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The exploration of the universe has recently entered a new era thanks to the multimessenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 ‘‘Quantum gravity phenomenology in the multi-messenger approach", is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers., Talent Scientific Research Program of College of Physics, Sichuan University 1082204112427, Fostering Program in Disciplines Possessing Novel Features for Natural Science of Sichuan University 2020SCUNL209, 1000 Talent program of Sichuan province 2021, Xunta de Galicia, European Commission European Union ERDF, "Maria de Maeztu'' Units of Excellence program MDM-2016-0692, Red Tematica Nacional de Astroparticulas RED2018-102661-T, La Caixa Foundation 100010434, European Commission 847648 LCF/BQ/PI21/11830030 754510, Ministry of Education, Science & Technological Development, Serbia 451-03-9/2021-14/200124, FSR Incoming Postdoctoral Fellowship Ministry of Education, Science and Technological Development, Serbia 451-03-9/2021-14/200124, University of Rijeka grant uniri-prirod-18-48, Croatian Science Foundation (HRZZ) IP-2016-06-9782, Villum Fonden 29405 DGA-FSE 2020-E2117R, European Regional Development Fund through the Center of Excellence (TK133) "The Dark Side of the Universe'' European Regional Development Fund (ESIF/ERDF), Ministry of Education, Youth & Sports - Czech Republic CoGraDS-CZ.02.1.01/0.0/0.0/15 003/0000437, Blavatnik grant, Basque Government IT-97916 Basque Foundation for Science (IKERBASQUE), European Space Agency C4000120711 4000132310, FNRS (Belgian Fund for Research), Programa de Apoyo a Proyectos de Investigacion e Innovacion Tecnologica (PAPIIT), Universidad Nacional Autonoma de Mexico TA100122, National University of La Plata X909 DICYT 042131GR, National Research, Development & Innovation Office (NRDIO) - Hungary 123996, FQXi, Swiss National Science Foundation (SNSF), European Commission 181461 199307, Netherlands Organization for Scientific Research (NWO) 680-91-119 15MV71, Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research (KAKENHI) 20H01899 20H05853 JP21F21789, Estonian Research Council PRG356, Julian Schwinger Foundation, Generalitat Valenciana Excellence PROMETEO-II/2017/033 PROMETEO/2018/165, Istituto Nazionale di Fisica Nucleare (INFN), European ITN project HIDDeN H2020-MSCA-ITN-2019//860881-HIDDeN, Swedish Research Council, European Commission 2016-05996 European Research Council (ERC) European Commission 668679, Advanced ERC grant TReX, Ministry of Education, Universities and Research (MIUR) 2017X7X85K, Fonds de la Recherche Scientifique - FNRS 4.4501.18, Ministry of Research, Innovation and Digitization - Romania PN19-030102-INCDFM PN-III-P4ID-PCE-2020-2374, United States Department of Energy (DOE) DE-SC0020262, Ministry of Science, ICT & Future Planning, Republic of Korea 075-15-2020-778, German Academic Scholarship Foundation German Research Foundation (DFG) 408049454 420243324 425333893 445990517 Germany's Excellence Strategy (EXC 2121 "Quantum Universe'') 390833306 390837967 Federal Ministry of Education & Research (BMBF) 05 A20GU2 05 A20PX1, Centro de Excelencia "Severo Ochoa'' SEV-2016-0588, CERCA program of the Generalitat de Catalunya, Agencia de Gestio D'Ajuts Universitaris de Recerca Agaur (AGAUR) Generalitat de Catalunya 2017-SGR-1469 2017-SGR-929 ICCUB CEX2019-000918-M, National Science Centre, Poland 2019/33/B/ST2/00050 2017/27/B/ST2/01902, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) 306414/2020-1, Dicyt-USACH 041931MF, National Science Fund of Bulgaria KP-06-N 38/11 RCN ROMFORSK 302640, Comunidad de Madrid 2018-T1/TIC-10431 2019-T1/TIC-13177 S2018/NMT-4291, UK Research & Innovation (UKRI), Science & Technology Facilities Council (STFC) ST/T000759/1 ST/P000258/1 ST/T000732/1 ST/V005596/1, Portuguese Foundation for Science and Technology UIDB/00618/2020 UIDB/00777/2020 UIDP/00777/2020 CERN/FIS-PAR/0004/2019 PTDC/FIS-PAR/29436/2017 PTDC/FISPAR/31938/2017 PTDC/FIS-OUT/29048/2017 