Despite doubts from quantum physicists: Einstein's theory of relativity reaffirmed

One of the most basic assumptions of fundamental physics is that the different properties of mass -- weight, inertia and gravitation -- always remain the same in relation to each other. Without this equivalence, Einstein's theory of relativity would be contradicted and our current physics textbooks would have to be rewritten. Although all measurements to date confirm the equivalence principle, quantum theory postulates that there should be a violation. This inconsistency between Einstein's gravitational theory and modern quantum theory is the reason why ever more precise tests of the equivalence principle are particularly important.

A team from the Center of Applied Space Technology and Microgravity (ZARM) at University of Bremen, in collaboration with the Institute of Geodesy (IfE) at Leibniz University Hannover, has now succeeded in proving with 100 times greater accuracy that passive gravitational mass and active gravitational mass are always equivalent -- regardless of the particular composition of the respective masses.

The research was conducted within the framework of the Cluster of Excellence "QuantumFrontiers." Today, the team published their findings as a highlights article in the scientific journal Physical Review Letters.

Physical context

Inertial mass resists acceleration. For example, it causes you to be pushed backwards into your seat when the car starts. Passive gravitational mass reacts on gravity and results in our weight on Earth. Active gravitational mass refers to the force of gravitation exerted by an object, or more precisely, the size of its gravitational field. The equivalence of these properties is fundamental to general relativity. Therefore, both the equivalence of inertial and passive gravitational mass and the equivalence of passive and active gravitational mass are being tested with increasing precision.

What was the study about?

If we assume that passive and active gravitational mass are not equal -- that their ratio depends on the material -- then objects made of different materials with a different centre of mass would accelerate themselves. Since the Moon consists of an aluminium shell and an iron core, with centres of mass offset against each other, the Moon should accelerate. This hypothetical change in speed could be measured with high precision, via "Lunar Laser Ranging." This involves pointing lasers from Earth at reflectors on the Moon placed there by the Apollo missions and the Soviet Luna programme. Since then, round trip travel times of laser beams are recorded. The research team analysed "Lunar Laser Ranging" data collected over a period of 50 years, from 1970 to 2022, and investigated such mass difference effects. Since no effect was found, this means that the passive and active gravitational masses are equal to approximately 14 decimal places. This estimate is a hundred times more accurate than the best previous study, dating back to 1986.

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Curved spacetime in a quantum simulator

The theory of relativity works well when you want to explain cosmic-scale phenomena -- such as the gravitational waves created when black holes collide. Quantum theory works well when describing particle-scale phenomena -- such as the behavior of individual electrons in an atom. But combining the two in a completely satisfactory way has yet to be achieved. The search for a "quantum theory of gravity" is considered one of the significant unsolved tasks of science.

This is partly because the mathematics in this field is highly complicated. At the same time, it is tough to perform suitable experiments: One would have to create situations in which phenomena of both the relativity theory play an important role, for example, a spacetime curved by heavy masses, and at the same time, quantum effects become visible, for example the dual particle and wave nature of light.

At the TU Wien in Vienna, Austria, a new approach has now been developed for this purpose: A so-called "quantum simulator" is used to get to the bottom of such questions: Instead of directly investigating the system of interest (namely quantum particles in curved spacetime), one creates a "model system" from which one can then learn something about the system of actual interest by analogy. The researchers have now shown that this quantum simulator works excellently. The findings of this international collaboration involving physicists from the University of Crete, Nanyang Technological University, and FU Berlin are now published in the scientific journal Proceedings of the National Academy of Sciences of the USA (PNAS).

Learning from one system about another

The basic idea behind the quantum simulator is simple: Many physical systems are similar. Even if they are entirely different kinds of particles or physical systems on different scales that, at first glance, have little to do with each other, these systems may obey the same laws and equations at a deeper level. This means one can learn something about a particular system by studying another.

"We take a quantum system that we know we can control and adjust very well in experiments," says Prof. Jörg Schmiedmayer of the Atomic Institute at TU Wien. "In our case, these are ultracold atomic clouds held and manipulated by an atom chip with electromagnetic fields." Suppose you properly adjust these atomic clouds so that their properties can be translated into another quantum system. In that case, you can learn something about the other system from the measurement of the atomic cloud model system -- much like you can learn something about the oscillation of a pendulum from the oscillation of a mass attached to a metal spring: They are two different physical systems, but one can be translated into the other.

