Spacetime is a noun which defines a physical state of the Universe as described by the general theory of relativity as specified originally by Albert Einstein.

Spacetime is a physical item which can be observed and effected. Mass warps spacetime to create a gravitational field.

Theoretically spacetime is expanding and has been doing so since the Big Bang which occured approximately 12 billion years ago.

When Hermann Minkowski first heard of Einstein's special theory of relativity, he realized that it described how space and time are folded into each other. He then began a famous paper with the statement:

"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.

Every person, thing, particle is always moving at the speed of light within spacetime (for us it will suffice to have one time dimension and three space dimensions). When we are at rest, the entirety of our speed is in the time direction. When we then move in one or more spatial directions, part of our speed is required to move in the new direction and therefore our speed in the time direction is reduced. (If our velocity vector doesn't lie entirely on time axis then the sum of the time vector and the spatial vector will be our velocity vetor)

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

Spacetime is a quasiriemannian manifold (it's almost a differential manifold, only instead of a metric you only get a quasimetric -- its square may be negative).

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,
as known to dear old Pythagoras. However, in space-time we use a different element, and call the result of integrating it interval rather than distance (you can use the speed of light as a constant to convert time to distance, to allow you to subtract the 2 quantities):
ds2 = dt2 - (dx2 + dy2 + dz2).
Note that if you want ds to be real, you have to ensure that nothing travels faster than the speed of light.

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.

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