SFRH/BD/137127/2018, Centre National de la Recherche Scientifique (CNRS), LabEx UnivEarthS ANR-10-LABX-0023 ANR18-IDEX-0001, Junta de Andalucia European Commission A-FQM-053-UGR18, Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN-2021-03644, National Science Centre Poland Sonata Bis 2019/33/B/ST2/00050 DEC-2017/26/E/ST2/00763, Natural Sciences and Engineering Research Council of Canada (NSERC) DGIID-DGA 2015-E24/2, Spanish Research State Agency and Ministerio de Ciencia e Innovacion MCIN/AEI PID2019-104114RB-C32 PID2019-105544GB-I00 PID2019-105614GB-C21 PID2019106515GB-I00 PID2019-106802GB-I00 PID2019-107394GB-I00 PID2019-107844GB-C21 PID2019-107847RB-C41 MCIN/AEI PGC2018-095328-B-I00 PGC2018-094856-B-I00 PGC2018-096663-B-C41 PGC2018-096663-B-C44 PGC2018-094626-BC21 PGC2018-101858-B-I00 FPA2017-84543-P FPA2016-76005-C2-1-P, Spanish 'Ministerio de Universidades' BG20/00228 Spanish Government PID2020-115845GBI00 Generalitat de Catalunya Comunidad de Madrid S2018/NMT-4291 Spanish Government PID2019-105544GB-I00, Perimeter Institute for Theoretical Physics, Government of Canada through the Department of Innovation, Science and Economic Development, Province of Ontario through the Ministry of Colleges and Universities, Centre National de la Recherche Scientifique (CNRS), Netherlands Organization for Scientific Research (NWO), Fundamental Questions Institute (FQXi), European Cooperation in Science and Technology (COST) CA18108, Research Council of University of Guilan, Iniziativa Specifica TEONGRAV Iniziativa Specifica QGSKY Iniziativa Specifica QUAGRAP Iniziativa Specifica GeoSymQFT, the Spanish Research State Agency and Ministerio de Ciencia e Innovacion MCIN/AEI PID2020-115845GBI00 PID2019-108485GB-I00 PID2020-113334GB-I00 PID2020-113701GB-I00 PID2020-113775GB-I00 PID2020-118159GB-C41 PID2020-118159GA-C42 PRE2019-089024, Rothchild grant UID/MAT/00212/2020 FPU18/04571

A short review of the characteristic features of the Maxwell equations in vacuum are recalled. Then some of the laboratory experiments and astrophysical observations aimed to test the physics of the electromagnetic field are described. These tests and observations include dispersion, birefringence, the Coulomb 1/r potential, tests of Special Relativity, charge conservation, and the superposition principle.

Tests of the Weak Equivalence Principle (WEP) by means of torsion balances have confirmed the WEP nearly to the 10−13 level. At this level, the coupling to changing gravitational environment on earth as well as seismic and thermal noise seem to establish a severe threshold for the improvement of accuracy. In order to overcome these difficulties, experiments in space offer new ranges of accuracy: Space platforms and satellites in a nearly free fall along geodesics offer unique possibilities to improve the accuracy of WEP‐tests by several orders of magnitude which is important as some quantum gravity inspired theories predict a WEP‐violation. At present, two satellite projects are planned and scheduled to test the WEP for neutral bulk matter: the French mission MICROSCOPE approved to be launched early 2008 is designed to measure on the 10−16 level and the ESA/NASA mission STEP which is still under study, will be precise on the 10−18 level. Modern space technology is not only interesting for WEP tests of neutral bulk matter, but can be used to carry out comprehensive EP‐tests (e.g. Lunar Laser Ranging). Beside tests with bulk matter, complementary tests with comparable results for other kind of matter or couplings (charged particles, atoms, neutrons, anti‐matter, or spin) are required. New ideas for space experiments to test the WEP for anti‐matter or charged matter have been discussed recently. Space also enables to test Newton’s Law on very small and huge distances. In the range below 0.1 mm, one can make use of the advantage of the weightlessness environment. For long range measurements above 1 astronomical unit, deep space satellites are and will be used to probe the gravitational field with improving accuracy.

