Light experiences a time dilation

REVOLUTIONARY

Albert Einstein recognized space, time, matter and energy as a unit. That not only turned physics upside down.

When Albert Einstein died in Princeton on April 18, 1955, the next day the Washington Post published a cartoon by Herb Block showing a multitude of worlds in desolate space. Only one of these cosmic specks of dust stands out: It has a huge sign with the inscription "Albert Einstein lived here". For Armin Hermann, who taught at the University of Stuttgart as a professor for the history of science and technology until 2001, this caricature hits "despite all the exaggeration something essential". And he emphasizes: “Whether we are physicists or not - we all have to deal with Einstein. Essentially stimulated by him, science has brought to light deep insights into the forces at work in the macrocosm and microcosm, and in doing so also achieved a completely new understanding of the essence of human knowledge. "

Einstein's contributions are varied and influential. The following pages deal with two highlights: the Special Theory of Relativity (SRT), which Einstein set up in 1905 in Bern, where he worked as a third-class technical expert at the Federal Patent Office because he was happy to have found a job at all, and the general theory of relativity (ART), which he completed in November 1915 in Berlin, where he had been appointed to the Prussian Academy of Sciences a year earlier.

With the SRT, Einstein linked space with time (as the fourth dimension) and recognized the relativity of time spans and distances. He also discovered that the speed of light is absolutely constant for all observers and that mass and energy are equivalent. In the ten field equations of the GTR, Einstein then mathematically linked space-time with matter and energy: Space and time are therefore not the passive stage of events, but are influenced by bodies and even by light - and vice versa. Therefore, according to Einstein, gravitation is actually not a force, but rather a property of spacetime geometry - the consequence of spacetime “curved” by mass. Because mass slows down time (relative to a reference system in a weaker gravitational field), deforms space and forces light rays onto the crooked path.

Experiments have meanwhile been brilliantly confirmed by SRT and ART. Even so, the theories still seem incomprehensible or even paradoxical to many people. This is also shown by the numerous letters from readers to Bild der Wissenschaft. After the great response to our introduction to the fundamentals of the Big Bang Cosmology (Bild der Wissenschaft 11/2009), you moved the editorial staff to present important aspects of the theory of relativity in a coherent manner, as far as the Space in a magazine is allowed - and true to Einstein's motto that things should be explained as simply as possible, but not more simply.

Because although SRT and ART are still considered very exotic, everyday life can hardly be imagined without them: Without them we would have neither navigation devices in the car nor antimatter in medical diagnostics or nuclear power plants for electricity generation. Our view of the world would also be completely different: Without special and general relativity, we would not be able to understand why the sun shines, how mechanical and electromagnetic processes fit together, how elementary particles behave, why space and time belong together and are able to vibrate, what it is with blacks Holes and also with space, which has been expanding since the Big Bang. ■

by Rüdiger Vaas

The light wall is absolute

The kinetic energy E of a body with mass m depends on its speed v. According to the special theory of relativity, E and m become infinite when the body approaches the speed of light c, so that it can never reach or even exceed the "light wall". Normal matter cannot therefore be accelerated to faster than the speed of light. In everyday life, in which classical mechanics approximately apply, the "relativistic increase in mass" of moving objects does not play a role. If you speed on the autobahn at 200 kilometers per hour, you only gain 10-12 percent of the mass. And even with a double supersonic flight it is only 10-10 percent.

What does the curvature of spacetime reveal?

The fact that the theory of relativity not only overcame the boundaries of knowledge, but also the borders of the countries became clear in the period after the First World War: Isaac Newton's theory of gravity was overthrown in nationalist Germany. But it was an Englishman, Arthur Stanley Eddington, who made the message from Berlin known worldwide and triumphantly confirmed Einstein's theory for the first time. Eddington knew Einstein's prediction of the deflection of light in the gravitational field and decided to check it out. A total solar eclipse on May 29, 1919 gave him the opportunity to do so. Eddington photographed the sky from Principe Island off the coast of Spanish Guinea and determined the position of the stars near the sun. The same thing happened in Sobral, Brazil, on another expedition led by Andrew Crommlin of the Greenwich Observatory. Result: The measured light deflection of 1.98 and 1.61 (plus / minus 0.30 arc seconds each) was in agreement with Einstein's prediction - and significantly greater than Newton's theory of gravity required. The researchers announced this on November 6, 1919 at a meeting of the Royal Astronomical Society, after preliminary results had been circulated a few weeks beforehand. When the London Times reported in detail the next day under the title “Revolution in Science”, Einstein became a star almost overnight. "This result is one of the greatest achievements of human thinking," commented the chairman of the meeting, Joseph John Thomson, who received the 1906 Nobel Prize in Physics for his discovery of the electron.

GHOST IMAGES IN THE SKY

It is true that the measurement errors were still large, and there would not have been much missing, then Einstein's prediction would have failed. But since then, numerous measurements have confirmed the deflection of light in the gravitational field. In 1991, for example, astronomers demonstrated the deflection of light with a measurement inaccuracy of 0.2 percent by precisely determining the position of distant radio galaxies at very different locations in the sky. And in 1997 an evaluation of the precise star position determinations of the European astrometry satellite Hipparcos yielded a similarly good confirmation (0.3 percent).

