Heisenberg's Uncertainty Principle Revisited

P Marquardt, G. Galeczki

Espen Gaarder Haug

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. Our modified theory indicates that renormalization is no longer needed. Further, Bell's Inequality no longer holds, as the breakdown of Heisenberg's uncertainty principle at the Planck scale opens up the possibility for hidden variable theories. The theory also suggests that the superposition principle collapses at the Planck scale. Further, we show how this idea 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.

Arthur L. Loeb

Paul Peter Urone, Roger A. Hinrichs

Haixing Miao

We revisit the Heisenberg uncertainty principle for continuous quantum measurement with the detector describable by linear response. When the detector is at the quantum limit with minimum uncertainty, the fluctuation and response of a single-input single-output detector are shown to be related via two equalities. We illustrate the result by applying it to an optomechanical device--a typical continuous measurement setup.