spacetime

"Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent realilty."

and then showed physicists how to think about spacetime, rather than space and time.

What all this explains is just that "folding" of space and time into one. This explains why, for example, when something travels at the speed of light that time for them ceases to pass. (The entire velocity vector whose magnitude is always equal to c (see above) then is in a spatial direction and there is none remaining for the time direction.)

I find this explanation to be very helpful in understanding the relationship of the space and time. And I like to think that I'm travelling at the speed of light, even as I sit here on my bum....

Concept from The Elegant Universe by Brian Greene

Imagine old-fashioned obsolete Galilean space. Given 2 points, if we wish to calculate the distance between them, we employ the distance element defined by

ds² = dx² + dy² + dz²,

ds² = dt² - (dx² + dy² + dz²).

Another way of talking about the second equation is to multiply dt not just by c, but also by i. Then ds² is simply minus the sum of squares of the 4 coordinates.

It is often said that Einstein's theory of special relativity shows that time and space are parameters of the same ilk and that, physically, spacetime is more fundamental. In fact, if we define a coordinate t*=ict, where i is sqrt(-1), then the set of coordinates (x, y, z, and t*) are invariant under Lorentz Transformations. In other words, the "length" between two points in such a coordinate system is the same regardless of the inertial reference frame of the observer. Note that the common-sense observation that a length sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2) is the same for all observers is false.

While special relativity is considered incontrovertible, there is, I think, a very clear difference between space and time, which is one of the greatest unanswered questions in science or philosophy. We cannot help but admit that the "coordinate" time flows forward in our consciousness, and we certainly don't have the freedom to move around in time as we do in space. From a mathematical point of view we can treat particles as functions defined by a few differential equations in 4 variables, and we can consider these 4 variables as equivalent, independent parameters. Particles (or more fundamentally quantum fields) exist over all time and all space. But in our human conscious world, which cannot be denied, the future has not been seen, the past cannot be returned to, and we are carried through time like a leaf in a stream is carried through space. And thus physics is philosophically at odds with everyday experience.