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Math 101
Добавлен 26 янв 2023
This channel is mainly about math and physics.
The Fascinating perspective of Geometric Algebra #SoMEpi
What's actually a magnetic monopole? Here we take a look at the mathematics of Electromagnetism and Gravitoelectromagnetism to see what kind of answer we can give to that question.
Links:
Here's a related paper accepted for publiccation:
iopscience.iop.org/article/10.1088/1402-4896/ad75d1
#SoMEpi #SoMEπ result:
some.3b1b.co/entries/ad09160a-8073-461c-906c-31c7db190034
Magnetic monopoles + duality transformation:
en.wikipedia.org/wiki/Magnetic_monopole
Gravitoelectromagnetism:
en.wikipedia.org/wiki/Gravitoelectromagnetism
Mathematical descriptions of the electromagnetic field:
en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field
Great introduction to Geometric Algebra:
ruclips.n...
Links:
Here's a related paper accepted for publiccation:
iopscience.iop.org/article/10.1088/1402-4896/ad75d1
#SoMEpi #SoMEπ result:
some.3b1b.co/entries/ad09160a-8073-461c-906c-31c7db190034
Magnetic monopoles + duality transformation:
en.wikipedia.org/wiki/Magnetic_monopole
Gravitoelectromagnetism:
en.wikipedia.org/wiki/Gravitoelectromagnetism
Mathematical descriptions of the electromagnetic field:
en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field
Great introduction to Geometric Algebra:
ruclips.n...
Просмотров: 27 410
Видео
A story about charged black holes
Просмотров 3,4 тыс.7 месяцев назад
Here we take a look at the mathematics of charged black holes from a different point of view, by analyzing the Reissner-Nordstrom metric. Slowmo bouncing ball, creds to Florian Knorn: ruclips.net/video/sVTJNv3-mWk/видео.html thank you The electromagnetic tensor at 10:35 link ruclips.net/video/J7-vJrRxR40/видео.html References: Reissner-Nordström metric en.wikipedia.org/wiki/Reissner–Nordström_m...
02 - Complex Electromagnetism
Просмотров 2,3 тыс.10 месяцев назад
This is how Maxwell's equations can be seen as the components of a complex set of equations along with Gravitoelectromagnetism. Paper accepted for publiccation iopscience.iop.org/article/10.1088/1402-4896/ad75d1 Gravitoelectromagnetism: en.wikipedia.org/wiki/Gravitoelectromagnetism VO: fliki.ai
01 - Complex Energy, Gravity and Electricity #SoME3
Просмотров 35 тыс.Год назад
Have you ever seen this equation before? This is about how we can put gravity and electricity under the same mathematical context, using complex numbers. 0:00 Motivation 2:36 Mathematics 3:24 Guess 01 - this one : Complex energy 02 - ruclips.net/video/dTa4Ridp4tE/видео.html : Complex Maxwell's equations VO: fliki.ai
Epic! #4Percent
Thank You
I am suspicious of the complex mass object, but the math of Maxwell's equations and this approximate gravity are the same, so I understand the relation. I also wonder what the full E^2 = p^2 +(mc^2)^2 equation would be in this form.
Suspicious is good ... E=mc² is still the expression for rest energy ... here I just make m complex ... thus, momentum would be also complex leading to E=ɣmc² , being ɣ the gamma factor and 'm' just a complex number
at one minute, it feels like an a^2+b^2=(a+b)^2 error
"child" in Schwarzchild is pronounced like "shield". Incidentally, it also means "shield". :)
Oh wow wow wow wow wow! I am a physicist, I mastered in GR, I understand the duality property, I've happened at bivectors more often than once and every time thought, "uh, interesting thing, I should perhaps grasp the thing, it looks like it may be useful". The bivectors describe an area, and the Ricci tensor on the left side describes a constant volume, absent sources on the right; I felt a connection there. But the stuff like complex‒valued mass has always looked suspicious to me. I'm not quite comfortable even with the negative mass that pops up on the cosmological scale in the effective field on the right side. Your vid packs a whole hour-long lecture! It's a good thing that you rolled it so quickly that I went full 🤯, pausing and rewinding oftentimes. I'll be working on your presentation today, explicitly writing down all derivations, and I won't be surprised at all if I end up with a full notebook of the elaborated lecture notes. And I'm so very much not 30 any more… So true were saying the Romans that growing a beard doesn't make one a wise man: why didn't I pick up this tool for my toolbox before! Thank you so very much for this quick intro, I now understand how useful the multivectors may be!
