From: intuitionist1@gmail.com   
      
   On Friday, November 2, 2018 at 1:21:57 AM UTC+3, Tom Roberts wrote:   
   > On 10/31/18 1:05 AM, Sabbir Rahman wrote:   
   > > In general people have to be more specific when they refer to "negative   
   > > mass". There are three mass types that enter into Newton's law of   
   > > gravitation for example - inertial, active and passive mass.   
   >   
   > Sure. But the context here is General Relativity, not Newton. In GR   
   > there is just a single "type" of mass: that which enters into the   
   > energy-momentum tensor in the field equation.   
      
   You must be reading this thread rather selectively then, as both have   
   definitely been discussed in previous posts.   
      
   > If one considers the motion of a "test particle" [#], then in the   
   > absence of any forces the particle follows a timelike geodesic path in   
   > the geometry determined by the (non-negligible) masses in the manifold.   
   > Note the mass of the test particle does not enter into its equation of   
   > motion (including its sign, if any).   
   >   
   > 	[#] An object whose size and mass are very much smaller   
   > 	than the scale of the geometry, so it can be neglected in   
   > 	determining the geometry.   
   >   
   > > [... 8 or 4 possibilities in Newtonian gravitation]   
   >   
   > But Newtonian gravitation is not very interesting, as it is solidly   
   > refuted. Nor is it relevant in this discussion in the context of GR.   
      
   Actually it is correct in the weak field limit. And actually, it is relevant   
   in the context of GR because, whereas it is merely _consistent_ for   
   particles of the four classes I have mentioned in Newtonian mechanics, I am   
   arguing that if the r<0 region of any of the Kerr solutions physically   
   exists, then class D particles _must_ exist (note that antiparticles are of   
   class D). Also if particles of class B (i.e. what are usually referred to   
   as 'negative mass' in the context of GR) exist, then particles of class C   
   must also exist.   
      
   > For a test particle and a mass, in GR there are only two cases: the mass   
   > is negative or the mass is positive. For these cases the structure of   
   > the geometry is known: for positive mass the geodesics converge on the   
   > mass, and for negative mass the geodesics diverge from the mass.   
   >   
   > 	Note that many authors consider at least one of the energy   
   > 	conditions to be part of GR, so the case of negative mass   
   > 	is excluded. Here, for the sake of discussion, I ignore the   
   > 	energy conditions.   
   >   
   > > If antimatter falls upwards [...]   
   >   
   > 	[I note that you switched from negative mass to antimatter   
   > 	 -- these are VERY different.]   
      
   Well, as I have explained, antiparticles are of class D, and they would   
   therefore fall upwards in the Earth's gravitational field.   
      
   > Attempting to argue about GR by analogy with NM is hopeless -- that boat   
   > has already sailed. For test particles the GR prediction is unambiguous:   
   > regardless of the test particle's mass (including sign, if any) it   
   > "falls downward" toward a positive mass and "falls upward" away from a   
   > negative mass.   
      
   Maybe you misread or misinterpreted what I wrote. I am not arguing about GR   
   by analogy with Newtonian mechanics. I discussed them separately and then   
   noted that all four classes of particle can appear in both (or rather in   
   the case of GR, in the bimetric extension of it, noting that the extension   
   is necessary if the r<0 region exists).   
      
   > While there is currently no experimental evidence of antimatter's   
   > behavior in gravity, the mass of every known antiparticle is   
   > unequivocally positive.   
      
   This is a rather strong statement. Please kindly a provide a reference to   
   the experiment that proves that this is the case.   
      
   > 	[There are theoretical arguments that imply that in   
   > 	 gravity antimatter must behave essentially the same   
   > 	 as matter. There are several efforts underway to   
   > 	 measure its behavior experimentally.]   
      
   Actually if you take a look at the literature, you will also find plenty of   
   theoretical arguments that imply that antimatter behaves the opposite to   
   matter.   
      
   > Note also that antimatter is described ONLY in quantum theories; no   
   > classical theory includes it. So it is stretching the boundaries to   
   > consider antimatter in GR.   
      
   This is not correct. I even referred to a paper by Vilatta in my earlier   
   post which explains why the r<0 region of the Kerr solutions can be   
   considered as the antimatter partner to the r>0 region.   
      
   > For two massive objects there are clearly four choices of their masses'   
   > signs in GR, but I don't know how the math works out for any case except   
   > "++", in which case they converge together. Given the absence of a   
   > general 2-body solution to the field equation, the other 3 cases require   
   > numerical calculations; I don't know how they work out [@]. I also don't   
   > consider them very relevant, as we have yet to observe anything with a   
   > negative mass, much less an object large enough to affect the geometry.   
      
   This is because we do not have instruments that are sensitive enough to   
   measure negative mass particles. The inability to measure negative mass does   
   _not_ imply that nothing with negative mass exists.   
      
   > 	[@] I also know enough about the subtleties of GR to not   
   > 	believe any claims without a calculation to back them up.   
   >   
   > > [... non-mathematical speculations about black holes]   
   >   
   > Your discussion here goes well beyond GR, seemingly into never-never   
   > land. To support it you need to formulate a complete theory, not just   
   > give idle speculations based on a fuzzy mish-mash of GR and a very   
   > different and refuted Newtonian theory. That's a challenge, as there is   
   > no expectation of ever being able to test it experimentally.   
   >   
   > Tom Roberts   
      
   Well, as I stated, if the r<0 region of any Kerr solution exists, then GR   
   has to be extended to the bimetric theory which has already been described   
   in some detail by Sabine Hossenfelder, and I provided you with a reference.   
      
   The argument for antigravitating particles I think is quite clear and   
   would also be of significant importance if true so it's not exactly 'idle   
   speculation'. Perhaps what you mean to say is that you do not _believe_   
   it to be the case because you do not believe that the r<0 region   
   physically exists. If you think that the argument itself is flawed, then   
   you should state where you think that the flaw is.   
      
   I would have thought that if the antihydrogen experiments that you yourself   
   referred to show that antihydrohen falls upwards in the Earth's   
   gravitational field then that would be pretty strong evidence of the   
   existence of antigravitating particles? Or do you mean that you have no   
   expectation of these experiments ever succeeding in making such   
   measurements?   
      
   [[Mod. note -- Those experiments have not (yet) succeeded in making   
   such measurements.  There's a nice overview of some of the theoretical   
   arguments (arging for antimatter falling "down" the same as matter) in   
     https://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter   
   -- jt]]   
      
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