Albert Einstein suggests, and empiricism seems to confirm, that space and time should not be treated as distinct from one another.
Actually space and time are different. There's a time arrow that clearly distinguishes past from future... even if most Mechanics seem to be symmetrical in time, Thermodynamics clearly shows that's not true. You must introduce that asymmetry somewhere or things won't work. What Relativity shows is that time and space are a whole that must be treated geometrically as a 4-dimensional thing, and not a 3-dimensional space where we let time flow... Space-time is the whole we live in (and some other theories, currently heteroclite (spelling?) superstrings quantum dynamic field theory (HSST), add more shrinking spatial dimensions, 6 more in the clockwise and 26 anticlockwise (or maybe vice versa, cannot remember well, but those 26 are reducible to the 10 ones, so the Universe is made of 10 dimensions (9 spatial, 1 temporal), 6 of which are continually shrinking since Big Bang, and 4 expanding, one of which is asymmetrical (time))
Yes, space and time are one thing. I've got this strong feeling that the universe isn't actually any bigger than it was just after the (postulated) Big Bang, it's just that the Metric Tensor has been unwinding, so the universe seems bigger. - What exactly is the difference between the two cases?
Well, that's interesting... From an inner observer, it wouldn't make any difference, I think... However we still have a problem with time... locally it's symmetric, but on a bigger scale it's asymmetric... That cannot be explained by the Metric Tensor... unless we put some expontaneous symmetry breaks here and there... but it's an interesting point of view. - The metric tensor can describe a temporally asymmetric universe just fine, thanks. It doesn't describe all the details, but that's because that tensor isn't meant to encapsulate all the details.
Why is it asymmetric on a larger scale? Is this an assumption or is there a specific example?
Time is a creation of man - it's a description not a thing. We use the word circle to describe the shape of the sun. We use the word time to describe the shape of change. Time is not a characteristic of the universe, but rather an artifice that we have created in order to organize change in our minds.
An alternate approach is to sit quietly alone in a room. Do not think. Just sit quietly with all your senses open and examine the flow of time. After a while, perhaps you will realize that there is nothing moving, nothing flowing and nothing passing. All change takes place in the same moment, and although the words spoken by some slave in Egypt four thousand years ago no longer make a sound it is always right now that he is speaking.
And perhaps you will realize that the universe was, in fact, sneezed from the nose of the great, green arkleseizure. With a sufficient amount of chemical substances, perhaps you will realize just about anything. Does that mean it has value? Does that inch closer to The Truth? -- Anonymous Donor (with due regard to Douglas Adams)
Of course this is nonsense, because a moment is a slice of time. The past and future, a priori, don't exist as part of the present. The above is probably trying to say they are all equally real, and that the division between them is a matter of perspective, but doing so in a terrible way.
As has been said, time is asymmetric because entropy must have a net increase. Perhaps the best definition of The Future is the time when the Universal Entropy is greater than it is now.
Explain again why entropy must have a net increase, or is this merely a local observation you have made?
Entropy is a human artifice even more so than "past", "present" and "future". Entropy is just the number of microstates (physical states) that correspond to a macrostate. A "microstate" is just what the human brain considers a "single" state because the differences between them are "insignificant".
If the universe is construed as a computer using Reversible Logic, as the Many Worlds Interpretation insists we must, then actual information stays constant across time, and the increase of "entropy" is just a human delusion/artifact. Hence time isn't asymmetric in any physically meaningful manner.
Incidentally, it may be worth noting that space and time are slightly distinguished in relativity. Associated with any two events is an interval, corresponding essentially to distance in space, but this is allowed to take on negative values. A positive interval is time-like while a negative interval is space-like, and these play different roles. Particles with mass can only follow time-like intervals, so go from their past to their future (and yes, the direction imposed on this is arbitrary), but not into their elsewhere.
See Rudy Rucker's "Geometry, Relativity, and the Fourth Dimension" ISBN: 0486234002
See original on c2.com 
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Spacetime is a model used in human language to encompass the physical sensation of embodiment within an environment and the conscious experience of sequences of identifiable events.