How is time taken as a dimension?

Yesterday and tomorrow are one

“Time is a strange thing”, wrote Hugo von Hofmannsthal in the libretto for Richard Strauss ‘1911 opera“ Der Rosenkavalier ”. “If you live like that, it is absolutely nothing. But then all of a sudden, you feel nothing but her. It is around us, it is also within us. It trickles in the faces, it trickles in the mirror, it flows in my temples. And between you and me it flows again, silently, like an hourglass. ”This flow of time is very familiar to us and at the same time extremely puzzling - but still a sheer illusion. Because more and more physicists and philosophers are coming to the conclusion that objectively time does not exist at all. "Recognizing this is perhaps the greatest intellectual challenge mankind has ever faced," says the philosopher and physicist Vesselin Petkov of Concordia University in Montreal, Canada.

This radical revolution of our worldview and self-understanding is a consequence of Albert Einstein's theory of relativity - or more precisely: its philosophical interpretation. But it took a surprisingly long time before this insight began to take hold - and there is still a lot of opposition to it today. “It is true that the theory of relativity stimulated more philosophical commentary and exerted more influence on mainstream philosophy than any other scientific theory - with the possible exception of Isaac Newton's theory of gravity. But it is a remarkable fact that its impact on metaphysics has been marginal, ”says Simon Saunders, who teaches philosophy at the University of Oxford.

How fast does time flow?

Even the metaphorical way of speaking causes problems: does time “flow” from the future through the present into the past, or does the interface of the present advance, as it were? Why does time have a direction at all? Does it make sense to talk about the passage of time? How fast does it go - about a second per second? (Of course, one shouldn't ask how long a meter is.) And what is this mysterious “now”, the razor-sharp cut of the present that separates the past, which is considered unchangeable, from the future, which is experienced as open and nebulous? According to many philosophers, strictly speaking, there is only the present. You called this worldview presentism (from Latin “praesens”: present, present). The past and the future are therefore not real, but merely exist as memories and ideas and, as it were, indicate a direction. The Greek philosopher Heraclitus was of the opinion that everything flows (“panta rhei”) and everything moves (“panta chorei”).

And according to Aristotle, everything is only real in the present, which connects the “past and future”, both of which do not exist: “One part of time was and is not, while the other will be and not yet is.” Yet this view has the paradoxical consequence that statements about Aristotle, who lived a good 2300 years ago and defined time as the “number of movements according to the earlier or later”, are actually meaningless. Just like statements about a station on Mars that is to be built in the next 40 years. Because the sentences about Aristotle or the Mars station lose their "referent" and the property of being true or false. As for Petkov and others, the theory of relativity has done presentism for Saunders: “Physical theories were once compatible with it, but they are no longer.” The scientific theorist Yuri Balashov of the University of Georgia puts it even more sharply: “Anyone who takes the theory of relativity seriously, cannot take presentism seriously. "

The reason: In contrast to the assumption of physics before Einstein, there is no universal simultaneity in the theory of relativity. Previously, you could imagine clocks at any point in the universe that were running exactly synchronized. But nature doesn't “tick” like that, as Einstein discovered. Rather, the time depends on the reference system. The faster a clock moves or the stronger the gravitational field it is in, the slower it goes. At the speed of light or at the edge of a black hole, there is virtually no time at all. The statement that time depends on the reference system, which is extremely unusual for the everyday mind, is not only a consequence of mathematics, but has also been confirmed by measurements - for example by comparing ultra-precise atomic clocks on earth and in satellites. In fact, the GPS navigation system would be unusable after a few minutes if the theory of relativity were not taken into account. In contrast to Einstein's own view, it has meanwhile even gained importance in everyday life. The physicist Roger Penrose from the University of Oxford has illustrated one consequence of the theory of relativity with the following paradoxical thought experiment: Two people who meet on the street can - if their speeds are extremely different - have completely different “presences”. The one who is moving in the direction of the Andromeda Nebula, for example, lives in a time when an invasion is being discussed there. And the other, although he is currently in the same place, lives in a time when the enemy spaceships have already made their way.

In this thought experiment, the present is so different for the two observers that they are practically in different worlds. But such a “relativization of existence”, as physicists call it, seems grotesque. “The concept of existence cannot be relativized without its meaning being completely destroyed,” contradicted Einstein's colleague at Princeton, the famous mathematician Kurt Gödel. Since he even found solutions to general relativity that describe rotating universes as time machines in which one can travel on suitable paths into one's own past, he came to a different conclusion: time must be an illusion (Bild der Wissenschaft 1/2006, "A whole universe as a time machine"). "The relativized existence also contradicts experiments that confirm the twin paradox," suggests Vesselin Petkov in the same notion.

