>>>/b/942166092theoretical basis of electrogravitic propulsion just dropped
Its cool seeing new schizos genuinely in a manic episode. What a little trooper. I wonder if he has incorporated anti-matter or spin...hrmm...
>>16838059bump
>it's just "muh longitudinal/scalar waves!!1!" for the bajillionth timewish these faggots would fuck off already
>>16840083No other framework posits the idea in this manner.The framework presented is mathematically consistent and extensive in elaboration, contrary to most 'works' shared on the idea. Discussion on the possibility of these phenomena is serious, as there are major gaps and inconsistencies within the mainstream standard framework in regards to the reality of the vector potential.Those like you who disregard concepts based on others opinions of such, are sheep and lack the due diligence and will to prove or support their stances, on their own accord. They simply state:>"look- see they said its wrong so its wrong... why? j-just look"
>>16840151Proponents of longitudinal EM waves have had over a century to demonstrate the effect.
>>16838059what am i even looking at, an antenna?Why is this "a theory" when the device is so simple. Just buy a wave generator on amazon for $50 and attach it to a copper plate."buh it need exotic material"so it doesnt work. The device should be based in the diagram you posted not on special materials
longitudinal waves sound cool but then you realize charge conservation forces you to only generate electric dipoles.These drawings dont consider that the "ground" would simply be the other leg of the dipole.
>>16840083I am sure you have an explanation for why scalar waves can't actually do that (they can, slow light is a thing)
>>16840294record yourself making this simple device and show us that it worksaav0x
>>16840211>What is displacement current within a spherical capacitor where- due to spherical geometry- any B field is null?'Displacement current' is a euphemism.>>16840228You are looking at a screen shot of a diagram taken from the elaboration of the framework, meant to quickly grab attention- then direct it towards the linked (now dead but archived) thread which is obviously right next to it.>>16840293Again, pic is a diagram with no context, not a proof of concept. Please don't take it as such.Pic related is a breakdown of the nature of specifically longitudinal waves.Ya Ya inb4 gauge invariance- I got something to mitigate that little nuance as well.
>>16840320Yea and get immediately suicided by global oil cabal? Publicity isn't the key here anon, information sharing is.>simpleMost definitely not. Building a functional prototype concerns observing and testing the magnetic vector potential under high frequency, anisotropic conditions.While the magnetic field inside a current carrying cylinder is zero, the magnetic vector potential moves in parallel with the current, and, as in pic related, is non-zero inside the tube. By utilizing high frequency currents, voltage impulses, and testing the circuit while piping liquid mercury, and to do a sort of coaxial concentric cylinder thing with different thin films/ electro-plates if different permitivities, permeabilities and anisotropy with the purposes of trying to get the harmonic component of the vector potential playing against itself, just like in the normal bohm -aharanov effect. Ideally try to get the vector potential phase component helixing within the pipe.
>>16840211https://sci-hub.se/https://doi.org/10.1134/1.1349267"Indeed, as was shown in the stationary case, the ABE is due to zero-field potentials, changing only the phase of the wave function. The necessary condition for the ABE is the presence of zero-field potentials that cannot be eliminated by gauge transformation. The notion of zero-field (redundant) potentials was first introduced for solving boundary problems in electrodynamics of anisotropic media [14–16] and is very seldom encountered in the physics literature. The authors of [17] argue that “electric and magnetic field vectors cannot be expressed in terms of vector potentials” in anisotropic media. The conventional approach to such problems was to use electric and magnetic field strengths or, for zero scalar potentials, vector potentials proportional to them as unknown functions (Coulomb gauge). Such an approach turned out to exclude the possibility of satisfying boundary conditions in anisotropic media due to the intrinsic structure of Maxwell’s equations (see Section 2). The use of electromagnetic potentials with nonzero scalar potential in order to regularly satisfy boundary conditions was first proposed by academician Tikhonov in 1959 [18].
>>16840322>Again, pic is a diagram with no context, not a proof of concept.All i'm saying is you cant have a machine with a varying electrical charge because that breaks charge conservation. You can have charge separation tho, and that is an electrical dipole.
>>16840330>and anisotropy with the purposes of trying to get the harmonic component of the vector potential playing against itselfthats such a good call outi wonder if adding any modeling around helmholtz-hodge. could garner any insighthttps://sci-hub.se/https://doi.org/10.1140/EPJD/E2008-00142-Y probably really good paper to cross reference here for this experiment and the classical analogue of bohm-aharonovi think that this is part of the minimum self induction section is important when reflection slowly varying the current.like the 1914 blondel experimenthttps://arxiv.org/pdf/1005.2350>linear solenoid in which a slowly varying current flows. In this case,since ρ = 0 everywhere, the scalar potential may be assumed to be zero
>>16840083>>16840211this youtuber did a really good historical expose on thishttps://www.youtube.com/watch?v=YHykWjtVdNMand if you want motivation and realize there might be startup capital in this from DARPA check outhttps://www.youtube.com/watch?v=mwDdX0wsv_Q
>>16840322>make claim>refuse to prove the claim>assume the claim is now trueYou are telling me this device is as simple as making an antenna yet you have not built one.Either you are retarded and this doesnt work or you are retarded and cant make a simple device
>>16840330>YOU DONT UNDERSTAND IF I MAKE A BATTERY WITH 5x THE CAPACITY I WILL GET KILLED BY BIG OIL
>>16840294Scalar waves aren't a thing. The entire basis for their supposed existence rests on a bunch of schizos making grandiose and claims about reactionless drives and free energy devices.>>16840913This is always the way with schizo theories. They constantly claim they can craft their free energy devices out of nothing more than paper clips and 9V batteries, but conveniently they can't measure the effects that supposedly make their widgets work without a fission reactor and 200 tons of liquid mercury that has been ritualistically sanctified by a one-eyed orthodox priest.
