time

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Physical size
Surname time
Formula symbol
Size and
unit system 		unit dimension
SI s T
cgs s T
Planck Planck time ħ 1/2 · G 1/2 · c −5/2

The time is a physical quantity . The common symbol of time is t , its SI unit is the second s.

Time describes the sequence of events, so it has a clear, irreversible direction. With the help of the physical principles of thermodynamics , this direction can be expressed as an increase in entropy , i. H. the disorder in a closed system . From a philosophical perspective, time describes the progression of the present coming from the past and leading to the future . According to the theory of relativity , time and space form a four-dimensional spacetime in which time plays the role of a dimensionoccupies. The concept of the present can only be defined in a single point, while other points of space-time that are neither in the past nor the future of this point are referred to as being “ spatially separated” from this point.

In the SI system of units, time is one of several basic quantities .

The time is used to specify a point in time . As civil time (UT, CET, etc.), it is based approximately on the position of the sun and is standardized within a time zone due to state regulations .

In philosophy one has always asked about the nature of time , which also touches on issues of worldview . For the physical, biological and human sciences, time is a central parameter that can also be measured using measurements . a. in all moving bodies ( dynamics , development), in chronobiology or the sociology of time . Psychology studies the perception and sense of time . The economy also regards time as an asset. In linguistics , “time” means the grammatical form of verbs, the tense .

introduction

Oscillation phases of a pendulum at different times. There is no flow of time in this representation of events.

Probably the most striking characteristic of time is the fact that there always seems to be a certain current and excellent place that we call the present , and which seems to move inexorably from the past towards the future . This phenomenon is also known as the flow of time. However, this flow eludes a scientific consideration, as will be explained below. The humanities cannot clearly clarify the question either.

In physics, time is used to describe events in an analogous manner, as does space . Physics only says that among all conceivable structures in three-dimensional space in combination with all conceivable temporal processes, only those that obey the laws of physics are observed . It could just as well be immovable structures in a four-dimensional space that are subject to certain geometric conditions by the laws of physics. According to Newton , the structure of space-time is given, with time having absolute significance; According to Albert Einstein, there is a special “relativity of simultaneity”. Something that could be interpreted as the flow of time occurs in physics only through probabilistic terms that are related to the concept of entropy (see below), although the terms past, present and future in Einstein's theories are mathematically precise and have measurable meaning. On closer inspection, however, it initially turns out to be completely unclear how a flow of time could be precisely described in the language of physics or mathematics or any other science.

For example, the statement that time flows only makes sense if an alternative that can be distinguished from it is conceivable. The obvious alternative of the idea of ​​a standing time, for example, leads to a contradiction, however, since it is only conceivable from the point of view of an observer for whom time continues to pass, so that the assumed standstill is perceptible as such at all (see also Critique of the pure Reason by Immanuel Kant ): If time could be stopped, how long would time then “stand”?

The apparent flow of time is therefore viewed by many physicists and philosophers as a subjective phenomenon or even as an illusion . It is assumed that it is very closely linked to the phenomenon of consciousness , which, like this, eludes a physical description or even explanation and is therefore one of the great riddles of natural science and philosophy. Our experience of time would then be comparable to the qualia in the philosophy of consciousness and consequently would have just as little to do with reality as the phenomenal content of consciousness in the perception of the color blue with the associated wavelength of light .

This would invalidate our intuitive notion that there would be an entity independent of oneself in the manner of a cosmic clock, which determines what point in time we all experience together at the moment, and which thus makes the present an objective now that connects us all .

Time as a physical quantity

In physics , time ( symbol : t or τ , from Latin tempus (time)) is the fundamental quantity which, together with space , can be used to determine the duration of processes and the sequence of events . Since it cannot yet be traced back to more fundamental phenomena, it is defined using methods for measuring it, as is the case with space and mass. In the SI system of units , time is measured in seconds ( unit symbol s). The units minute and hour are derived directly from this, indirectly (via earth movement and legally stipulated leap seconds) also day and week , plus (depending on the calendar ) month , year , decade , century and millennium .