The curvature of spacetime can also cause the light not only to get on the wrong path, but also to split it up and, in extreme cases - in the vicinity of black holes - even bend it back by 180 degrees. The split leads to ghosting in the sky. With such a gravitational lensing effect, a galaxy in the foreground influences the path of the light of a distant primordial galaxy behind it in such a way that it can be seen twice, four times or more often, is sometimes distorted like an arc and also often appears brighter. If the foreground and background galaxies are exactly one behind the other as seen by the observer, the light of the background galaxy is fanned out to form a so-called Einstein ring. Like a cosmic mirage, it surrounds the foreground galaxy, which acts like a scattering lens. Several hundred such ghost images have been photographed since 1979, including several Einstein rings. Astronomers can even use it to determine distances.

Albert Einstein had described their existence in principle in an article published in 1936, but never dreamed that they could ever be observed. In fact, he had discovered the gravitational lensing effect as early as 1912. This only became known in 1997 when science historians Jürgen Renn and Tilmann Sauer from the Max Planck Institute for the History of Science in Berlin and John Stachel from Boston University analyzed his notebooks. Einstein's early discovery shows the importance of qualitative thinking for the development of scientific theories: Einstein was able to set up the simple model and draw his conclusions before he had fully formulated the GTR. "More important than the mathematical elaboration was his approach of bringing very different areas of physics into a conceptual context, in this case the theory of gravity and geometric optics." ■

Untitled

When Einstein gave his lectures, his driver always sat in the back of the hall. One day he thought that he could give a lecture himself, because he had heard it so often. Einstein took him at his word: they exchanged clothes, and the driver did his job flawlessly while Einstein listened secretly. Then a listener asked a difficult question about a tricky detail. The driver replied: "The answer is so simple that it can be given by my driver, who is sitting here in the hall."

(The joke is a popular one - but it's far too good to be true.)

Untitled

Albert Einstein's theory of relativity has always been considered difficult to understand. According to a widespread but not necessarily true anecdote, the physicist Ludwik Silberstein once said to Arthur Eddington, who measured the light deflection predicted by Einstein in the gravitational field, after a lecture: "Professor Eddington, you must be one of the three people in the world, who really understand the general theory of relativity. "When Eddington was silent, Silberstein continued:" Don't be so humble! "To which Eddington:" On the contrary - I wonder who the third person is. "

Silberstein, who came from Poland, had published a textbook on special relativity as early as 1914 and supplemented it ten years later with a description of general relativity and regularly lectured on it. In 1935 he published an article in which he believed to prove an error in the ART. After a debate with Einstein, he even turned to the press. But he wasn't right.

Untitled

“I admire the general theory of relativity like a work of art,” said Max Born, who received the Nobel Prize in Physics 32 years after his friend Albert Einstein. The theory of relativity is now the best-confirmed scientific theory. How it turned the conception of space, time, matter, energy and gravity inside out and shook the classic building of physics, is explained by Bild der Wissenschaft based on the fundamental questions in this cover story.

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revolutionary

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What is new about the special theory of relativity?

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Why are space and time relative?

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How can time expansion and length contraction be demonstrated?

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What does E = mc² mean?

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Why are light-fast flights through space impossible?

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How did Einstein come up with general relativity?

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What does the curvature of spacetime reveal?

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What are gravitational waves?

What is new about the special theory of relativity?

Max Planck emphasized the philosophical value of the special theory of relativity, which goes far beyond its physical value. The Nobel laureate in physics was one of the first to understand the importance of Einstein's epoch-making insight. The then 26-year-old Albert Einstein, who was far away from the academic world as an unknown technical expert III. Class and "venerable federal ink shit" (Einstein about himself) examined applications at the patent office in Bern, had published in the Annalen der Physik a paper in less than six weeks with the title "On the electrodynamics of moving bodies" in 1905. It led to a completely new understanding of space and time.

Rest or run? No matter!

The starting point of Einstein's considerations was a fundamental contradiction between two well-confirmed physical theories - mechanics, largely developed by Galileo Galilei and Isaac Newton, on the one hand, and electromagnetism, on the other, as it was completely formulated by James Clerk Maxwell around 1860 after preliminary work by others. The contradiction is that the two theories contain different “conversion rules” for coordinate transformations - that is, for the description of physical processes from the different perspectives of observers who move relative to one another. This is of great importance because the laws of nature do not depend on the random sensibilities of scientists. Newton therefore postulated an absolute time and an absolute space: clocks and linear scales would have to show the same conditions everywhere in the universe and from the perspectives of all observers, regardless of their speed. So whether someone almost runs his lungs out in the 100-meter run or lies motionless on the holiday beach should not have any influence on the physics.

But Maxwell's equations look different, depending on whether they are formulated in a stationary or a moving frame of reference. The dormant system was still considered fundamental at the beginning of the 20th century. It was linked to a hypothetical medium in which the electromagnetic waves were supposed to propagate like sound waves in the air. This medium, called “ether”, should rest in Newton's absolute space, as it were. Accordingly, the speed of light rays on earth would have to differ - depending on the direction in which they race through the ether. Because the earth moves around the sun at a certain speed, and the light would sometimes spread with it and sometimes, half a revolution later, run in the opposite direction. However, such differences have never been measured.

