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Stability of natural constants in space and time confirmed

Comparisons of atomic clocks have improved previous tests by a factor of 20

PTB News 2.2021
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fundamental research in physics

A natural constant should always have the same value, regardless of when or where it has been determined. Einstein’s famous general theory of relativity exploits this fundamental assumption, which is known as local position invariance (LPI). The validity of this assumption has now been confirmed by means of a comparison of optical ytterbium clocks at PTB with an accuracy increased by a factor of 20.

The outcome of an experiment that does not depend on gravitation should not depend on when or where it is performed. This assumption is known as local position invariance (LPI) and is a core element of Einstein’s general theory of relativity. LPI also implies that natural constants do not vary in time and space. However, our present understanding of physics has reached its limits when it comes to describing phenomena such as dark matter or the disequilibrium between matter and antimatter. String theories that endeavor to describe such phenomena predict violations of LPI which could materialize, for instance, in the form of changes in natural constants.

Commonly known natural constants are the fine-structure constant α, which describes the strength of the electromagnetic interaction, and the proton-to-electron mass ratio μ. These quantities are involved in the setup of all atoms and molecules. They influence the atomic energy scales – and thus also energy differences between atomic states that are used as a reference frequency in atomic clocks. The sensitivity of the energy differences to the natural constants considerably depends on the atomic system considered. For example, the frequency of the caesium clock, with which the base unit of time, the second, is realized, changes when μ and α are varied. Frequencies of optical atomic clocks show no dependence on α but can be used to detect variations of α. The ytterbium ion seems to be particularly well suited for this purpose, since it has two optical reference transitions whose dependences on αstrongly differ from each other. A combined comparison of ytterbium clocks and caesium clocks thus allows such changes of both α and μ to be detected.

Following this approach, ytterbium clocks and caesium clocks of PTB were compared over a period of several years. The results showed that changes in the value of α (α = 0.007297) each year may occur only from the 21st decimal place on. With an accuracy improved by a factor of 20, this has been the first significant improvement of the limit of a possible temporal variation of α within 12 years. For changes in the value of μ, the previous limit has been improved by a factor of 2. Besides the limitation of a potential temporal change, the data also limit a possible spatial dependence of the natural constants on the gravitational potential of the sun on the earth’s orbit.


Nils Huntemann
Department 4.4 Time and Frequency
Phone: +49 531 592-4430
Opens local program for sending emailnils.huntemann(at)ptb.de

Scientific publication

R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, Chr. Tamm, S. Weyers, E. Peik: Improved limits for violations of local position invariance from atomic clock comparisons. Phys Rev. Lett. 126, 011102 (2021)