Are fields projections in spacetime of higher dimesions?

I am initiating my learning on QFT and my question might be really basic, but I am having difficulties finding an answer, I would appreciate any help to find this in the literature.

Here is my question:

If all dimensions are independent and co-exist (here and now).
If humans are not able to see all dimensions, but we might be able to measure them.

My question is when we observe projections of other dimensions on spacetime they should be observed as fields, right? And in spacetime any equation should be an equation of motion to make sense, right?

If this is true…

Can we find these equations (electromagnetic field, for example) accounting for the dimensions the projection misses?

I appreciate the time anyone put to answer my questions.

Thanks!

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Let me try to rephrase my question.

Imagine a 2D parabolic equation y=x^2. If you look at it as 1D, in x, what you would see a lot of values "closer to each other" (higher density) as x goes -∞ and +∞.

In my mind, this density of values would look like a "field" in x, instead of being described as a higher dimension function.

If you have measured enough values of x, is it possible to get to y=x^2?

If fields are projections in spacetime, can we find the other dimensions if we have enough measurements?