From: goldenfieldquaternions@gmail.com   
      
   On Sunday, January 20, 2019 at 1:20:31 AM UTC-6, Gary Harnagel wrote:   
   >> [[Mod. note -- Note that your observation of A "halting" as it   
   >> approaches the event horizon of a black hole is in some sense an   
   >> optical illusion.  An observer colocated with A itself does not   
   >> observe this.   
   >   
   > I'm wondering if this is relevant to the distant observer.  What does   
   > A see looking back at said distant observer?  Does A see the observer's   
   > time passing more quickly than his?   
   >   
   > Suppose A reverses direction just before he reaches the event horizon   
   > and meets up with the observer.  Won't A be younger and the observer   
   > be older?   
   >   
   > OTOH, if A continues on and reaches the event horizon, he will pass   
   > on through in no time at all, but won't an infinite amount of time   
   > have passed for the observer?   
   >   
   > Gary   
      
   If one is to think of computation according to halting one needs to   
   think according to nilpotent operators. For a group G with elements g   
   these act on vectors v so that gv = v'. These vectors can be states in a   
   Hilbert space or fermionic spinors. The group elements are generated by   
   algebraic operators A so that g = e^{iA}. Now if we have the nilpotent   
   situation where Av = 0 without A or v being zero then gv ≈ (1 + iA)v =   
   v.   
      
   A time ordered product of fields, often used in path integral, is a   
   sequence of operators similar to g and we may then have that g_1g_2g_3 …   
   g_n as a way that a system interacts. We might then have some condition   
   that at g_m for m < n the set of group operations all return the same   
   value, so the group has a nilpotent condition on its operators. This   
   would then bear some analogue to the idea of a halted computation.   
      
   The question of whether there are nonhalting conditions is then most   
   likely relevant to spacetime physics of quantum fields. If we have a black   
   hole of mass M it then has temperature T = 1/(8pi GM). Suppose this sits   
   in a spacetime with a background of the same temperature. We might be tempted   
   to say there is equilibrium, which is a sort of halted development. However,   
   goldenfieldquaternions@gmail.comit the black hole emits a photon by Hawking   
   radiation of mass-energy &m   
   (delta mass) so M --> M - &m it is evident its temperature increases.   
   Conversely if it absorbs a photon from the thermal background then  M -->   
   M + &m and its temperature decreases. This will then put the black hole   
   in a state where it is now more likely to quantum evaporate or to grow   
   unbounded by absorbing background photons.   
      
   This might then be a situation of nonhalting, and with gravitation or   
   quantum gravity the moduli space is nonHausdorff with orbits of gauge   
   equivalent potentials or moduli that are not bounded. We might then   
   consider quantum gravitation as an arena where the quantum computation   
   of its states are nonhalting, or might they be entirely computable.   
      
   LC   
      
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