Timing

Astronomical clock in the old town of Prague

Time measurement is one of the oldest tasks in astronomy . After it was proven in the first half of the 20th century that the length of the mean solar day is subject to irregular fluctuations and increases in the long term, the ephemeris time was introduced, which was based on the more uniform planetary motion. Its time unit, the ephemeris second, was adopted in 1960 as the second in the International System of Units . Since 1967/68 the definition of the SI second has been based on a transition in the 133 Cs atom, with the original length being retained as precisely as possible. The most important time scales are today

  • the international atomic time TAI, the unit of which is the SI second on the geoid .
  • the Universal Time UT1 , which depends on the current angle of rotation of the earth, i.e. is a form of the mean solar time. It runs irregularly and can be measured with an accuracy of a few microseconds.
  • the Coordinated Universal Time UTC, which follows the second cycle of the TAI, but only deviates from UT1 by a maximum of 0.9 s due to the occasional insertion of leap seconds . It or a zone time that depends on it is civil time.
  • the terrestrial time TT, which in 1984 replaced the ephemeris time in astronomy in order to be able to correctly handle the relativistic time dilation caused by movement and gravity. It corresponds very precisely to TAI + 32.184 s on the geoid. There is also the related barycentric dynamic time TDB, which differs from TT on the geoid by a maximum of 2 ms, as well as the two coordinate times TCG and TCB; see dynamic time .

Astronomical dates and times are often conveniently given as Julian Date (JD) or modified as Modified Julian Date (MJD).

Today, like other measurands , time in physics is operationally defined, i.e. using a measurement method. For time measurement, systems are mainly used that periodically return to the same state. The time is then determined by counting the periods. Such a device is called a clock . But also monotonous movements can be the basis of the time measurement, e.g. B. in the earlier sand and water clocks .

Atomic clock

A watch is the better, the more precisely the periodic process can be reproduced and the less it can be influenced by external conditions, for example mechanical disturbances such as temperature or air pressure . Therefore, quartz watches are much more precise than mechanical watches. The most accurate clocks are atomic clocks that are based on atomic oscillation processes. This means that a relative rate error of 10 −15 can be achieved, which corresponds to a deviation of one second in 30 million years. The time and thus also the frequency , its mathematical reciprocal value , are the physical quantities that can be measured with the greatest possible precision, which has led to the definition of length being reduced to that of time by referring to the meter as the one Defines the distance that the light travels in a vacuum for 1 / 299.792.458 seconds.

Newtonian physics

Isaac Newton describes the phenomenon of time in the following words:

"Absolute, true and mathematical time flows in itself and, by virtue of its nature, is uniform and unrelated to any external object."

- Isaac Newton : Mathematical Principles of Natural Science ; London 1687

The basic concept of “absolute time” was long considered “naturally applicable” in physics, from around 1700 to 1905, i.e. H. up to the formulation of the special theory of relativity by Albert Einstein . The Newtonian concept of time is still the basis for everyday understanding of the phenomenon, although many precision measurements have shown that it was not Newton but rather Einstein who was “right”.

Quantum mechanics

Although the energy-time uncertainty relation appears at first glance to be Heisenberg's uncertainty relation, it is of a different nature. In quantum mechanics, time is a parameter. There is no operator for the time. When trying to introduce it, one encounters contradictions.

theory of relativity

Due to the discoveries in connection with the theory of relativity , the Newtonian concept of an absolute time that is the same in every place in the universe had to be abandoned. For example, observers who move relative to each other assess temporal processes differently. This applies to both the simultaneity of events that take place in different locations and the length of time between two meetings of two observers who move relative to each other between these meetings ( time dilation ). Since there is no absolutely static coordinate system , the question of which observer is correctly assessing the situation does not make sense. Therefore, each observer is assigned his so-called proper time . Furthermore, the presence of masses influences the passage of time, so that it elapses at different speeds in different places in the gravitational field . Newton's assumption that time flies without reference to external objects is no longer tenable.

In the basic equations of the theory of relativity, time and space appear to be almost completely equivalent and can therefore be combined into a four-dimensional space - time . Mathematically, however, you are not dealing with a four-dimensional Euclidean space, the , but with a so-called Minkowski space . In this room, and do not have an analog metric structure, but z. B. and , where is the speed of light and the "imaginary unit" of the complex numbers. Space and time are not completely identical in the special theory of relativity either, but the possibility of thermodynamic behavior remains, see below.

