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 While the discussion in this section related to relativity has now been superseded by the specific discussion of both ‘special and general relativity’, there may still be some benefits to presenting some of the basic tenets of general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, in 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 primary 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.