The twin paradox is actually not one, but another bizarre consequence of the theory of relativity. It is also based on "time dilation": the faster a system moves relative to another, the more the time of this racing system is stretched - that is, the slower it passes. If a spaceman were to travel through space at almost the speed of light, his twin brother who remained on earth would have aged much more when they met again than the spaceman or, depending on the speed and duration of the journey, would have been dead for a long time.

The fact that time dilation really does occur in nature is proven by the speed dependence on the decay of short-lived unstable particles such as muons. These are heavy siblings of electrons. Resting muons have a half-life of 1.5 millionths of a second. When physicists accelerated muons to 99.94 percent of the speed of light in an experiment in 1976, they found that they existed around 29 times longer. In fact, the special theory of relativity says that the “proper time” of the muons is stretched by a factor of 29. The detection of muons at sea level also proves the time dilation. Otherwise these particles, which are generated in the upper layers of the atmosphere by the impact of cosmic rays, would almost all have to decay before they reach the earth's surface. By the way, another relativistic effect also plays a role here - the length contraction already discovered by the Dutch physicist Hendrik Antoon Lorentz, but only explained by Einstein: Near the speed of light, distances and objects in the direction of movement shorten (see graphic on the left “The relativity of space and time "). For the muons, the way to the ground is almost compressed. Time dilation and length contraction contradict our everyday understanding, which assumes an absolute presence and simultaneity, because in the course of its evolution it has only been adapted to slow speeds. But the theoretical and experimental objections cannot be dispelled. Petkov says: "The presenterism contradicts the special theory of relativity and is therefore wrong." The conventional three-dimensional descriptions are quite possible, as Petkov emphasizes. Einstein himself had used this way of speaking. But in reality the reality behind it is four-dimensional if you take the theory of relativity seriously. "If the world were three-dimensional, then the consequences of special relativity and the experiments that confirm it would be impossible," summarizes Petkov. "Physical objects are extended in time, which means that they are four-dimensional."

The time becomes the shadow

Time as the fourth dimension - what is so easy to read here is a radically new view of the world. Because in a certain way the time is spatialized, even if it differs in the equations from the three spatial dimensions by an inverted sign, i.e. a minus sign if the spatial coordinates are set positive. Even more: In the theory of relativity, space and time are fused into an inseparable unit: space-time. Hermann Minkowski was the first to recognize this consequence, when Einstein had attended mathematics lectures at the Zurich Polytechnic - but mostly skipped it. On September 21, 1908, the brittle mathematician gave a lecture to the Assembly of German Natural Scientists and Doctors in Cologne about the special theory of relativity formulated by Einstein three years earlier. In his lecture he said the following, pathetic and often quoted words, the scope of which, however, was not fully understood for a long time: “The tendency is radical. From hour ‘on, space for oneself and time for oneself should completely sink into shadow, and only a kind of union between the two should preserve independence."

Neither Lorentz nor Einstein had attacked the spatial concept. But from the perspective of the special theory of relativity there is no absolute space, but rather an infinite number of spaces - similar to how an infinite number of two-dimensional planes can be thought of in a three-dimensional volume. The union of space and time, that is the astonishing teaching of the theory of relativity, results in a four-dimensional spacetime block. In Minkowski's words: “Three-dimensional geometry becomes a chapter in four-dimensional physics.” This Minkowski space-time can either be interpreted as a four-dimensional mathematical space that represents the time development of the three-dimensional world, or as a mathematical model of a four-dimensional world in which time is the fourth dimension. This second interpretation is appropriate for Petkov, Saunders, and others because it is the only way to avoid the paradox that existence is relative. This block universe of spacetime (see box “From the fourth dimension to the block universe”) is quasi timeless or eternal. Accordingly, presenterism is replaced by another philosophical view of the world: eternalism (from the Latin “aeternus”: eternal). In eternalism, all points in time and their reference systems are real equally. Time is a real fourth dimension analogous to the three spatial dimensions.

The future is already fixed

Future and past are real too. And objects do not only exist in the present, but also in the past and future - Aristotle and the Mars station are, as it were, fixed in the spacetime of the block universe: as a so-called world line. The objects are spatially and temporally - more precisely "spatiotemporal" - extended. This seems difficult to imagine, but it is analogous to a bicycle that has been parked in a doorway. This bicycle, too, consists of coherent spatial parts that are located outside and inside the door: the rear wheel, for example, is still outside, the front wheel is already in the hallway. In addition, the bicycle consists of temporal “parts”, such as a stage with a flat tire and the increasing number of rust spots in one “direction” of the world line. These parts should not, of course, be interpreted as a sequence of stages.