The gravitational lensing effect

"We have now been able to show that we can produce effects in this way that can be used to resemble the curvature of spacetime," says Mohammadamin Tajik of the Vienna Center for Quantum Science and Technology (VCQ) -- TU Wien, first author of the current paper. In the vacuum, light propagates along a so-called "light cone." The speed of light is constant; at equal times, the light travels the same distance in each direction. However, if the light is influenced by heavy masses, such as the sun's gravitation, these light cones are bent. The light's paths are no longer perfectly straight in curved spacetimes. This is called "gravitational lens effect."

The same can now be shown in atomic clouds. Instead of the speed of light, one examines the speed of sound. "Now we have a system in which there is an effect that corresponds to spacetime curvature or gravitational lensing, but at the same time, it is a quantum system that you can describe with quantum field theories," says Mohammadamin Tajik. "With this, we have a completely new tool to study the connection between relativity and quantum theory."

A model system for quantum gravity

The experiments show that the shape of light cones, lensing effects, reflections, and other phenomena can be demonstrated in these atomic clouds precisely as expected in relativistic cosmic systems. This is not only interesting for generating new data for basic theoretical research -- solid-state physics and the search for new materials also encounter questions that have a similar structure and can therefore be answered by such experiments.

"We now want to control these atomic clouds better to determine even more far-reaching data. For example, interactions between the particles can still be changed in a very targeted way," explains Jörg Schmiedmayer. In this way, the quantum simulator can recreate physical situations that are so complicated that they cannot be calculated even with supercomputers.

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Curved spacetime in the lab

In a laboratory experiment, researchers from Heidelberg University have succeeded in realising an effective spacetime that can be manipulated. In their research on ultracold quantum gases, they were able to simulate an entire family of curved universes to investigate different cosmological scenarios and compare them with the predictions of a quantum field theoretical model.

According to Einstein's Theory of Relativity, space and time are inextricably connected. In our Universe, whose curvature is barely measurable, the structure of this spacetime is fixed. In a laboratory experiment, researchers from Heidelberg University have succeeded in realising an effective spacetime that can be manipulated. In their research on ultracold quantum gases, they were able to simulate an entire family of curved universes to investigate different cosmological scenarios and compare them with the predictions of a quantum field theoretical model. The research results were published in Nature.

The emergence of space and time on cosmic time scales from the Big Bang to the present is the subject of current research that can only be based on the observation of our single Universe. The expansion and curvature of space are essential to cosmological models. In a flat space like our current Universe, the shortest distance between two points is always a straight line. "It is conceivable, however, that our Universe was curved in its early phase. Studying the consequences of a curved spacetime is therefore a pressing question in research," states Prof. Dr Markus Oberthaler, a researcher at the Kirchhoff Institute for Physics at Heidelberg University. With his "Synthetic Quantum Systems" research group, he developed a quantum field simulator for this purpose.

The quantum field simulator created in the lab consists of a cloud of potassium atoms cooled to just a few nanokelvins above absolute zero. This produces a Bose-Einstein condensate -- a special quantum mechanical state of the atomic gas that is reached at very cold temperatures. Prof. Oberthaler explains that the Bose-Einstein condensate is a perfect background against which the smallest excitations, i.e. changes in the energy state of the atoms, become visible. The form of the atomic cloud determines the dimensionality and the properties of spacetime on which these excitations ride like waves. In our Universe, there are three dimensions of space as well as a fourth: time.

In the experiment conducted by the Heidelberg physicists, the atoms are trapped in a thin layer. The excitations can therefore only propagate in two spatial directions -- the space is two-dimensional. At the same time, the atomic cloud in the remaining two dimensions can be shaped in almost any way, whereby it is also possible to realise curved spacetimes. The interaction between the atoms can be precisely adjusted by a magnetic field, changing the propagation speed of the wavelike excitations on the Bose-Einstein condensate.