For Einstein, the contradictions and inconsistencies were "unbearable". And he found that they disappear when one gives up the assumption of an ether, an absolute time and an absolute space. Instead, he made two other requirements that have proven themselves to this day:

· The principle of relativity: The physical laws have the same form in all non-accelerated reference systems.

· The constancy of the speed of light: The speed of light in a vacuum is the same in all frames of reference.

This made it unnecessary to assume that the “resting” frame of reference was somehow fundamental or something special. And a single conversion rule was sufficient for all coordinate transformations - for both mechanical and electromagnetic processes. The SRT created great uniformity and dealt with all problems in one fell swoop. Even more: it revealed a fundamental connection not only between matter and energy, but also between space and time. Einstein saved both as absolute and independent categories and, as it were, merged them into space-time. "From hour‘ on, space and time should completely sink into shadow, and only a union of the two should preserve independence, "was the classic interpretation of the mathematician Hermann Minkowski in 1908, with whom Einstein had studied in Zurich.

It's not all RELATIVE

The price for this theoretical breakthrough, which experiments have since confirmed and corroborated many times, is a new concept of simultaneity: There is no absolute time, but rather proper times dependent on the reference system. And what appears simultaneously to one observer - say two independent events in the starry sky - is not necessarily simultaneous to another observer who is in a different place at the same speed or who is moving in the same place at a completely different speed. Spatial and temporal distances are not universal, but relative: time can, as it were, stretch and space shorten. This completely contradicts our everyday experience. But not everything is relative. The speed of light, which Einstein recognized as constant in contrast to all relative locations, movements and speeds, is independent of the reference system. It is a universal natural constant that has the same value everywhere, namely 299,792.458 kilometers per second in a vacuum. It is absolutely true, and it is the fundamental link between space, time, matter and energy. In this respect, the theory of relativity could also have been called “absolute theory”. ■

Why are space and time relative?

Time dilation is one of the most confusing conclusions from the theory of relativity: time passes more slowly for fast moving clocks than for slow or motionless clocks. (At that time, Einstein could not have known that, strictly speaking, nothing is at rest because space is expanding, and it does not play a role for the SRT either.) Incidentally, such a time expansion can also be caused by gravity: clocks in the gravitational field tick more slowly than such isolated in space. But this is an effect of general, not special, relativity.The time dilation in rapid movements has caused heated discussions.

The phenomenon is often illustrated with the so-called twin paradox: According to this, an astronaut racing through space at high speed would have aged much less when he returned to Earth than his twin brother who stayed at home. Assume that a 27-year-old astronaut flies at 98 percent of the speed of light to the star Vega, which is around 25 light-years away, and back again. Then 10 years have passed on his return, so he is 37 years old - while his twin brother, who remained on earth, has already celebrated his 77th birthday and is now 40 years older than the astronaut. (The example is simplified because the time-consuming acceleration and braking phases were omitted.) At 98 percent speed of light, the time in the spaceship passed considerably more slowly than on earth.

The TWIN PARADOXON is false

This age difference is irritating enough, but it is a measurable fact. It becomes paradoxical when one argues that the twin who remained on earth also moved away from their brother at 98 percent of the speed of light - after all, the special theory of relativity teaches that no reference system is preferred. Seen in this way, the spaceman from whom the earth moved would have to be 40 years older than his brother when the earth returned to him.

But that is wrong - as is the whole argument. Because the twins' movements must not be viewed as symmetrical. Only reference systems that are at rest or move at a constant speed are equal. But in the example, the spaceman first speeds up, then flies a curve at Wega to return, and finally brakes again near the earth. Such accelerated movements are not an object of the special, but of the general theory of relativity. However, if two astronauts were to fly past each other at high constant speed and compare their clocks several times, then they could both actually find that the other clock is ticking more slowly.

JOURNEY INTO THE FUTURE

In principle, time dilation can even be used for a journey through time into the distant future. For example, if you were to fly to a star 500 light-years away at up to 99.9992 percent of the speed of light with the acceleration and braking pressure of 1 G - this corresponds to the force of gravity - you would only have aged almost 25 years while on the Earth 1000 years would have passed. A way back to their own youth would of course be blocked. So if you are planning a trip into the future, you should submit your tax return beforehand - otherwise the terrible impatience of the tax office awaits you when you return.

The length contraction, which is also a consequence of the constant speed of light, is complementary to time dilation. Because like time, distance is also relative. In the direction of movement, all scales are shortened by the same factor that time expands. For example, if an astronaut flies to Vega at 98 percent the speed of light, he is on the way for 5 years and has covered a distance of 5 times 0.98 light years, i.e. 4.9 light years, in his reference system, while from the perspective of the earth it is 25 light years .

The length contraction was described by George FitzGerald before Einstein in 1889 and Hendrik Antoon Lorentz in 1892. These physicists also tried to resolve the formal contradictions between classical mechanics and electromagnetism. However, they were still caught up in pre-relativistic thinking and wanted to explain the phenomenon through velocity-dependent forces in the ether between the atoms. In contrast, the relativity theory's length contraction does not mean that a meter stick will shorten, as if it were being compressed. Rather, the length contraction is a matter of the - thoroughly "objective" - ​​reference system. So if you want to lose weight, you can't just whiz through the world at almost the speed of light and trust that the length contraction will make your bulbous belly disappear. ■

What does E = m c2 mean?

