You can check out our answer to the question "What is a dimension"
for some more information about space, time, and dimensionality. You
ask some good additional questions, though.
I'm not sure that "perceiving space as one unified thing" is
really all that strange even though there are three spatial dimensions
we are familiar with. There are different ways to go (up, to the right,
and forwards), even though empty space is really the same in all
directions (we say it's "isotropic"). Spacetime gets bent around due to
the presence of matter and energy, but that's another story.
Our explanations of the physical phenomena we observe make sense
only if we use Einstein's theories of special and general relativity.
Using these theories, we treat the time coordinate as another number we
need to specify an event -- we need three space coordinates and a time
in order to say when and where something happened. If we express the
coordinates of some event as viewed by someone else, we use Einstein's
prescriptions, and these usually involve formulas which include the
spatial coordinates and the time coordinate in one observer's frame of
reference combined together to calculate the space coordinates and time
coordinates of the same event viewed in another observer's frame of
reference. It was Einstein's work that showed us just how much like a
space coordinate time really was (and just how unlike it is! See the
dimensionality answer for an explanation of how time comes in with an
opposite sign in the "distance" formula).
As for your question: "how are we sure that's all the dimensions
there are?" the answer is "We're not sure at all". There could be more
dimensions lurking out there. Some may be very small -- you may only be
able to go a tiny fraction of a proton's radius in one of the proposed
extra dimensions before winding up back where you started. We sometimes
call these extra dimensions in these models "rolled up" or
"compactified". One reason why these models seem kinda kooky is that we
also have to come up with some explanation for why we may have not
noticed these extra dimensions yet in experiments. Maybe we just
haven't done the right experiment yet, and the smaller the rolled-up
extra dimensions are, the harder it is to test them with today's
equipment. But the predicted effects are testable -- one predicted
effect is that gravity gets stronger than the usual 1/r^2 dependence if
you get within a radius similar to the size of the curled-up extra
dimensions of something.
Also the distinction between space dimensions and time dimensions
really comes down to how many dimensions have the opposite sign
contribution to the distance formula (physics jargon: the "metric").
Time also has some interesting special properties. One is that
thermodynamics gives rise to the "arrow of time" entropy inceases with
time; stuff spontaneously breaks much more often than it spontaneously
fixes itself. The different gases in the atmosphere spontaneously mix
(by random diffusion even if no stirring is going on), but do not
spontaneously unmix. We remember the past and not the future. Space
dimensions seem to be equally good going either way, but time has this
"arrow" pointing from the past to the future, and past events can
effect future events but not the other way around (we have found no
reason to believe that this rule, called "causality" is violated).
Most explanations of time's arrow are historical -- for some
reason the universe started in a very special 'unscrambled' state, and
the odds are overwhelming that it will fall into more 'scrambled'
states, because they are much more numerous. We don't understand the
reason for the special starting state.
Evidence for a different arrow of time comes from particle
physics experiments. Exchanging particles for antiparticles, changing
the signs of all the spatial coordinates, and making time run backwards
is a combined symmetry operation which is supposed to leave all the
laws of physics unchanged (this is called the "CPT theorem"). Some
experiments have shown that by swapping particles for antiparticles and
changing the signs of the space coordinates produces measurable
differences in some reactions ("CP violation"). The inference here is
that the time symmetry by itself is not a good symmetry of nature. The
laws of physics would be different if time ran forwards instead of
backwards. Direct violation of +-time symmetry was found in the neutral
kaon system in the mid 1990's.
One last thought on your question whether there can be more
dimensions. Occam's razor is a principle expounded centuries ago that
our explanations should be no more complicated than necessary. In fact,
the original formulation is that "entities should not be multiplied
beyond necessity" (a very rough paraphrase of the original Latin). In
short, if we do not need to invoke the idea of any extra dimensions to
explain what we observe in nature, then we shouldn't do it -- it just
makes our models more cumbersome without improving their ability to
explain nature. And furthermore, it opens the number of ways the models
can be wrong to possibilities limited only by our imagination.
That's not to say Occam's razor prevents thought and even
speculation -- it merely pares down the possible final explanations we
are willing to accept as "the best we can do". Science proceeds by
formulating hypotheses and checking them with experiment. I am
delighted when people come up with ideas that add things (like extra
dimensions, or extra particles) to what we think we already know, but I
am even happier if these ideas can predict something we can test in the
laboratory so we can tell the difference between these models and
simpler ones not including the extra dimensions or particles.
Tom (w. a little editing by Mike)
(published on 10/22/2007)