Waiting for the case of the equivalence principle

The microscope experiment, launched in 2016, confirmed with unprecedented precision the equivalence principle at the heart of Einstein’s general theory of relativity. Two physicists explain the implications of this result.

What is the equivalence principle?
Serge Reynaud . According to the principle of equivalence, two bodies released at the same time in a vacuum fall with the same speed and the same acceleration, even if they have different masses or compositions. Galileo had already studied this phenomenon, particularly with the help of pendulums. The idea was reinforced by Newton’s laws, which involve two types of masses: the inertial mass (the one that “resists” the acceleration of a massive body, editor’s note) and the bass mass (that which causes the acceleration of a massive body under the action of gravity, n.d. editorial). While nothing a priori obliges them to be the same, Newton established that they are visibly identical. Experiments with pendulums were refined by the early 20th centurye They showed that two bodies in free fall had the same acceleration with a relative accuracy of 10-6. Since then, the accuracy has been increased to about 2×10-13 Use of torsion balances. By analyzing the first data from the mission in 2017, Microscope had achieved a record precision of 2×10-14still significantly improved this year in our final results with an equivalence principle verified at 2.7 x 10-fifteen.

Why are we trying to confirm or disprove this principle?
SR If the principle of equivalence was already known to Newton, the concept became really essential with Albert Einstein, who built his general theory of relativity on the basis of the assertion that the principle of equivalence was true. In particular, this allowed him not to include mass in the motions associated with gravity, which is then no longer described as attraction between two objects, but as a deformation of the geometry of space-time. General relativity successfully predicted many phenomena, such as gravitational waves, discovered a century later, but we know that it will one day be superseded because it belongs to classical physics. This means that quantum phenomena are not taken into account. The unification of gravitational theories with those of the quantum domain is one of the greatest challenges of contemporary fundamental physics. However, most theses that come close to it predict a violation of the equivalence principle. Knowing the accuracy to which the equivalence principle is verified allows both testing of general relativity and narrowing the space of possibility for unification theories.

Giles Metris. The very notion of the equivalence principle is ambiguous, since a principle is usually accepted and does not need to be tested. While this is a principle within the framework of general relativity and classical theory, it is not an absolute principle for all of physics.

How does the microscope experiment investigate the equivalence principle?
GM Basically, the principle of the experiment is very simple, since we are only comparing the case of two bodies. For this we try to achieve the longest possible free fall under perfectly controlled conditions and with extremely careful timing. On Earth there are weightless towers like that of the University of Bremen. They make it possible to observe the free fall very closely for four seconds. With the microscope, the total free fall time used in our measurements reaches one hundred and thirty-eight days.

The zero gravity tower at the Center for Applied Space Technology and Microgravity at the University of Bremen.

The microscope was successful because the experiment took place in a satellite, but the orbiting bodies are in permanent free fall. The objects were placed in a cage that protected them from interference from atmospheric debris. This casing also acted as an accelerometer, ensuring that the free masses did not hit the walls of the satellite itself, which was slowed down by this friction. Thus the two masses fell but remained held by an electrostatic force. By measuring the force necessary to thwart their movements, we could then calculate their acceleration.

The precision of the microscope boils down to detecting the weight of a fly landing on a supertanker. It’s impossible to do this directly, and we circumvented this difficulty through two complementary strategies. Since the cylindrical masses and the satellite are in free fall, we initially only measured acceleration differences on the order of the famous fly and not the total acceleration. Then the Microscope satellite was equipped with a complete micropropulsion system, which made it possible to compensate for fluctuations in the satellite’s acceleration due to friction in the residual atmosphere. This system made it possible to stabilize the rotation of the satellite on itself at a level never before achieved. The microscope was stopped in 2018 when the gas supplying the micro-drive system ran out.

So where do the precision gains that have made it possible to achieve these end results come from?
GM Since the publication of the first results in 2017, we have continued to work to reduce two categories of errors. Statistical errors decrease with time and accumulation of measurements. So we improved our accuracy by a factor of ten. In doing so, however, we expose ourselves to systematic errors that arise when we measure a signal that is actually not what we want to examine. We have therefore made great efforts to account for various effects, particularly thermal ones, in order to reduce their contribution to bias.

Exploded view of the instrument at the heart of the microscope satellite. We see two masses of full prints in platinum for the reference unit and two masses of cross-section prints in golden titanium (external and internal).

What possibilities are there to verify this principle even more precisely in the future?
SR Many teams are working on these topics. In any case, Microscope offers exceptional feedback, we can analyze what worked well and what limited the final precision so that the next missions go further. After that, there are two main approaches. The first is to use Microscope’s lessons to set up a similar project but more precisely. The second would be to conduct the experiments with laser-cooled atoms playing the role of masses to be compared. This area has benefited from many advances in recent years, offering ever greater control and precision.

GM. The National Office for Aerospace Studies and Research (Onera) and the GéoAzur laboratory, under the aegis of the National Center for Space Studies (Cnes), have already carried out initial studies for a successor to Microscope, with the aim of making it a hundred times better. In addition, a project based on cold atoms has already passed a first selection filter by the European Space Agency (ESA). These processes are therefore already underway, but in the space sector the completion of projects is always quite long.

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The equivalence principle remains valid!

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