Hi, I'm very glad you liked it ... Geometric Algebra is awesome, it makes things so easy to understand and manipulate ... could you share your notes, I'm very curious about what people can take out of it
@@math.101 I certainly will! -Do you have the email or Xwitter DM in your profile? YT isn't kind to links to private stuff, even if it's on Google Drive...- Found your e-mail in the profile. Is it the best one to send stuff to?
@@cykkm profile email, yep
AI voice has gotten reaaallllyy good, daaaamn
Can you explain how an imaginary charge is a mass? I don't see how you arrived at that.
Short answer: think about what if it's not an imaginary quantity ... because the conversion from Coulombs to mass units is something so simple, that it's out of the question, right?
@@math.101 I'm still not sure I follow. A charge assembled to a certain distance is a certain amount of work or energy. But there are other units in there, to get an energy expression. I don't see how a charge can be dimensionally equivalent to an energy or a mass.
@@vwcanter Now I think I get you ... when you say "A charge assembled to a certain distance is a certain amount of work or energy" I think you mean potential energy, which is different from rest energy. This is a big part of this channel's topic, to ask something about electric charge contribution to rest energy.
The voice works really well!
Have you considered that the negative potential energy in the interior of your new electric case black hole could counteract the energy of the singularity, leading to a regular interior solution and a usual exterior solution?
Hey, nope, I haven't ... how would that go?
Crappy title … especially for a math page
how would you call it?
The math of quantum mechanics is simple but its implications are incomprehensible. The implications of General Relativity are comprehensible but the math is incomprehensible.
Is this ai generated?
just the voice over
I mean, nope
nice video
Wouldn't it be great if all the forces were actually just the result of geometry from some common thing acting on spacetime
It would indeed, Kaluza‒Klein style, but without an extra 5th dimension and an additional scalar field, difficult to make physical sense of. Definitely try it.
The electrostatic force can be written as [Fe=(1/4.π.e)(Q^2/R^2).G/G=G.(Q/√(4.π.e.G))(Q/√(4.π.e.G)(1/R^2)], where mass M=∆Q/√(4. π.e.G) and gravitational force as [F=(G.M.M/R^2).(4.π.e/4.π. e)=(1/4. π.e)√(4.π.e.G)M.√(4.π.e.G)M(1/R^2)], where charge is equal to Q=√(4.π.e. G)∆m and ∆m can be the particle's mass loss or the binding energy between the charge and the particle ∆E=c^2.Q/√(4.π.e.G)=∆m.c^2
Trying not to lie but if AI has been taught to lie in the name of security, we're struggling.
sorry, what?
@@math.101 would only try to induce sorrow on any person who's done damage to others so that they can come to a resolution of what they've been trained or forced to do that makes harm for others.
Gravity is always an attractive force, whereas electric charges can either attract or repel. Also, electromagnetic forces, carried by photons, do not affect gravity.
I don't get it ... do you think this video states otherwise?
🤍
Math 505 ?
almost 😊 ... love that guy
Just wondering, is there a reason why you didn't use the wedge/outer product to replace i times the cross product?
yes, it's just a shortcut, 100% for animation purposes, so that I skip a step when dealing with Maxwell's equations
Very good 👍👍👍
Thank you very much
I enjoyed this presentation very much. Well done. ⭐️
Thank you so much
Very interesting. Thank you for making this video
My pleasure!
I mean, using E=mc² is kind of wrong, because we are always making the fundamental assumption that inertial mass = gravitational mass. The mass ypu talked about in the major part of the video is the gravitational mass, but the mass in E=mc² has nothing to do with gravity, but everything to do with kinematics, being actually inertial mass. That's why the final equation is so weird
good point, next video I'm gonna disclose that assumption ... yet, Einstein himself made use of this assumption to explain Mercury's perihelion precession, right?