"For the waves on the condensate, the propagation speed depends on the density and the interaction of the atoms. This gives us the opportunity to create conditions like those in an expanding universe," explains Prof. Dr Stefan Flörchinger. The researcher, who previously worked at Heidelberg University and joined the University of Jena at the beginning of this year, developed the quantum field theoretical model used to quantitatively compare the experimental results.

Using the quantum field simulator, cosmic phenomena, such as the production of particles based on the expansion of space, and even the spacetime curvature can be made measurable. "Cosmological problems normally take place on unimaginably large scales. To be able to specifically study them in the lab opens up entirely new possibilities in research by enabling us to experimentally test new theoretical models," states Celia Viermann, the primary author of the "Nature" article. "Studying the interplay of curved spacetime and quantum mechanical states in the lab will occupy us for some time to come," says Markus Oberthaler, whose research group is also part of the STRUCTURES Cluster of Excellence at Ruperto Carola.

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Dark energy: Neutron stars will tell us if it's only an illusion

A huge amount of mysterious dark energy is necessary to explain cosmological phenomena, such as the accelerated expansion of the Universe, with Einstein's theory. But what if dark energy was just an illusion and general relativity itself had to be modified? A new SISSA study, published in Physical Review Letters, offers a new approach to answer this question. Thanks to huge computational and mathematical effort, scientists produced the first simulation ever of merging binary neutron stars in theories beyond general relativity that reproduce a dark- energy like behavior on cosmological scales. This allows the comparison of Einstein's theory and modified versions of it, and, with sufficiently accurate data, may solve the dark energy mystery.

For about 100 years now, general relativity has been very successful at describing gravity on a variety of regimes, passing all experimental tests on Earth and the solar system. However, to explain cosmological observations such as the observed accelerated expansion of the Universe, we need to introduce dark components, such as dark matter and dark energy, which still remain a mystery.

Enrico Barausse, astrophysicist at SISSA (Scuola Internazionale Superiore di Studi Avanzati) and principal investigator of the ERC grant GRAMS (GRavity from Astrophysical to Microscopic Scales) questions whether dark energy is real or, instead, it may be interpreted as a breakdown of our understanding of gravity. "The existence of dark energy could be just an illusion," he says, "the accelerated expansion of the Universe might be caused by some yet unknown modifications of general relativity, a sort of 'dark gravity'."

The merger of neutron stars offers a unique situation to test this hypothesis because gravity around them is pushed to the extreme. "Neutron stars are the densest stars that exist, typically only 10 kilometers in radius, but with a mass between one or two times the mass of our Sun," explains the scientist. "This makes gravity and the spacetime around them extreme, allowing for abundant production of gravitational waves when two of them collide. We can use the data acquired during such events to study the workings of gravity and test Einstein's theory in a new window."

In this study, published in Physical Review Letters, SISSA scientists in collaboration with physicists from Universitat de les Illes Balears in Palma de Mallorca, produced the first simulation of merging binary neutron stars in theories of modified gravity relevant for cosmology: "This type of simulations is extremely challenging," clarifies Miguel Bezares, first author of the paper, "because of the highly non-linear nature of the problem. It requires a huge computational effort -months of run in supercomputers -- that was made possible also by the agreement between SISSA and CINECA consortium as well as novel mathematical formulations that we developed. These represented major roadblocks for many years till our first simulation."

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Not all theories can explain the black hole M87*

As first pointed out by the German astronomer Karl Schwarzschild, black holes bend space-time to an extreme degree due to their extraordinary concentration of mass, and heat up the matter in their vicinity so that it begins to glow. New Zealand physicist Roy Kerr showed rotation can change the black hole's size and the geometry of its surroundings. The "edge" of a black hole is known as the event horizon, the boundary around the concentration of mass beyond which light and matter cannot escape and which makes the black hole "black." Black holes, theory predicts, can be described by a handful of properties: mass, spin, and a variety of possible charges.

In addition to black holes predicted from Einstein's theory of general relativity, one can consider those from models inspired by string theories, which describe matter and all particles as modes of tiny vibrating strings. String-inspired theories of black holes predict the existence of an additional field in the description of fundamental physics, which leads to observable modifications in the sizes of black holes as well as in the curvature in their vicinity.

