Is it possible to define 4-dimension world in one formula?

Question

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Answer 1

Depends on what you mean. Do we have an equation (or set of equations) to adequately describe our universe (be it 4 dimensions or more), no. We're working on it. For the small scale, the 4-D equations of Quantum Field Theory work very well, and on the large scale GR equations work well. The number of equations required depends on the number of independent variables that we need to describe reality. These vary depending on the theory.

The goal of theoretical physics is to write one equation (known as a Lagrangian) to describe reality. The Lagrangian is fed through the Euler-Lagrange equations from Calculus of Variations, which then gives N "equations of motion" where N is the number of independent variables.

Now that talks about how to describe the Laws of our 4D world. If you just want an equation to describe a 4D space-time, the simplest one to understand is the metric. The metric is an equation that defines how to measure a geometric length, and is used to describe gravity and spacetime (which are equivalent) in General Relativity.

First consider a flat 3D space (Euclidean space - the space you talk about in high school geometry) with coordinates given by (x,y,z). If I wanted to measure the distance (denoted by s) from the origin to the point (x,y,z), it is given by the formula s^2 = x^2 + y^2 + z^2; this is just the Pythagorean Theorem extended to 3D. Now, not every space is flat, so we really need to measure distances on only the small the scale using differentials from calculus. All this means is we're taking the (x,y,z) to be really close to the origen (keep in mind we can define the origin to be at any point of interest). We denote this by using a "d" in front of the coordinates. All this means is that the total length is very small. So we write: (ds)^2 = (dx)^2 + (dy)^2 +(dz)^2.

Now GR says that space and time are part of the same thing called spacetime, but they are different by a sign. So going to a flat space time as in Special Relativity (I'm dropping the parenthesis, but they are implied), we get ds^2 = dt^2 - dx^2 - dy^2 - d^z^2.

Going to a curved space time, each of the terms above gets a function in the front to describe the curvature. There can also be cross terms (like dx*dy) with functions as well if the system isn't symmetric. These functions form a metric tensor. Using the metric tensor with the metric equation one can derive what a "straight line" would look like in a curved space.

So, yes, we can describe a 4D space very, just not OUR 4D space as well as we would like to (at very small scales or extremely high energy).

Answer 2

if u think nothing is impossible then the ans is yes.... ya the thing is that we still don't have a good understanding about the four dimensions i.e the space-time as we are in four dimensional

we can get a better answer when we have the "gravity-quantum" theory that is the unification of physics

Answer 3

h * w * l multiplied or displaced by time = reality

one's reality as far as worlds go, is the world on which one lives their alloted time in life.

This is just my opinion.... works for me.

Answer 4

4th dimension is not properly defined yet,,,,,, hence cannot be written in formula