Einstein discovered in 1905 that energy E and mass m are two sides of the same coin because they are equivalent over the square of the speed of light c. A few months later he added a three-page addendum to his article “On the electrodynamics of moving bodies”, which was published in the Annalen der Physik and which founded the special theory of relativity, which was only named in 1915, the headline of which he cautiously formulated as a question: “Is inertia one Body depends on its energy content? ”In this, Einstein showed that an object that radiates energy also loses mass. E = mc2 - he used this notation later - only indicates the rest mass of the body. If it moves with momentum p, the equation is: E2 = (mc2) 2 + (pc) 2. (By the way, the c stands for “constant” - or for “celeritas”, Latin for “speed”). The astonishing consequence: mass is nothing more than a certain form of energy.

"DO NOT THE LORD LAUGH AT IT"

Einstein did not come to this result through experimental data, but through a mathematical derivation. “The thought is funny and captivating; but whether the Lord is laughing about it and fooling me, I cannot know ”, he wrote to his friend Conrad Habicht in the fall of 1905. Einstein hoped, however, that the validity of the formula could be tested when measuring radioactive decay. "It cannot be ruled out that a test of the theory will succeed in bodies whose energy content is highly variable (e.g. with the radium salts)," he wrote at the end of his article.

Confirmation came in 1932 when John Cockcroft and Ernest Walton at the Cavendish Laboratory in Cambridge used the world's first particle accelerator to shoot protons at lithium atoms, creating alpha particles. The balance was only correct if the energy was included in addition to the initial and final product masses. Shortly afterwards, Irène and Frédéric Joliot-Curie observed in Paris that particles can arise from high-energy radiation. So Einstein was right: energy and mass can transform into one another and are not essentially different at all.

This also makes it understandable that a body in motion has energy - and cannot be accelerated to the speed of light, because this would require an infinite amount of energy and it would be infinitely heavy. The mass of an aircraft that flies at almost 1000 kilometers per hour is, for example, 0.0000000001 percent greater than when standing at the gate. But bodies at rest also contain energy. The mass of a brick weighing one kilogram, for example, could theoretically supply a 100 watt lightbulb with electricity for 30 million years. However, this energy can never be extracted in practice.

That E = mc² still has a very real meaning - this is also a confirmation of the special theory of relativity - became evident at the latest in 1945 with the detonation of the first atomic bombs. And nuclear power plants demonstrate it every day: The fission of heavy atomic nuclei releases large amounts of energy. In the case of the bombs that killed over 100,000 people in Hiroshima and Nagasaki, only about one gram of uranium or plutonium was used. The reverse process, the merging of light atomic nuclei, is also an enormous source of energy. This was first used destructively in the form of the hydrogen bomb in 1952, but has not yet been implemented in a constructive manner in the form of nuclear fusion reactors.

Nature is still there: our sun has been shining for 4.6 billion years due to the fusion of hydrogen to helium. 1038 nuclear fusion processes take place in its 15.7 million degree hot center every second. In the process, 500 million tons of hydrogen are converted - and around 4 million tons of this are converted into energy, 0.7 percent of the total mass involved. That would meet mankind's current energy needs for a million years. Within 45 million years the sun will be “lightened” by the mass of the earth due to nuclear fusion and E = mc². Of this wasteful annihilation - the luminosity of the sun is 3.8 · 1026 watts - on average only 1367 joules of energy per second and square meter arrive on earth - but that is enough to drive all life processes here. In this respect, even our existence cannot be understood without the theory of relativity. ■

How can time expansion and length contraction be demonstrated?

The time dilation and the length contraction are not illusions, but measurable effects. This is shown by muons, for example. They arise, among other things, through reactions of high-energy particles of cosmic radiation (predominantly protons that are almost light-fast) with atomic nuclei in the earth's atmosphere. These muons, the heavy siblings of electrons, can be detected with special detectors. This is surprising because they are unstable and disintegrate with a half-life of only 1.5 millionths of a second. Since they are formed by nuclear reactions at a height of 30 kilometers, they can - although they are almost as fast as light - cover a mere 450 meters in 1.5 millionths of a second. After 30 kilometers, almost all of them should have disintegrated. But this is not the case for terrestrial observers, because the time dilation greatly extends the lifespan of the muons. To put it another way: Due to their high speed, the path for the muons is greatly shortened. From the perspective of their reference system, they do not travel 30 kilometers to the surface of the earth, but only a few hundred meters.