>>16840913It was more like:>points to thread outlining nuanced mechanics behind field theory>retards lacking any understanding of the material shout proof while simultaneously showing their severe lack of knowledge>gives documented examples of evidence/experiments- as well as examples of quieted or ignored fundamentals such as amperes law>retards ignore documentation and default to their echo chambers instead of engaging in real debate& if you want proof of this^^ claim, simply observe this amygdaloid who thinks I'm talking about making a battery: >>16840914>>16840962You idiots see the word "scalar" and immediately assume the context revolves around "scalar wave" propaganda. Read again. 'Scalar' (each point in the field is single value) - 'super' (above/primal/first) - potential (field of potentiality). Its unit is the Weber rather than Wb/m^2 as with the B field.You people have no idea what any of this means because you have no background in vector calculus or its prerequisites and it shows.How about you show me some math- contextually related- regarding my framework, which mathematically disproves the possibility of anything which has been postulated?Can you even do that? Or will you continue to pull the schizo card while claiming to know something? Choose. Or acquiesce and wear the dunce cap.
>>16840973>You people have no idea what any of this means because you have no background in vector calculusVector calculus is second year math for most undergrad majors that regular /sci/, anon. Vector calculus is not that impressive.
>>16840985Yet I see no one sharing a shread of contrived mathematics by any individual claiming I'm schizos. I've only seen supporting math so far.
>>16841115You've posted a screencap of what I can only assume is the last line of a derivation from some self-published manifesto, what the fuck do you expect people to do with that? Read your mind?
>>16841160This entire thread was created to serve as a pointer to another.Its called due diligence anon and you have none. >posted a screencap of what I can only assume is the last line of a derivation from some self-published manifestoI've done more than that and you know it. Maybe if you tried- beyond moving just your eyeballs- to observe the reference material, it's source, and the validity behind the claims, you wouldn't default to assumption as you main form of deductive reasoning. I've done my part in sharing links to peer reviewed papers, screen caps of entire chapters of books related to the subject, do yours and put the pieces together in your own head so you can grasp what's being posited here, and maybe come up with some contrary mathematics?All you can do is question my character. You can't and never will address the actual material directly, BECAUSE you have no grasp of it.Your brain is pure amygdala.
>>16841172>The entire thread was created to point to a thread on another board where threads rarely survive an hour and which has no archive of any sort.Sounds like you didn't think this through.
>>16840973>Words words wordsPost some math. /sci/ even has [math]\LaTeX[/math]-support you /b/-tard
>>16841205Here, you homunculus: https://archived.moe/b/thread/942166092/>>16841231The math is already posted, see the link above. Not doing it twice, was a lot of effort.Once again:>All you can do is question my character. You can't and never will address the actual material directly&>Maybe come up with some contrary mathematics?Until either of those things happen, no one here has actually 'knocked me off the podium'- so to speak. Just thrown tomatoes and heckles from the side lines. No actual proponent of the contrary and a complete lack of diligence has been observed so far.
>Inb4 more attacks of character & defaulting to assumptions instead of legitimate discourse.
>>16840973>thinks I'm talking about making a battery>cant understand ironyyou are <90 iq
>>16840973>no background in vector calculusI took calc 3 while in high schoolhow about impressing me with some gauge theory, after all the true definition of E&M beyond high school is by using differential forms
>>16841253Its not my fault your irony comes off as idiocy anon. Get a grip.>>16841256Sure, fine, but first, understand at least the history behind the ideology of longitudinal electromagnetic forces and why they have some value in terms of theory development and experimentation:In 1820 Ampère stood before the French Academy and demonstrated: two parallel currents attract each other. Currents in opposite directions repel, the opposite of stationary charges. But he didn’t stop there. Over the next several years, he developed an entire theory of electrodynamics. He designed clever experiments, isolating tiny current elements and measuring the forces between them. What he found was remarkable. Yes, moving charges attract sideways, the magnetic force we all learn about. But they also don’t stop repelling each other along their path. Ampère’s experiments made this clear: charges moving in the same direction still push each other away head-to-tail, a longitudinal repulsion that standard models don’t include. He derived this force mathematically, not as a correction to magnetism, but as a fundamental part of how current elements interact. And in the lab, he found ways to isolate and test it. One of his cleverest setups used tightly wound coils, what he called helices. Each turn of the coil contributed a small element of current, some running side-by-side, others aligned head-to-tail. Now, according to standard thinking, these coils should have repelled each other, like two bar magnets aligned the same way. But instead… they attracted. This wasn’t evidence of a new attractive force, it was evidence that the standard picture was missing something.
>>16841269Cont.Ampère realized that in the geometry of the helices, some of those longitudinal repulsions didn’t cancel, they shifted the balance. The sideways attractions and head-to-tail repulsions combined in a way that reversed the expected outcome. It was a powerful demonstration, not of magnetism, but of direct forces between moving charges, acting in ways the magnetic field alone couldn’t explain. It was all one force, but with two distinct faces. One pulled sideways. The other pushed along the path. Both effects were real. Both were measured. Both were written down in his magnum opus. But that head-to-tail repulsion wasn’t a separate force, but a different aspect of the same law. Ampère’s equation describes a single interaction, one that changes with geometry. When current elements run side-by-side, the dominant effect is attraction, the magnetic force we learn in school. When they’re aligned head-to-tail, that same interaction becomes repulsion. It’s a powerful force, but only when the charges are organized. If their motion is random, like drifting ions in a gas, the net force cancels out. It’s not just motion that matters, it’s coherence. Standard theory ignores this repulsion entirely. It treats magnetism as a separate field, and assumes that any longitudinal effects are either negligible or cancel out. But Ampère showed something deeper: That one law, properly applied, could explain both the magnetic attraction we know, and the hidden repulsion we’ve forgotten. At the time, this wasn’t controversial. Newton’s gravity and Coulomb’s law were already understood as instantaneous forces acting at a distance, and Ampère assumed electrodynamics worked the same way. He even emphasized that the forces must obey Newton’s third law in its strongest form, equal and opposite, and aligned along the straight line connecting the elements. In his view, a force that acted off-axis or failed to reciprocate would violate basic mechanics.
