In what sense speed of light could be changing in solar system?
There have been continual claims that the speed of light in solar system is decreasing. The latest paper about this is by Sanejouand and to my opinion must be taken seriously. The situation is summarized by an excerpt from the abstract of the article:
The empirical evidences in favor of the hypothesis that the speed of light decreases by a few centimeters per second each year are examined. Lunar laser ranging data are found to be consistent with this hypothesis, which also provides a straightforward explanation for the so-called Pioneer anomaly, that is, a time-dependent blue-shift observed when analyzing radio tracking data from distant spacecrafts, as well as an alternative explanation for both the apparent time-dilation of remote events and the apparent acceleration of the Universe.
Before one can speak about change of c seriously, one must specify precisely what the measurement of speed of light means. In GRT framework speed of light is by definition a constant in local Minkowski coordinates. It seems very difficult to make sense about varying speed of light since c is purely locally defined notion.
- In TGD framework space-time as abstract manifold is replaced by 4-D surface in H=M4×CP2 (forgetting complications due to the hierarchy of Planck constants). This brings in something new: the sub-manifold geometry allowing to look space-time surfaces "from outside", from H-perspective. The shape of the space-time surface appears as new degrees of freedom. This leads to the explanation of standard model symmetries, elementary particle quantum numbers and geometrization of classical fields, the dream of Einstein. Furthermore, CP2 length scale provides a universal unit of length and p-adic length scale hypothesis brings in an entire hierarchy of fixed meter sticks defined by p-adic length scales. The presence of imbedding space M4×CP2 brings in light-like geodesics of M4 for which c is maximal and by a suitable choice of units could be taken c=1.
- In TGD framework the operational definition for the speed of light at given space-time sheet is in terms of the time taken for light to propagate from point A to B along space-time sheet. In TGD framework this can occur via several routes because of many-sheeted structure and each sheet gives its own value for c. Even if space-time surface is only warped (no curvature) this time is longer than along light-like geodesic of M4(×CP2) and the speed of light measured in this manner is reduced from its maximal value. The light-like geodesics of M4 serve as universal comparison standards when one measures speed of light - something which GRT does not provide.
What TGD then predicts?
- TGD inspired cosmology predicts that c measured in this manner increases in cosmological scales, just the opposite for what Louise Riofrio claims. The reason is that strong gravitation makes space-surface strongly curved and it takes more time to travel from A to B during early cosmology. This means that TGD based explanation has different cosmological consequences as that of Riofrio. For instance, Hubble constant depends on the space-time sheet in TGD framework.
- The paradox however disappears since local systems like solar system do not normally participate in cosmic expansion as predicted by TGD. This is known also experimentally. In TGD Universe local systems could however participate cosmic expansion in average sense via phase transitions increasing Planck constant of the appropriate space-time sheet and thus increasing its size. The transition would occur in relatively short time scales: this provides new support for expanding Earth hypothesis needed to explain the fact that continents fit nicely together to form single super continent covering entire Earth if the radius of Earth is by a factor 1/2 smaller than its recent radius (see this).
- If one measures the speed of light in local system and uses its cosmic value taken constant by definition (fixing particular coordinate time) then one indeed finds that the speed of light is decreasing locally and the decrease should be expressible in terms of Hubble constant.
- TGD based explanation of Pioneer anomaly can be based on completely analogous reasoning.
For background see for instance the chapter TGD and Astrophysics of "p-Adic length Scale Hypothesis and Dark Matter Hierarchy".