/sci/ - Science & Math

>>15331342

Son you need to learn how to be more concise.

>>15332325
here is TLDR
Scientists shouldn't interpret the lack of unique solutions to A as a causus belli for Gauge theory, it just kicks the problem down the road. Scientists should instead focus on discerning unique A's for thier given problem. A isn't arbitrary, just alot of different ones are possible. A source of arbitrariness is only using the first and second derivatives in the equations and holding medium dependent variables constant, there just isn't enough information. I suggest, that instead of adding the logical step above laplacian, to go a step below the gradient, and allow permitivity and permeability to vary with the field. This will further constrain A, providing inspiration for experiments that can accurately determine the nature of the magnetic vector potential

>>15332363
>Scientists shouldn't interpret the lack of unique solutions to A as a causus belli for Gauge theory
No one is attacking gauge theory. Modern physics is all about gauge theory and it's used in places you wouldn't expect like condensed matter physics.

>I suggest, that instead of adding the logical step above laplacian, to go a step below the gradient, and allow permitivity and permeability to vary with the field.
It's not exactly clear to me what you are intending to do, but no doubt it's completely unphysical. There's a good reason for gauge fields. You can derive them in reverse by trying to construct a quantum field theory that has massless spin 1 particles.

tldr, you have a lot to learn about physics still

>>15332394
>No one is attacking gauge theory. Modern physics is all about gauge theory and it's used in places you wouldn't expect like condensed matter physics.
I am attacking gauge theory, Its a coping mechanism that entrenched itself as its founders didn't have python nor insight of Bohm-Aharonov. The potentials are real and physical, one shouldn't go lopping them off. Gauge theory is a black box function. sure, you might get some valuable stuff out, but the how and why is completely obscured between destroying the field equations are recovering it with ones gauge. It doesn't help that there is serious critiques of the lack of insight modern physics has revealed, bolsters undoubtedly by too big to fail particle collider experiments.

>It's not exactly clear to me what you are intending to do, but no doubt it's completely nonphysical
Scientists see the speed of light in their physics equations and totally forget that its really 1/ sqrt(mu * rho). permitivity and permeability are functions of the media. Change the natural impedence of your space and you now have more information in your field equation that can reduce the arbitrariness of A

>tldr, you have a lot to learn about physics still
Perhaps, i'll say, that you have alot less to mimic

>>15331342
Nice work anon. This is very understandable. Can you explain this in terms of differential forms?

>>15331342
I don't the see problem? If I just gave you the constant acceleration of a projectile, then you'll still need to know the initial conditions to deduce the position. Same story here, but with B and A.

>>15332469
My quandary is best illustrated within the differential forms of the potentials formulation of geometric algebra found here

https://ieeexplore.ieee.org/abstract/document/6876131

IT clearly exposes 1) what information one is giving up in they engage in gauge theory by "setting l = 0" and 2) it clearly shows how the vector and scalar potentials are related to the current, solely through the differences in temporal and spatial second order derivatives. Its an illustration of inertia, a particle being whacked a certain way that satisfies the same constraints that informed maxells, i mean gibbs-heaviside's equations.

We see however in these equations that the speed of light is held constant, meaning that nothing is being said about a particle going through a difference in the impedence of space, a partial gradient with respect to permitvity and another with respect to permeability. Visually stacking two thin layers of crystals atop each other. Whilst i've yet to perform the math, its a topological tautology that increasing constraints reduces possible solution sets, so it aught to motivate a new class of experiments targeted at exposing unique solutions to A

>>15332509
So in what way is your particular solution related to not setting "l" to 0?

>>15332479
The issue at hand is that, with simply a constant acceleration, one does not have enough information to stop this 'exploit' found in the first pdf. We get a bunch of possible initial conditions and we cant tell which one is the true initial condition. Metaphorically, Gauge theorists say thats okay, we can draw a circle around all the possible combinations with our gauge and call it a day. I am not content, I want the real initial conditions.