>>16841270Cont. For decades, Ampère’s ideas didn’t vanish. Wilhelm Weber even built on them, formulating a more general law that applied to individual moving charges, and included their relative velocities and accelerations. For a time, it was widely used, especially in Europe.But by the 1840s, the tide had begun to shift. In 1844, Hermann Grassmann introduced a novel mathematical technique, a kind of early vector algebra, to express physical forces geometrically. His formulation inspired what would later become the cross-product structure of the Lorentz force law. But unlike Ampère’s original law, it didn’t allow for longitudinal forces, those acting along the line of motion. Instead, it only described sideways interactions between currents. It was a shift in how electrodynamics could be framed, more compact and mathematically elegant, but subtly incomplete. A few years later, Franz Neumann took a different approach. Instead of focusing on the forces between current elements, he re-expressed the interaction in terms of energy, introducing the concepts of potential energy and mutual inductance between circuits. This shift made it easier to incorporate energy conservation into electrodynamics, and it laid the groundwork for practical applications like generators and transformers, and introduced the concept of the vector potential. But it also pulled attention away from the underlying forces themselves, replacing them with more abstract, system-level descriptions that didn’t preserve the directional detail of Ampère’s original law.
>>16841272The final steps in abandoning Ampère’s picture came with Maxwell and Lorentz. James Clerk Maxwell, inspired by Faraday’s idea of invisible lines of force, recast electrodynamics in terms of local fields, electric and magnetic, propagating at a finite speed. His equations were brilliant. They unified electricity, magnetism, and light into a single framework. But in doing so, they excluded any concept of instantaneous action at a distance. There was no longer room in the math for Ampère’s direct force between current elements. Maxwell didn’t deny those findings, on the contrary, he called them “one of the most brilliant achievements in science,” and praised Ampère’s law for satisfying Newton’s third law more directly than any other formulation. But practically speaking, his formalism couldn’t accommodate it. Then came Hendrik Lorentz. Building on Maxwell’s field equations, he introduced a new, compact expression for how fields act on individual point charges. This brought clarity and consistency, especially in understanding how light, charge, and radiation interact. But it also finalized the shift: electrodynamics was now a story of fields acting on particles. The idea of charges interacting directly, of forces between current elements, was considered unnecessary, even obsolete. Later generations mistook omission for disproof, and quietly erased Ampère’s original force law from the textbooks, along with the longitudinal effects it predicted. Even though it was never disproven.
>>16841274For much of the 20th century, even those curious about Ampère’s force had no easy way to study it. His seminal Mémoire was never widely translated. That began to change thanks to Brazilian physicist André Koch Torres Assis. He not only translated Ampère’s work into English, but became one of its few modern defenders, arguing that we’d abandoned a crucial part of electrodynamics. Then in the late 1970s, Peter Graneau at MIT picked up the question again. He ran high-current experiments, sending powerful pulses through thin wires. To his surprise, he measured forces acting along the length of the conductor, much stronger than Maxwell’s equations predicted, and entirely in line with what Ampère had described. According to standard electromagnetic theory, two main effects should dominate: the magnetic pinch force squeezing the wire radially, and resistive heating gradually vaporising it from within. Yet in Graneau’s tests, the wires didn’t simply pinch or melt, they fragmented violently along their length, as though being pulled apart head-to-tail. The speed of the breakup and the magnitude of the forces were far greater than the pinch force or heating could explain. When he measured these forces directly, they matched the predictions of Ampère’s original law, including the longitudinal repulsion between current elements, completely absent from the Maxwell–Lorentz formulation. These weren’t fringe results. Peter published them in peer-reviewed journals, where they passed review but sparked fierce debate. And the more he measured, the more convinced he became: the problem wasn’t just with the experiments. It was with the theory.
>>16841275In Peter’s view, and later his son Neal’s, the field-based model had missed the point entirely. We don’t observe electromagnetic fields. We observe the forces that matter feels. And Ampère’s law described those forces directly, not as a delayed field effect, but as an instantaneous interaction between currents, falling off with distance, but never truly vanishing. They argued that what we call an electromagnetic wave is not a self-sustaining interplay of electric and magnetic fields moving through empty space, but the collective effect of countless direct interactions between charges, nearest neighbours giving the strongest nudges, more distant ones giving smaller nudges. This is one of the phenomena I've attempted to model & in Ampère’s view, the “wave” is simply the cascading pattern of those interactions, which we interpret as having electric and magnetic components, but which are in fact two aspects of the same underlying force. Together, their work stood as a modern echo of Ampère’s discovery. Measured. Published. And quietly ignored.
