Albert Einstein's theory of General Relativity is a little bit complex for most of us. There are famously sixteen equations that can be interpreted in a variety of ways in modern cosmological models, and us non-mathematicians want to learn the basics of space curvature and time dilation that happens in relation to mass.
The more mass is present the more space is curved. The sun has a lot of mass and much space curvature. Gravity is regarded in the paradigm as curving space, while all mass attracts other mass as if it had only a positive charge attracted to positive, and that mass curves space in proportion to its amount of mass.
I was reading a book called 'Faster Than Light' about the variable speed of light theory, and the author mentioned that Einstein's special theory of relativity was made with the paradigm that space is empty and did not account for the effect of curved space upon light or mass travelling through it. He needed to improve the theory and make it a General Theory of Relativity that would in one fell swoop surpass Newton's theory of gravitation.
I found a nice little book named 'One to Nine' published in 2007-2008 by Andrew Hodeges that covers a lot of ground about each number and some of its deeper, even philosophical significance. So one reaches the number four and finds a mathematical phrase that provides a really simply idea for understanding basic parameters of G.R.
A three-dimensional space-imagine a Cartesian coordinate x,y grid with another line penetrating through it like an arrow to make three dimensions (the flat grid like a computer screen is two dimensions) can be used to draw a sphere upon. With another dimensions of time allowing the sphere to expand or contract one has the number four that is usefully presented in the expression T2 - x2 - y2 -z2.
Wikipedia has an useful article on Algebra. Describing many dimensions mathematically is something that is apparently a project with a major investment of time, yet of course math is purely abstract at heart. http://en.wikipedia.org/wiki/Algebra
I was wondering about some of the discussion on the topic of time in the context of the special theory, yet maybe one must use the general theory to describe the relationship of time to experience subjectively.
There are innumerable illustrative examples of the special theory, yet it is G.R. with the contraction of time with speed letting one travelling near the speed of light experience time passing much slower than for those stationary on a planet (its really impossible though because as mass approaches relativistic speed it increases its relative mass infinitely and that requires an infinite amount of energy to accelerate it closer to light speed.
With the cosmic microwave background radiation and measurement of personal time from qualitative analysis of the elapse of time since the 300,000 years from Time = 0 in the history of the Universe when light first escaped from a super-hot plasma cloud in theory) anyone in the Universe should be able to tell what their time is objectively in the history of this Universe even with relativity.
It is amazing that mass itself and ties into space somehow 'curving' it perhaps by association with particular small dimensions in it, yet space is increasing in size outside concentrations of mass as if the dimensions of space were expanding along a time dimensions and unaffected by gravity enough to localize at any given clump of mass through space curvature.
Space is observed to be nearly 'flat' by astrophysicists I believe, and the intense curvature of space around mass especially about neutron stars and black holes is an anomalous or minority phenomenon in the context of space. It is a little challenging to think of dimensions expanding without mass, as if they should have any size or substance to increase. It is almost easier to imagine all of mass contracting in the Universe and space remaining the same size, yet of course that probably isn't so.
Hodges does provide Minkowsky's equation for the separation of two events in time (0,0,0,0) and (t,x,y,z). he is using complex numbers in the example (the book is easy to read for non-mathematicians and self-explanatory). An easy version Hodges provides where the speed of light is represented by 'c' and the value is one is:is c2t2 - x2 - y2 -z2...
That makes everything clear.
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