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Pretty straightforward question. Does there exist a theoretical upper bound for the acceleration of a point mass? If not, what is the greatest acceleration of a point mass ever recorded, or that will be reached by new technology in the next few years?

Federico
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    Does an electron qualify as a point mass? – David White Oct 10 '23 at 16:18
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    It probably will be Planck acceleration, i.e. light speed achieved per Planck time (ignoring relativistic effects of course), it's about $10^{51}~m/s^{2}$. – Agnius Vasiliauskas Oct 10 '23 at 16:27
  • @DavidWhite It does! – Federico Oct 10 '23 at 16:51
  • @DavidWhite neutrinos are better. – JEB Oct 10 '23 at 18:13
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    @AgniusVasiliauskas Why can't you achieve c in less time? Planck units are not the "smallest possible units". It's not true that the Planck length represents the shortest length possible or that the Planck time is the shortest duration possible. The Planck mass is big enough to contain trillions upon trillions of hydrogen atoms. – Nuclear Hoagie Oct 10 '23 at 19:59
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    I think some but not all of the Planck units are, not the smallest possible units, but the smallest measurable units. Like somehow a photon small enough to give resolution smaller than the Planck length would instantly become a black hole or something. I don't know though, this is pure speculation. – CPlus Oct 10 '23 at 21:00
  • Possible duplicates: https://physics.stackexchange.com/q/3334/2451 and links therein. – Qmechanic Oct 11 '23 at 00:48
  • Also see https://physics.stackexchange.com/a/185943/123208 "the Planck length is more numerology than physics at this point" – PM 2Ring Oct 11 '23 at 01:13
  • @NuclearHoagie You interpret Planck mass wrongly. It's the greatest mass for a charged particle which it can have before collapsing into black hole. Similarly, exceeding my given acceleration limit means that ordinary matter composed from hadrons will not stand-up such pressure and will convert into quark plasma. In other words,- Plank units indicates that at such high energy conditions matter state changes and for describing that we need new type of Physics, which we doesn't have yet (no accepted quantum gravity theory). – Agnius Vasiliauskas Oct 11 '23 at 10:02
  • @AgniusVasiliauskas Why can't you accelerate a particle smaller than a Planck mass faster than the Planck acceleration? The argument seems to be that accelerating a Planck mass to $c$ in less than the Planck time requires too much force, but accelerating something smaller than the Planck mass doesn't require that much force. It's not clear to me how we can find an upper limit of acceleration without having a lower limit of mass - for a fixed force applied to a particle, we need simply halve the particle's mass to double its acceleration. – Nuclear Hoagie Oct 11 '23 at 13:03
  • @NuclearHoagie Seems you haven't checked given links in comments. Mass is not everything. Due to extensive Unruh radiation, extreme temperature of body will be reached, about $10^{31}~K$, approximately Hagedorn temperature. Upon this point of evaporation, there's no solid body left which could "double the acceleration". Clear ? – Agnius Vasiliauskas Oct 11 '23 at 14:42
  • Btw, due to Hawking/Unruh radiation smaller mass will probably mean that body, upon transforming into black hole at such accelerations, will evaporate faster, because evaporation time is proportional to black hole mass. And for micro-back holes this will really be an instant event. – Agnius Vasiliauskas Oct 11 '23 at 14:58

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