>>16841276We like to think of electromagnetism as neat and local. Forces that propagate at the speed of light. Carried by invisible fields. No faster than they need to be. But Ampère’s force hints at something deeper, a direct, immediate connection between moving charges, not mediated by a field at all. And here’s the strange part: Even with instantaneous action-at-a-distance, you still get what looks like a delayed effect.Imagine a current being switched on in a mile-long wire. In Ampère’s view, the first charges would feel the force right away. But those ahead are further away, so they feel it less. Only when the first few charges start to move, do their neighbors feel a stronger push. And so the signal builds… cascading forward, like a pressure wave. Not because the force is delayed, but because it’s distributed. It’s exactly what field theory predicts, but for a very different reason. In Ampère’s view, there is no field doing the work. The charges act directly on one another. And that changes everything. It means that the so-called “field” is just a convenient summary, a pattern that emerges from the sum of all interactions. And if that’s true… then the work isn’t being done by empty space. It’s being done by the matter itself, by the currents. And that raises a deeper possibility. Because if those interactions are instantaneous, but fall off with distance, then the vast network of cosmic currents might be more than just structure. It might be connection. A real, physical link between moving charges, across galaxies, across clusters, across time. That may sound like metaphysics, but it’s not. It’s exactly what Mach proposed: that inertia and motion arise from the instantaneous influence of the entire universe.
>>168412391. Maxwell’s equationsOn Minkowski spacetime [math]( M = \mathbb{R}^{1,3} )[/math] with coordinates [math]( (t, x, y, z) )[/math],let [math]( F )[/math] denote the electromagnetic field 2-form and [math]( J )[/math] the current 3-form.Maxwell’s equations are[eqn] dF = 0, \qquad d\star F = \mu_0 J,[/eqn]where [math]( \star )[/math] is the Hodge dual associated with the Minkowski metric.Since [math]( dF = 0 )[/math], we can introduce the potential 1-form [math]( A )[/math] such that[eqn] F = dA.[/eqn]In the Lorenz gauge [math]( d\star A = 0 )[/math], Maxwell’s equations reduce to the wave equation[eqn] \Box A = \mu_0 J,[/eqn]where [math]( \Box = d\star d\star + \star d\star d )[/math] is the spacetime d’Alembertian.In coordinates, [math]( \Box = \frac{1}{c^2}\partial_t^2 - \nabla^2 )[/math].2. Geometry of the square antennaConsider a thin, conducting square patch located at [math]( z = 0 )[/math] with side length [math]( a )[/math]:[eqn] S = \{ (x, y, 0) \mid |x| \le \tfrac{a}{2},\ |y| \le \tfrac{a}{2} \}.[/eqn]Let the antenna carry a tangential surface current density [math]( \mathbf{K}(x, y, t) )[/math]that oscillates harmonically with angular frequency [math]( \omega )[/math]:[eqn] \mathbf{K}(x, y, t) = \Re \left\{ \tilde{\mathbf{K}}(x, y)\, e^{-i\omega t} \right\}.[/eqn]
>>16841239>>16841281Part 23. 3-form for a surface currentA tangential surface current at [math]( z = 0 )[/math] can be represented by the 3-form[eqn] J = \Re \left\{ \left( \tilde{K}_x\, dy \wedge dz + \tilde{K}_y\, dz \wedge dx \right) \wedge e^{-i\omega t}\, dt \; \delta(z)\, \chi_S(x, y) \right\},[/eqn]where [math]( \chi_S(x, y) )[/math] is the indicator function of the square [math]( S )[/math], and[math]( \delta(z) )[/math] confines the current to the plane [math]( z = 0 )[/math].4. Solution for the potentialIn the Lorenz gauge, the potential satisfies[eqn] (\nabla^2 + k^2)\, \tilde{\mathbf{A}}(\mathbf{r}) = -\mu_0\, \tilde{\mathbf{J}}(\mathbf{r}), \qquad k = \frac{\omega}{c}.[/eqn]The spatial Green’s function of the Helmholtz operator is[eqn] G(\mathbf{r}, \mathbf{r}') = \frac{e^{ik|\mathbf{r} - \mathbf{r}'|}}{4\pi |\mathbf{r} - \mathbf{r}'|}.[/eqn]Hence, the complex vector potential is[eqn] \tilde{\mathbf{A}}(\mathbf{r}) = \mu_0 \int_S \tilde{\mathbf{K}}(\mathbf{r}') \frac{e^{ik|\mathbf{r} - \mathbf{r}'|}}{4\pi |\mathbf{r} - \mathbf{r}'|}\, dS',[/eqn]and the field strength 2-form is [math]( F = dA )[\math].QEDcheck mate
>>16841281Hoping the latex embeds, learning its functionality on 4chan for the first time rn.Anyhow...Your calculation assumes curl-free [math]A[/math] only in gauge choice, but scalar [math]\chi[/math] unifies: [math]A = \nabla \chi[/math], [math]F = dA = d(d\chi) = 0[/math] trivially satisfies [math]dF = 0[/math], but singularities in [math]\chi[/math] allow nonzero [math]\star dA[/math] (B-field via curl).>I've outlined this in the archived thread.For antenna [math]K[/math], solve [math]\square \chi = \mu_0 \int G(r,r') \frac{\delta J}{\delta \chi} dr'[/math] where [math]J[/math] derives from [math]\frac{\partial^2 \chi}{\partial t^2}[/math] and [math]\nabla^2 \chi[/math];gravity emerges as [math]\phi = \beta \nabla^2 \chi[/math], extending to time dilation [math]t = t_0 \sqrt{1 + \frac{2\phi}{c^2}}[/math]. Standard omits this depth, reducing to special case without exotic potentials.
>>16841290The value of the constant of proportionality denoted by beta is currently unknown to me, which is why experimentation is so important.You may object because the curl of a gradient is said to always be zero. But that is only true for simply connected regions.If there is a singularity at the center, then there can be a nonzero curl around the center even though everywhere else, the curl of the gradient is indeed zero. >I can demonstrate this.
