I'm really happy I discovered your channel. You have a gift for teaching and am very grateful you took time to share your knowledge. Please don't stop making videos!
Hi there, this metrices discuss is really awesome to think about 2*2 to 4*4 matrix version of Pauli Matrices to Quaternion Matrices. While when the 3 dimension spinor simulation has virtualized in standard model, more so-called spacetime engineering or say holographic symmetrical twin universe model has assumed reverse to paradox to observable vacuum hyperspace. Then from matrix transformation to spacetime engineering ds^=c^dt-(dx^+dy^+dz^), we'll get new spinor waveforms to gravitometrix and traversable principles, so these matrix transformation has brings larentz variation to hyperspace geometric engineering system. Some main higher dimension matrix has also considered sliptime functions to quantum timemetrix field, so more elastistic aether would interact in mathematics to spinor simulation. ...
@18:00 yes, but the _false_ idea "spin is discrete" came from Stern-Gerlach. In Dirac theory spin is just an eigenvalue of σ_3 (so outcome of a measurement detecting the circulating part of the Dirac current). The reason the electrons or silver atoms come out of a Stern-Gerlach filter in only two beams is because the device is a filter, as so will be any measurement of spin. This is clear if you numerically solve the Dirac equation and follow streamlines. As the electrons pass through the region of inhomogeneous B-field the Dirac current orientation rotates _smoothly_ and ends up aligned either 'up' or 'down' relative to the magnet orientation, as well as deflected accordingly. The magnet is imposing the beam splitting. If the magnet was rapidly rotating then the S-G beam would not split, it'd spread out in a cone or something.
Yes, I agree that the magnet imposes the split and it is NOT a function of the electron in the silver atom at all. But my reasoning is a little different than yours. In my reasoning, Yes, the large magnet causes the dipole moment of the small "magnet" to align with the large magnet. If the silver atom is just a little bit above the central plane of the magnet, it will go up and if the atom is just a little big below the central plane, it will go down. In my way of thinking, there are not TWO orientations of the magnetic moment, but ONE. The S-pole of the dipole points towards the N-pole of the big magnet and the S-pole of the dipole points toward the S-pole of the big magnet analogously to how a small magnet would behave if place between the N and S poles of the big magnet in the Stern-Gerlach experiment.
It can happen in physical space if you want it to happen in physical space via "the belt trick". "square root of probability" is just the probabilistic way of looking at the problem. I prefer reality to probability. The animations that Chantal and I are working on are a physical implementation of "the belt trick".
@@FractalWoman But the minus sign of a wave function does not make any physical sense to me. There is no such thing as negative probability. We only measure the square of a wave function anyway. So I am not sure if it is reasonable to translate the doubling of angles to a physical space.
Hi. Is there a way in which I could contact you? I'd like to share some insights into what you say, as I was very surprised about how close our understanding of the ether is. I think I could provide additional context to help you in your project.
This is the best way to contact me. If you have something to say that is insightful, then I would like the rest of my team (my subscribers) to be able to see it too. You could maybe write something up, then put a link to it here. If I like what I see, then maybe we could collaborate more directly. For now, I am trying to limit my collaborations a very small group of people. Too many cooks sometimes spoils the meal, if you know what I mean.
@@FractalWoman Fair enough. Would it be ok if I uploaded a vid to my channel and shared it in the comments of a recent video, or would you prefer a written format?
@@FractalWoman Lori, I just finished watching your second conversation with Chantal. Unfortunately I don't have the time with work and all to make the videos I suggested, but there's some videos I think you would find very useful for your simultations and understanding. Have you delved into geometric algebra?
@@Ottmar555 For the time being, I am trying to avoid the language of vectors. I know they are important in the grander scheme of things, but I have been able to do a lot without the invocation of the complicated symbolic language of algebra. I am using matrices ONLY and am trying to see how far that gets me. I am trying to get to the root of the math that "nature does" and I'm pretty sure that nature doesn't "do" algebra. That said, I did spend a bit of time studying Clifford algebra.
I'm really happy I discovered your channel. You have a gift for teaching and am very grateful you took time to share your knowledge. Please don't stop making videos!
You are making me love math.
Thank you very much for your content and a great thank you in advance for providing this code.