In three-dimensional space, the choice of the three coordinate axes is arbitrary, so that terms such as left and right, up and down, front and back are relative. In the special theory of relativity it turns out that the time axis is not absolute either. Thus, with the state of motion of an observer, the orientation of his time and space axes in space-time also change. It is a kind of shear movement of these axes, which is mathematically closely related to the rotations. This means that space and time can no longer be clearly separated, but depend on each other in a non-trivial way (so-called Lorentz transformations ). The consequences are phenomena such as the relativity of simultaneity , time dilation and length contraction . These properties of time and space, which were discovered in connection with the theory of relativity, are largely beyond our view. However, they can be precisely described mathematically and - as far as experimentally accessible - also optimally confirmed. However, the time axis cannot be turned around by a movement, that is, past and future cannot be interchanged; the emerging theory retains the fundamental property of causality .

Time is not necessarily unlimited in general relativity . Many physicists assume that the Big Bang is not only the beginning of the existence of matter , but also represents the beginning of space and time. According to Stephen W. Hawking , there was no point in time "a second before the Big Bang" or a point on earth 1 km north of the North Pole .

In 2008, however, Martin Bojowald developed a theory within the framework of loop quantum gravity (SQG) according to which the universe already existed before the Big Bang. The usual cosmological models of general relativity have their limits due to the singularity shown.

Time travel

The relativistic effects mentioned can in principle be interpreted as time travel. The extent to which journeys into the past are also possible in principle via the curvature of spacetime and other phenomena has not been conclusively clarified. Possible candidates are so-called wormholes , which could connect areas of space-time with different times, also special trajectories in the vicinity of a sufficiently fast rotating black hole and finally the vicinity of two cosmic strings that fly past each other sufficiently quickly. The effort required to put any of these potential possibilities to practical use would, however, far exceed the means available to mankind today.

The paradoxes that arise when traveling into the past could be avoided within the framework of Everett's many-worlds theory . After that, the past you are traveling to would be located in a parallel world . The original course of things and the one modified by time travel would both take place in parallel and independently of one another.

Time and causality

The concept of time is closely related to the concept of causality . So we take it for granted that the cause occurs before its effect; more precisely, every observer of correlated events will describe the process in such a way that the effect is conditioned by the cause in his model of the process. The past is immutable, it cannot be influenced by present events. The future, on the other hand, is causally dependent on the present, i.e. it can be influenced by events or actions in the present.

In the theory of relativity, the chronological order of some events that take place in different places is judged differently by observers who are moving relative to one another. This is precisely the case if the two events could only come into contact through a signal with faster than light speed . If an interaction could take place at faster than light speed, then one could send a message into the past with the following system:

  1. The signal is sent at faster than light speed to a relay station far enough away.
  2. This accelerates conventionally away from the original transmitter (alternatively: it conventionally transmits it to another relay station moving away from the receiver, e.g. the other side of a rotating platform). This “postpones” the sending event from the past into the future.
  3. Finally the signal is sent back at faster than light speed. If the speeds involved are high enough, the signal arrives before the original signal is sent out.

Therefore the principle of causality would be violated. In the middle of the 20th century it was assumed that there could be tachyons faster than light . Should they be able to interact with ordinary matter, the causality would be violated. The hypothesis of the existence of tachyons therefore has hardly any supporters.

To the symmetry of the two directions of time

The laws of physics, which underlie the basic forces of the phenomena of our everyday life, are invariant with respect to an inversion of time . This means that for every process that obeys these laws, the reverse of the time is also possible in principle. This statement contradicts our everyday experience. If a ceramic cup falls on the floor, it breaks into pieces. Conversely, it has never been observed that these shards reassemble by themselves to form an intact cup. However, such a process would not in principle contradict the laws of nature. It's just extremely unlikely.

The background of this fact is a probability consideration that in the second law of thermodynamics is formulated. According to this, the entropy , which indicates the degree of disorder of a closed system, always increases and thus its order decreases. A temporary increase in order cannot be ruled out in principle, but is more or less unlikely depending on the size. In order to provoke the spontaneous reunification of broken pieces into a cup, one would have to create and observe a more than astronomical number of broken pieces.

The second law of thermodynamics - and the related friction phenomena  - violate the symmetry with respect to the two directions of time. It cannot therefore be derived from the basic laws of physics, but has the property of a postulate . The two directions of time lose their equivalence, and one speaks of the thermodynamic time arrow . It is seen as a potential basis for the flow of time from the past into the future, as we experience it in our everyday world.