>>16841292>>16841292Demonstration: >Hoping the latex is rightConsider a vector potential field of the form:[math]\tilde{A}_{\rm cylindrical} = \frac{1}{s} \hat{\phi}[/math] [math]\tilde{A}_{\rm cartesian} = \frac{-y}{x^2 + y^2} \hat{x} + \frac{x}{x^2 + y^2} \hat{y}[/math] This represents a circulating field that drops off linearly with distance from the vertical axis. Its curl is zero everywhere except along the z axis, where it is undefined. [math]\nabla \times \vec{A} = -\frac{\partial (1/s)}{\partial z} \, \hat{s} + \frac{1}{s} \frac{\partial}{\partial s} \left( s \frac{1}{s} \right) \hat{z}[/math]Whereas the electric singularity is a point, the magnetic singularity is a string. Here it is oriented vertically along the z axis with the field circulating around it.The proper approach to this problem is to use Stoke's Theorem to first calculate the amount of circulation around the origin, which gives the value of magnetic flux that is present.[math]\oint_P \vec{A} \cdot d\vec{l} = \int_S \nabla \times \vec{A} \cdot d\vec{a} = \chi[/math][math]\oint_P \vec{A} \cdot d\vec{l} = \oint_P \frac{1}{s} \hat{\phi} \cdot (s\, d\phi\, \hat{\phi}) = \oint_P d\phi = 2\pi[/math]The singularity string contributes a flux of 2π for a circular path drawn around it. From Stoke's Theorem we see that the surface integral of the curl must equal this value.[math]\int_S \nabla \times \vec{A} \cdot d\vec{a} = 2\pi[/math]Here we can invoke the 2 dimensional Dirac delta function defined as:[math]\delta_2(s) = \begin{cases} +\infty, & s = 0 \\ 0, & s \neq 0 \end{cases}[/math][math]\int_S \delta_2(s)\, d a = 1[/math]For the surface, we may use a unit disc lying in the xy plane. Then:[math]\int_S (\nabla \times \vec{A}) \cdot d\vec{a} = \int_S (\nabla \times \vec{A}) \hat{z}' \cdot \hat{z}'\, da = \int_S (\nabla \times \vec{A})\, da = 2\pi[/math]By comparing this to the delta function integral, we see that:[math]\nabla \times \tilde{A} = 2\pi \delta_2(s)[/math]
>>16841335Cont.This is the fundamental 'superpotential' field of an irrotational vector potential, which has a singularity at the central axis of rotation that produces a nonzero B at the origin. Since B is zero everywhere else, χ is allowed to have a gradient everywhere else besides the origin.What does this mean? The χ field is a corkscrew of infinite width that winds around the z axis. The infinite width is not a problem, it simply means that phenomena that depend on the path around the flux do not depend on distance from it.One example is the Aharonov–Bohm effect, where an electron traveling around a long thin solenoid picks up a phase factor that depends on the magnetic flux inside the solenoid, but not distance from it. If this solenoid were bent into a closed toroid so that all flux were absolutely confined inside, the effect would still exist.Another example is a loop of wire wound around a ferromagnetic rod in which there is a changing magnetic field. The electromotive force induced by the changing magnetic flux is independent of the diameter of the loop. If the flux were completely confined inside a toroidal core, it would still produce the same electromotive force. That is because the electron isn’t actually experiencing the flux itself, but rather the corkscrew superpotential surrounding the flux lines.A changing flux creates a changing gradient in the superpotential, and an electron in that path will be pumped along the gradient. Stated another way, a changing gradient generates an electric field, which places a force on the electron as expected.
>>16841290>chatgptlmaoYou dont even understand what I typed>Your calculation assumes curl-free A only in gauge choiceIf by A you mean A(r) as i typed before then A is already a bivector retard so i am not assuming anything>but scalar X unifiesX is already a scalar just read the equationyou cannot define [math]A = \nabla \chi [/math] i already defined [math]A[/math][math]d(d\chi) = 0 [/math] is irrelevant because [math] \chi [/math] is a scalar>but singularitiesah yes, schizo time>gravity emerges asthe units dont matcheverything is garbage i wont bother try to make sense off
>>16841335>this mouth breather is making chatgpt calculate magnetic flux on a cylinder and passing it off as pseudo science
>>16841338Yes, but also no, I used grok to help translate the math into 4chan suitable latex format because you complained about it, that's it. The math existed much before this conversation.The magnetic vector potential is not a bivector; it is a polar vector quantity defined such that its curl equals the magnetic field.>dunce cap confirmedAlso, Jesus Christ... you need to actually LOOK at the archived thread because our definitions of chi are completely different and you haven't even realized that because of your lack of diligence.>>16841340More irony that comes off as idiocy, never gets old, always gets noticed.
>>16841347>The magnetic vector potential is not a bivector; it is a polar vector quantity defined such that its curl equals the magnetic field.high school math, lmaohave a look at the faraday tensor and tell me that the magnetic field is not a bivector
>>16841350>the magnetic field itself is fundamentally a bivector because in muh special relativity fields are combined into muh tensorYes, the FORCE FIELD is a bivector, not the POTENTIAL FIELD exhibited by Aharonov & Bohm.When you combine fields like that, of course you'll need more than one value vector to describe it... Only makes sense.Doesn't mean that actually describes anything physical.The whole idea of my theory is to posit that divergence of the magnetic vector potential is proportional to the gravitational potential and details a mathematical framework concise with known derivations which outlines the proportionality, positing Chi as key element.