Physicists Dr Prashant Kocherlakota and Professor Luciano Rezzolla from the Institute for Theoretical Physics at Goethe University Frankfurt, have now investigated for the first time how the different theories fit with the observational data of the black hole M87* at the centre of the galaxy Messier 87. The image of M87*, taken in 2019 by the international Event Horizon Telescope (EHT) collaboration, was the first experimental proof of the actual existence of black holes after the measurement of gravitational waves in 2015.

The result of these investigations: The data from M87* are in excellent agreement with the Einstein-based theories and to a certain extent with the string-based theories. Dr Prashant Kocherlakota explains: "With the data recorded by the EHT collaboration, we can now test different theories of physics with black hole images. Currently, we cannot reject these theories when describing the shadow size of M87*, but our calculations constrain the range of validity of these black hole models."

Professor Luciano Rezzolla says: "The idea of black holes for us theoretical physicists is at the same time a source of concern and of inspiration. While we still struggle with some of the consequences of black holes -- such as the event horizon or the singularity -- we seem always keen to find new black hole solutions also in other theories. It is therefore very important to obtain results like ours, which determine what is plausible and what is not. This was an important first step and our constraints will be improved as new observations are made."

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Timekeeping theory combines quantum clocks and Einstein's relativity

 A phenomenon of quantum mechanics known as superposition can impact timekeeping in high-precision clocks, according to a theoretical study from Dartmouth College, Saint Anselm College and Santa Clara University.

Research describing the effect shows that superposition -- the ability of an atom to exist in more than one state at the same time -- leads to a correction in atomic clocks known as "quantum time dilation."

The research, published in the journal Nature Communications, takes into account quantum effects beyond Albert Einstein's theory of relativity to make a new prediction about the nature of time.

"Whenever we have developed better clocks, we've learned something new about the world," said Alexander Smith, an assistant professor of physics at Saint Anselm College and adjunct assistant professor at Dartmouth College, who led the research as a junior fellow in Dartmouth's Society of Fellows. "Quantum time dilation is a consequence of both quantum mechanics and Einstein's relativity, and thus offers a new possibility to test fundamental physics at their intersection."

In the early 1900s, Albert Einstein presented a revolutionary picture of space and time by showing that the time experienced by a clock depends on how fast it is moving -- as the speed of a clock increases, the rate at which it ticks decreases. This was a radical departure from Sir Isaac Newton's absolute notion of time.

Quantum mechanics, the theory of motion governing the atomic realm, allows for a clock to move as if it were simultaneously traveling at two different speeds: a quantum "superposition" of speeds. The research paper takes this possibility into account and provides a probabilistic theory of timekeeping, which led to the prediction of quantum time dilation.

To develop the new theory, the team combined modern techniques from quantum information science with a theory developed in the 1980s that explains how time might emerge out of a quantum theory of gravity.

"Physicists have sought to accommodate the dynamical nature of time in quantum theory for decades," said Mehdi Ahmadi, a lecturer at Santa Clara University who co-authored the study. "In our work, we predict corrections to relativistic time dilation which stem from the fact that the clocks used to measure this effect are quantum mechanical in nature."

In the same way that carbon dating relies on decaying atoms to determine the age of organic objects, the lifetime of an excited atom acts as a clock. If such an atom moves in a superposition of different speeds, then its lifetime will either increase or decrease depending on the nature of the superposition relative to an atom moving at a definite speed.

The correction to the atom's lifetime is so small that it would be impossible to measure in terms that make sense at the human scale. But the ability to account for this effect could enable a test of quantum time dilation using the most advanced atomic clocks.

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Nobel Prize in Physics 2020: Discoveries about black holes

 

Abstract illustration of black hole.

The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics 2020 with one half to Roger Penrose, University of Oxford, UK, "for the discovery that black hole formation is a robust prediction of the general theory of relativity" and the other half jointly to Reinhard Genzel, Max Planck Institute for Extraterrestrial Physics, Garching, Germany and University of California, Berkeley, USA and Andrea Ghez, University of California, Los Angeles, USA "for the discovery of a supermassive compact object at the centre of our galaxy."

Black holes and the Milky Way's darkest secret

Three Laureates share this year's Nobel Prize in Physics for their discoveries about one of the most exotic phenomena in the universe, the black hole. Roger Penrose showed that the general theory of relativity leads to the formation of black holes. Reinhard Genzel and Andrea Ghez discovered that an invisible and extremely heavy object governs the orbits of stars at the centre of our galaxy. A supermassive black hole is the only currently known explanation.

