Invariance under Scale Transformations

Gerard't Hooft的一片论文《Quantum Gravity without Space-time Singularities or Horizons》给出：

Turning this observation around, one might assume that, whatever the equations are, they define information to flow around. The density of this information flow may well define the Planck length locally, and with that all scales in Nature. Obviously, this leaves us with the problem of defining what exactly information is, and how it links with the equations of motion. The notion of information might not be observer-independent, as the scale factor ω isn’t.