How can we calculate 4D space - time characteristics in a larger space - time ?
Answers
Answer:
Einstein's theory of special relativity created a fundamental link between space and time. The universe can be viewed as having three space dimensions — up/down, left/right, forward/backward — and one time dimension. This 4-dimensional space is referred to as the space-time continuum.
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Answer:
How does 4D space link with time?
Via geometry.
We don’t know there there is a 4D space to link with time… we only know about a 3D space to link with time.
However, I would expect that it would link with time the same way that 3D space would.
A position in 3D space space — the kind you are used to — would be described by 3 coordinates (x,y,z) , they are linked together by the way we find a distance ie. from the origin:
If we define r so that r2=x2+y2+z2 , then r is the distance of point (x,y,z) from the origin. It’s just the 3D theorem of Pythagoras.
In 4-space, the equivalent 4-position would be: (w,x,y,z) and the expression that links these 4 dimensions together would be: r2=w2+x2+y2+z2
If we want to link either space with a time dimenstion, we need only subtract the equivalent distance in time. vis:
s2=r2−(ct)2
… so “ s ” would be the interval in space-time that is analogous to a distance from the origin in regular space. Just set up r to be the distance for the number of dimensions you want.
If you choose the 3-space r, then you get a 4D space-time.
The constant “c” is a conversion factor from the time units you use for t and the distance units you use for r .
Another connection between the dimensions is the Lorentz transformation for relativity. At least that is how it works in this Universe.
Aside: all these descriptions assume the space-time being used is “flat”.
Explanation:
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