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A Suggested Boundary for Heisenberg's Uncertainty Principle

Espen Gaarder Haug

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

In this paper we are combining Heisenberg's uncertainty principle with Haug's suggested maximum velocity for anything with rest-mass. This leads to a suggested exact boundary condition on Heisenberg's uncertainty principle. The uncertainty in position at the potential maximum momentum for subatomic particles as derived from the maximum velocity is half of the Planck length.

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In this paper we are combining Heisenberg's uncertainty principle with Haug's suggested maximum velocity for anything with rest-mass. This leads to a suggested exact boundary condition on Heisenberg's uncertainty principle. The uncertainty in position at the potential maximum momentum for subatomic particles as derived from the maximum velocity is half of the Planck length.
Background: There has been altercation for and against Heisenberg uncertainty principles, whose earlier mathematical form has assumed other forms. This is despite the fact that the original form ought to be for the hydrogen atom only. Methods: the method is purely theoretical and computational, involving the use of spectroscopic data in the literature. Aim and objectives: The aim of the research was to show that half of reduced Planck’s constant (ℏ/2) cannot be restricted to a lower limit to the product of the uncertainty in the momentum and the uncertainty in the position. The objectives were: 1) to undertake the derivation of an equation unifying the Heisenberg uncertainty principle and atomic principles; and 2) to give evidence that half of the reduced Planck’s constant (ℏ/2) is strictly for hydrogen. Results and discussion: With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position and momentum increases with decreasing radii. Conclusion: The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen only. The possibility of linking the product of uncertainties in position and momentum to Pa may be reserved for a future study.
We propose that Heisenberg's uncertainty principle is a consequence of gravity. While quantum mechanics and gravity are widely considered incompatible, we show that Heisenberg's uncertainty principle, which is a central tenet in quantum mechanics, in fact, arises from non-diminishing finite gravity between a particle and another identical particle. We observe that it is impossible to know the position or momentum of the particle with unlimited precision, unless the gravity is infinite or zero, respectively, between the particles. We derive upper and lower bounds on the uncertainties in position and momentum of the particle, based on the uncertainty principle emerging from gravity. Accordingly, the quantum-classical boundary is identified, beyond which gravity behaves classically.
A prevailing formulation of the Heisenberg uncertainty principle is re-examined that measuring position with noise epsilon\\epsilonepsilon brings the momentum disturbance no less than hbar/2epsilon\\hbar/2\\epsilonhbar/2epsilon. With rigorous formulations of noise and disturbance, a model of a measuring interaction demonstrates that this formulation of the Heisenberg uncertainty principle is by no means universally valid. An experimental realization of the model is also suggested.
In this paper we show that Heisenberg’s uncertainty principle, combined with key principles from Max Planck and Einstein, indicates that uncertainty collapses at the Planck scale. In essence we suggest that the uncertainty principle becomes the certainty principle at the Planck scale. This can be used to find the rest-mass formula for elementary particles consistent with what is already known. If this interpretation is correct, it means that Einstein’s intuition that “God Does Not Throw Dice with the Universe” could also be correct. We interpret this to mean that Einstein did not believe the world was ruled by strange uncertainty phenomena at the deeper level, and we will claim that this level is the Planck scale, where all uncertainty seems to collapse. The bad news is that this new-found certainty can only can last for one Planck second! We are also questioning, without coming to a conclusion, if this could have implications for Bell’s theorem and hidden variable theories.
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.
The Heisenberg equation may not be as well-known as Einstein’s e=mc^2. But the Heisenberg equation’s implications that there is an irreducible uncertainty with regard to the position of an object are no less intriguing than the implications of Einstein’s relativity equation that time slows to a stop when the relative velocity of an object approaches the speed of light. Using elementary mathematics and science, this paper begins by examining the physics of motion of an everyday object such as a tennis ball. The paper shows that the same physics that applies to everyday objects in fact also applies when it comes to subatomic particles, such as an electron in motion. And by taking gradual incremental steps in developing the mathematics of the underlying physics, the paper leads to the conclusion that the universe is inherently uncertain, that it is impossible to know the exact position of any object.