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Moby-Dick (Mar 08 2026 at 14:26):I recently watched the video Negative Mass. I remember learning in secondary school that mass is a proxy for the amount of matter. Following this approach, let's suppose that matter is modeled as a CW-complex. Let's define mass as its Euler characteristic. Notice that if all cells have an even dimension, it is obvious that the mass will be non-negative. However, the presence of odd-dimensional cells can produce entities with negative mass. Why would matter be modeled in that way? I don't know, but I suspect this might be justified within a model involving quantum entanglement. I am not a physicist, and this is just speculation. Perhaps other people would like to share other proposals on how a negative mass can arise.
John Baez (Mar 08 2026 at 20:46):The main point of my video was to explain that in modern physics "mass" is not really a thing, only "mass squared" (which deserves some new name of its own), so negative mass is not something that arises physically. There are some equations where mass shows up in the fundamental laws of physics, like the Dirac equation for spin-1/2 particles. However, these equations have a symmetry that says only mass squared is experimentally accessible.
Moby-Dick (Mar 08 2026 at 21:05):In statistical terms, we would say that only mass squared is identifiable, not mass itself.
Moby-Dick (Mar 08 2026 at 21:28):These researchers produced a negative mass as an emergent property.
M.A. Khamehchi, Khalid Hossain, M.E. Mossman, Yongping Zhang, Thomas Busch, Michael McNeil Forbes, and Peter Engels, "Negative mass hydrodynamics in a spin-orbit--coupled Bose-Einstein condensate", Phys. Rev. Lett. 118(15), 155301 (2017). (Preprint: arXiv:1612.04055.)
John Baez (Mar 08 2026 at 21:43):Yes, in non-fundamental physics there are situations where "negative mass" is a useful abstraction. One of the most commonly seen is a helium balloon: it acts roughly like it has negative gravitational mass but positive inertial mass, so it falls up. (If both types of mass were negative it would fall down, as explained in the video.)
But in the fundamental description of a helium balloon, we don't need to invoke negative mass.