Frenzy near Geneva

At the European Center for Particle Physics CERN near Geneva, the time dilation of muons was measured directly for the first time in 1976. The physicists created muons there, which rushed through a storage ring at 99.94 percent of the speed of light. Their half-life was 44.6 millionths of a second - 30 times the resting value. The result is consistent with the prediction of the SRT (measurement uncertainty: 0.2 percent). In the meantime, particles at CERN are accelerated much closer to the speed of light - with a correspondingly life-extending effect. If you could do that to people born when Stonehenge was built, they would still be children now. The length contraction is also noticeable in particle accelerators. Physicists have to take this into account when, for example, they shoot gold or lead cores at one another in order to briefly achieve physical conditions in the collision zone such as those that prevailed in space less than a billionth of a second after the Big Bang (Bild der Wissenschaft 2/2009, " When space was fluid "). The heavy nuclei, which are almost as fast as light, no longer appear spherical, but rather flat like flounder due to the contraction in length, which increases the collision front and has measurable effects. ■

MORE ON THE SUBJECT

READ

Generally understandable brief introductions: Thomas Bührke E = mc² dtv, Munich 1999, € 8.90

Domenico Giulini Special Theory of Relativity Fischer, Frankfurt am Main 2004, € 8.90

Claus Kiefer Gravitation Fischer, Frankfurt am Main 2003, € 8.90

Black holes, time travel, faster than light speed and quantum gravity: Rüdiger Vaas tunnel through space and time cosmos, Stuttgart 2010, € 19.95

Understanding the theory of relativity with the help of middle school mathematics: Gottfried Beyvers, Elvira Krusch Small 1 x 1 of the theory of relativity Springer, Heidelberg 2009, € 24.95

Einstein's life and work: Michio Kaku Einstein's Cube Piper, Munich 2010, € 19.95

Jürgen Neffe Einstein Rowohlt, Reinbek 2007, € 9.95

Thomas Bührke Albert Einstein dtv, Munich 2004, € 10, -

Scientific biography of Einstein: Abraham Pais The Lord God is refined ... Spectrum Akademischer Verlag Heidelberg 2000, € 14.95

INTERNET

Comprehensive introduction to the theory of relativity: www.einstein-online.info

Einstein Archive of the Hebrew University of Jerusalem: www.alberteinstein.info

Einstein's impact to this day: www.aip.org/history/einstein

Experiments for Einstein

Numerous experiments and astronomical observations have verified and very precisely confirmed various effects that are described and predicted by the special and general relativity theory:

Michelson-Morley experiment: The speed of light is constant, even on small scales, and is independent of the movement and direction of movement of the reference system in a vacuum, 299,792.458 kilometers per second.

Time dilation: The faster a system moves relative to another, the more its time is stretched - that is, the slower it passes.

Length contraction: bodies that are almost as fast as light appear shortened in the direction of movement.

Turning away effect: objects that are almost as fast as light appear deformed.

Optical Doppler Effect: The wavelengths of light appear compressed or stretched when an object approaches or moves away from the observer.

Relativistic aberration: Fast particles emit radiation primarily in the direction of movement and therefore glow particularly intensely when viewed from a certain angle.

Equivalence of mass and energy: In nuclear reactions (fission, fusion, matter-antimatter annihilation), matter is converted into energy according to the formula E = m c².

Relativistic increase in mass: the faster an object moves, the more energy it requires to accelerate.

Equality of inert and heavy mass: very precisely confirmed for macroscopic and microscopic objects.

Perihelion of the planets: The point of a planetary orbit closest to the Sun shifts slightly in the plane of the orbit with each revolution.

Lunar Laser Ranging: Laser beams from the earth, which are reflected by mirrors on the moon, measure the increase in the distance to the moon with centimeter precision and check various relativistic parameters.

Light deflection in the gravitational field: mass changes ("bends") the geometry of the room.

Shapiro effect: light needs a little more time for the slightly curved path in the gravitational field than for the straight path.

Lense-thirring effect: A rotating body drags the space-time surrounding it with it when it rotates. This has been measured on the earth and on black holes.

Gravitational redshift: photons lose energy in the gravitational field.

Time dilation in the gravitational field: under the influence of gravity, clocks tick more slowly.

Gravitomagnetic effects: They arise from the rotation of masses and are analogous to magnetic forces.

Gravitational lens effect: gravity can not only deflect light, it can even simulate double and multiple images or "Einstein rings" from distant light sources.

Microlensing: In addition, gravitational lenses cause short-term light amplification.

Gravitational waves: They are created by rotating, colliding or collapsing masses. The indirect detection was successful in double pulsars. Direct measurements are currently being attempted.

Black holes: there is a lot of independent evidence for them.

Cosmological: Big Bang, expanding space, cosmological constant

How relative is the time?

According to the theory of relativity, clocks move more slowly in a gravitational field and when moving quickly. These two effects can be measured with high-precision atomic clocks based on the relative frequency changes and also play a decisive role in satellite navigation (GPS). At an altitude of 9,550 kilometers, the gravitational and speed effects just balance each other out. The clocks on the International Space Station lag behind the Earth, while the clocks on the GPS and geostationary satellites move ahead.

Why are light-fast flights through space impossible?

In the theory of relativity, 1 plus 1 is not necessarily 2. At least not when it comes to speeds that are greater than the police allow. In our everyday life, the relative speed vrel of two objects results from the addition of their individual speeds v1 and v2. The following applies: vrel = v1 + v2 (when moving in the opposite direction, a number is negative). Not so at speeds close to light - otherwise, for example, the laser beam fired by a spaceship that is almost as fast as light would have to be almost twice the speed of light. However, this is not the case according to the SRT. Rather, a relativistic addition formula comes into play: vrel = (v1 + v2) / (1+ (v1v2 / c2)). Only if v1 and v2 are small relative to c does the usual sum result as a limit value. The road traffic regulations are therefore not in danger, and you can hit your opponent in the face of your opponent even without studying the SRT.

