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This Concept Map, created with IHMC CmapTools, has information related to: TGD and GRT.cmap, TGD AND GRT 3. Entropic gravity and TGD. Does temperature have spa- cetime correlate? a) Entropic gravity was a buzz world for few years ago. b) The basic objection is standard QM against it is that gravitational interaction of neutrons with Earth's gra- vitational field is describable by Schrödinger equation and this does not fit with thermo- dynamical description. c) In Zero Energy Ontology quantum theory can be seen as a square root of thermody- namics formally and this rai- ses the question whether or- dinary temperature could pa- rametrize wave functions ha- ving interpretation as square roots of thermal distributions in ZEO. The model for cell membrane gives support for this idea. If this were the case temperature would have by quantum classical correspon- dence direct space-time cor- relate. d) A less radical view is that temperature can be associa- ted with the effective space- time metric only., TGD AND GRT 2. Possible answers to the ques- tions a-c. a) The replacement of superpo- sition of fields with superposition of their effects means replacing superposition of fields with the set-theoretic union of space-ti- me surfaces. Particle experien- ces sum of the effects caused by the classical fields at the space-time sheets. b) This is true also for the clas- sical gravitational field defined by the deviation from flat Min- kowski metric instandard M^4 coordinates for the space-time sheets. One could define effect- ive metric as sum of M^4 metric and deviations. This effective metric would correspond to that of General Relativity. This resol- ves long standing issues relating to the interpretation of TGD. c) Einstein's equations could hold true for the effective metric. They are motivated by the underlying Poincare invariance which cannot be realized as global conservation laws for the effective metric. d) The breaking of Poincare in- variance could have interpreta- tion as effective breaking in zero energy ontology (ZEO), in which various conserved char- ges are length dependent and defined separately for each causal diamond (CD)., TGD AND GRT 2. Possible answers to the questions d-e. a) EP at classical level would hold true if Einstein's equations hold true for the effect- ive metric. b) The value of gravitational constant is in principle a prediction of theory containing only CP_2 radius as fundamental scale and Kähler coupling strength as only coupling constant analogous to critical temperature. c) In GRT inspired quantum theory of gravi- tation Planck length scale given by L_P=sqrt(hbar_eff×G) is the fundamental length scale. In TGD CP_2 size R defines it and it is independent of h_eff. The predicti- on for gravitational constant is as the TGD counterpart of L_P: L_P^2= R^2/n, n di- mensionless constant. The prediction for G would be G= R^2/n×hbar_eff. d) This could have important implications if the hierarchy of Planck constants is reali- zed. In particular, Planck mass becomes M_P= hbar_eff/sqrt(n)R rather than sqrt(hbar_eff/G). For instance, if blackhole entropy is given by S ∝ GM^2/h_eff would, S would scale as R^2M^2/h_eff^2 and ap- proach zero for large values of h_eff. If formula h_eff=h_gr= GM^2/v_0, v_0 of order rotation velocity of blackhole holds true, one has S=v_0/cə would true: black- hole would be purely quantal object. h_gr=h_eff is supported by the anomalo- usly high value of gravimagnetic moment of rotating super-conductor, TGD AND GRT 1. Questions: a) Is it really possible to obtain a realistic theory of gravitation if general space-time metric is replaced with induced metric depend- ing on 8 imbedding space coordinates (ac- tually only 4 by general coordinate invariance. b) What happens to Einstein equations? c) What about breaking of Poincare invariance. which seems to be real in cosmological scales? Can TGD cope with it? d) What about Equiva- lence Principle (EP)? e) Can one predict the value of gravitational constant? f) Does one obtain TGD counterpart of blackho- le?, TGD AND GRT 2. Blackholes and TGD. a) Blackhole metric as such is quite possible as effecti- ve metric of M^4. It is how- ever imbeddable in M^4× CP_2 partially. b) The direct imbedding of blackhole metric fails at some radius which can be smaller than Schwarschild radius. This is due to the compactness of CP_2. A general result is that the embedding carriers non- vanishing gauge charge - say em charge. This need not (but could!) have phy- sical significance if the met- ric of GRT corresponds to the effective metric obtain- ed by the proposed recipe. c) TGD forces to challenge the standard view about black holes. For instance, could it be that blackhole interior corresponds to Euc- lidian space time region? Could holography hold true in the sense that blackhole horizon would be replaced with a partonic 2-surface with astrophysical size and having light-like orbit as also black-hole horizon has. If the radial compo- nent of metric is required to be finite one indeed ob- tains metric with vanishing determinant at horizon.