Roger Penrose used ingenious mathematical methods in his proof that black holes are a direct consequence of Albert Einstein's general theory of relativity. Einstein did not himself believe that black holes really exist, these super-heavyweight monsters that capture everything that enters them. Nothing can escape, not even light.

In January 1965, ten years after Einstein's death, Roger Penrose proved that black holes really can form and described them in detail; at their heart, black holes hide a singularity in which all the known laws of nature cease. His groundbreaking article is still regarded as the most important contribution to the general theory of relativity since Einstein.

Reinhard Genzel and Andrea Ghez each lead a group of astronomers that, since the early 1990s, has focused on a region called Sagittarius A* at the centre of our galaxy. The orbits of the brightest stars closest to the middle of the Milky Way have been mapped with increasing precision. The measurements of these two groups agree, with both finding an extremely heavy, invisible object that pulls on the jumble of stars, causing them to rush around at dizzying speeds. Around four million solar masses are packed together in a region no larger than our solar system.

Using the world's largest telescopes, Genzel and Ghez developed methods to see through the huge clouds of interstellar gas and dust to the centre of the Milky Way. Stretching the limits of technology, they refined new techniques to compensate for distortions caused by the Earth's atmosphere, building unique instruments and committing themselves to long-term research. Their pioneering work has given us the most convincing evidence yet of a supermassive black hole at the centre of the Milky Way.

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Einstein's general relativity theory is questioned but still stands for now

Black hole illustration

More than 100 years after Albert Einstein published his iconic theory of general relativity, it is beginning to fray at the edges, said Andrea Ghez, UCLA professor of physics and astronomy. Now, in the most comprehensive test of general relativity near the monstrous black hole at the center of our galaxy, Ghez and her research team report July 25 in the journal Science that Einstein's theory of general relativity holds up.

"Einstein's right, at least for now," said Ghez, a co-lead author of the research. "We can absolutely rule out Newton's law of gravity. Our observations are consistent with Einstein's theory of general relativity. However, his theory is definitely showing vulnerability. It cannot fully explain gravity inside a black hole, and at some point we will need to move beyond Einstein's theory to a more comprehensive theory of gravity that explains what a black hole is."

Einstein's 1915 theory of general relativity holds that what we perceive as the force of gravity arises from the curvature of space and time. The scientist proposed that objects such as the sun and the Earth change this geometry. Einstein's theory is the best description of how gravity works, said Ghez, whose UCLA-led team of astronomers has made direct measurements of the phenomenon near a supermassive black hole -- research Ghez describes as "extreme astrophysics."

The laws of physics, including gravity, should be valid everywhere in the universe, said Ghez, who added that her research team is one of only two groups in the world to watch a star known as S0-2 make a complete orbit in three dimensions around the supermassive black hole at the center of the Milky Way. The full orbit takes 16 years, and the black hole's mass is about four million times that of the sun.

The researchers say their work is the most detailed study ever conducted into the supermassive black hole and Einstein's theory of general relativity.

The key data in the research were spectra that Ghez's team analyzed this April, May and September as her "favorite star" made its closest approach to the enormous black hole. Spectra, which Ghez described as the "rainbow of light" from stars, show the intensity of light and offer important information about the star from which the light travels. Spectra also show the composition of the star. These data were combined with measurements Ghez and her team have made over the last 24 years.

Spectra -- collected at the W.M. Keck Observatory in Hawaii using a spectrograph built at UCLA by a team led by colleague James Larkin -- provide the third dimension, revealing the star's motion at a level of precision not previously attained. (Images of the star the researchers took at the Keck Observatory provide the two other dimensions.) Larkin's instrument takes light from a star and disperses it, similar to the way raindrops disperse light from the sun to create a rainbow, Ghez said.

"What's so special about S0-2 is we have its complete orbit in three dimensions," said Ghez, who holds the Lauren B. Leichtman and Arthur E. Levine Chair in Astrophysics. "That's what gives us the entry ticket into the tests of general relativity. We asked how gravity behaves near a supermassive black hole and whether Einstein's theory is telling us the full story. Seeing stars go through their complete orbit provides the first opportunity to test fundamental physics using the motions of these stars."