Other everyday variables also appear in a new light due to the theory of relativity. Mathematically, this is expressed using a relativistic factor called the Lorentz or Gamma factor. This factor has a stronger effect the closer a speed v comes to the speed of light c and amounts to g = 1 / (1 - v2 / c2). The time dilation and length contraction can be calculated with g: A period of time expands by the gamma factor, and a distance is shortened by its reciprocal value, i.e. by 1 / g.

The gamma factor affects not only space and time, but also mass and energy. That's the bad news for science fiction fans who'd love to whiz spaceships across the galaxy. Because the energy expenditure for an acceleration does not increase linearly, but exponentially. Bodies with a rest mass can never be brought to the speed of light, because this would require an infinite amount of energy. This has to do with the relativistic mass increase that Einstein discovered: In addition to the rest mass m, there is also the relativistic mass g m of an object in a given frame of reference. The mass of a particle increases with its velocity v by the factor 1 / (1 - v2 / c2).

INCREASE WITH ENERGY

An astronaut who weighs 80 kilograms in bed at home would therefore have a mass of more than half a ton if he were racing through space at 99 percent the speed of light. Nevertheless, he would not feel heavier, because it would not be his heavy mass that increases, but his inert mass, which in a way counteracts the acceleration. (However, why one feels relatively heavy in bed when the alarm clock goes off in the morning cannot be explained by the theory of relativity either.) This makes flights through the Milky Way that are almost as fast as light difficult. For example, in order to achieve a tenfold time expansion relative to earth, corresponding to over 99 percent of the speed of light, in addition to a payload mass of around 1.25 tons with which you want to return, you would have to carry over 243,000 tons of fuel as take-off mass - and that only applies for a hypothetical photon rocket that converts all fuel into light and thus has the maximum possible outflow speed for the thrust. That is utopian, if not impossible in principle. For comparison: the Saturn V rockets that people used to take off to the moon had a mass of around 2,700 tons.

The gamma factor also plays a major role in the world of particle physics, and the relativistic increase in mass is even part of the everyday business of researchers. If, for example, protons are accelerated to 99.999999 percent of the speed of light in the LHC (Large Hadron Collider) near Geneva, they are 7,000 times heavier than at rest. At DESY (German Electron Synchrotron) in Hamburg, electrons were even brought up to such high speeds that their mass increased 55,000 times. ■

What are gravitational waves?

As Einstein recognized in 1916, analogous to light waves, there must also be gravitational waves. The name goes back to a work by the French mathematician Henri Poincaré from 1905. It is based on an idea by the Dutch physicist Hendrik Antoon Lorentz five years earlier. But it was not until the ART that it could be brought into a mathematical form and formulated as a physically testable hypothesis. Einstein found the decisive description - the quadrupole formula - in 1918. In 1937 he turned to the subject again.

Gravitational waves do not consist of electromagnetic radiation, but rather of vibrations of space-time. They are extremely weak periodic compressions and expansions of spatial and temporal intervals. A typical value is a frequency of around 1 kilohertz. Gravitational waves arise when masses revolve around one another, collide with one another or collapse. Even with planets, these ripples in space-time carry away a tiny part of the kinetic energy. On earth, for example, this is around 200 joules per second. This results in a gradual shrinking of the radius of the orbit. For planets this only becomes relevant when the universe is billions by billions of years older than it is today, but with much more massive objects in space it is already leading to catastrophic collisions.

The best indirect indication of the existence of gravitational waves as well as the first application example for relativistic effects of strong gravitational fields is an exotic object 21,000 light years away in the constellation eagle named PSR 1913 + 16. Joseph Taylor and Russell Hulse discovered it with the Arecibo radio telescope in Puerto Rico in 1974. In 1993 they received the Nobel Prize in Physics for this. PSR 1913 + 16 is a system of two neutron stars, which alternately orbit each other every 7 hours and 45 minutes on highly elliptical orbits. Neutron stars are the collapsed cores of burned-out giant stars, the outer shells of which exploded into space as supernovae. One of the two star corpses of PSR 1913 + 16 is a pulsar, whose radio radiation periodically sweeps over our solar system like the light cone of a lighthouse and can therefore be measured. The pulsar rotates around 17 times per second. With the Arecibo telescope, the arrival times of the radio signals could be determined with an accuracy of around 20 millionths of a second - the precision has now been increased tenfold. The regularity of their “pulse sequences” make pulsars into highly precise “clocks”. This makes it possible to use them to test the subtle effects of general relativity. In addition to five classic parameters such as orbital eccentricity and period, which are now known with an accuracy of better than 1 to 1 million, eight different relativistic measured variables can be determined - and this has now been the case for more than three decades. This made it possible for the first time to test the ART for strong gravitational fields. Result: The measurements are in excellent agreement with the predictions.

