Is cosmic expansion a mere coordinate effect?
There is a very interesting article about cosmic expansion or rather a claim about the absence of cosmic expansion.
The argument based on the experimental findings of a team of astrophysicists led by Eric Lerner goes as follows. In non-expanding cosmology and also in the space around us (Earth, Solar system, Milky Way), as similar objects go further away, they look fainter and smaller. Their surface brightness remains constant. In Big Bang theory objects actually should appear fainter but bigger. Therefore the surface brightness- total luminosity per area - should decrease with distance. Besides this cosmic redshift would be dimming the light.
Therefore in expanding Universe the most distant galaxies should have hundreds of times dimmer surface brightness since the surface are is larger and total intensity of light emitted more or less the same. Unless of course, the total luminosity increases to compensate this: this would be of course total adhoc connection between dynamics of stars and cosmic expansion rate.
This is not what observations tell. Therefore one could conclude that Universe does not expand and Big Bang theory is wrong.
The conclusion is of course wrong. Big Bang theory certainly explains a log of things. I try to summarize what goes wrong.
- It is essential to make clear what time coordinate one is using. When analyzing motions in Solar System and Milky Way, one uses flat Minkowski coordinates of Special Relativity. In this framework one observes no expansion.
- In cosmology one uses Robertson-Walker coordinates (a,r, θ,φ). a and r a the relevant ones. In TGD inspired cosmology R-W coordinates relate to the spherical variant (t,rM,θ,φ) of Minkowski coordinates by formulas
a2= t2-rM2, rM= a×r.
The line element of metric is
ds2= gaada2 -a2[dr2/(1+r2)+r2dΩ2]
and at the limit of empty cosmology one has gaa=1.
In these coordinates the light-cone of empty Minkowski space looks like expanding albeit empty cosmology! a is just the light-cone proper time. The reason is that cosmic time coordinate labels the a=constant hyperboloids (hyperbolic spaces) rather than M4 time=constant snapshots. This totally trivial observation is extremely important concerning the interpretation of cosmic expansion. Often however trivial observations are the most difficult ones to make.
- In Zero Energy Ontology (ZEO) - something very specific to TGD - the use of these coordinates is natural since zero energy states are pairs of positive and negative energy states localized about boundaries of causal diamonds (CD), which are intersections of future and past directed light-cones having pieces of light-cone boundary as their boundaries. The geometry of CD suggests strongly the use of R-W coordinates associated with either boundary of CD. The question "Which boundary?" would lead to digression to TGD inspired theory of consciousness. I have talked about this in earlier postings.
- Thus the correct conclusion is that local objects such as stars and galaxies and even large objects do not participate in the expansion when one looks the situation in local Minkowski coordinates - which by the way are uniquely defined in TGD framework since space-time sheets are surfaces in M4×CP2. In General Relavity the identification of the local Minkowski coordinates could be highly non-trivial challenge.
In TGD framework local systems correspond to their own space-time sheets and Minkowski coordinates are natural for the description of the local physic since space-time sheet is by definition a space-time region allowing a representation as a graph of a map from M4 to CP2. The effects caused by the CD inside which the space-time surfaces in question belong to the local physics are negligible. Cosmic expansion is therefore not a mere coordinate effect but directly reflects the underlying ZEO.
- In General Relativity one cannot assume imbeddability of the generic solution of Einstein's equations to M4 × CP2 and this argument does not work. The absence of local expansion have been known for a long time and Swiss Cheese cosmology has been proposed as a solution. Non-expanding local objects of constant size would be the holes of Swiss Cheese and the cheese around them would expand. The holes of cheese would correspond to space-time sheets in TGD framework. All space-time sheets can be in principle non-expanding and they have suffered topological condensation to large space-time sheets.
- Einstein-Yang-Mills space-time is obtained from the many-sheeted space-time of TGD by lumping together the sheets and describing it as a region of Minkowski space endowed with an effective metric which is sum of flat Minkowski metric and deviations of the metrics of sheets from Minkowski metric. Same procedure is applied to gauge potentials.
- The motivation is that test particle topologically condenses at all space-time sheets present in given region of M4 and and the effects of the classical fields at these sheets superpose. Thus superposition of fields is replaced with superposition of their effects and linear superposition with set theoretic union of space-time sheets. TGD inspired cosmology assumes that the effective metric obtained in this manner allows imbedding as vacuum extremal of Kähler action. The justification of this assumption is that it solves several key problems of
GRT based cosmology.
- The number of field patterns in TGD Universe is extremely small - given by preferred extremals - and the relationship of TGD to GRT and YM theories is like that of atomic physics to condensed matter physics. In the transition to GRT-Yang-Mills picture one gets rid of enormous topological complexity but the extreme simplicity at the level of fields is lost. Only four CP2 coordinates appear in the role of fields in TGD framework and at GRT Yang-Mills limit they are replaced with a large number of classical fields.