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
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?
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.
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?
The math of quantum mechanics is simple but its implications are incomprehensible. The implications of General Relativity are comprehensible but the math is incomprehensible.
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
@@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 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
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 ...
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
@@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).
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
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.
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.
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.
@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.
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
