Preprint Hypothesis Version 3 Preserved in Portico This version is not peer-reviewed

The Theory of Quantum Uncertainties and Quantum Measurements

Harsh Anand
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Version 1 : Received: 17 January 2022 / Approved: 20 January 2022 / Online: 20 January 2022 (10:30:56 CET)
Version 2 : Received: 7 March 2022 / Approved: 7 March 2022 / Online: 7 March 2022 (13:42:08 CET)
Version 3 : Received: 29 October 2022 / Approved: 31 October 2022 / Online: 31 October 2022 (04:32:16 CET)

How to cite: Anand, H. The Theory of Quantum Uncertainties and Quantum Measurements. Preprints 2022, 2022010297. https://doi.org/10.20944/preprints202201.0297.v3 Anand, H. The Theory of Quantum Uncertainties and Quantum Measurements. Preprints 2022, 2022010297. https://doi.org/10.20944/preprints202201.0297.v3

Abstract

1) We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time $t$. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time $t_0$ under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove that both these situations cannot arise under ordinary circumstances and thus measurement processes cannot be modelled by physical Hamiltonians.

Keywords

Quantum speed limits; quantum information; Quantum computing

Subject

Physical Sciences, Mathematical Physics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1
Received: 31 October 2022
Commenter: Harsh Anand
Commenter's Conflict of Interests: Author
Comment: We wish to extend the idea of a time bound to a spacial bound. We had seen that to bring  arbitrary states in close time,  more energy must be given to the system.  If now, we wish to bring together two points on the real line close to each other, can we hope that adding more momentum will do it?  It will be so upto an extent but we are left with some undefined quantities and it is difficult to attach physical meaning to it. Thus we leave the problem here.
We now delve into an attempt to theoretically model a quantum measurement process. And then we look into the fundamental interpretation of the Quantum uncertainty relations and produce some new insights .
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