Can you make a follow up video of the relation with the Lagrange points in space. Which also James Web is using?

Don at 8:10 "This section is a bit technical". Yes, Don, that's the technical part 😂

Do the sub and super scripts indicate that there are Tensors involved in the equation?

@drdon5205

3 ай бұрын

Yes, but simple ones

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?

@drdon5205

3 ай бұрын

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.

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"?

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 👍

@hanks.9833

3 ай бұрын

​@@RockBrentwoodnope

@Untoldanimations

3 ай бұрын

@@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.

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

8:06 "...kind of technical.." . And the rest wasnt? - Said us with high school math degree 😂

Does the recent Muon g-2 experiment results call for a modification of this equation?

@juliavixen176

3 ай бұрын

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.

Question from a non-physicist: Is the section about "ghost particles" and "cleanup" just a fudge factor? If not, why not?

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!

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.

@sleepyjohn2695

3 ай бұрын

Wowww now this is what i can call a Flex!!😅😅

@sleepyjohn2695

3 ай бұрын

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 😂😂😂

@wj9494

3 ай бұрын

You've covered a lot of ground here, but I ask, is there any way to prove/disprove the idea of a twisted tube?

@Dragrath1

3 ай бұрын

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.

@SpotterVideo

3 ай бұрын

@@wj9494 If you watch some of the animations/simulations on KZread 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?

Any book suggestions where I can learn about the derivation of this equation in depth? Note: I am not a beginner physics student.

@thstroyur

3 ай бұрын

Michael E. Peskin, Daniel V. Schroeder - An Introduction to Quantum Field Theory; Walter Greiner, Joachim Reinhardt - Field Quantization

you shloud do clip for hologram quantum gravity

Great. Now explain all the formules on the black board behind you...

I was at a party tonight and saw someone wearing a T-shirt with a graphic of Fermilab on it. I was so excited and asked the guy if he was into physics. He said no, he just thought the shirt was cool. I died a little.

@drdon5205

2 ай бұрын

Well, at least you go to the best parties...

Some of those equations remind me of looking at some Regex that I'm supposed to understand and modify that were written a decade ago

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**

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?

My old engineering mentor was always leaving something as an exercise for the student. In time I became a very fit engineer.

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?

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….

@juliavixen176

3 ай бұрын

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.)

Just found this vid. My brain said to me: "thank you for studying philosophy."

Hey , Dr Don, unrelated question. Can leptons be used instead of electrons to power our devices. Leptronics?

@narfwhals7843

3 ай бұрын

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.

@Italianjedi7

3 ай бұрын

@@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.

@narfwhals7843

3 ай бұрын

@@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.

@Italianjedi7

3 ай бұрын

@@narfwhals7843 Wow. Yeah I think Isaac said it was Clarketech. Thanks for the response!

Nobody could do that whole standard model Lagrangian by hand! Good thing we have supercomputers to calculate for us… 😁

Sir, please create and publish the math video. I would appreciate it very much.

@thedeemon

3 ай бұрын

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. :)

I love this channel is a secret vote for our country

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.

Dr. Don who is your tailor? Where is your T-shirts and merchandise?

Partial differential equations are nemesis.

Aren't the "ghost fixes" basically an indication, that there is an incoming paradigm shift to replace the Standard Model?

@soaringvulture

3 ай бұрын

I just figured that they were fudge factors added to make the math come out right, meaning that the math is wrong.

@Dragrath1

3 ай бұрын

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.

Okay, now what about that stuff on the chalkboard? That should make a pretty good episode.😊

Never knew that Physics involves Ghosts who also give headaches 😁

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

Okay so like where do I get the shirt now though

I keep hoping that if I watch long enough I'll see the announcement of the boxing match between Fermilab and Brookhaven.

PBS space time covered this topic also. A real deep dive.

"this 4th section is kind of technical" Me an engineer: yes hmmmm very nice

Interesting video Dr. Don. Seems like one would need a room full of computers to solve that equation! Interestingly, in celestial mechanics, the Lagrange points are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies.

@KaiHenningsen

3 ай бұрын

To quote Wikipedia: _The three collinear Lagrange points (L1, L2, L3) were discovered by the Swiss mathematician Leonhard Euler around 1750, a decade before the Italian-born Joseph-Louis Lagrange discovered the remaining two.[5][6]_ _In 1772, Lagrange published an "Essay on the three-body problem". In the first chapter he considered the general three-body problem. From that, in the second chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits.[7]_

@zackyezek3760

3 ай бұрын

The SM Lagrangian ISN’T actually fully solvable with normal calculus or even numerical approximations on supercomputers. It’s mostly that gluon & quarks QCD part- it takes extremely powerful supercomputers and all sorts of advanced simulation tricks to get results accurate to 1% or less from it, and that’s for minimally complicated systems like a muon interacting with the vacuum (muon g-2 theory work) or the detailed innards of a proton. The good news is that most of the time, you can ignore all but a few terms because their effects would be too tiny (e.g. all of the QCD stuff if you’re working with neutrinos).

The Big Picture! Thanks!

would love to see the more advanced cut

At 4:59 which one is the psi? Or is it phi? It doesn't look like it...

@juliavixen176

3 ай бұрын

Ψ = PSI Φ = PHI

I wonder why the Higgs part of that equation isn't written in a more compact way

@KaiHenningsen

3 ай бұрын

You probably could, at the expense of making the other parts more complicated.

‘The solution is left as an exercise to the students’ - this is how we will get the theory of everything, remember these words😅

My favorite moment is at 8:07 - "This fourth section is kind of technical.". Yep. Sure.

Goldstein's "Classical Mechanics" concludes with relativistic field theory. Too bad it never get covered in class.

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?

@juliavixen176

3 ай бұрын

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.

@thedeemon

3 ай бұрын

One way to give it meaning is looking at en.wikipedia.org/wiki/Path_integral_formulation

@Vatsek

3 ай бұрын

@@thedeemon Feynman used the L = T - V approach in his path integral formulation. If you look closely at it, it has very little meaning.

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?

@Arikayx13

3 ай бұрын

While not a concrete answer, think of it a bit like a map projection. Our normal flat map does great at predicting distances of things in the center, and with a little conversion can still predict distances well enough further north or south but if you get right to the exact edge, you're suddenly in a position where any lateral changes happen at infinite or near infinite speed. The map needs to be adjusted to again start predicting the right distances. In a similar way sometimes infinities can start replicating out of control and a bunch of complicated readjustment is used to wrangle them back in to keep the predictions matching reality. And indeed understanding that in some cases infinities are controllable and not a sign to dump the whole idea was part of the quantum electro dynamics revolution.