SPIRAL OF DESTRUCTION

More importantly, it was shown that the orbital period of PSR 1913 + 16 decreases by about 75 millionths of a second per year. That means: The two celestial bodies dance faster and faster around each other in an increasingly narrow spiral path. This shrinks by more than 3 millimeters per orbit (or by around 3.5 meters every earth year), so that the two neutron stars will collide with each other in about 300 million years. The reason for the decrease in orbital velocity is that accelerated masses radiate energy in the form of gravitational waves - analogous to the emission of electromagnetic radiation when forces act on charged particles.

A direct measurement of the gravitational waves is still pending. It would open a new window to space. Physicists are on the verge of this, because the gravitational wave detectors are now so sophisticated that it is only a matter of time before the first vibrations of space-time can be caught: If tomorrow the light of a new star explosion should reach us somewhere in the Milky Way, then it will the highly sensitive gravitational wave detectors LIGO (Laser Interferometer Gravitational Wave Observatory) in the USA and GEO600 near Hanover register this cosmic vibration. ■

How did Einstein come up with general relativity?

“I was sitting on my armchair in the Bern patent office when the following thought suddenly occurred to me: When a person is in free fall, they cannot feel their own weight. I was amazed. That simple thought made a deep impression on me. It drove me in the direction of a theory of gravitation. "In 1922 Albert Einstein told in a lecture at the Japanese University of Kyoto, how he had written in November 1907 in an overview article about the consequences of the SRT and recognized" that all natural phenomena are involved Exception of the law of gravitation in the terms of the special theory of relativity could be represented. I felt a deep longing to see the reason for it. ”With his idea at the patent office, Einstein had“ the happiest thought ”of his life. This is how he put it in a review for the magazine Nature in 1920, but it was not printed because it seemed too long to the editors.

“For an observer who is in free fall from the roof of a house, there is no gravitational field - at least in his immediate vicinity. If the falling observer drops some other bodies, then they are in a state of rest or uniform movement in relation to him, ”continued Einstein at the time. And he wrote: "The experimentally proven independence of the acceleration of gravity is a strong argument for the fact that the postulate of relativity must also be extended to coordinate systems that are in non-uniform motion to one another."

Heavy makes you sluggish

In doing so, Einstein went beyond the scope of the SRT, because what is “special” about the SRT is that it only describes special reference systems: those that are uniform. It does not deal with accelerations and the effects of gravity. That these are in principle the same was Einstein's basic idea in Bern. He postulated what he called the equivalence principle, for which there is still no physical explanation, although experiments have confirmed the principle with ever greater accuracy. Einstein made it the starting point of the ART: The heavy mass in the gravitational field, measurable, for example, with a spring balance, and the inert mass that opposes acceleration, are the same size. "The general theory of relativity owes its origin to the fact of experience of the numerical equality of the inert and the heavy mass of bodies," said Einstein. In fact, a physicist in a closed room would not be able to find out whether the sandwich that falls from the breakfast table to the floor (of course with the butter side first ...) is doing this because of gravity - or because the room is actually a cabin in a spaceship, which is constantly accelerated against the direction of fall of the sandwich.

The reverse also turns out to be a principle: Far from any source of gravity, one is weightless - but also in free fall, if, for example, the line of an elevator car breaks. This effect is used in parabolic flights, for example for astronaut training and microgravity research, by allowing an aircraft to sag for 10 to 20 seconds. The result is a brief weightlessness - a very bearable lightness of being, as the author experienced firsthand (Bild der Wissenschaft 5/2006, “Flying high in a crash”). In fact, astronauts in Earth orbit, for example in the International Space Station, are not weightless because they are flying through space. The earth's gravity is still quite strong at an altitude of 400 kilometers. Rather, the astronauts float around because they are, as it were, in permanent free fall - in a continuous circular fall around the globe.

Einstein drew an astonishing conclusion from the equivalence principle: gravity should influence rays of light. On the one hand, it should reduce their frequency ("gravitational redshift"), on the other hand, it should deflect the path of the rays when they pass a heavy body. Einstein thought the effect was far too weak to be able to measure it.

GRAVITATION Bends the light

It was not until 1911 that he dealt with the subject again, meanwhile as a physics professor in Prague. In his article "About the Influence of Gravitation on the Propagation of Light", he described how the deflection of light might be detectable after all: by means of an exact determination of the position of stars close to the edge of the sun during a total solar eclipse. In his article, he predicted an angle of light deflection of 0.87 arc seconds. At that time Einstein did not yet know that mass bends space and that the predicted value is therefore too low by a factor of 2. Incidentally, Isaac Newton could already have calculated a deflection of 0.87 arc seconds from his law of gravitation and his corpuscular light theory.

The curvature of space, which is difficult to visualize (see graphic “On crooked tours”), was discovered by Einstein in 1912. At that time, frustrated by the overflowing administrative tasks in Prague - “the ink shitting is endless” - he returned to his alma mater as a full professor. the ETH Zurich. In the summer he realized that he needed non-Euclidean geometry for his theory of gravity (which was already called general relativity at the time). His former fellow student Marcel Grossmann, who was meanwhile a mathematics professor at the ETH, helped him to understand and apply this difficult mathematics to describe the curvature of space.

