This answer https://worldbuilding.stackexchange.com/a/8525/1991 claims that no particle can accelerate further after its de Broglie wavelength becomes Planck length.

Given that speed at this point is smaller than the speed of light, this means that the theoretical maximum of a particle's speed is below speed of light actually.

It this true? Does it mean that the particle will experience some additional force prohibiting its further acceleration besides what is predicted by Special Relativity?

  • $\begingroup$ The answer has since been removed by its owner. $\endgroup$ – HDE 226868 Jan 10 '15 at 19:20

The linked answer is wrong. The Planck length has no currently agreed physical significance - it is just a scale. Current theories beyond the Standard Model interpret it differently, for example, in loop quantum gravity it is indeed the shortest conceivable length, but in string theory it is just the scale at which the notion of particles emerges from strings of that length scale.

In the currently uneqivocally accepted theories of relativity and quantum field theory, there is no limit to how close a particle can come to the speed of light, and hence no limit to the kinetic energy it might hold.

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    $\begingroup$ I'd be curious to know how this is actually resolved in string theory though--is it in fact possible for a string to have a wavelength much shorter than the Planck length in some inertial frame? And if anyone knows, I'm also curious about how it would be resolved in continuous theories that (as I understand it) postulate the Planck length is frame-invariant along with the speed of light, like doubly special relativity and De Sitter invariant special relativity. $\endgroup$ – Hypnosifl Jan 10 '15 at 17:58
  • $\begingroup$ That answer has been edited since to respond to your criticism. Is it correct as of now? It currently claims the kinetic energy cap applies only to photons. $\endgroup$ – Anixx Jan 10 '15 at 18:14
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    $\begingroup$ @Anixx: It is still false because it relies on the idea that the Planck length is the shortest achievable wavelength, which is not established. It might become true if we find that one of the theories that treats the Planck length as such is the right theory to describe nature, but with our current knowledge, there is no upper limit to the energy of photons, either (except the practical limitation of how you would produce such a high-energy photon in the first place). $\endgroup$ – ACuriousMind Jan 10 '15 at 18:19
  • $\begingroup$ @Hypnosifl Does De Sitter invariant special relativity imply invariant Planck length? I think it only implies the invariance of the De Sitter radius, i.e. that of the cosmological constant essentially. $\endgroup$ – Dvij Mankad Jun 21 '17 at 9:28

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