Lorentz invariant mass and length scales

Understand

We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale.

• In other words, the frame independence of such scale is built-in within those transformations, and one does not need to invoke the principle of relativity for their invariance.
• This automatically ensures the frame-independence of the spectrum of geometrical operators in quantum gravity.
• Furthermore, we show that the above predicts a small but measurable difference between the inertial and gravitational mass of any object, regardless of its size or whether it is elementary or composite.