time as magnitude of dimensions

[supernova_smash]

Maybe I'm lost, I still know little about physics (so please don't judge to harshly ), but this whole time as a 4th dimension is really triggering some weird and probably absurd thought. I read that to visualize time being another dimension, we must somehow add another axis to the x/y/z grid in such a way that it is perpendicular to these axis. I know that this is impossible to visualize, but I don't see how this logically makes sense. Is time a dimension that can be depicted visually, or is just a component of space? If it is a component of space, why don't we visualize a "unit sphere" on the x/y/z grid, and then use time as a magnitude of all the axis and thus the sphere? In this way, an event would be described in space and time. It also seems analogous to the Bing Bang theory, maybe because it's a ball expanding from an infinitely small point (the origin of x,y,z). It is also a good visual for the "end" of the universe (that is if this whole idea isn't too far off), because it would show that the universe doesn't end (at least it would appear that way to us) because we are simply too far behind in time to catch up to the "surface", if you will, of the sphere. If this could be possible, what would the negative values of each axis mean, anything? Or do they just represent all directions? I'm so lost, be gentle

 

[Crisp]

Hi supernova_smash,

The unit sphere in XYZ-space is a 2 dimensional surface in a 3 dimensional mathematical space and hence not independent of the three spatial dimensions you refer to. Since time is independent of space (in the sense that time can pass without movement in space), this construction will not work out. The only way to add an independent coordinate to a set of coordinates is to add an extra dimension (this can be mathematically proved using linear algebra).

Also, the analogy of the big bang and an expanding "sphere" is perhaps one you should not stretch too far: we are talking about spheres in a 4-dimensional spacetime that can be curved in strange ways, so the visualisation trick of an expanding sphere does not always predict what the math would .

Bye!

Crisp

 

[Boris2]

"...but this whole time as a 4th dimension..."

It is only the fourth dimension when talking about spacetime. It is not the fourth dimension when talking geometry.


"....we must somehow add another axis to the x/y/z grid in such a way that it is perpendicular to these axis. "

I think this only applies when talking of a fourth spacial dimension. In spacetime all the axis are travelling forwards in time, so there is no need to visualise another axis at 90^o to the xyz ones.