"NOBODY WILL BELIEVE YOU"

Einstein wrote to the physicist Arnold Sommerfeld on October 29, 1912 that he “hadn't bothered nearly as much in his life” and that “he had received great respect for mathematics, which I until now in its more subtle parts in my simplicity for pure Luxury looked at! The original theory of relativity is child's play against this problem. "Nobel laureate in physics, Max Planck, who had made the special theory of relativity well known and visited Einstein in 1913, even considered the venture to be hopeless:" As an old friend, I have to advise you against it, because you on the one hand will not get through; and if you get through nobody will believe you. "

But Einstein persisted and continued to work, partly with Grossmann, on the non-Euclidean theory of gravity, which even the brilliant Isaac Newton could not have found because the mathematical tools of the trade were not available at the time. Einstein was only able to work intensively in 1915, after moving to Berlin. “At Easter I go to Berlin as an academician without any obligation, as a living mummy,” he wrote in 1914 to his friend and former colleague Jakob Laub and reported that he had been appointed a member of the Prussian Academy of Sciences where he was no longer had to teach and supervise students. “I'm looking forward to this difficult job!” Einstein “had enough of the lectures. All he wanted was to think, ”said the quantum physicist Abraham Pais in the first scientific biography of the genius of the century.

Breakthrough in Berlin

In the second half of 1915, Einstein did mainly that: thinking. He revised his results several times. “It's easy with the Einstein. Every year he revokes what he wrote the previous year, ”he remarked self-deprecatingly in a letter to his friend, physicist Paul Ehrenfest. In November things happened in quick succession: First, Einstein succeeded in fully describing the perihelion of Mercury, which had been puzzling for decades, using the general theory of relativity (see graphic "Mercury on the wrong track"). "I was stunned with excitement for a few days," he later recalled.

On November 18, 1915, Einstein announced that he had calculated a value of 1.74 arc seconds for the deflection of starlight by the sun - twice the prediction of Newton's theory of gravity. So this was now in direct contradiction with Einstein's theory. In principle, it should be possible to decide this by taking measurements. On November 25th, the last errors in the building of the general theory of relativity were eliminated. It stood before the astonished and critical eyes of physicists in its form that is still valid today. By the time the account was published in the Annalen der Physik in 1916, Einstein had “written more than twelve papers on gravity, each time revoking the conclusions of the previous work,” said Abraham Pais in a nutshell. Einstein later said: “In the light of knowledge that has already been achieved, what has been successfully achieved appears almost natural, and every intelligent student grasps it without much effort. But the foreboding, years-long search in the dark with its tense yearning, its alternation between confidence and weariness and its finite breakthrough to clarity, only those who have experienced it know. ”■

Shrinking web

Because bodies that orbit each other emit gravitational waves, they come closer and closer on a spiral path. This effect is particularly great with neutron stars. It was measured with the greatest precision in the PSR 1913 + 16 double pulsar discovered in 1974 in the constellation of Adler, where it corresponds exactly to the predictions of the general theory of relativity. This not only excellently confirms the theory for strong gravity fields, but is also the first indirect evidence for the gravitational waves predicted in 1916.

Mercury going astray

The elliptical orbit of the planet Mercury (shown here greatly exaggerated) is not closed. Rather, its closest point to the sun, the perihelion, slowly moves around the sun, at around 1.5 degrees per century. This has been known since around 1860. The effect is mainly due to the influence of gravity on the other planets in the solar system, especially Venus and Jupiter. But a remainder of 43 arc seconds (about 1/80 of a degree) per century was inexplicable for a long time. It was not until 1915 that Einstein was able to solve the riddle with the general theory of relativity. Later, the perihelion rotation was also measured for Venus, Earth, Mars and the planetoid Icarus.

The tremor of space-time

Gravitational waves make themselves felt as tiny periodic compressions and stretching of spatial and temporal distances. The graphic illustrates the effect of a gravitational wave arriving perpendicular to the plane of the paper.There are two directions of polarization, also referred to as “plus” (above) and “x” (below), which usually overlap.

On crooked tours

Albert Einstein calculated how mass bends space. As a result, light gets on the wrong track, as it were - it has to follow the gravitational geometry and can no longer propagate “in a straight line” as in almost empty space. This effect was first measured in 1919 during a total solar eclipse: Stars were still visible close to the edge of the sun covered by the moon, which were actually behind the sun. The graphic illustrates the “true” and the “apparent” light paths. The room is symbolized as a two-dimensional rubber blanket, its curvature due to the great mass of the sun as a hollow in it. (The low mass of the moon is negligible for the greatly exaggerated effect.)

In the wake of spacetime

The Austrian physicists Hans Thirring and Joseph Lense investigated from 1918 how rotating masses slightly “drag along” space-time around them. This co-rotation causes a tiny deflection from freely swinging pendulums or rotating spheres. The Gravity Probe B satellite was launched in 2004 to measure the Lense Thirring Effect - an angular deflection of only 0.04 arc seconds in Earth orbit. In the meantime he has proven the much stronger deflection of 6.6 arc seconds due to the space-time curvature of the terrestrial gravitational field to an accuracy of better than 0.5 percent. The data are still being evaluated for the lens thirring effect.

January 18, 2011

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