Could There Be Distances Beyond Planck Length in Discrete Space?

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The discussion explores the concept of discrete space at the Planck length and questions whether other distances, such as those near proton width, have been considered. It highlights that in discrete space-time, energy and momentum conservation occurs modulo the inverse lattice spacing. The conversation references Leonard Susskind's notion of a "desert" in energy scales from TeV to 10^19 GeV, suggesting a gap in current theories. Participants are curious if alternative lengths beyond the Planck scale have been proposed or studied. The inquiry emphasizes the need for further exploration of potential distances in the context of discrete space-time theories.
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Discrete space has been proposed at Planck length. But has any other distance been proposed(studied), like near proton width.
 
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Discrete space time means that energy and momentum are only conserved modulo the inverse lattice spacing.
 
Count Iblis said:
Discrete space time means that energy and momentum are only conserved modulo the inverse lattice spacing.

Yes, but my question was about if anybody tried or thought that the Planck length might not be the only length possible. Since, as Susskind puts it the desert from TeV to 10^19 GeV. Of course, I know the rarional for Planck length case.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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