>>16841353>bivector because in muh special relativity>because relativity>special >special relativity>Doesn't mean that actually describes anything physical.oh like singularities dont describe reality>magnetic vector potential is proportional to the gravitational potentialwell earth has a gravitational potential we can measure, surely we should be able to detect a magnetic vector potentialpost your findings
>>16841280On a globally hyperbolic Lorentzian 4‑manifold [math]M[/math], classical electromagnetism is a [math]U(1)[/math] gauge theory with connection 1‑form [math]A \in \Omega^1(M)[/math] and curvature 2‑form [math]F=dA \in \Omega^2(M)[/math]. Maxwell’s equations are the linear, local system[eqn]dF=0,\qquad d{*}F=J,[/eqn]with [math]J \in \Omega^3(M)[/math] the conserved current (a 3‑form), [math]dJ=0[/math]. This is the sharpest way to encode "no magnetic monopoles" and charge conservation, and it is invariant under the de Rham cohomology (gauge) [math]A \mapsto A + d\chi[/math].The force density on matter is the covariant Noether current contraction [math]f^\nu = F^{\nu\mu}J_\mu[/math], i.e. in forms, [math]f = \iota_{j^\sharp}F[/math], with [math]j^\sharp[/math] the vector field metrically dual to the current 1‑form. Longitudinal, transverse, “sideways,” etc. are observer‑dependent splittings; the invariant object is [math]F[/math].Momentum conservation does not come from a pairwise Newton III on particles; it comes from the local divergence-free condition for the total stress‑energy tensor:[eqn]\nabla_\mu\big(T_{\text{matter}}^{\mu\nu} + T_{\text{EM}}^{\mu\nu}\big)=0,\qquadT_{\text{EM}}^{\mu\nu}=F^{\mu\alpha}F^{\nu}{}{\alpha} - \tfrac{1}{4}g^{\mu\nu}F{\alpha\beta}F^{\alpha\beta}.[/eqn]Your insistence on a "strong" Newton III applied to matter alone is a category error; the missing reaction is carried by field momentum [math]\mathbf{g} = \varepsilon_0,\mathbf{E}\times\mathbf{B}[/math] and transmitted by the Maxwell stress [math]T_{ij}[/math]. That is the end of the story.
>>16841270On any Cauchy slice [math]\Sigma_t[/math] with induced metric [math]\gamma[/math], Hodge–Helmholtz decomposes [eqn] \mathbf{E} = \nabla \phi + \nabla \times \mathbf{A}_T,\qquad \nabla \cdot \mathbf{A}_T = 0. [/eqn] Gauss’ law is an elliptic constraint [math]\nabla^2 \phi = -\rho/\varepsilon_0[/math], which is “instantaneous” in the same trivial sense that constraints in any symmetric‑hyperbolic PDE system are instantaneous. The evolution of [math](\mathbf{A}_T,\mathbf{B}=\nabla\times\mathbf{A}_T)[/math] is hyperbolic with characteristics on the light cone. Conflating an elliptic constraint with physical nonlocality is a first‑semester PDE mistake.In Coulomb gauge the scalar potential looks instantaneous; in Lorenz gauge both potentials propagate at [math]c[/math]. Gauge‑dependent “instantaneity” has zero physical content. Observables are [math]F[/math] and its stress; they are causal.
>>16841270>Standard theory ignores this repulsion entirely. It treats magnetism as a separate field, and assumes that any longitudinal effects are either negligible or cancel out. it literally encodes them lol. Just decompose relative to an observer [math]u^\mu[/math]: [math]E^\mu = F^{\mu\nu}u_\nu[/math], [math]B^\mu = ({*}F)^{\mu\nu}u_\nu[/math]. Whether a force component is “longitudinal” to [math]\mathbf{v}[/math] depends on [math]u^\mu[/math]; it is not an invariant classification. What is invariant are the two scalars [math]I_1 = F_{\mu\nu}F^{\mu\nu}[/math], [math]I_2 = F_{\mu\nu}{*}F^{\mu\nu}[/math]. Your narrative obsesses over a frame‑dependent decomposition and then mistakes gauge choice for physics. Literally Jefimenko’s equations give the retarded fields of arbitrary [math](\rho,\mathbf{J})[/math]; the near zone includes longitudinal [math]\mathbf{E}[/math] components exactly as required by charge conservation. None of that rescues an instantaneous force.
>>16841269>>16841270>muh coils and helices doeTwo coaxial, like‑wound solenoids attract in plain Maxwellian magnetostatics. The field energy is[eqn]U = \tfrac{1}{2} L_1 I_1^2 + \tfrac{1}{2} L_2 I_2^2 + M(z) I_1 I_2,\qquad F_z = -\frac{\partial U}{\partial z} = - I_1 I_2 \frac{\partial M}{\partial z}.[/eqn][math]M(z)[/math] decreases with separation [math]z[/math] for coaxial loops, hence [math]F_z>0[/math] (=attraction) when currents are codirected. This is literally undergrad lol.invoking “hidden longitudinal repulsion” to explain a sign that falls straight out of [math]U(B)[/math] is performative confusion
>>16841276>strongest nudges, more distant ones giving smaller nudges. This is one of the phenomena I've attempted to model & in Ampère’s view, the “wave” is simply the cascading pattern of those interactions, which we interpret as having electric and magnetic components, but which are in fact two aspects of the same underlying force.This "cascading pattern" literally is just a field though lol. The Maxwell system is symmetric hyperbolic and the wavefront set of [math]F[/math] propagates along null bicharacteristics. Singular support lives on the light cone, i.e. there is no spacelike transport. Your cascading nearest‑neighbor pushes is a verbose re‑description of a local hyperbolic PDE with retarded Green’s function.