I really appreciate it 🙏
please don't delete this. I'm almost there to understand what you're talking about, i need a month or two more XD
Thanks for the work anyway
No problem. Will not delete this. Hopefully, I will be adding more that will help you more.
Hi there, this metrices discuss is really awesome to think about 2*2 to 4*4 matrix version of Pauli Matrices to Quaternion Matrices. While when the 3 dimension spinor simulation has virtualized in standard model, more so-called spacetime engineering or say holographic symmetrical twin universe model has assumed reverse to paradox to observable vacuum hyperspace. Then from matrix transformation to spacetime engineering ds^=c^dt-(dx^+dy^+dz^), we'll get new spinor waveforms to gravitometrix and traversable principles, so these matrix transformation has brings larentz variation to hyperspace geometric engineering system.
Some main higher dimension matrix has also considered sliptime functions to quantum timemetrix field, so more elastistic aether would interact in mathematics to spinor simulation.
...
@18:00 yes, but the _false_ idea "spin is discrete" came from Stern-Gerlach. In Dirac theory spin is just an eigenvalue of σ_3 (so outcome of a measurement detecting the circulating part of the Dirac current). The reason the electrons or silver atoms come out of a Stern-Gerlach filter in only two beams is because the device is a filter, as so will be any measurement of spin. This is clear if you numerically solve the Dirac equation and follow streamlines. As the electrons pass through the region of inhomogeneous B-field the Dirac current orientation rotates _smoothly_ and ends up aligned either 'up' or 'down' relative to the magnet orientation, as well as deflected accordingly. The magnet is imposing the beam splitting. If the magnet was rapidly rotating then the S-G beam would not split, it'd spread out in a cone or something.
Yes, I agree that the magnet imposes the split and it is NOT a function of the electron in the silver atom at all. But my reasoning is a little different than yours. In my reasoning, Yes, the large magnet causes the dipole moment of the small "magnet" to align with the large magnet. If the silver atom is just a little bit above the central plane of the magnet, it will go up and if the atom is just a little big below the central plane, it will go down. In my way of thinking, there are not TWO orientations of the magnetic moment, but ONE. The S-pole of the dipole points towards the N-pole of the big magnet and the S-pole of the dipole points toward the S-pole of the big magnet analogously to how a small magnet would behave if place between the N and S poles of the big magnet in the Stern-Gerlach experiment.
You saved the cool animation till the end!
Huh. I had to slow it down, but it just occurred to me that it's doing a figure 8. The 'belt'
I am confused. I thought that doubling of angles happens not in physical space but in "square root of probability" space.
It can happen in physical space if you want it to happen in physical space via "the belt trick". "square root of probability" is just the probabilistic way of looking at the problem. I prefer reality to probability. The animations that Chantal and I are working on are a physical implementation of "the belt trick".
@@FractalWoman But the minus sign of a wave function does not make any physical sense to me. There is no such thing as negative probability. We only measure the square of a wave function anyway. So I am not sure if it is reasonable to translate the doubling of angles to a physical space.
Hi. Is there a way in which I could contact you?
I'd like to share some insights into what you say, as I was very surprised about how close our understanding of the ether is. I think I could provide additional context to help you in your project.
This is the best way to contact me. If you have something to say that is insightful, then I would like the rest of my team (my subscribers) to be able to see it too. You could maybe write something up, then put a link to it here. If I like what I see, then maybe we could collaborate more directly. For now, I am trying to limit my collaborations a very small group of people. Too many cooks sometimes spoils the meal, if you know what I mean.
@@FractalWoman Fair enough. Would it be ok if I uploaded a vid to my channel and shared it in the comments of a recent video, or would you prefer a written format?
@@Ottmar555 Yes. That would work perfectly. I prefer videos.
@@FractalWoman Lori, I just finished watching your second conversation with Chantal. Unfortunately I don't have the time with work and all to make the videos I suggested, but there's some videos I think you would find very useful for your simultations and understanding.
Have you delved into geometric algebra?
@@Ottmar555 For the time being, I am trying to avoid the language of vectors. I know they are important in the grander scheme of things, but I have been able to do a lot without the invocation of the complicated symbolic language of algebra. I am using matrices ONLY and am trying to see how far that gets me. I am trying to get to the root of the math that "nature does" and I'm pretty sure that nature doesn't "do" algebra. That said, I did spend a bit of time studying Clifford algebra.
goated