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A New Concept of Information Based on Heisenberg's Uncertainty Principle and Its Experimental Verification

Frank Z. Wang

Published Jul 7, 2021• 1 citation
Publisher

Abstract

Abstract This study is the first use of Heisenberg's energy-time uncertainty principle to define information quantitatively from a measuring perspective: the smallest error in any measurement is a bit of information, i.e., 1 (bit)=(2∆E ∆t)⁄ℏ. If the input energy equals the Landauer bound, the time needed to write a bit of information is 1.75x10-14 s. Newton's cradle was used to experimentally verify the information-energy-mass equivalences deduced from the aforementioned concept. It was observed that the energy input during the creation of a bit of (binary) information is stored in the information carrier in the form of the doubled momentum or the doubled “momentum mass” (mass in motion) in both classical position-based and modern orientation-based information storage. Furthermore, the experiments verified our new definition of information in the sense that the higher the energy input is, the shorter the time needed to write a bit of information is. Our study may help understand the fundamental concept of information and the deep physics behind it.

DOI
10.21203/rs.3.rs-654447/v1

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Frontiers in Physics•Dec 8, 2022•3 citations
Abstract This study is the first use of Heisenberg's energy-time uncertainty principle to define information quantitatively from a measuring perspective: the smallest error in any measurement is a bit of information, i.e., 1 (bit)=(2∆E ∆t)⁄ℏ. If the input energy equals the Landauer bound, the time needed to write a bit of information is 1.75x10-14 s. Newton's cradle was used to experimentally verify the information-energy-mass equivalences deduced from the aforementioned concept. It was observed that the energy input during the creation of a bit of (binary) information is stored in the information carrier in the form of the doubled momentum or the doubled “momentum mass” (mass in motion) in both classical position-based and modern orientation-based information storage. Furthermore, the experiments verified our new definition of information in the sense that the higher the energy input is, the shorter the time needed to write a bit of information is. Our study may help understand the fundamental concept of information and the deep physics behind it.
In 1961, Landauer [R. Landauer, IBM J. Res. Develop. 5, 183 (1961)] pointed out that resetting a binary memory requires a minimum energy of kBTln(2){k}_{B}Tln(2)kB​Tln(2). However, once written, any memory is doomed to lose its content if no action is taken. To avoid memory losses, a refresh procedure is periodically performed. We present a theoretical model and an experiment on a microelectromechanical system to evaluate the minimum energy required to preserve one bit of information over time. Two main conclusions are drawn: (i) in principle, the energetic cost to preserve information for a fixed time duration with a given error probability can be arbitrarily reduced if the refresh procedure is performed often enough, and (ii) the Heisenberg uncertainty principle sets an upper bound on the memory lifetime.
A vast number of internal “time” quantities, intrinsically associated with some particular phenomena, is all that can be consistently defined in physics. This leads us to interpret the notion of “uncertainty in time” specifically, for each of the considered phenomena. However, a universal conception of “time” can be proposed from the unifying point of view of the Observer, considering only the information process underlying any phenomenon. A change in the available information relative to that phenomenon can be calculated with the use of a universal “time”-information operator. This operator computes the algorithmic information content of the predictive tool associated with any experimental situation. Its standard deviation is then used to interpret the notion of “uncertainty in time” as a limit of predictability for any evolution. Heisenberg’s principle of “time”-energy uncertainty can then be rigorously regarded as a cognitive principle governing the evolution of any physical system.
One of the most striking deviations of quantum mechanics from classical mechanics is that any measurement of a microscopic system involves the interaction with the measuring instruments. The interaction cannot be neglected and in fact leads to uncontrollable disturbance on the system. In 1927, Werner Karl Heisenberg in his celebrated paper established the quantitative expression for unavoidable momentum disturbance caused by any position measurement. The crucial word here is simultaneously. The uncertainty relation gives the lower bound on the product of the uncertainties of two pairs of variables. But it says nothing about the accuracy with which individual observables can be measured. The physical meaning of energy-time uncertainty is different from that of x-px uncertainty. Position and momentum are observables to which Hermitian operators are assigned and which are measured at a particular time. An important implication of the uncertainty principle is that quantum systems do follow classical trajectories which conflict with our everyday experience.
Abstract Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays an important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is well known that the case of energy and time principally differs from more familiar examples of two non‐commuting observables. Since quantum theory was originated, many approaches to energy–time uncertainties have been proposed. Entropic way to formulate the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, uncertainty relations of the “energy–time” type are obtained in terms of Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state‐dependent and state‐independent formulations are of interest. Some of the derived state‐independent bounds are similar to the results obtained within a more general approach on the basis of sandwiched relative entropies. The developed method allows us to address the case of detection inefficiencies.
Since every substance has a price tag of information that includes all the building blocks in our universe, one cannot simply ignore information when dealing with science. We have shown that there is a profound connection between information and entropy, a quantity that has been well accepted in science. Without this connection, information would be more difficult to apply in science. Two of the most important pillars in modern physics must be Einstein’s relativity theory and Schrödinger’s quantum mechanics. However, there exists a profound connection between them, by means of Heisenberg’s uncertainty principle. Due to the uncertainty relation, we see that every bit of information takes time and energy to transfer, create, and observe. Since one cannot create something from nothing, anything to be created needs a huge amount of energy and a great deal of entropy to make it happen.
Heisenberg guessed, after he established the matrix quantum mechanics, that the non-commutativity of the matrices of position and momentum implied that the position and momentum of a particle could not be precisely simultaneously determined. He consequently conjectured that time and energy should also have a similar relationship. Soon after, Robertson derived an inequality concerning the space coordinate and momentum, which was thought to be the mathematical expression of the uncertainty relation guessed by Heisenberg. Since then, people have tried various devices to prove the correctness of these two relations. However, no one conducted a careful analysis of Heisenberg’s primary paper. In this work, we point out some serious problems in Heisenberg’s paper and the literature talking about the uncertainty relationships: the physical concepts involved in the uncertainty relations are not clear; one physical concept had more than one explanation, i.e., switching concepts; there has never been measurement experiment to support the relations. The conclusions are that the so-called coordinate–momentum uncertainty relation has never been related to actual measurement and there does not exist a time–energy uncertainty relation.