This thread touches on many interesting issues, so I wanted to see if there was any consolidation of opinion on a number of the key issues discussed:
1)
N-spatial dimensions:
While the analogy of flatlander and 4D animals are useful visualisations, do they really provide any meaningful picture? While mathematics is free to conceptually imagine any number of spatial dimensions is there any empirical evidence to support a physical existence? The only example I can think of relates to string theory, but I understand that most of these dimensions would have to exist on a quantum scale?
think the truth is that there is no such thing as time, only space. Time is an illusion created by our limited perception.
In post #18, it was suggested that time was only a manifestation of the mind. This was backed up by an example of a pencil moving from A to B and therefore, in this definition of 4D spacetime, simultaneously existing at all points between A & B. While this may be the case, it seems to require a new science in the sense that another pencil moving from C to D, but intersecting the path AB, would violate Pauli’s exclusion principle?
2)
4D Spacetime
As I understand it, the definition of 4D spacetime, as used in relativity and cosmology, is typically referring to 3 spatial dimensions and 1 time dimension. Therefore, while accepting that 4D spacetime is a useful concept for explaining time dilation and space contraction in terms of the spacetime interval, it would seem that an intuitive distinction between time and space can still be retained?
3)
Geometry of Space and Time
In the context of general relativity, the Schwarzschild metric suggests that the perception of both space and time can be affected by the presence of a large gravitational mass. However, these effects are only observed at a distance and not by whose within the observed frame of reference. Equally, the more dramatic effects of this form of spacetime curvature are typically
localised to points of extreme gravitational mass, e.g. black holes. As such, we seem to require a centre of mass or centre of energy density?
In contrast, the FRW metric, based on the assumptions of a cosmological model being both homogeneous and isotropic, seems to reflect that only space expands as a function of time as defined by the scale factor a(t). As such, this leads to a geodesic nature of spacetime, which might be visualised in terms of 2 photons moving in parallel, 1 metre apart. After a period of time, the original separation must be subject to expansion and therefore our parallel photons follow a geodesic and not a classical straight line. As such, this seems to be the definition of spacetime curvature?
Again, while accepting that it might be convenient to fully embrace spacetime as a single entity, it is not clear to me that space and time do not remain different and distinct concepts?
4)
The Geometry of the Universe
Within cosmology, there is an additional definition of spatial curvature [k]. With reference to Friedmann’s equation, [k] can be defined as an energy density, which is inversely proportional to the square of the scale factor a(t), i.e. 1/a^2. However, based on this definition, the effects of spatial curvature will have been swamped by matter and radiation in the past and by dark energy in the future. Overall, the current model suggests that [k] reflects an essentially flat spatial geometry.
Therefore, while the balloon analogy might be a useful visualisation of an expanding universe, it is unclear to me how the geometry of the physical universe can be liken to the curved surface of the balloon?
Many of the posts seem to be quite adamant about the issue of the universe having no edge or centre. While taking no issue with this position within the context of the standard model, this does not automatically preclude other models leading to other conclusions. I am not forwarding the following model in opposition to the standard model, see link below, but some of the readers of this thread might be interested in some of the ideas expressed by people with some obvious academic background.
http://arxiv.org/abs/gr-qc/0602102
Would be interested in any clarifications or additional comments on any of the points raised. Thanks
) or flatlanders, note that they also permit the animals/flatlanders to move around, have a rather decent life (If you read 'Flatland' you know what I mean), i.e. there is dynamics. Therefore a flatland is not just a 2D space, it is 2+1 spacetime, i.e. 2 spatial dimension and 1 temporal dimension. A silly 4D creature would therefore live in a 4+1 spacetime, 5 dimensions if you will in that sense. It is quite standard for people who talk about higher dimensions in the pure mathematical sense not to mention the time dimension (since they weren't talking about GR).
