Planck acceleration

The Planck acceleration is the acceleration of an object which accelerates from zero to the speed of light during one Planck time. It is a derived unit in the Planck system of natural units.

Formula and value

The formula for the Planck acceleration, from which its value is calculated, is:





where aP is the Planck acceleration, c is the speed of light, tP is the Planck time[1] and g is the standard acceleration of gravity.[2]

Meaning

The Planck acceleration is the highest acceleration conceivable in the Universe, as the speed of light is the highest possible speed and the Planck time is the shortest possible duration of any meaningful physical process. This limitation does assume that relativity has natural units.[3]

However, it is not clear whether any object in the Universe actually reaches or can reach the Planck acceleration. Photons emanating from their subluminal source (for example, a particle-antiparticle collision) experience zero acceleration, as they always travel at the speed of light. One event where the Planck acceleration was possibly reached was the Big Bang, in regard to the acceleration of the expanding Universe during the Planck epoch. Also, within a black hole, such acceleration might be possible, but that is certainly unknown.

If the mass of the body is given, then a second limit, Caianiello's maximal acceleration, also applies:[4]

See also

References

  1. ↑ "CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2016-07-24.
  2. ↑ "CODATA Value: standard acceleration of gravity". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2016-07-28.
  3. ↑ "Why is there no limit on maximum acceleration similar to one on maximum velocity (i.e. speed of light)? - Quora".
  4. ↑ Papini, Giorgio (2006). "Caianiello's Maximal Acceleration. Recent Developments". Imagination and Rigor. p. 119. arXiv:quant-ph/0407115Freely accessible. doi:10.1007/88-470-0472-1_10. ISBN 88-470-0320-2.
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