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The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

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Related Experiment Video

Updated: Dec 21, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Noise-resolution uncertainty principle in classical and quantum systems.

Timur E Gureyev^1,2,3,4, Alexander Kozlov⁵, David M Paganin⁶

¹ARC Centre of Excellence in Advanced Molecular Imaging, the University of Melbourne, Parkville, VIC, 3010, Australia. timur.gureyev@unimelb.edu.au.

Scientific Reports

|May 14, 2020

Summary

This study reveals a fundamental limit: function width and value distribution width cannot both be minimized simultaneously. This noise-resolution uncertainty principle impacts communication and imaging systems.

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Last Updated: Dec 21, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

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Published on: April 4, 2017

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Published on: August 12, 2013

Area of Science:

Physics
Information Theory
Signal Processing

Background:

Classical and quantum systems often face inherent limitations in simultaneously resolving signal features and noise.
Existing uncertainty principles, like Heisenberg's, govern quantum mechanical measurements but do not fully address noise-resolution trade-offs in broader contexts.

Purpose of the Study:

To establish a novel uncertainty relationship for the product of correlation length and variance in ergodic stochastic processes.
To investigate a related uncertainty principle for bosonic quantum fields concerning coherence and spatial width.
To explore whether non-classical states can overcome classical noise-resolution limits.

Main Methods:

Mathematical derivation of uncertainty relations for function width and value distribution.
Analysis of ergodic stochastic processes to define correlation length and variance.
Application of quantum field theory to bosonic modes and coherence properties.
Investigation of sub-Poissonian statistics and photon number squeezed states.

Main Results:

Demonstrated that function width and value distribution width cannot be simultaneously minimized.
Established an uncertainty relation for correlation length and variance in stochastic processes.
Derived a similar uncertainty principle for bosonic quantum fields.
Showcased that non-classical states can surpass the classical noise-resolution uncertainty limit.

Conclusions:

A new uncertainty relationship, distinct from Heisenberg's, limits simultaneous minimization of function width and value distribution width.
This principle has implications for the information capacity of communication and imaging systems.
Non-classical states offer potential advantages in overcoming classical noise limitations.