According to widespread expectations, we will shortly witness a new era in experimental gravitation. More accurate measurements of classical, weak field effects will soon be performed. Examples of these classical effects are the bending of light rays by the solar mass (or its modern counterparts, based on radio propagation effects), and the relativistic perturbations of the orbit of Mercury. In addition, we will shortly probe a new domain, where predicted but not yet measured effects (e.g. the Lense-Thirring effect, gravitational waves) will provide significant new tests of general relativity and its foundations. Particularly promising are the relativistic tests in space. Some of these experiments require the use of dedicated missions (e.g. GPB, STEP, LISA), while others are part of complex missions dedicated to astronomy or space exploration in general (e.g. Cassini, BepiColombo, GAIA). The aim of this book is to provide a detailed review of the subject of experimental gravitation in space. These are the proceedings of an international advanced school which took place in 1999 in Bad Honnef. A positive aspect of this book is that both experimental techniques and theoretical background are presented side by side. Particular emphasis is given to tests of the Lense-Thirring effect and the equivalence principle, and to applications of spaceborne atomic clocks. In such a rapidly developing field, it is almost inevitable that some experimental techniques are left out, and the editors quite rightly decided to focus on only some of the topics in the field of experimental gravitation. The book starts with an excellent review by Nordtvedt on solar system tests of general relativity. The second section is dedicated to the Lense-Thirring effect, offering a very good introduction for readers unfamiliar with gravitomagnetism. On the experimental side, this part is dominated by the review by Everitt et al on the status of GPB. Also well covered is the equivalence principle (EP). We mention Haugan and Lammerzahl's review of the role of the EP in gravitational field theories. From the experimental side, Nordtvedt gives an update on the status of the LLR experiment, now able to test the validity of the EP to an accuracy of the order of 10-13, along with a confirmation of the de Sitter precession and an upper limit on the time variation of Newton's constant. In the future, experiments like STEP will be able to test the EP to an accuracy several orders of magnitude better than that currently available from LLR. Lockerbie et al give an updated review of the status of STEP, which gives a clear idea of the very challenging technical progress required in order to meet these expectations. I found the section on gravitational waves somewhat disappointing. It includes theoretical papers by Blanchet et al on the generation of gravitational radiation, and by Grishchuk on the cosmological background. However, the experimental part is very poorly covered, with a single presentation by Rudiger et al on the GEO600 ground-based laser interferometer (thus, not even a space experiment). Completely missing are contributions on space experiments based on laser interferometry (e.g. LISA) or on the Doppler technique (e.g. Cassini). The book would have certainly gained from the inclusion of a detailed discussion on the status and plans of such detectors. Finally, like other titles from Springer-Verlag's series on Lecture Notes in Physics, this book is very well produced, although it would certainly have benefited from accurate editing before going to press. Several typos were found (the most evident case being the misspelling of Thirring in the title of Part II). Cited references are extensive and very useful, although, again, they could have been produced with a single and more accurate format throughout the book. In summary, I strongly recommend this book, in particular to professionals and graduate students interested in learning some theoretical aspects of modern experimental gravitation. Giacomo Giampieri

