Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Revisiting the Derivation of Heisenberg's Uncertainty Principle: The Collapse of Uncertainty at the Planck Scale

Version 1 : Received: 17 May 2018 / Approved: 18 May 2018 / Online: 18 May 2018 (08:01:26 CEST)
Version 2 : Received: 5 September 2018 / Approved: 5 September 2018 / Online: 5 September 2018 (09:34:51 CEST)

How to cite: Haug, E. Revisiting the Derivation of Heisenberg's Uncertainty Principle: The Collapse of Uncertainty at the Planck Scale. Preprints 2018, 2018050258 (doi: 10.20944/preprints201805.0258.v2). Haug, E. Revisiting the Derivation of Heisenberg's Uncertainty Principle: The Collapse of Uncertainty at the Planck Scale. Preprints 2018, 2018050258 (doi: 10.20944/preprints201805.0258.v2).

## Abstract

In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton `clock' frequency in elementary particles.

## Keywords

Heisenberg's uncertainty principle; certainty; wave function; Planck scale; Planck mass; Planck particle; Bell's Inequality; superposition; entropy; Compton clock

## Subject

PHYSICAL SCIENCES, General & Theoretical Physics

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