Spectral gaps, additive energy, and a fractal uncertainty principle

Energy - Time Uncertainty Principle typeset

| This paper contains a simple but powerful statement and proof of the Energy-Time uncertainty principle.

Notes on fractal uncertainty principle version 0.5 (October 4, 2017)

"Weighing" a closed system and the time-energy uncertainty principle

A gedanken experiment is proposed for "weighing" the total mass of a closed system from within the system. We prove that for an internal observer the time tau, required to measure the total energy with accuracy DeltaE, is bounded according to tauDeltaE>Planck's over 2pi. This time-energy uncertainty principle for a closed system follows from the measurement backreaction on the system. We genera...

Covariant energy-momentum and an uncertainty principle for general relativity

We recognize the natural covariant extension for energy-momentum in general relativity: energy-momentum in spacetime as opposed to space. The key indicator is the Tolman energy integral for stationary systems. The demand that the general expression for arbitrary dynamic systems reduce to the Tolman integral in the case of stationary bounded distributions leads to the matter-localized Ricci inte...

A new uncertainty principle

By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or uncertainty principle) while the average distribution function over each predetermined finite velocity solid-angle element can be calculated.