@@math.101 Firstly, loved your video 👏👏🎉🥳🥳🎉🥰😍 But that inertial mass = gravitational mass is the strong relativity principle, and is basically taken as one of the most fundamental axioms in physics. Yet, there is no reason why the relation is linear, or why it should behave the same in extreme situations. He did use it for Mercury's Perihelion, but, then again, he (and everyone else) used that for everything else too. Only in MOND's (Modified Gravity Models) do we see, sometimes, speculations around the violation of that axiom. Many experiments are all the time trying to see if there is any distinction between the masses. Obs.: m_inertial := mi, m_gravitational := mg mi = k*mg, through a neat change of variables results in mi = mg (technically they are quantities of different units, the inertial kg and the gravitational kg, with a conversion constant of 1 kg/kg) What physicists are looking for is weird stuff like mg=f(mi, v), with f(mi, 0)=mi
Thank you so much 🥰
If you expand M1M2, you will get m1q2 and m2q1 terms, how do you interpret those two imaginary terms?
That's a good question, for one side the imaginary part of a vector is interpreted as a bi-vector which is often associated with rotations in the perpendicular plane, so it wouldn't modify the distance between the objects ... on the other hand that multiplication is similar to the Dirac quantization condition take a look here en.wikipedia.org/wiki/Magnetic_monopole which is associated with angular momentum ...but honestly, I don't know at this point 😊 ... yet I find the whole thing quite interesting ... I hope you enjoyed the video, thanks for taking the time to write a comment ...
geometry is all you need. nature tells all her secrets, you just gotta look deep.
This is nice. Thank you.
Thank you too!
It's very elegant rolling those equations into one, but I doubt you'd have more insight in whats going on, if you'd be introduced to those forces in this form. Not sure, I was taught classical linear algebra projective geometry and Gibbs' Vector calculus, perhaps this formulation would be intuitive with someone who is trained in Geometric Algebra instead. It's kinda sad, when I was at Uni here was no one seriously pursuing Geometric Algebra, I wish the theory would have been part of the standard curriculum. It's time consuming and slow learning it on your own. Cheers!
How can I start studying geometric algebra? I am at the second year of physics at uni, and this seems quite important and something that should be taught, but isn't
yeah, they should ... I've learned about it from the internet ... there is a good introduction in the description ... there is also a good book called Doran, Lasenby - Geometric Algebra for Physicists (2003)
These equations imply that magnetic monopoles would carry a mass of ~m_S (the Stoney mass), and thus a quantum field of said monopoles would have a maximum interaction distance of hbar/(m_S * c) = L_P /(srt(alpha_EM)) = ~11 Planck lengths. Such a small field interaction cross section implies the half life of such monopoles would be ~12 Planck times, which is highly unstable to say the least. Such a quantum field would get lost in the quantum vacuum foam if it exists at all
Thank you for showing where the elusive monopoles are hidden, in the plank level transients 😅
I didn't know about Stoney mass
@@math.101 Stoney units are a relatively obscure unit system from the late 1800's that was replaced by the Planck unit system after the development of QM. The unique mass you're proposing in this video (M= m + iq/srt(4piepsilonG)) is roughly equivalent to the Stoney Mass (with the exception that it's an imaginary component of a complex mass).
How does this relate to the GEM theory of John Brandenburg, which uses one extra dimension (Kaluza-Klein theory)?
no idea 😊, yet many people point this out ... so perhaps there is a connection, if you come across with something, let me know, I would be happy to hear about it
This only works for slow moving masses right?
Ok nvm this shit way too complex for me lmao
Superb!!!❤❤
Thanks 🤗
Пусть школьники, студенты, измеряют сами Вселенную её тёмную энергию, чёрные дыры, … Соберём учебно/практические пособия? «лазерную рулетку *+опорное расстояние* в 1000000 м» и «ГИБРИД гироскоп Майкельсон Морли». (мы, не ищем эфир, Мы *увидим* как работает квантовая гравитация) Обращаюсь к Вам с предложением на совместное изобретения ГИБРИД гироскопа ИЗ НЕКРУГЛЫХ, двух катушек с новым типом оптического волокна с «полой сердцевиной из фотоно-замещенной вакуумной зоной или (NANF)», где - свет в каждом *плече* проходит по 250000 (в дальномере 1000000) метров при этом, не превышает параметры 84/84/84 см., и вес - 24кг. Предприятия по выпуску "Волоконно-оптических гироскопов" может выпускать ГИБРИД гироскопы и дальномеры, для учебно практического применения в школах и высших учебных заведений. Эйнштейна мечтал измерить скорость поезда, самолёта - через опыт Майкельсона Морли 1881/2024 г., и только тогда, опыт будет выполнен для СТО больше чем 70%. Это возможно выполнить с помощью оптоволоконного ГИБРИД гироскопа. Вот исходя из выполненного более 70% опыта Майкельсона, возможно доказать постулаты: Свет - это упорядоченная вибрация гравитационных квантов и доминантные гравитационные поля корректируют скорость света в вакууме. Думаю получится совершать научные открытия; по астрономии, астрофизике, космологии, высшей теоретической физике,.. В итоге *увидите* теорию всего в простых ❤учебных устройствах.
