From: carlip@physics.ucdavis.edu   
      
   On 5/5/18 8:50 AM, SEKI wrote:   
   > On Friday, May 4, 2018 at 4:59:21 PM UTC+9, Steven Carlip wrote:   
   >> On 5/1/18 1:41 PM, SEKI wrote:   
      
   [...]   
   >> First of all, what you've described is not the actual derivation   
   >> of Hawking radiation, but rather a hand-waving after-the-fact   
   >> description of the mathematics.  If you were right, it wouldn't   
   >> mean Hawking radiation was unrealistic, it would just mean that   
   >> the description isn't a very good one.  You really can't dodge   
   >> the math; reading pop sci descriptions can sometimes lead to   
   >> good questions, but it won't give you answers.   
      
   > I am sorry, I am neither a professional physicist nor young to   
   > become one. I merely would like to carry out a thought experiment.   
      
   >> But your argument is wrong, too.  According to the equivalence   
   >> principle, the trajectory of an object in a gravitational field   
   >> is independent of its mass.  In a vacuum, a hammer falls with the   
   >> same acceleration as a feather; a negative mass hammer would do   
   >> the same.  It's simply not true that a negative mass particle   
   >> would be repelled by a black hole, in either general relativity   
   >> or Newtonian gravity.   
      
   > I am not sure this argument is right or not.   
      
   What would it take to make you "sure"?   
      
   >> It *is* true that a particle, of positive or negative mass, would   
   >> be repelled by a negative mass black hole.   
      
   > Isn't this inconsistent with what you wrote above?   
      
   No.  A positive mass attracts everything (including both positive   
   and negative mass objects); a negative mass repels everything.   
      
   > Anyway, I acknowledge that mathematical models of modern physics   
   > is based on Einstein's equation as far as gravitation is concerned.   
   > As I wrote previously, Einstein's gravitational equation is   
   > presented in terms of linear expression of energy-momentum tensor.   
   > So, negative energy is considered to curve the space-time in the   
   > opposite direction to positive one. And, I suppose that particles   
   > with negative energy, if actually present, are to be repelled by   
   > the black hole.   
      
   Spacetime is four dimensional, and its curvature can't really be   
   described in terms of a "direction."  You guess is roughly right,   
   though -- a positive mass source produces an attractive gravitational   
   field, and a negative mass source produces a repulsive gravitational   
   field (up to some subtleties about what counts in "mass").   
      
   The point, though, is that an attractive gravitational field attracts   
   *everything*, and a repulsive gravitational field repels *everything*.   
   In Hawking radiation, in particular, the black hole mass is positive,   
   and it's simply not true that it repels negative energy particles.   
      
   > If you give me a proof that my supposition is wrong, my question   
   > is to be resolved and it is really appreciated.   
      
   Again, what kind of "proof" do you want?   
      
   -- You could take the word of people who actually know general   
   relativity.  (I've been teaching GR for more than 25 years, have   
   a textbook coming out soon, and have more than 100 published   
   papers, including a recent review paper on Hawking radiation,   
   https://arxiv.org/abs/1410.1486, with more than 50 citations in   
   Google Scholar.)   
   -- You could learn enough GR to see for yourself.   
   -- You could... well, I don't know.  What else would be a "proof"   
   you'd accept?   
      
   Steve Carlip   
      
   --- SoupGate-Win32 v1.05   
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