ok now imagine that dirac imagined everything and much more but without a computer and today's technology.

You sound so much like @thorskywalker you will never be able to convince me you aren’t the same person. Especially since I love both of your content. Math and Star Wars!

1:23 so does the second photon always put the atom in the 210 state ??????

I thought electrons were prevented from falling back in by one of those nuclear forces pushing back on them, not this... uncertainty thing I half understand. Is that nuclear force just a classical-ish description of this quantum effect?

I like the idea of explicitly showing the 4D spaces you're talking about, it kinds of demystifies them in a nice, visual way.

2:38:00 At this point I want to point out that we derived Dirac equations by kind of taking square root of wave equation. And out of Dirac equation fiddling for the Gauge invariance, we derived maxwell equations, which would lead to the wave equation. We have proven 0 = 0. I like this video.

I was about to say definitely yes to a video on electromagnetism as a gauge theory, then I saw the three hour video at the top of my recommended! Very glad to have stumbled across this video and this channel, it's already helping a lot of things to click for me. Appreciate the in-depth references, too.

enjoyed this

Well, you sure spun me up... subscribed!

Here is the proof.. *The universe is chiral* at the galactic and therefore down to the atomic level from our perspective and we are not able to see the influence... yet.

"and it's more zen..." I like it. Skipping forward... what if the world is much more bizarre than it appears (at first glance)? Maybe "add" a dark matter "wind" to everything. Very weak interaction, which is why we don't see it or account for it. We are in a slurry...

I got excited, then I saw it was over an hour long video and it’s late as hell

Quick question: it was mentioned that the Dirac matrices are just one way to solve the set of constraints and other mathematical objects would do the same... Do we reach the same conclusions with those other objects (eg spin, antimatter)? Do we get any nonphysical predictions? Or do they turn out to be mathematically identical to matrices?

My favorite part of this was taking an object in my hands and spinning it around twice, and then repeating that but slightly differently each time according to the diagram of an octopus (but with only two loops) as it gradually pulled in, convincing myself that there really is no difference between two turns and zero turns. It's not every day that you get to understand quantum mechanics using physical objects in your hands.

KZfaq is too good to exist.

Ti voglio tanto bene sempre 💕💕

Fyi another great derivation of the Schrödinger equation is shown in the video "What is the Schrödinger Equation?" by the channel Physics Explained. Amazing stuff, thanks for this! Oh how I wish we had these sorts of visuals back in my undergrad days.

thank you❤️❤️❤️

I feel like that's all I needed in my life, thank you so much

Is the photon that bounces back from objetcs into our eyes the same one that the object received from the source of light? No right? It is a new one... actuallly can i talk about different photons or electrons? Isn't the concept of individuallity insufficient to describe them?

Hi at 34:10 the conjugate meant flipping the sign of the imaginery part [conventional] since switching real with imaginary is not making sense to me [please explain] thanks

is digital space real space

Agree that you cannot push something beyond the speed of light but this is more reasonable and intuitive to see that the pushing efficiency drops when reach the speed of pushing. A bullet cannot catch up something faster than its speed. But rockets can accelerate faster than pushing, the gas pushed behind from a very fast rocket can be leaving us on earth that is stationary. I.e. Galilean relativity.

A lot of areas of mathematics would be so much more fun (and easy to understand) if we were four-dimensional beings! Complex analysis comes to mind...

What if I tilt my head and lean back without skepticism? Will my neck suddenly twitch? :-) Click my name to see my use of spinors as I fire off bank shots...

Your description regarding the "apparent teleportation" reminded me of the flat earther's talk about how their fantasy Earth exists. I got a little chuckle thinking about them explaining how the Sun pops from one side of their flat Earth to the other in an instant.

very nice

absolutely massive, huge, gigantic.

The 'Einstein' comment about his name might be the dad joke of the year! lol

So help me autism, I WILL learn what these equations mean. I just need to reteach myself calculus, learn new calculus, differential equations, special and general relativity, and rewatch this video 6 or 7 times

Are they not pronounced like: Spine-ors? Like a spine that bends and flexes to connect things together with a cord that communicates all as a unit?

it might be better to visualize higher dimensions like this: instead of stereographic projection while rotating along a plane, show it as a sequence of slices each with a different w-coordinate (so you could range the w coordinate from -5 to 5, and show 10 total slices on screen next to eachother). this allows you to see the whole object at once without resorting to distorting it in a way that human brains aren't really meant to make sense of.

What would have happened with a different number of spatial dimensions? We can only make 4 gamma matrices out of combinations of 1 and i. Is the number of dimensions fundamental to why we have electrons, or vice versa?

Sorry, my brain can't handle the complexity without a graphic app illustrating the ideas in combination. The only way an average person can handle this is a simulation mentoring the person trying to understand. Something beyond what Brilliant does.

Great

A new one for Sheldon Cooper's FUN WITH FLAGS 😂🎉

What this guy is basically saying ' for the laymen ' is that 1x1=2. =D Kidding aside, I grew up in a low income home. I wasn't able to go to college. Being 48, that doesn't mean I cant [try] to understand this. It is beautiful. 99% of what was said was over my head. But I'm a history nut, and love Newton, Durack, Feynman, Krauss, there are just to many to list. I love the way you explain things....which makes it sounds like I understood what you said in this video lol, but it's very unique to come across someone that teaches the way you do. I person can go to school and get a major, that DOES not mean they are good at explaining or teach said topic. I'm a guitar teacher and guitarist of over 34 years. So sir, I didn't understand pretty much any of this. BUT I want to learn. And you have a great way of talking / teaching. I know this video took you a long time to put together. Your right, we live in a time where a person like me can learn this stuff because of the resources we are able to obtain that you couldn't get back in the 90's unless you went to a university. Thank you.