In this context, there is often talk of a reversibility or irreversibility of time. However, this is a linguistic and logical inaccuracy. If someone could reverse the time, he would see all processes going backwards. This reversed course of time would only be recognizable from the point of view of an observer who is subject to a kind of personal time that continues to run forward unchanged. However, such a division of time into one subject to an experiment or thought experiment and another unchanged makes no sense.

The laws of physics that describe the phenomena of weak and strong interaction are not invariant with respect to a time reversal . For a process in the field of nuclear and elementary particle physics , the time reversed is therefore not necessarily compatible with the laws of physics. The CPT theorem states that the process is again in harmony with the laws of nature if it is not only viewed in reverse time, but also as a mirror image and is built up from antimatter . From the CPT theorem it follows that processes that represent a so-called CP violation , as is the case with some particle decays, cannot be invariant with respect to a time reversal.

In the formalism of describing antimatter, antiparticles are equivalent to ordinary particles, which in a certain sense move backwards in time. In this sense, the pair annihilation of a particle with its antiparticle has a formal similarity to a single particle that begins to move back into the past at this point, so that it exists twice there and does not exist at all in the future.

Limits of the physical concept of time

There are clear indications that the phenomenon of time loses  its properties as a continuum in the Planck time range of 10 −43 s . The consistent application of the known physical laws leads to the result that every process that is shorter than Planck's time can only be assigned to one object that must immediately collapse into a black hole (see Planck units ). This consideration shows that the known physical laws fail beyond Planck's time. It is hoped that the related questions will be clarified by a theory of quantum gravity , which has yet to be developed , and which would combine the two fundamental theories of physics, relativity theory and quantum physics . In such a theory, the time would possibly be quantized in the area of ​​Planck time. In loop quantum gravity , for example , a candidate for the theory of quantum gravity, it is assumed that the structure of spacetime is a four-dimensional, foam-like spin network with "bubbles" of the order of magnitude of Planck units. However, one must be this "foam" not in imagine embedded space and time, but the foam is in this theory space and time.

philosophy

In antiquity u. a. the philosophers Heraklit, Plato, Aristotle and Augustine dealt with the concept of time, in modern times especially Newton, Leibniz, Kant, Heidegger and Bergson.

Heraclitus' river pictures, which are symbolized by the constant river bed in which everything flows ( panta rhei ), are a metaphor for time. Immutable periodic transitions between day and night, i.e. the stability of the course of the river and the dynamics of its flow, stand as the unity of opposites .

For Plato , space and time have no essence, but are only moving images of what actually is ( theory of ideas ). For Aristotle the concept of time is inextricably linked to changes; time is the measure of every movement and can only be measured by this . It can be divided into an infinite number of time intervals ( continuum ).

For the first time Augustine differentiates between a physically exact (measurable) and a subjective, experience-related time. Time and space only came into being through God's creation , for whom everything is a presence . Augustine sums up the mystery of time in the following saying:

“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. ”(Confessiones XI, 14)

For Isaac Newton , time and space form the “containers” for events; for him they are just as real as representational objects: “Time is, and it ticks evenly from moment to moment.” Newton's view dominates in natural philosophy because it enables time and to describe space independently of a reference point or observer.

In contrast, Gottfried Wilhelm Leibniz thinks that time and space are only mental constructions to describe the relationships between events. They have no “essence” and therefore there is no “flow” of time. He defines time as follows: “Time is the order of that which does not exist at the same time. It is therefore the general order of changes, in which one does not look at the specific type of changes. "

According to Immanuel Kant , time, like space, is a “pure form of perception” of the inner sense. They are our access to the world, so they belong to the subjective-human conditions of world knowledge, in the form of which human consciousness experiences sensory impressions.

However, Kant ascribes an empirical quality to it for time measurements and distant events. We can set the time from our experience not think away and not tell whether they are a - world - whatsoever in itself belongs. In a similar way, Martin Heidegger's main work “ Being and Time ” describes the latter as a reality that deeply shapes being human.

psychology

There are often clear differences between the subjectively perceived time and the objectively measurable time. The following sections are intended to present these briefly and clearly.

The perception of duration

The perception of the duration depends on what happens in the time. An eventful period appears briefly, "flies by". In contrast, uneventful periods can sometimes be excruciatingly long. The terms amusement and boredom are derived from this observation.

Paradoxically, looking back, one perceives the times the other way round: In eventful times, a lot of information has been stored, so that this period seems long. Conversely, low-event times appear briefly in retrospect, as hardly any information is stored about them.