My position here is that, instead of adding third order Laplacian (whatever their called) or adding jerk, jaunt, etc- to reduce the amount of possible solutions, we introduce permittivity and permeability gradients instead. In the analogue, adding an area of greater friction or elasticity. But the added benefit is that the impedence of space has self resonant effects once they hit a boundary condition (pic in >>15332363) so it seems logical that one will get more information by tuning a resonance condition in their experiment, than simply adding higher order derivitives

>>15332509
>https://ieeexplore.ieee.org/abstract/document/6876131
Thanks for the link. Looks very interesting.

>>15332529
>I am not content, I want the real initial conditions.
You can't with only E and B, the EM 4-potential is a deeper physical object, which was demonstrated by Aharonov-Bohm. The speed of light in vacuum is constant, so I don't see what you mean by these 'permittivity and permeability' gradients.

>>15332527
My fundemental desire is to no longer hide behind gauge theory and accurately deduce what the potentials, given a specific usecase, actually exist. Simply seeing the divergence (or inner product) of the Magnetic Vector Potential to zero and defining a class of valid potentials under a gauge theory for myself is insufficient. Especially with the inertial relationship of the scalar and vector potentials with the current density.

My solution is try to reduce the amount of valid potentials for a given instance by introducing material gradients, expose 1/sqrt(epsilon * mu) to their own differential forms, create setups that induce standing wave resonance through the impedence over the space. Perhaps than can one zero in on what exactly the potential one is seeing, and can dispense with truncating their equations mid calculation

>>15332536
I don't know what a material gradient would be. Are you saying the field potential is different in vacuum and in air? That should be a testable hypothesis.

>>15332535
>You can't with only E and B, the EM 4-potential is a deeper physical object, which was demonstrated by Aharonov-Bohm.
Indeed,
>The speed of light in vacuum is constant
but i'll still posit, contrary to popular verbage, that true vacuum has no permittivity and permeability, in every other wave equation the analogues to these variables are medium dependent, so using things like thin films of crystals in self resonance circuits

>>15332452
this, im suprised we dont have boom of new theories since computers become available
its only 100+ year old bullshit being amplified over and over

>>15332452
Bohm-Aharanov is standard gauge theory, and everyone uses the gauge potentials, they are the basic fields in the Lagrangian. You are attacking some strawman version of undergraduate physics, that is why I say you have a lot to learn.

>>15332540
>I don't know what a material gradient would be
consider the Functional graded materials expounded in this paper (what >>15332452
pic here is from)

The idea being we can now, with it seems a good precision, grade a material in such a fashion that its permitivity and permeability changes with distance (or x,y,z for ones field calculations) If considering a wire with a finite length, it also than possess unique impedence effects that would inform novel harmonic resonance conditions. This is important, as the alternative is to simply add the 3rd order gradients to the equation, but you dont get anything back after the imparting of inertia from that, there is more information here!)

>>15332552
and more information density, logically would likely reduce the arbitrariness of the the vector potential (for completeness)

>>15332545
It doesn't help this subject of gauge theory seems to be a rite of passage in the emag community and has come to rest as a cornerstone for modern physics, so touching it agitates tenureships and billion dollar experimental setups.

>>15332546
Yes Bohm-Aharanov employed guage theory in their work, but than reveiled the 'primacy of the potentials' and cast caution to the growing climate that the vector potential was simply 'a mathematical convenience' that conveyed no physical meaning (how many even learned this in their undegrand 50 years after the experiment, i did in my undergrad!) This experiment showed without a doubt that, while gauge theory may provide a path around discerning the true character of A to reach an observable, something very deep and perhaps foundation is being missed by neglecting its true character in a given experiment.

>>15332562
(cont)
As the geometric algebra potentials formulation of emag expounds, not only is the vector potential important, but it very well be the most important part of the whole theory

>>15332562
I don't think you understand Gauge theory, you have to FIRST choose a gauge to deduce the potential. Then all other gauges would lead to the same physical results.

>>15332581
>sets divergence of the potential to zero
>voila, i deduced the potential

from paper
>Subsequent developments led to the discovery that different forms of the vector potential result in the same
observable forces. The partial arbitrariness of the vector potential A brought forth various restrictions on it

leading to setting, declaring, removing maths, to restrict the vector potential. The rules for a valid guage being Focks equations in above pic >>15332566 .