I really like your video and it inspired me to study gravitoelectromagnetism. A question, how did you obtain the mass in complex form M=m+(\frac{q} {\sqrt(4 \pi \epsilon _{0} G)}) i. That makes me very curious.
Hi, I'm super glad you like it ... Long story short, I came across a silly integral that kind of took me there 😄 ...
Where is the silly integral in order to reading
This is really good but as I said in another video: rhô,J (4-mass current) is not Lorentz invariant... But gamma (rhô,J) is, it is the four momentum, with gamma lorentz factor. Did you try some computations of GR tests with the 4-momentum as a source ? What I say is just replacing the rhom et Jm by gamma rhom and gamma Jm, but I have no idea of the results because I did not try to compute it 😅
How do you prove that black holes spin 3 times the velocity of light the other way relative to our galaxy the milky way. Otherwise it can't hold our galaxy. For example a flight is spinning at 1 Mac then to counter the effects you need 3 Mac the other way like breaking systems. 2 Mac to set it right and one for acceleration. Somewhat like 3 sticks to hold a heavy weight.
I bet this video is probably pretty good. But the robot voice is a dealbreaker for me. Sorry
yeah, I'm not a fluent English speaker, sorry
@@math.101 i'll narrate the video for you
Thank you for considering it good anyways, I think I'll try next time 🤔
@@math.101 yesss, many people prefer a genuine voice over a robot, and the accent of the narrator just makes the video even more real and genuine
1:17 How? it's not incorrect M_1*M_2 is not m_1*m_2 + m_q1*m_q2. Where you lost m_1*m_q2 + m_2*m_q1 ?
hmm, perhaps I should've said more about that, yes (I thought it was clear that we can find both laws in the real part) ... I only say that "now its components wouldn't be just real numbers anymore" ... It's so difficult to come up with a good script without messing things up 🤔
Too quick for me as an amateur observer, but also an obvious aspect-version of Singularity-point/functional i-reflection vortex-vertex containment in Polar-Cartesian self-defining vector-value e-Pi-i @1-0-infinity coordination-identification positioning system. Excellent Teaching Observations.
too quick 🤔 yep, I have to improve that aspect. When you are making the video it feels like an eternity 😅 thank you so much
1000th like 😊
😚
It _really_ doesn't help that you use the same synthetic voice that 'Spirit Science' does. 😮
🤦 is that about spiritualism? ... I couldn't find them
@math.101 Spirit Science talks about electric mass and stuff, using the same synthetic voice, but is complete nonsense. Sir Sic often debunks Spirit Science on his channel. All this off topic if course, just a pity about the voice.
jaja, Sir Sic, is hilarious ... I've just discovered him, thanks 😅
Im doing a PhD on physics and I love your video! So Beautiful, Thanks !
Thank YOU so much
I forget why a basis vector multiplied by itself is one. Why not 0? When you use the rule that flipping order flips the sign, shouldn't xx = -xx Nevermind, I remember, silly me x is in the same direction as x, where two distinct basis vectors sit at right angles
There is a very good introduction to it in the description
Wonderful video!
Thank you very much!
Excellent presentation!
Glad you liked it!
I'd love to see this video revisited with general relativity and electroweak theory.
yeah, I don't know exactly what, but a future video is gonna be about something around those lines
Interesting video. I've been thinking about looking into kaluza klein for a while. Definitely a rewatcher for sure.
Thank you so much, I'm glad you like it
??? This video is a lie I found a magnetic monopole in my backyard