invoking a 200‑year‑old nonlocal kernel is not bold, it's just mathematically illiterate kek
>>16841239Brother, you're confusing the type (form degree), the gauge role, and the natural pairing that defines physical units. Just stop posting you're embarrassing yourself
>/b/tard cant into physicsriveting thread
>>16840973calling a 0-form a "scalar superpotential" with unit Weber is a unit fallacy: the electromagnetic field is a 2-form [math]F=dA\in\Omega^2(M)[/math], current is a closed 3-form [math]J\in\Omega^3(M)[/math] with [math]dJ=0[/math], and the equations [math]dF=0[/math], [math]d{*}F=J[/math] fix what can carry flux; flux is the pairing [math]\langle F,\mathcal{S}\rangle=\int_{\mathcal{S}}F\in\mathrm{Wb}[/math] for any oriented 2-current [math]\mathcal{S}[/math], i.e. Weber is attached to the 2-form-2-current pairing, not to an arbitrary 0-form; a 0-form [math]\phi\in\Omega^0(M)[/math] pairs with 0-currents (weighted points), so declaring [math][\phi]=\mathrm{Wb}[/math] merely ensures that [math]\sum_i \phi(x_i)[/math] has units Weber, which is irrelevant to magnetic flux and cannot replace [math]\int_{\mathcal{S}}F[/math]; the only scalar with units of Weber that naturally appears is the gauge function [math]\chi\in\Omega^0(M)[/math] in [math]A\mapsto A+d\chi[/math], [math]\varphi\mapsto \varphi-\partial_t\chi[/math], with [math][A]=\mathrm{Wb}/\mathrm{m}[/math], [math][\chi]=\mathrm{Wb}[/math], and [math]F=dA[/math] unchanged, i.e. pure redundancy, not a physical superpotential; if you try to elevate that scalar to a potential of a potential by setting [math]A=d\phi[/math], then [math]F=dA=d^2\phi=0[/math] and all fluxes vanish (by Stokes, [math]\oint_{\partial \mathcal{S}}A=\int_{\mathcal{S}}F=0[/math]), contradicting any nontrivial [math]\langle F,\mathcal{S}\rangle[/math].
>>16840973Vector algebra cant distinguish between polar and axial vectors and the cross product only exists in R^3The wtf is this equation in the quaternionic formThat two vectors each with 0 scalar potentials cant interfere to produce a region of positive scalar potential Tracing how this scalar changes over ab action though the field can be considered a wave of scalar potential or scalar waves
>>16840973>>16841392attempting to salvage the claim via a differential operator [math]\mathcal{D}:\Omega^0\to\Omega^2[/math] with [math]F=\mathcal{D}(\phi)[/math] collapses under the constraints [math]dF=0[/math] and [math]d{*}F=J[/math] for arbitrary [math]J[/math]: you would need [math]d\mathcal{D}=0[/math] as an operator identity and, simultaneously, [math]\phi\mapsto { *}\mathcal{D}(\phi)[/math] to be surjective onto exact 3-forms, which in turn recreates the usual potential [math]A[/math] (up to gauge) rather than a new scalar; in vacuum one can introduce Hertz/Debye superpotentials [math]\Pi\in\Omega^2[/math] with [math]A=\delta\Pi[/math], [math]F=d\delta\Pi[/math], but these are 2-forms (not scalars), metric-dependent through [math]\delta=-{*}d{*}[/math], and their dimensions follow [math][\Pi]=[A]\cdot\mathrm{length}=\mathrm{Wb}\cdot\mathrm{m}[/math], not Weber; units are fixed unambiguously by the kinematics and the action [math]S=\int \tfrac{1}{2\mu_0}F\wedge{*}F + A\wedge J[/math], giving [math][F]=\mathrm{Wb}/\mathrm{m}^2[/math] (hence the spatial [math]\mathbf{B}[/math] has [math]\mathrm{Wb}/\mathrm{m}^2[/math]) and [math][A]=\mathrm{Wb}/\mathrm{m}[/math], while the electric scalar potential has [math][\varphi]=\mathrm{V}[/math] and the magnetostatic scalar potential (when it exists on [math]\mathbf{J}=0[/math] simply connected regions via [math]\mathbf{H}=-\nabla\psi_m[/math]) has [math][\psi_m]=\mathrm{A}[/math]; confusing [math]\mathrm{Wb}[/math] (the unit of the integrated flux [math]\int_{\mathcal{S}}F[/math]) with [math]\mathrm{Wb}/\mathrm{m}^2[/math] (the areal density represented by the 2-form’s spatial components) is precisely the “integrand vs integral” mistake. declaring a pointwise scalar to "have unit Weber" does not make it a flux density, and it cannot reproduce F without either trivializing the field ([math]d^2=0[/math]) or smuggling in a noncanonical metric-dependent operator that reduces to the standard potentials anyway
>>16840973>>16841397>>16841360finally, nontrivial flux sectors are encoded by the cohomology class [math][F]\in H^2(M\setminus \mathrm{worldtubes})[/math], obstructing even a global 1-form potential [math]A[/math] when [math][F]\neq 0[/math]. a fortiori no global 0-form can capture a 2-class; so the only consistent “scalar with Weber” in sight is the gauge parameter [math]\chi[/math], which changes nothing observable, while the field strength remains a 2-form with [math]\mathrm{Wb}/\mathrm{m}^2[/math] components and Weber-valued surface pairing
>>16841353If you actually couple [math]\delta A[/math] to a "gravitational potential" [math]\Phi_g[/math] via a Lagrangian term [math]\lambda,\delta A\cdot \Phi_g[/math], you either (i) break [math]U(1)[/math] gauge symmetry (Proca‑like, ruining AB holonomy and contradicting precision bounds on photon mass), or (ii) introduce a Stueckelberg field [math]\chi[/math] with [math]A\mapsto A+d\chi[/math], [math]\chi\mapsto \chi-\sigma[/math] to keep gauge invariance, in which case the observable is a massive scalar mixed with [math]\delta A[/math], not gravity, and the AB sector is unaffected (monodromy remains a [math]\pi_1[/math]-character). None of this produces a coordinate‑independent scalar equal to [math]\partial_\mu A^\mu[/math]. In the weak‑field Newtonian limit, gravity is encoded by the metric perturbation [math]h_{00}=-2\Phi_g/c^2[/math], i.e. a component of a symmetric 2‑tensor (a section of [math]S^2 T^*X[/math]), living in a completely different functorial world than [math]A\in \Omega^1(X)[/math]; there is no natural transformation of sheaves sending a gauge‑equivalence class of [math]A[/math] to a diffeomorphism‑invariant scalar [math]\Phi_g[/math].
