Relativistically accurate

A research team has measured the geographical difference in altitude between Munich and Braunschweig using the most accurate clocks in the world.

July 04, 2024

Time passes faster in Munich than in Braunschweig – at least physically speaking, this is a fact according to Einstein's general theory of relativity. The difference has to do with the fact that Munich is geographically higher. Although it is miniscule at around one second in a million years, it can be measured very accurately using optical atomic clocks. Such chronometric altitude measurements have the revolutionary potential for measuring and observing the Earth. Researchers from the Max Planck Institute of Quantum Optics  (MPQ), the Physikalisch-Technische Bundesanstalt (PTB) and Leibniz University Hannover (LUH) have now measured the difference in altitude between Munich and Braunschweig using two optical clocks. Their results were published in Physical Review Applied.

Time passes more slowly in the lowlands of northern Germany than in Munich,  which is a few hundred metres higher up, because it is a little closer to earth. Time passes more slowly closer to a massive body (such as the Earth). This relativistic effect is one of the core predictions of  Einstein's general theory of relativity and has been experimentally verified many times since the middle of the last century. At different locations on Earth, however, the difference is so small that it can only be measured with the most accurate clocks: atomic clocks. It is,  however, difficult – especially over long distances – to connect the clocks at the two locations to compare their time.

The solution: optical atomic clocks connected to each other via optical fibres. Christian Lisdat, head of the working group at the  Physikalisch-Technische Bundesanstalt, explains: "Using chronometric  levelling, we can measure the differences in the Earth's gravitational  field directly and very accurately using differences in the  frequencies of the clocks." This enables a wealth of new applications in geodesy, the science of measuring the earth and its gravitational field: for example, differences between the elevation networks of different countries can be resolved, which can be particularly large if there is no direct land connection - such as between islands and the mainland. Sea levels could also be monitored more accurately by better networking water levels or comparing them with a virtually unchanging reference point in space.

But back to the difference in altitude between Munich and Braunschweig: for their measurement experiment, PTB scientists have developed a state-of-the-art transportable optical clock based on laser-cooled strontium atoms. In addition, the MPQ, PTB and other European partners are operating a fibre network that transmits light in a phase-stable manner. "The north-south connection via fibre optic links has already existed for 15 years and was the first to be set up worldwide," explains Dr Ronald Holzwarth, research associate in the Department of Laser  Spectroscopy at the MPQ and Managing Director of Menlo Systems GmbH. Two optical clocks can be connected and compared via this fibre network –  in this case the frequency difference between the MPQ in Garching near  Munich and the PTB in Braunschweig.

For this purpose, the transportable optical clock was first synchronised with another strontium clock at the PTB and then transported to the MPQ. There, the researchers compared this clock with the clock left behind at PTB via an optical fibre connection and measured how much the frequencies had changed relative to each other. The two clocks were then compared again at PTB to ensure that nothing had changed apart from the relativistic redshift. The difference in altitude of around 400 metres was determined from the measurement data with an uncertainty of 27  centimetres. The chronometric measurement agrees with comparative measurements using established conventional methods.

The measurement, the results of which were recently published in the journal Physical Review Applied, demonstrates the practical feasibility of chronometric height measurements with optical clocks and paves the way for practical applications in relativistic geodesy. At the same time, it is only the beginning. In the meantime, the PTB researchers have developed a significantly improved transportable atomic clock that is intended to determine the difference in altitude between Munich and  Braunschweig even more reliably. "We expect a significant improvement with the last measurement campaign – with the optimised optical PTB  clock, the uncertainty in the height measurement will only be a few centimetres”, explains Ronald Holzwarth

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