Everyday language finds it very difficult to interpret the world in this way. But that's the point: "Change, passing away, temporal becoming have their usual meaning only in the three-dimensional world," says Petkov. Einstein, who had initially described Minkowski's spacetime as “superfluous erudition”, had to realize the importance of the knowledge of his former teacher a little later. In 1916 he admitted: "Without Minkowski's important thoughts, the general theory of relativity might have got stuck in a nappy." Later Einstein had also adopted eternalism - not yet known at the time. In 1952 he emphasized in the 5th appendix to the 15th edition of his book "Relativity: The Special and General Theory" that it seems more natural to think of physical reality as a four-dimensional existence instead of the development of a three-dimensional existence. And in 1955 - shortly before he died - he wrote in a letter of condolence on the occasion of the death of a friend: "For us believing physicists, the division between past, present and future has only the meaning of an albeit stubborn illusion." , but is merely an illusion, then in reality there is no sequence of events at all. This is just our subjective erroneous perception - although it is difficult to believe when you often have far too little time or fearfully staring at your aging process. The mathematician Hermann Weyl described this in his book “Philosophy of Mathematics and Natural Science” in 1927 as follows: “The scene of reality is not a standing three-dimensional space in which things are developing over time, but the four-dimensional world in which Space and time are inextricably fused. This objective world does not happen, but it is - absolutely; a four-dimensional continuum, but neither space nor time. Only in front of the gaze of the consciousness creeping up in the world lines of the bodies does ‘a section of this world live zieht and pass it as a spatial, temporal change."

If it didn't sound so paradoxical, one could say that Weyl was way ahead of his time with this description. His words also make it clear which problem eternalism raises: How does the perception of time come about in an eternally static block universe? Weyl implicitly defined our consciousness as something that moves along the world lines of the body - the "flow of time" would therefore be dependent on consciousness. This is either a contradicting claim or it means that consciousness may not have any physical reality at all.

the holy grail of physics

In fact, philosophers like René Descartes have maintained over and over that consciousness is in time but not in space. Such a body-soul or mind-brain dualism is of course not acceptable to many philosophers - and it does not follow from eternalism either. But the uncomfortable question remains why we experience a “present” and a “flow of time” - and not all at once - and why our consciousness does not extend simultaneously to the world line of our spatiotemporal body. "Can we be sure that some of the people we meet are not just unconscious bodies?" Asks Petkov, half joking and half scared.

For some researchers, such questions are, of course, an indication that something fundamentally cannot be right with eternalism. They suspect that the ghost will pass as soon as the theory of relativity can be combined with the quantum theory to form a "world formula". Such a theory of quantum gravity is a kind of "Holy Grail" of contemporary physics. But the chances of success in going back to the good old days with the help of a theory of quantum gravity are pretty slim.

· One reason is the quantum cosmology, which is supposed to explain the Big Bang, among other things. The Wheeler-DeWitt equation plays a decisive role in this (Bild der Wissenschaft 4/2004, “Quantum Cosmology for the Curious”). Nobody yet knows the exact solution of this “formula for everything”. But the researchers already know that time in it - in contrast to space - no longer appears and therefore cannot be a fundamental quantity.At most, time substitute forms can be defined, for example via the expansion parameter that describes the expansion of space.

· Another reason is that the development of quantum gravity research tends to identify the “building blocks” of reality - and time does not belong to them either. According to the theory of loop quantum gravity, these building blocks are the spin networks - a web of one-dimensional structures. Space-time emerges from it. That is why it is not a foundation of nature, but a subordinate product - ultimately it is actually an illusion. Abhay Ashtekar from Pennsylvania State University, who played a key role in developing this theory, likes to quote the writer Vladimir Nabokow in this context: "The room is a rapture in the eyes, the time a singing in the ears."

Ashtekar's colleague Carlo Rovelli, a physics professor at the University of Marseille, also regards time as an illusion: “Even if I cannot prove it, I am convinced that time does not exist. I believe that there is a way to describe how nature works without using the terms time and space. 'Space' and 'time' will only make sense within certain approximations - just as the term 'water surface' loses its meaning when we look at the atoms of water in detail: If you look closely enough, there is such a thing as a water surface Not at all. ”It is very similar with time and space:“ They are only macroscopic approximations - illusions that our consciousness has created in order to understand reality. ”■

Rüdiger Vaas

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“So what is time? If nobody asks me about it, I know; if I want to explain it to someone who is asking, I don't know, ”the Church Father Augustine wrote over 1500 years ago. Since then, time has hardly lost any of its mystery. There is not even agreement about the status of space and time: space and time are

· Independent objects or things?

· Properties of objects?

