Waiting for the fall of the principle of equivalence

Launched in 2016, the Microscope experiment confirmed with unprecedented precision the equivalence principle that is at the heart of Einstein’s theory of general relativity. Two physicists explain the implications of this result.

What is the principle of equivalence?
Serge Reynaud . According to the equivalence principle, two bodies released simultaneously into vacuum fall with the same velocity and the same acceleration, even if of different mass or composition. Galileo had already studied this phenomenon, in particular using pendulums. The idea was reinforced by Newton’s laws, where two types of masses are involved: the inertial mass (the one that “opposes” the acceleration of a massive body, ed) and bass mass (what causes the acceleration of a massive body due to gravity, ed). Although nothing a priori forces them to be the same, Newton found that they are visibly identical. Experiments with pendulums were perfected until the early 20th centuryAnd century, where they verified that two free-falling bodies had the same acceleration with a relative accuracy of 10-6. The accuracy has since been increased to around 2×10-13 using torsion balances. Analyzing the first data from the mission in 2017, Microscope achieved a record accuracy of 2×10-14still greatly improved this year in our final results with a verified equivalence principle at 2.7×10-15.

Why do we try to verify or invalidate this principle?
SR If the equivalence principle was already known to Newton, the term really became essential with Albert Einstein, who built his theory of general relativity by postulating that the equivalence principle was true. This allowed him in particular not to involve the mass in the movements linked to gravity, which is then no longer described as an attraction between two objects, but as a deformation of the geometry of space-time. The theory of general relativity has successfully predicted many phenomena, such as gravitational waves which were discovered a century later, but we know that one day it is destined to be replaced, because it belongs to classical physics. This means that it does not take into account quantum phenomena. Being able to unify the theories of gravitation with those of the quantum domain is one of the main challenges of contemporary fundamental physics. However, most propositions that come close to it involve a violation of the principle of equivalence. Knowing with what precision the equivalence principle occurs allows both to verify general relativity and to reduce the space of possibilities for unifying theories.

Gilles Metris. There is ambiguity about the term equivalence principle itself, because normally a principle is accepted and does not need to be tested. This is indeed a principle within the framework of general relativity theory and classical theory, but it is not an absolute principle for all physics.

How does the microscope experiment explore the equivalence principle?
GM Basically, the principle of the experiment is quite simple as we are only comparing the fall of two bodies. This is why we try to achieve the longest free fall possible, under perfectly controlled conditions and with extremely accurate timing. On Earth there are weightless towers like that of the University of Bremen in Germany. They allow you to observe free falls with extreme precision for four seconds. With Microscope, the cumulative total time of free fall used in our measurements reaches one hundred and thirty-eight days.

The zero gravity tower of the Center for Applied Space Technology and Microgravity, 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 installed in a cage that protected them from disturbances deriving from atmospheric residues. This enclosure also acted as an accelerometer which ensured that the free masses did not hit the walls of the satellite itself, which were held back by these frictions. Thus, the two masses fell, but remained held by an electrostatic force. It is by measuring the force needed to counter their movements that we could then calculate their acceleration.

The precision of the microscope is equivalent to detecting the weight of a fly landing on a supertanker. It is impossible to do it directly and we have circumvented this difficulty with two complementary strategies. To begin with, since the cylindrical masses and the satellite are in free fall, we only measured acceleration differences, of the order of magnitude of the famous fly, and not the total acceleration. The Microscope satellite was then equipped with an entire micropropulsion system that made it possible to compensate for the variations in acceleration of the satellite due to friction in the residual atmosphere. This system made it possible to stabilize the rotational movement of the satellite on itself to a level never reached before. The microscope came to a halt in 2018, with the exhaustion of the gas that fed the micro-propulsion system.

So where do the gains in accuracy come from that made it possible to obtain these final results?
GM Since the first results were published in 2017, we have continued to work to reduce two categories of errors. Statistical errors decrease with time and accumulation of measurements. This is how we improved our accuracy by a factor of ten. But in doing so we expose ourselves to systematic errors, which arise when we measure a signal that is not really what we want to study. We have therefore made great efforts to take into account the different effects, in particular the thermal ones, in order to reduce their contribution to systematic errors.

Exploded view of the instrument in the center of the Microscope satellite. We see two masses of complete tests, in platinum, for the reference unit, and two masses of tests in section, in gold titanium (external and internal).

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

GM. The National Office for Aerospace Studies and Research (Onera) and the GéoAzur laboratory have already undertaken, under the aegis of the National Center for Space Studies (Cnes), the first studies for a successor of Microscope with the aim of do a hundred times better. Furthermore, 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 field, the completion of projects is always quite long.

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The principle of equivalence remains valid!

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