>>16841335Hunh a helicity?Interesting,Mind taking a look at this experiment for me?Its teslas hairpin circuit but we hollow out the bars into pipes.Could it be that if ths pipe was filled with mercury, switching the circuit on will make the mercury helix inside the pipe due to the vector potential inside the pipe?
>>16840151t. watched 3 Curt Jaimungal interviews and thinks he knows physics now
>>16841335>>16841337Anon, the circulation computation [math]\oint_{C_s} A = \int_0^{2\pi} d\phi = 2\pi[/math] says nothing mystical about a corkscrew of infinite width. it is the period of the closed 1‑form [math]A[/math] on [math]X[/math], i.e. the generator of [math]H^1(X;\mathbb{Z})\cong\mathbb{Z}[/math]. Concretely, [math]A[/math] is flat, with curvature zero on [math]X[/math] and monodromy [math]\exp\big(\oint A\big)=e^{2\pi i}[/math] around [math]L=\{x=y=0\}[/math]; multiplying by a flux [math]\Phi[/math] gives [math]A_\Phi=(\Phi/2\pi)\,d\theta[/math], [math]dA_\Phi=\Phi\,\delta_L[/math], and holonomy [math]\exp(i\Phi)[/math]. This is exactly the AB background: a flat connection on [math]X[/math] with nontrivial period, i.e. a nontrivial class in [math]H^1(X;\mathbb{R}/\mathbb{Z})[/math], encoded on a C̆ech cover [math]\{U_0,U_1\}[/math] by local primitives [math]A_i=d\theta_i[/math] with transition [math]\theta_1-\theta_0=\phi[/math] and constant cocycle [math]e^{i\Phi}[/math] on [math]U_0\cap U_1[/math]. The “string” is the support of the curvature current [math]\delta_L[/math]; call it “singularity” if you insist, but it is just the Poincaré dual cycle that saturates Stokes.Your vector‑calculus curl algebra fails because you are differentiating across a branch cut; the correct statement is the distributional identity above. The claim "nonzero [math]B[/math] at the origin" is sloppy: [math]\mathrm{supp}(dA)=L[/math], not a point. The assertion that this constructs a "superpotential field" is absolute /b/tardation: [math]A=d\theta[/math] is exact on any simply connected chart and globally represents a nontrivial period; rebranding [math]\theta[/math] as "superpotential" doesn’t upgrade a multivalued gauge function into physics.
>>16841337Your last sentence literally asserts [math]E[/math] is exact while invoking a nonzero [math]\oint E[/math]; pick one.
>>16841242looks like you shut up once people explained basic EM to you kek
>>16838059>/b/What's with schizos and spamming /b/? Mandlbaur did the same shit, took him a few weeks to even discover /sci/
>>16841409it won't, meds
>>16840332Should've asked Grok to explain it to you since it doesn't say what you think it does. It basically just repackages a triviality (flat but nontrivial holonomy) as a medium‑dependent miracle and then garbles boundary‑value analysis into a claim about the nonexistence of potentials. The Aharonov-Bohm effect lives in the connected component of flat U(1)‑connections with nontrivial monodromy; anisotropy in constitutive laws has zero bearing on that classification.
>>16838059The worst thing to come out of widespread access to AI has been the ridiculous number of schizos being convinced that their retarded ramblings are deep and secret knowledge. Every Mandlbaur-tier faggot out there is convinced they're fucking Einstein or Feynman now, just because ChatGPT sycophantically sucks their dick every time they prompt it.>Hye Copilot, what if liek, realty is just an alien silmulshun?>Wow! That's a really insightful idea! You're so smart! Have you considered upgrading to a Premium account?
>>16840330No. You are trying to manufacture Aharonov-Bohm holonomy in a domain with trivial first cohomology and then blame "high frequency, anisotropy, thin films" for the absence of gauge invariants. Let D be the fluid-accessible region (the interior of the hollow tube); topologically D ≅ {(r<a)}×R, hence [math]H^1(D;\mathbb{Z})=0[/math] and [math]\mathrm{LocSys}_{\mathbb{G}_m}(D)\cong 0[/math]. Consequently, whenever [math]F=dA=0[/math] on D (your B=0 inside), the connection is pure gauge: [math]A=d\chi[/math]; all periods vanish [math]\oint_\gamma A=0[/math] for every closed [math]\gamma\subset D[/math]. There is no AB sector to play against itself, no monodromy to helix and no gauge‑invariant source of angular momentum.
>>16841353>my theory is to posit that divergence of the magnetic vector potential is proportional to the gravitational potentialThere’s no basis for that postulate though. When Einstein postulated a constant speed of light, it was based on the results of the Michelson and Morley interferometry experiments indicating a constant speed of light. When Bohr postulated the existence of stationary states it was because the discovery of braking radiation ruled out a classical model for electron dynamics. There are no experimental observations to support your postulate that magnetic vector potentials produce gravitational fields.Glancing through the shit you’re posting in the thread, many of the equations you’re asserting aren’t even dimensionally correct, nor is there any indication that you’ve bothered to confirm if teh Lagrangian is still invariant under this choice of gauge other than to make some vague statement that you’ve ‘solved’ the need for gauge invariance.
