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Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Relative Risk

Relative Risk

Relative risk (RR) is a statistical measure commonly used in epidemiology to compare the likelihood of a particular event occurring between two groups. This metric is important for evaluating the relationship between exposure to a specific risk factor and the probability of a particular outcome. It plays a crucial role in medical research, public health studies, and risk assessment. Relative risk quantifies how much more (or less) likely an event is to occur in an exposed group compared to an...

Relative Velocity in One Dimension

Relative Velocity in One Dimension

The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...

Relative Frequency Histogram

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...

Relative Velocity in Two Dimensions

Relative Velocity in Two Dimensions

Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing...

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Related Experiment Video

Updated: Feb 16, 2026

Implementation of a Reference Interferometer for Nanodetection

Implementation of a Reference Interferometer for Nanodetection

Published on: April 26, 2014

The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer.

Andrew J P Garner^1,2, Markus P Müller^3,4,5,6, Oscar C O Dahlsten^2,7,8

¹Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore.

Proceedings. Mathematical, Physical, and Engineering Sciences

|January 2, 2018

Summary

This summary is machine-generated.

Relativity of simultaneity limits interference phenomena in interferometers, restricting theories to standard complex quantum theory. Relaxing relational assumptions allows for quaternionic quantum theory, but requires careful experimental design to observe beyond-quantum effects.

Keywords:

Mach–Zehnder interferometer axioms of quantum theory general probabilistic theories interference quantum foundations quantum information

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Last Updated: Feb 16, 2026

Implementation of a Reference Interferometer for Nanodetection

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Area of Science:

Quantum physics
Interferometry
Relativity

Background:

Interferometers test physical theories, historically contrasting quantum and classical mechanics.
Recent experiments explore exotic alternatives to quantum theory, including theories with higher-dimensional state spaces.
Relativity of simultaneity poses a challenge to complex interference phenomena.

Purpose of the Study:

To investigate the impact of relativity of simultaneity on interference phenomena in two-armed interferometers.
To determine which theoretical state spaces are compatible with relativity of simultaneity.
To guide the design of future experiments searching for beyond-quantum effects.

Main Methods:

Analysis of interference patterns in a two-armed interferometer under the framework of relativity of simultaneity.
Comparison of interference phenomena predicted by classical bits, real, complex, and quaternionic quantum theories.
Examination of the role of relational properties in interference experiments.

Main Results:

Relativity of simultaneity forbids interference phenomena more complex than those in standard complex quantum theory.
If interference depends on relational properties, only complex quantum theory or subspaces are permitted.
Quaternionic quantum theory is compatible with relativity of simultaneity if relational assumptions are relaxed.

Conclusions:

Relativity of simultaneity significantly constrains the types of interference observable in interferometers.
Experimental designs must account for relativity of simultaneity to avoid obscuring beyond-quantum effects.
The study highlights the interplay between fundamental physics principles and experimental capabilities in exploring quantum foundations.