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/sci/ - Science & Math

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15849797 No.15849797 [Reply] [Original]

Could we predict more dimensions by reformulating our current physics equations into algebraic formulations instead of fields equations?

I remember that Maxwells equations were orginally formulated in a quaternionic form. I see this as evidence of the prediction of the 4th dimension of time before SR, with (-1,i,j,k) being (t,x,y,z) & with the diagonal of the quaternion table being the same as the diagonal for the Minkosiki metric (being: diag(-1,1,1,1)). I feel more substance will be given if we take a look.

>> No.15849811

>algebraic
You're 150 years too late. Erlangen program is over. Try category theory instead.

>> No.15849815

>>15849811
Would category theory predict dimensions?

>> No.15849846

>>15849811
>category theory
when will this meme die?

>> No.15849849

>>15849797
This has to do with the fact that the Clifford algebra describing Lorentz representations is related to the quaternion algebra
https://link.springer.com/book/10.1007/978-3-7643-7791-5

>> No.15850094

>>15849797
>I feel more substance will be given if we take a look.
I feel it's you who should take a look - at basic textbooks, that is - before larping as a physicist or mathematician on 4chin.
Quaternions arise as the even subalgebra of the Clifford algebra of a 3-dimensional Euclidean space. This has been generalised and used in theoretical physics decades ago, including arbitrary spaces with non-trivial metric signature.
It would have literally taken you less time to google that up than to post this.

>> No.15850634
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15850634

>>15849797
yes,
https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6876131

>> No.15850730
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15850730

>>15850094
>This has been generalised and used in theoretical physics decades ago
indeed, but somehow the vector potential is still taught as just a 'mathematically conveinence' with no basis in reality decades later.

Such a travesty could only be tolerated by being stuck in the vector algebra formulation of the gibbs-heaviside equations. Exterior products are generalizable beyond R^3 unlike the curl, ignoring the scalar term of the quaternion hides a vital part of wave interference, and the currents fundemental relationship with the vector potential obsures whats reallying being destroyed when implementing a guage

quaterions are the way
enjoy https://www.youtube.com/watch?v=3AAK-4KdGXs

and have https://www.researchgate.net/publication/237501522_Electrodynamics_with_the_Scalar_Field

>> No.15850755 [DELETED] 
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15850755

are these invisible extra dimensions in the room with us right now?

>> No.15851695

>>15850730
>indeed, but somehow the vector potential is still taught as just a 'mathematically conveinence' with no basis in reality decades later.
>t. I have never read a single QED book

>> No.15851896

>>15851695
>>t. I have never read a single QED book
no that's the halfway cope. [math]\textbf{A}[/math] has an explicit physical meaning, and direct measurability already in classical situations