Knowledge Limited: Deep Time, Deep Space

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis A4: The concept of probability is problematic in the context of existence of only one object.
It is useful to distinguish between the experimental sciences—physics, chemistry, microbiology for example—on the one hand, and the historical and geographical sciences—astronomy, geology, evolutionary theory for example, on the other.

In the experimental sciences, one is usually free to both observe and experiment.  For example, we can observe at what temperature water freezes with different concentrations of various salts such as sodium chloride.  But in the historical and geographical sciences, one can observe but we are seldom, if ever, able to experiment.  We can observe the properties of the Sun and other stars, but we cannot create a star nor modify its properties to see how that alters its development.  We must infer how individual stars or classes of stars change with time by observing many stars of different masses at various points along their continuum of existence.  And what of objects that are unique or that happened only once?  The evolution of life on Earth, the Grand Canyon, and the Universe itself?  The greatest challenge in the historical and geographical sciences besides not being able to run experiments is the enormous amount of time it takes for measurable changes to occur.  How can we humans—who seldom live more than a century—begin to comprehend changes that occur over a million, let alone a billion, years?

Thesis B1: Astronomical observations are confined to the past null cone, fading with distance.
Uncertainty grows with distance and time.  The vast scale of the universe implies we can effectively only view it from one spacetime event (“here and now”).

Cosmology is both a geographic and a historical science combined into one: we see distant sources at an earlier epoch, when their properties may have been different.  As we are looking back in the past, source evolution must be taken into account; their properties at the time they emitted the light may be quite different from their properties now.  We can only determine the distances of objects if we understand this evolution; but in practice it is one of the unknowns we have to try to determine.

Distant sources appear very small and very faint, both because of their physical distance, and because their light is highly redshifted (due to the expansion of the universe).  Simply detecting them, let alone determining their characteristics, becomes rapidly more difficult with distance.  Furthermore absorption by intervening matter can interfere with light from distant objects.  The further back we look, the worse these problems become; thus our reliable knowledge of the universe decreases rapidly with distance.

Another name for the “null cone” Ellis mentions above is light cone.  A light cone is a two-dimensional model of our three spatial dimensions, plus time.  We build up the cone using a series of circles along the time dimension.

First, let’s consider that you, the observer, as experimenter, produce an isotropic flash of light sometime this year at a particular location.  The flash of light will move outward in all directions at the speed of light.  The concentric circles below show the location of the wavefront from your flash in the year 2027, 2037, and 2047 when it is 10 light years, 20 light years, and 30 light years from Earth, respectively, and so on.  If we add a time axis that is perpendicular to the plane of our two-dimensional “Flatland” and points away from you, we see that we can build up a cone from the ever-expanding circular wavefront at every instant of time.  This is the future light cone.

Similarly, when you look out into the depths of space on a clear night you are also inexorably looking back in time.  Light from a star 10 light years away left on its journey to Earth in 2007.  If the star is 20 light years away, the light began its journey in 1997.  If 30 light years away, in 1987, and so on.  Again, if we add a time axis perpendicular to our two spatial dimensions, now pointing towards you (coming from the past), we see that we can build up a cone from the incoming wavefront’s location at each moment of time in the past.  This is the past light cone.

Now, if we put the past and future light cones together we get the full view of our location in spacetime, as shown below.  The two cones meet at the “here and now”.  Keep in mind that the diagram below is a two-dimensional representation of a 3D object (two spatial dimensions and one time dimension), but in reality, this should be a four-dimensional object (three spatial dimensions and one time dimension).

So, our view from the “here and now” is small and provincial.  Instead of obtaining a panoramic snapshot of our universe as it currently exists today, we are being served up old photos instead.  But quite useful, nonetheless.

Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.

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