Ghez's research team was able to see the co-mingling of space and time near the supermassive black hole. "In Newton's version of gravity, space and time are separate, and do not co-mingle; under Einstein, they get completely co-mingled near a black hole," she said.

"Making a measurement of such fundamental importance has required years of patient observing, enabled by state-of-the-art technology," said Richard Green, director of the National Science Foundation's division of astronomical sciences. For more than two decades, the division has supported Ghez, along with several of the technical elements critical to the research team's discovery. "Through their rigorous efforts, Ghez and her collaborators have produced a high-significance validation of Einstein's idea about strong gravity."

Keck Observatory Director Hilton Lewis called Ghez "one of our most passionate and tenacious Keck users." "Her latest groundbreaking research," he said, "is the culmination of unwavering commitment over the past two decades to unlock the mysteries of the supermassive black hole at the center of our Milky Way galaxy."

The researchers studied photons -- particles of light -- as they traveled from S0-2 to Earth. S0-2 moves around the black hole at blistering speeds of more than 16 million miles per hour at its closest approach. Einstein had reported that in this region close to the black hole, photons have to do extra work. Their wavelength as they leave the star depends not only on how fast the star is moving, but also on how much energy the photons expend to escape the black hole's powerful gravitational field. Near a black hole, gravity is much stronger than on Earth.

Ghez was given the opportunity to present partial data last summer, but chose not to so that her team could thoroughly analyze the data first. "We're learning how gravity works. It's one of four fundamental forces and the one we have tested the least," she said. "There are many regions where we just haven't asked, how does gravity work here? It's easy to be overconfident and there are many ways to misinterpret the data, many ways that small errors can accumulate into significant mistakes, which is why we did not rush our analysis."

Ghez, a 2008 recipient of the MacArthur "Genius" Fellowship, studies more than 3,000 stars that orbit the supermassive black hole. Hundreds of them are young, she said, in a region where astronomers did not expect to see them.

It takes 26,000 years for the photons from S0-2 to reach Earth. "We're so excited, and have been preparing for years to make these measurements," said Ghez, who directs the UCLA Galactic Center Group. "For us, it's visceral, it's now -- but it actually happened 26,000 years ago!"

This is the first of many tests of general relativity Ghez's research team will conduct on stars near the supermassive black hole. Among the stars that most interest her is S0-102, which has the shortest orbit, taking 11 1/2 years to complete a full orbit around the black hole. Most of the stars Ghez studies have orbits of much longer than a human lifespan.

Ghez's team took measurements about every four nights during crucial periods in 2018 using the Keck Observatory -- which sits atop Hawaii's dormant Mauna Kea volcano and houses one of the world's largest and premier optical and infrared telescopes. Measurements are also taken with an optical-infrared telescope at Gemini Observatory and Subaru Telescope, also in Hawaii. She and her team have used these telescopes both on site in Hawaii and remotely from an observation room in UCLA's department of physics and astronomy.

Black holes have such high density that nothing can escape their gravitational pull, not even light. (They cannot be seen directly, but their influence on nearby stars is visible and provides a signature. Once something crosses the "event horizon" of a black hole, it will not be able to escape. However, the star S0-2 is still rather far from the event horizon, even at its closest approach, so its photons do not get pulled in.)

Ghez's co-authors include Tuan Do, lead author of the Science paper, a UCLA research scientist and deputy director of the UCLA Galactic Center Group; Aurelien Hees, a former UCLA postdoctoral scholar, now a researcher at the Paris Observatory; Mark Morris, UCLA professor of physics and astronomy; Eric Becklin, UCLA professor emeritus of physics and astronomy; Smadar Naoz, UCLA assistant professor of physics and astronomy; Jessica Lu, a former UCLA graduate student who is now a UC Berkeley assistant professor of astronomy; UCLA graduate student Devin Chu; Greg Martinez, UCLA project scientist; Shoko Sakai, a UCLA research scientist; Shogo Nishiyama, associate professor with Japan's Miyagi University of Education; and Rainer Schoedel, a researcher with Spain's Instituto de Astrofsica de Andalucia.

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