Our reality is essentially four dimensional:
left-right
by
back-front
by
up-down
by
before-after.
Gravity is described by General Relativity as mass distorting a four dimensional field “called” spacetime.
Are the four dimensions of GR in fact identical to our own four dimensional reality?
Or, just degrees of freedom which take place within reality…like paint on a canvas?
As I understand it, various fields like electric, magnetic, Higgs, etc. are said to be superimposed upon spacetime.
Furthermore, various branches of physics describe systems with 10, 11, 26, or as many as 248 dimensions (with tiny, curled-up geometries) doing their thing within what appears to us a four dimensional reality.
What if Gravity’s four dimensions are distinct from our reality…one just sitting atop the other, like the higher dimensional forces seem to be?
Yes, general relativity (GR) operates in four spatial dimensions and one time dimension. You can describe those spatial dimensions as x,y,z or you can coordinate transform to any other coordinate system you want (spherical coordinates: r, theta, phi are usually better for a lot of applications). In order to do calculations and stuff in GR you basically have to have a working understanding of tensor calculus as well as differential geometry (this is harder than it sounds).
The differential geometry component allows you to treat spacetime as locally flat. This is analogous to the trick in special relativity where you change to someone else’s “inertial reference frame” through a coordinate transformation in order to do a calculation and then “boost back” to the original reference frame to get your answer. A simple example of this would be if you’re standing next to some train tracks and a train is going by and there’s an old western gunfight happening on top of the train. If you were making calculations on where people are / shooting it would be easier to “boost” to the reference frame of the moving train, do your calculation, then coordinate transform back to you as the observer. In this case, you’d be removing the velocity of the train from the equation and then “putting it back in” after the fact.
With differential geometry you can make your local calculation in a flat spacetime but then you can still do curved spacetime problems. I guess we can skip other more complicated details if that answers your question?
As for your other questions: Yes, the 4-dimensions that describe your GR scenario (the technical term is a metric) are equivalent to the 3 spatial and 1 time dimension you’re (hopefully) very familiar with. The point of GR is to describe reality.
Electromagnetism has its own set of equations that describe the electric and magnetic fields and those also take place in x,y,z,t space.
Other fields (the quantum fields of which the Higgs is one) do not mesh with GR and are independent. Situations where both GR spacetime curvature and quantum effects are both relevant are unable to be described by our current understanding. As for the concept of higher dimensions - some theorists suggest that if we had more spatial dimensions (where are they? curled up really really really tiny so we don’t perceive them) that you could fix that problem and have one theory that encompasses general relativity as well as quantum effects. These theories make other predictions (new quantum particles) which have so far gone unobserved, and the space for which those new particles could exist continues to shrink as new observations are done. So you absolutely should not take higher number of dimensions as given or established.