From: intuitionist1@gmail.com   
      
   On Friday, August 17, 2018 at 10:07:39 AM UTC+3, Phillip Helbig (undress to   
   reply) wrote:   
   > In article <2c0366cf-d2b2-4d5e-ad1b-47cd027030e5@googlegroups.com>,   
   >  writes:   
   >   
   > > > If you had two negative masses they would attract. Because with the   
   > > > negative mass acceleration is towards a positive mass this experiment   
   > > > may not be able to determine if antimatter is really negative mass.   
   >   
   > If I recall correctly, not long ago Steve Carlip pointed out here that   
   > positive mass attracts everything, including negative mass, and negative   
   > mass repels everything.   
      
   I am a little bit late to join this thread (sorry), but I wanted to make a   
   few important points.   
      
   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. If the signs of   
   these three masses are I, A and P respectively, then the particle type can   
   be specified by (I,A,P) - so there are 8 types, (+++), (++-), (+-+), (+--),   
   (-++), (-+-), (--+) and (---). Obviously (+++) corresponds to ordinary   
   matter and the remaining 7 have at least one kind of negative mass, so you   
   need to be specific which type you mean. If you mean by negative mass type   
   (---), which is the one allowed by the WEP, then this will indeed fall   
   `downwards'. This type is also repels itself.   
      
   Newton's law depends only on the product IP, so there are actually only 4   
   types of particle in terms of mutual interactions. Let's call them class A,   
   B, C and D:   
      
   Class A: (+++) and (-+-) act like normal matter   
   Class B: (---) and (+-+) act like the negative mass of GR and falls   
   downwards and is mutually repulsive   
   Class C: (++-) and (-+-) falls upwards and is mutually repulsive   
   Class D: (+-+) and (--+) falls upwards and is mutually attractive   
      
   If antimatter falls upwards, it is of class C or D. If it is of class C,   
   then the Earth will be attracted; if it is of class D, the Earth will be   
   repelled. Obviously you will not be able to tell between the two   
   possibilities.   
      
   Now, Lawrence in his response to ben... is clearly assuming that the   
   negative mass particle is of class B. Note that if it were of class C, both   
   particles would still accelerate away together off to infinity but in the   
   opposite direction. But then he goes on to say that two negative masses   
   would attract. This is _incorrect_ as for both class B and class C, the   
   particles are mutually repulsive. Only class D particles are mutually   
   attractive, but class A and class D particles repel each other and they do   
   not accelerate in the same direction.   
      
   The AEGIS experiment will be able to distinguish between class B (antimatter   
   falls downwards) or class C or D (falls upwards). It will not be able to   
   distinguish between class C or class D if antimatter falls upwards.   
      
   Now Philip reminds us of Steve Carlip's statement that positive mass   
   attracts everything and negative mass repels everything. Of course Steve is   
   referring to the particles of class A and B, which satisfy the WEP and are   
   allowed by GR.   
      
   HOWEVER, I think that the belief that only particles of class A and B are   
   allowed by GR is _INCORRECT_.   
      
   The reason I say this is because if we consider the r<0 side of the Kerr   
   solution, which is the CPT dual of the r>0 side (see e.g. "The matter-   
   antimatter interpretation of Kerr spacetime" by Villata), in this region   
   mass changes sign and particles turn into their antiparticles, i.e. from the   
   perspective of observers in the region r>0, class A and class B particles   
   turn into their antiparticles, i.e. of class D and class C respectively, and   
   also appear to be falling towards the disc at r=0. Obviously the particles   
   which pass into r<0 are totally oblivious to this change, and still think   
   that they are normal particles. Now, this means first of all that antimatter   
   is _not_ of class B, but of class D, so antiparticles fall _upwards_ in the   
   Earth's gravitational field.   
      
   Also, it means that WEP does not hold in r<0 as I and P have opposite sign   
   there. However, all is not lost, because the WEP only actually requires that   
   the _ratio_ of I and P need to be the same for all particles, I=-P is okay   
   in r<0 as long as it is true for all particles there, which it is.   
      
   Thus although the particles in r>0 and r<0 have different ratios of I to P,   
   the WEP still holds _locally_ independently on each sheet. As long as a   
   class A or B particle does not somehow enter the region r<0, everything   
   should still be fine.   
      
   HOWEVER, things are _not_ necessarily fine. Suppose that there are more than   
   one Kerr black hole (or fast Kerr solution), and suppose that the discs   
   bounded by the ring singularity connect just two spacetime sheets, rather   
   than a new universe popping up every time a ring singularity is formed   
   (which IMO seems rather implausible). The former double-sheeted spacetime   
   is, in fact, the scenario envisaged by Einstein and Rosen in their 1935   
   paper "The particle problem in the general theory of relativity" for the   
   multiparticle case (and IMO is mor plausible).   
      
   Well, in this case, depending on which sheet you are sitting on at the time,   
   it appears that the Kerr black hole/fast Kerr solution is formed either by   
   collapse of particles of class A and B (r>0 sheet) or of particles D and C   
   (r<0 sheet). This means that _both_ sheets must have pre-existed the   
   formation of the first Kerr black hole/fast Kerr solution.   
      
   Now, the sheets themselves are both just ordinary spacetime sheets, so if   
   only ordinary particles of class A and B are present on one sheet initially,   
   then they can be present on the other as well. So, this is where the problem   
   appears - once the first Kerr black hole/fast Kerr solution forms, the   
   floodgates open and class A and B particles start crossing the r=0 disc into   
   the other sheet, and class C and D particles suddenly become present on both   
   sheets. Moreover, applying the same argument as above, they must have pre-   
   existed the formation of the ring singularity/wormhole, and thus initially   
   there must have been particles of all four classes, A, B, C and D present on   
   both sheets.   
      
   But this _does_ violate the WEP. However, it must also be the case if we do   
   not want to throw away the r<0 region, and have only a single spacetime   
   sheet, which is unjustified. Therefore, the WEP does not hold, and we must   
   have two metrics present - one for particles of class A and B, and one for   
   particles of class C and D. But this bimetric theory is precisely the one   
   proposed by Sabine Hossenfelder in "Bimetric theory with exchange symmetry".   
      
   Thus, I claim, for consistency and completeness, general relativity must be   
   extended to a bimetric theory on a double-sheeted spacetime in which all   
   four particle classes, A, B, C and D, can be  (and indeed are) present.   
      
   [[Mod. note -- Two points:   
      
   [continued in next message]   
      
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