# The Concept of Space-Time

At this point, we probably should try to qualify the previous description
of the ‘*nature of the universe*’
by adding some additional concepts related to spacetime. While the discussion
in this section related to relativity has been now been superseded by
the specific discussion of both ‘*special
and general relativity*’, there may still be some benefits to
presenting some of the basic tenets of general relativity for reference
within the current discussion:

As far back as 1908, Hermann Minkowski proclaimed that our intuitive understanding of space and time was fundamentally flawed and that only spacetime existed.

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
reality. |

While not arguing with one of the great mathematicians of his day,
it is possible that the concept of spacetime needs to be put into some
practical context. While accepting that 4D spacetime is an important
concept for explaining time dilation and space contraction in terms
of a `*spacetime interval*`,
it is not clear that an intuitive distinction between time and space
cannot still be retained for most general descriptions. In many respects,
the real paradigm shift between Einstein and Newton was the notion that
time was relative and not an absolute concept, rather than necessarily
implying that space and time could not still be treated as distinct
quantities, especially within a single frame of reference. After special
relativity, in 1905, Einstein published general relativity, 1915, which
expanded on the idea of spacetime curvature, which might be most readily
understood in terms of the *Schwarzschild
metric*, which describes the effects on both space and time caused
by a specific mass [M] with an unambiguous centre of gravity. However,
the primarily effects of general relativity are normally subject to
interpretation by a distant observer and not normally within the observed
frame of reference itself, i.e. an observer in free-fall can be subject
to both relativistic velocity and gravitation but does not perceived
local time dilation or spatial curvature. Equally, as suggested, the
more dramatic effects of this form of space-time curvature are typically
localised to points of extreme gravitational mass, e.g.
*black holes*. In stark contrast,
the *FRW metric* is based on the
assumptions of a homogeneous density universe, which reflects the expansion
of space as a function of time as defined by the scale factor a(t).
For example, if we assumed the spatial curvature is flat, by setting
[k=0], the large-scale geodesic nature of spacetime might be initially
visualised in terms of 2 photons moving in parallel, e.g. 1 metre apart,
but after a sufficiently long period of time this space would be subject
to expansion and therefore our parallel photons might be described as
following a curved or geodesic path in spacetime rather than a classical
straight line.

However, it is not the goal of this section to appear to be rejecting any of the ideas of relativity; simply that some aspects of theoretical physics, such as N-spatial dimensional manifolds, may not be that meaningful to anybody, but a trained mathematician, and therefore counter-productive when simply trying to acquire a general understanding of cosmology. As such, the focus will be put on examining the basic ideas that support the accepted cosmological models, and in doing so, try to understand and question what aspects of these models remain essentially unverified hypothesis. Therefore, the following sub-sections will try to review some of the key concepts that collectively define the nature of spacetime prior to some further discussion of the specific assumptions underpinning the ΛCDM concordance model.