Andromeda paradox

Sabine Hossenfelder has a nice Youtube video (see this) about Andromeda paradox (see this) introduced by Penrose. This paradox had escaped my attention.

Special relativity predicts that time= constant hyper-surfaces defining moments "Now" are different for observers in relative motion. It is of course far from clear whether moments "Now" correspond geometrically to this kind of hyper-surfaces. In special relativity one might argue that this is the case but in general relativity general coordinate invariance makes this kind of identification questionable since the Lorentz invariance of special relativity is only approximate.

If one assumes that the special relativistic notion is a good approximation, one ends up with the Andromeda paradox. Assume two observers at Earth moving towards and away from Andromeda. Their time= constant hypersurfaces are tilted with respect to each other. Suppose that Andromedans discuss sending a rocket to Earth. The first observer sees them still discussing whether to do this whereas the second observer sees that the rocket is already sent. This looks paradoxical.

What can one say about the Andromeda paradox in the TGD framework?

1. TGD can be seen as a hybrid of special and general relativities so that Poincare invariance becomes exact at the level of the 8-D embedding space H=M⁴× CP₂ but is lost at the level of space-time surfaces. Therefore the naive definition of simultaneity at the level of H could make sense.
2. In TGD, the standard quantum ontology in which the physical states correspond to 3-D hypersurfaces is replaced with zero energy ontology (ZEO) in which the quantum states are superpositions of Bohr orbit-like 4-surfaces as time evolutions of 3-surfaces. The basic classical object is Bohr orbit satisfying holography = holography principle rather than a 3-surface: this conforms nicely with general coordinate invariance (see this).
3. The "subjective now" in this framework is defined by the sensory input. As far as light signals are considered, it would correspond to a past-directed light-cone beginning from the position of the observer. The tips of these light-cones would be at slightly different positions for the two observers in the situation considered.
4. This argument relates to consciousness and volitional action since there is a subjective moment at which some-one sends the rocket. In TGD inspired theory of consciousness, one must distinguish between subjective and geometric time and this moment corresponds to a moment of subjective time as a quantum jump in which the superposition of space-time surfaces involving sender and environment, in particular rocket, is replaced with a new one. In zero energy ontology (ZEO) this moment could correspond to a pair of "big" state function reduction (BSFR) changing temporarily the arrow of geometric time in Andromeda.

   The two observers would receive signals from zero energy states before and after the pair of BSFRs that is from geometric time before after the decision was made and these signals would correspond to topological light rays starting from zero energy states before and after the BSFR pair. These superpositions of space-time surfaces can be approximated with a single "average" space-time surface. There would be no paradox in ZEO.

To sum up, in general relativity the paradox results from the assumption that space-time is a fixed arena of dynamics. In TGD, the description of the act of free will as a pair of BSFRs however forces us to give up this assumption. The act of free will replaces the zero energy state with a new one and the superposition of space-time surfaces changes.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.