From McTaggert to AdS5 geometry The purpose of this note is to show how an 'AB-series' interpretation of time, given in a companion paper, leads, surprisingly, directly to the physicists' important AdS5 geometry. This is not a theory of 2 time dimensions. Rather, it is a theory of 1 time dimension that has both A-series and B-series characteristics. To summarize the result, a spacetime in terms of 1. the earlier-to-later aspect of time, and 2. the related future-present-past aspect of time, and 3. 3-d space, automatically gives us AdS5. I must assume the reader is already familiar with the theory of time proposed in the companion paper Merriam (2019). In 1+1 spacetime, in terms of t and x, in one convention, we have the invariance of (1) 2 2 2 2c t xt = - + under Lorentz transformations. The Minkowski 1+3 invariant is in terms of (t, x^3), such that, in the same convention, t → ict, for the imaginary unit i and the speed of light c. We want a generalization to a new invariant τ' in terms of the A-series and the B-series and x3, (gsystem, t, x^3) and the transformations that leave it invariant. That's because 1 dimension of time has 2 related parameters, in this theory, 1 for the A-series and 1 for the B-series. But it's not immediately obvious in what way(s) such a generalization is possible, because probability gets involved. Nevertheless we can try. (And this, also, has to do with whether the future is branching.) In what might be called 1+1+1 spacetime, in terms of g, t, and x, it would be nice if there were some kind of invariant (2) 22 2 2 2 2 2 1' c k g c t xt = - + for some complex number c1, and some new constant k in units of meters per e. This is a new constant, a 'conversion factor' in meters/e, in analogy to the speed of light, which is a constant or 'conversion factor', c, in meters/sec. (Yes they can each be rescaled such that, in their respective units, k = 1, and c = 1, but that's discussed in the companion paper and is not important right now.) k is the rate the position changes as it becomes from Alice's future into her present and then into her past. c is the rate the position changes when going from earlier to later times. These are, in this theory, not the same thing. Consider (3) 3 22 2 2 2 2 2 1 1 ' i d c k dg c dt dxt = = - +å (Wu, 2016) The minus sign between t and g, it was argued in the companion paper, comes from their opposite orientation: earlier-to-later times go into the future while future-present-past times come out of the future. Obviously other ideas are possible, but the simplest thing to try is therefore (4) g → -ikg. In which case (5) 3 2 2 2 2 2 2 1 ' i d k dg c dt dxt = = - - +å (Another thing to try is g → -ih'g for the imaginary unit i and some constant h' based on Plank's constant h, but the dimensions might be off.) I don't have a degree in physics. But, if I am not mistaken, (5) is the AdS5 invariant. Let's be clear on the interpretation of (3). It does not have 2 dimensions of time. It is a proposal for an invariant on a different kind of 'spacetime'. It has 3 dimensions of space, and it has one dimension of time, but that dimension has related A-series and B-series characteristics. This might be called AB-spacetime. The Aseries characteristics are, of course, 'ontologically private', as defined in the companion paper. Thus, (3) is an invariant on Alice's 'private' AB-spacetime. To summarize again, a spacetime in terms of (1) the earlier-to-later aspect of time, and (2) the related future-present-past aspect of time, and (3) 3-d space, automatically gives us AdS5. References Merriam, Paul (2019), A theory of time: bringing McTaggart into physics, https://philpapers.org/rec/MERATO-4 Wu, Yuxiao, (2016), p. 1, A Very Introductory AdS/CFT, http://theory.uchicago.edu/~ejm/course/JournalClub/Basic_AdS-CFT_JournalClub.pdf