One did not deduce anything, they declare and assume it to be a certain way. They found a set of constraints that given a hypothetical potential it fits inside the field theory. It says nothing about what the potential actually is. All it reveals is a set of possible potentials

>>15332596
Are you actually retarded? You need a gauge to deduce the fucking potential, the gauge != initial conditions. To draw on the projectile analogy from earlier (but with known initial velocity), the gauge is NOT the initial condition (elevation from ground), but is the choice of origin.

>>15332634
>Are you actually retarded?
no just unbrainwashed by gauge magic.

>You need a gauge to deduce the fucking potential
gauge theory is a reaction to the arbitrariness of potentials, one utilizes gauge theory because they have no idea what the initial conditions are. One isn't deducing anything with gauge theory they are assuming the character of the potentials.

Again setting the divergence of the vector potential to 0 is not a natural following of the maxwells equations, it a truncation, a lopping off of the mathematics, a simplying assumption to help work with the equations

>>15332552
Indeed, even in Hivelys gauge free extended electrodynamics, he opts to begin utilizing the time derivative on the permittivity

>>15333251
>gauge theory is a reaction to the arbitrariness of potentials, one utilizes gauge theory because they have no idea what the initial conditions are.
Dude, did you even read my response? A gauge transformations leads to physically identical results, this is true for QED as well, which demonstrated the 'primacy of potentials'. These aren't conflicting concepts, you're just retarded.

>>15334173
>A gauge transformations leads to physically identical results,
I've reiterated this many times in this thread already and is my central point. Namely that it is insufficent that it leads to identical results. By doing so it is masking the valuable physical insight concerning the nature of the potentials, and leading scientists astray from concerning themselves with probably the most important question in electrodynamics- that given a usecase, what is the exact character of the potential.

To recap

>>15331342
>A is indeed something- far from a 'mathematical conveinience' and its precise character aught to be the subject of inquiry, not simply finding a gauge that can justify ones observations, but leaves step-by-step procedure of how a particle got from A to B in a black box.

>>15332562
>This experiment showed without a doubt that, while gauge theory may provide a path around discerning the true character of A to reach an observable, something very deep and perhaps foundation is being missed by neglecting its true character in a given experiment.

>>15334224
Gauge invariance is a fundamental aspect of QED, are you saying that QED is wrong despite admitting to its predictions(Aharonov-Bohm)? This isn't even in the realm of classical EM, which you seem to be struggling with.

>>15331342
>The truncation of the field equations to accomodate gauge theory hides mathematically interesting possibilities and blurs actually the most important part of a emag theory, the precise character of the A field itself.
Which is why you must make sure that your differential chain complex in the given domain has trivial cohomology before you try and work with the potentials.

>>15334283
Elaborate pls? I dont know diff geo :(

>>15334303
In simple terms, make sure to work on a "star-shaped" domain with no holes if you want to define single-valued scalar or vector potentials owing to that differential chain complex's trivial cohomology as inferred from the Poincaré lemma.

>>15334269
There is nothing fundemental about gauge invariance, it is coping mechanism to deal with the reality that an observer doesn't have complete information about their field. I am not saying QED is wrong, i am saying theories that build on top of gauge invariance are, quite litterally, missing the point.

Before Bohm-Aharonov, especially after the advocacies by Weyl, the potentials were being relegated, to a mere mathematical artifact. Its actually still largely taught this way. Why bother deducing the exact character of the vector potentials if its just an intermediate, purely mathematical step in the calculations, Bohm-Aharonov proved that A is physical, so one shouldn't just skip over it with gauge theory, attention should be paid to using gauge free field equations and experiments should be conducted to overcome the 'exploit' found in the first pdf.

This largely concerns the the unification of CED and QED, needn't i remind you that this too is a coping mechanism, a schizm derived from the irreconsilability of the macro and micro

>>15334303
I think this video explains it succinctly
https://www.youtube.com/watch?v=2ptFnIj71SM

>>15334320
>cohomology
yep u lost me :p
>"star-shaped" domain
what do u mean by this?

>>15334320
>>15334283
thank you for your contribution, I am not familiar with these maths, but if it motivates an experimental construction that condemns a charged particle to come from only a single vector or scalar potential than the endevour shall be worth while.

>>15334340
>what do u mean by this?
https://en.wikipedia.org/wiki/Star_domain
Make sure to watch this >>15334327 video too.