🔥🔥🔥

Thank you so much. I had sworn off trying to learn particle physics because I felt like I was getting nowhere. Finally this has opened the door to understanding what people are talking about when they refer to gauge symmetry. Your calculations are very easy to follow and deriving Maxwell’s equations is extremely satisfying. It’s still deeply mysterious to me why U(1) symmetry is a thing but I’m convinced it creates EM!

Congratulations.... Again! : ) Your videos always bring bright insights from an educated physics who I assume loves what he is talking about and had spent long hours enjoying thinking about the physics and maths behind it. And I love the balance between raw physics math and equations that are usually preceded by animations and insights about the problem... In my case, I self study Quantum Mechanics with Griffiths book and also followed the MIT openware course on QM I and part of QM II and i use your videos to review things that I supposedly learnt, and see them visually and wonderfully expressed in your rigurously accurate animations.. But I always get great insights and a taste for the more complicated things that lay beneath QM... QM is amazing and hard to learn for a 52 year old mechanically engineer... But I love it... And I love your videos.... Great effort in the script... Great care in the animations and editing.... No shortcuts, no potholes.... Congratulations!!! And thanks a lot for sharing your thoughts on this hard QM matter!!! And I love also your next videos.. The Klein Gordon Dirac series.. I already viewed them twice, and now I will enjoy them again for the third time in preparation for the 3rd part of your hydrogen series... Those Dirac videos are the first time I understood completely the Dirac equation... Now I'm the quest to understand or at least have solid knowledge about spin mathematics and physics, and I use your videos and eigenchris and Noah_explains_physics...and other math resources and buff... And I'm anxious to review all of them again adding an additional onion layer or understanding!! I also have in the wish list your video on electromagnetism as a gauge theory... But I'm preparing for it as you ask for.... I think I'm probably the kind of public that can enjoy the most your videos... And I think there are thousands or hundreds of thousands of viewers like me... So your videos are wonderful and are helping lots of people.... So keep this way!!!! Congratulations!!! And many thanks!!!!! : )

2:55:39 Your Faraday tensor should be contravariant, i.e. superscript mu and nu.

I learned more than from any other KZfaq Video on QM! Best Introduction to Spinors ever.

The speed of light is not a constant as once thought, and this has now been proved by Electrodynamic theory and by Experiments done by many independent researchers. The results clearly show that light propagates instantaneously when it is created by a source, and reduces to approximately the speed of light in the farfield, about one wavelength from the source, and never becomes equal to exactly c. This corresponds the phase speed, group speed, and information speed. Any theory assuming the speed of light is a constant, such as Special Relativity and General Relativity are wrong, and it has implications to Quantum theories as well. So this fact about the speed of light affects all of Modern Physics. Often it is stated that Relativity has been verified by so many experiments, how can it be wrong. Well no experiment can prove a theory, and can only provide evidence that a theory is correct. But one experiment can absolutely disprove a theory, and the new speed of light experiments proving the speed of light is not a constant is such a proof. So what does it mean? Well a derivation of Relativity using instantaneous nearfield light yields Galilean Relativity. This can easily seen by inserting c=infinity into the Lorentz Transform, yielding the GalileanTransform, where time is the same in all inertial frames. So a moving object observed with instantaneous nearfield light will yield no Relativistic effects, whereas by changing the frequency of the light such that farfield light is used will observe Relativistic effects. But since time and space are real and independent of the frequency of light used to measure its effects, then one must conclude the effects of Relativity are just an optical illusion. Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton. Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity. It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles. *KZfaq presentation of above arguments: kzfaq.info/get/bejne/qcuAl61o27m1poU.html *More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145 *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1 Dr. William Walker - PhD in physics from ETH Zurich, 1997

I have a question! During the Inhomogeneous Maxwell's equations part 1 around 2:08:58 the boundary term was determined to be zero, i.e. that the nudges in the photon field go to zero at the boundary but I am not super convinced of this. The telephone pole analogy works because we have a macroscopic string rigidly attached at the boundary, but a photon obeys the Heisenberg uncertainty principle. Thus, if we know where a photon is being nudged, like away from the boundary, we do not know it's momentum and thus whether it can have a small chance to nudge the boundary and be nonzero, or if we know it's momentum we do know if the photon is nudging the boundary. With the nonlocality of electromagnetism how can we guarantee vanishing of the boundary term?

This was beautiful and brings joy

Great video! One question I still have by the end, is why did we square the residuals? How do we know that’s the best way to represent how well our line fits (compared to say taking the raw value or the square root or something else)?

You skipped right over Nelson's 4th theory of homotopic counter clockwise nonexistent right angles and concave wedges.

Trypiilians were burning down their cities to increse its magnetism, trust me....they DID NOT start with Dirac eq. :)

Last night I had a dream of partying with 1836 spinning elephants.

I didn't understand a thing you just said, I enjoyed listening to it nevertheless.