Planck length - Greene versus classics

[nomadreid]

Planck length -- Greene versus classics

Brian Greene, in Chapter 10 of "The Elegant Universe", offers a sketch of string theory's version of why massive particles have a minimum size of the Planck length. I give my summary of the argument in the next paragraph, and the question in the following paragraph is based on this summary. If you are familiar with the argument, please correct my summary if it is faulty before answering the question.


(a) The massive particles are strings that are wound around small dimensions, and hence the minimum size of these particles is the minimum size of the dimension around which they wind.
(b) Probes (photons, etc.) have two modes: wound and unwound. They have two kinds of energy: vibrational and winding energies. The unwound ones have higher vibrational and lower winding energies; the wound ones have lower vibrational and higher winding energies. They come together in a particle as reciprocals of each other (when using natural units).
(c) The higher the vibrational energy, the smaller the distance which can be measured, by the Heisenberg Uncertainty Principle; however, below the Planck length, the coordinate systems for the laws of Physics are inverted, so that the Planck distance becomes a maximum, and the relations using these distances remain isomorphic to the relations using the distances above the Planck distance.
(d) In any case, when one gets down to the Planck distance, it requires less energy to use probes with higher winding energies, so these are the natural probes to use. However, the more energy one uses for these probes, the less precision for the distance is possible, so that the Planck length once again becomes a minimum.

Now, these are interesting arguments, but given the classic arguments for the shielding of anything of the Planck length-- summarized nicely for example by John Baez in http://math.ucr.edu/home/baez/lengths.html, that long before getting to that point one would be putting in enough energy to create new particles, losing the original target, or with even more energy one could create a black hole which, as a black hole, would shield all knowledge of the size of the original target, and then upon evaporation would also lose the original target -- isn't the argument (c) above irrelevant?

 

[LightHero]

No, the argument (c) is not irrelevant. While it is true that one could put enough energy into a particle to create a new particle or a black hole, this does not mean that the Planck length is not still a minimum size for the particle. In fact, the shielding of anything of the Planck length is exactly what is needed in order for the Planck length to be the minimum size for massive particles. The argument (c) is simply pointing out that at the Planck length, the Heisenberg uncertainty principle works in reverse: the higher the vibrational energy, the smaller the distance which can be measured. This means that even if one were to put enough energy into a particle to create a new one or a black hole, the distance which can be measured would still be limited by the Planck length. Thus, the Planck length remains the minimum size for massive particles.