· Relations between objects?

· Issues?

· Innate forms of perception or thought in the human mind and conditions for the possibility of experience in general, but not something objective outside of subjective reality?

· Constructs of our brain, consciousness or the grammar of our language?

In physics, since Galileo Galilei at the latest, time (t) has been a variable in equations such as h = 1/2. g. t2 and v = g. t. Here, h denotes the height, g the acceleration due to gravity and v the velocity of fall. This operationalizes time - which Albert Einstein later expressed with his bon mot that time is what the clock shows. This of course hides a deep controversy in physics and philosophy:

· According to the reductionism or relationism of time, as championed by Aristotle, Gottfried Wilhelm Leibniz and Ernst Mach, time only exists because and when there are changes and thus relationships between things.

· According to the Platonism or absolutism of the time, favored by Plato and Isaac Newton for example, time can also pass without change. So it would be possible that the whole universe would freeze and still an “empty” time would pass - perhaps billions of years between reading this sentence and the next.

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· The theory of relativity and the work on a “world formula” have virtually erased time.

· Instead, there is a four-dimensional space-time - a "block universe" in which everything is fixed at once.

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The British writer Herbert George Wells described time as the fourth dimension as early as 1895 - in his novel “The Time Machine”. And even earlier, in 1884, the British mathematician Charles Howard Hinton speculated about a four-dimensional space-time in which ordinary particles appear as threads - an almost prophetic anticipation of the “world line” that plays a central role in the theory of relativity.

The four-dimensional reality is often referred to as the “block universe” because it does not develop, but is there as a whole and all at once. If God existed and he existed outside of time, as the Church Father Augustine believed, he could, as it were, survey the world in its totality from beginning to end. The concept of the immutable block universe goes back to the American psychologist and philosopher William James. In his essay "The Dilemma of Determinism" from 1884 he criticized the idea of ​​determinism, which would contradict the idea of ​​free will. For determinism claims “that the areas of the universe that are already established have absolute control over what is to become of the other areas. Various possibilities are not hidden in the womb of the future. [...] The whole is in every single part and is welded into an absolute unit, an iron block in which there can be no ambiguity or a shadow of a change.

An impressive literary implementation of the quasi-spatial all-at-once experience was achieved in 1970 by the American science fiction author Norman Spinrad in his story “The Weed of Time”. In it, an extraterrestrial herb abolishes the illusion of temporality: when you eat it, you can see your entire life from birth to death - and yet you can't change anything about it. Ted Chiang's “Story of Your Life” from 1999 has a similar plot. In it he describes how a new view of language and thinking changes the experience of time in such a way that one sees one's whole life quasi simultaneously in front of one.

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only the past is determined, the future, on the other hand, is a scope of possibilities, of which only one is realized at any point in time. This thesis of evolving spacetime is an alternative to the static spacetime block universe. The graphic illustrates this with the random trajectory of a particle: It shows the world line of events at two points in time. But it is controversial whether such an “open future” even exists and also an absolute coincidence that cannot be reduced to the fact that an observer does not know the future.

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For Isaac Newton, time was absolute - everywhere in the universe one could imagine clocks set up that run synchronously for any observer, the time of a “now” should be universal. Albert Einstein, on the other hand, recognized that time is inextricably linked with space, appears stretched at high speeds and gravity fields that warp space-time, and that it is different for different observers. Therefore there is no objective simultaneity (the “surface of the present” in Newton's), but for every observer an infinite amount of arbitrary “hypersurfaces”, which all together give the spacetime of the block universe. In it the world lines of the observer are fixed from beginning to end.

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The “flow” of time is an illusion in the context of the theory of relativity. Everything is fixed “at once” in space-time, so to speak. The graphic illustrates this illusion with a swinging pendulum. The “space-time block” is represented with the time coordinate t and two space coordinates x and y, the third dimension of space cannot be shown here.

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If two observers A and B meet at a point P at very different speeds, then their measurements of space and time do not agree. These relativistic effects - called time dilation and length contraction - contradict common sense. However, they have been proven experimentally and an indication that space and time are not separate, but are united as four-dimensional space-time. The diagrams above show the separate location and time coordinates x and t for both observers. The two digital clocks (left) and the meter stick (right) - each drawn as a "world line" extended in space-time - are at rest in the coordinate system of A while B races past them. The two digital clocks show the same time for A (here: 5 seconds), but not for B. So there is no universal, objective simultaneity. The same object also appears to be of different lengths for A and B, because B sees the yardstick shortened. The past at point P is clear: In the theory of relativity, it is characterized by the light cone of the past, which includes everything that can influence an event at P at the maximum speed of light.

February 18, 2008

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