Die von Albert Einstein begrundete moderne Gravitationstheorie ist eines der faszinierenden Gebiete der Physik. Nicht wenige Studierende der Physik haben ihr Studium unter anderem deshalb aufgenommen, weil sie mehr uber diese Theorie wissen wollten. Zudem tragt die Gravitationsphysik wesentlich zum Erscheinungsbild und zur Akzeptanz der Physik in der Offentlichkeit bei. Wenn jedoch nichts geschieht, wird in 5 Jahren nur noch an einer einzigen deutschen Universitat Gravitationsphysik hauptamtlich in Forschung und Lehre betrieben. Wahrend die Allgemeine Relativitatstheorie bis in die sechziger Jahre hinein eine Domane der Theoretiker war, hat sie seitdem auch fur Experimentalphysiker grose Bedeutung gewonnen. Ermoglicht durch wesentliche Fortschritte in den experimentellen Methoden wurden viele Grosprojekte der experimentellen Gravitation in Angriff genommen. Von besonderer Bedeutung sind dabei unter anderem Gravitationswellendetektoren, die nicht nur eine wesentliche Vorhersage der Allgemeinen Relativitatstheorie testen, sondern auch ein neues “Fenster” zum Weltall aufstosen, welches sowohl einen Blick zuruck in die fruhesten Phasen des Universums, als auch die Beobachtung neuer astrophysikalischer Phanomene ermoglicht – Beobachtungen, die wiederum viele theoretische Arbeiten nach sich ziehen werden. Weiterhin denke man an die Kosmologie, die Physik Schwarzer Locher, die Raumfahrt und nicht zuletzt das GPS (Global Positioning System), was schon Einzug in unseren Alltag gehalten hat. Dazu kommt die groste Herausforderung, der sich die theoretische Physik heute gegenubersieht, namlich die Vereinheitlichung von Gravitation und Quantentheorie. An all diesen Entwicklungen und Fragestellungen sind Relativisten aus Deutschland (oder entsprechend gebildete Geodaten, Astrophysiker oder Quantenoptiker) wesentlich beteiligt. Demgegenuber last die Situation der Gravitationsforschung in Deutschland schon heute sehr zu wunschen ubrig: Es gibt zur Zeit nur an 5 Universitaten ausgewiesene, mit permanenten Stellen ausgestattete Arbeitsgruppen auf diesem Gebiet. Daruber hinaus zeichnet es sich immer deutlicher ab, das 4 dieser Gruppen in den nachsten 5 Jahren mit der Emeritierung bzw. Pensionierung ihrer Leiter ersatzlos gestrichen werden. Dann gabe es in ganz Deutschland (neben dem MPI fur Gravitationsphysik in Potsdam) nur noch eine einzige Universitat (Jena) mit einer entsprechenden Arbeitsgruppe auf diesem Gebiet. Dabei sind insbesondere die folgende Punkte zu bedenken: 1. Die Allgemeine Relativitatstheorie ubt, insbesondere mit ihren Anwendungen in Astrophysik und Kosmologie, eine grose Anziehungskraft auf Studierende aus und steigert die Attraktivitat einer physikalischen Fakultat betrachtlich. Vorlesungen uber Relativitatstheorie und auch popularwissenschaftliche Vortrage zu diesem Thema gehoren zu den meistbesuchten Veranstaltungen. 2. Die Allgemeine Relativitatstheorie ist fur andere Gebiete der Physik (Astrophysik, Teilchenphysik, Quantenoptik, mathematische Physik, Geodasie) und zudem auch fur andere Wissenschaften (Mathematik, Wissenschaftstheorie, Informatik) von grosem Nutzen und hat viele wichtige Entwicklungen auf diesen Gebieten angeregt. Die Vertreter dieser Fachrichtungen sollten an mehr als einer deutschen Universitat Diskussionspartner finden. 3. Es ware auserst kontraproduktiv und geradezu absurd, in einer Zeit, in der verschiedene unter erheblicher deutscher Beteiligung durchgefuhrte Grosprojekte in der experimentellen Gravitationsphysik ihre ersten und mit Sicherheit aufsehenerregenden Ergebnisse liefern, Forschung und Lehre auf diesem Gebiet an den deutschen Universitaten praktisch einzustellen.