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Atomic clocks confirm the constancy of fundamental constants in space and time

Comparisons of high-performance atomic clocks improve previous tests by up to 20 times


It sounds trivial: A fundamental constant should always have the same value, regardless of when or where it is determined. Einstein’s famous theory of general relativity also uses this fundamental assumption, which is known as local position invariance (LPI). In the current issue of Physical Review Letters, scientists from the Physikalisch-Technische Bundesanstalt (PTB) in Germany have confirmed the validity of LPI with a significantly improved experimental test. Their investigations are motivated by modern string theories that predict LPI violations – for example temporal variations of fundamental constants. In their search for the experimental confirmation of such “new physics”, the PTB researchers used the comparison of their high-precision atomic clocks and were able to improve the results of previous experiments by up to 20 times.

Comparisons between ytterbium and caesium atomic clocks at different locations (x) and times (t) confirm the constancy of fundamental constants.

The outcome of an experiment that does not depend on gravity should be independent of when and where it is performed. This assumption is known as local position invariance (LPI) and is a central part of Einstein’s general theory of relativity. LPI also implies that fundamental constants do not change in time and space. However, the current understanding of physics is reaching its limits, for example in describing dark matter or the imbalance between matter and antimatter. Modern theories that strive to describe these phenomena predict violations of LPI, which could manifest themselves, for example, in variations of fundamental constants.

Well-known fundamental constants include the fine structure constant α, which describes the strength of the electromagnetic interaction, and the mass ratio of the proton to the electron µ. These quantities are relevant for the structure of all atoms and molecules. They affect the atomic energy scales and thus also energy differences between atomic states, which are used as reference frequencies in atomic clocks. The sensitivity of the energy differences to the fundamental constants depends strongly on the particular atomic system. For example, the frequency of the caesium clock, which is used to realize the base unit of time, the second, changes when µ and α vary. Frequencies of optical atomic clocks show no dependence on µ, but they can be used to detect α-variations. The ytterbium ion, which has two optical reference transitions, each with a very different dependence on α, appears particularly suitable for this purpose. A combined comparison of ytterbium and caesium clocks thus allows the search for changes in both α and µ. Following this approach, researchers at PTB compared their high-precision atomic clocks over a period of several years and found that changes in the value of α (which is α=0.007297...) per year can occur at most from the 21st decimal place. This is the first significant improvement in the limit of a possible temporal variation of α in over 12 years, with an accuracy that is a factor of 20 higher. For changes in µ, the previous limit was improved by a factor of 2. In addition to limiting a potential temporal variation, the data also limit a possible spatial dependence of the fundamental constants on the gravitational potential of the Sun on the Earth’s orbit.

During the measurements, the frequency of one of the two ytterbium clocks was also determined with highest precision: The frequency, which is 642×1012 Hz, was determined with an accuracy of 0.08 Hz and represents the most accurate measurement of an optical frequency with caesium clocks to date.


Dr. Nils Huntemann
WG 4.43 “Optical Clocks with Trapped Ions”
Phone: +49 531 592-4430
E-mail: nils.huntemann@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).journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.011102