The perception of simultaneity

Simultaneous perception is more complex than it appears at first glance. There are different thresholds:

  • The threshold from which two events are recognized as separate depends on the respective sense organ . In humans , for example, visual impressions must be 20 to 30 milliseconds apart in order to be separated in time, while three milliseconds are sufficient for acoustic perception .
  • The threshold from which the sequence of two stimuli can be differentiated is about 30 to 40 milliseconds, regardless of the type of perception, but is always based on the slowest stimulus transmission.
  • In addition, the perception of the present is indicated by a three-second period, this period is called the present duration .

biology

Almost all living things , including single-cell organisms , have a biological internal clock that is synchronized with the day-night cycle and other natural cycles. The internal clock for the daily rhythm also runs without daylight, as was shown in plants in the dark, but also in people in bunker experiments in which the volunteer test subjects lived without any reference to external time rhythms. After a while, a constant wake-sleep rhythm averaged around 25 hours was established. It is known as the circadian rhythm (from Latin circa , approximately, and Latin dies , day).

Comparative cultural studies

Comparative cultural studies and philosophical reflection on it lead more and more to the insight that time as an anthropological constant that applies to all people equally, does not exist at all. Rather, there are culture-specific conceptions of time with various structures, such as:

  • the cyclical of the pre-Socratics and the natural ethnicities, which is documented in the assumption of the eternal return of the same,
  • the eschatological one, which has a beginning and is directed towards an end goal and also determines the premodern conception of history,
  • the straight and continuous, coming from the past and going via the present into the future, which is the basis in traditional physics and which we today mostly assume as universal, but which is a western cultural product,

Sociology and Society

From a sociological point of view, time structures are necessary in order to relieve citizens of the stress of decision-making (A. Gehlen), to determine their civil duties, to administer their affairs and to coordinate their actions. Calendars with fixed time rhythms (year, months, weeks, Sundays and public holidays, etc.) and functions (e.g. church, national or international recurring events to commemorate) are helpful for this. Depending on the complexity of the social order, time windows are determined for the division of the ages with their respective functions: infancy, childhood, adolescent age, adulthood, old age or: kindergarten, school, time of study or apprenticeship, employment, leisure. Citizens thread their individual biographies within these social time specifications: B. Birth, initiation rites (baptism, etc.), school entry, school career, study or entry into the profession, marriage, etc.

Time and right

Which legal time applies in which place is a political decision of the respective state. In Germany, the right to determine the time according to Article 73, Paragraph 1, No. 4 of the Basic Law belongs solely to the Federation . Time in Germany was regulated by the law on time determination until July 12, 2008 and has since been regulated by the Units and Time Act.

Time in literature

“Human existence is realized in designing the future, in retaining what has been and in letting the present arise. Therefore it is to be understood in terms of the process of its timing. A preferred form of telling ahead is telling. When and how the process of giving birth begins, how it unfolds and how it ends - all that is the narrator's creation. "

- Walter Biemel
  • Walter Biemel examines newspaper and novel structure in his book . Philosophical analyzes of the interpretation of the modern novel using the example of the five novels Der Nachsommer by Adalbert Stifter , Madame Bovary by Gustave Flaubert , Der Zauberberg by Thomas Mann , A Fable by William Faulkner and La Casa Verde ( The Green House ) by Mario Vargas Llosa die manifold of the present, whereby in each novel a different emphasis, a different interpretation of reality becomes visible.
  • In the novel The Magic Mountain by Thomas Mann is the time a central motif, interwoven with the life / death issue. In it u. a. discusses the extent to which “the interestingness and novelty of the content pass the time, that is: shorten it, while monotony and emptiness weigh down and inhibit your walk” (short-term). The issue of the “narrative” of time is also discussed, the relationship between the length of a report and the length of the period to which it relates (narrative time, narrated time). The last two chapters bring together six years of routine and monotony for the hero of the novel. Here Arthur Schopenhauer's man processes “timeless now”, lat. Nunc stans . On the narrative level, the asymmetry in the novel structure corresponds to a distorted perception of time by the protagonist himself.
  • In the novel In Search of Lost Time by Marcel Proust , the novel hero noticed that the past is the only preserved in his memory. At the end of his life he realizes that a novel of his memories is the last chance to create the work of art that he had planned. So the book ends with the author starting to write it. The "lost time" is ambiguous:
    • Time wasted by the narrator
    • Time that is irretrievably lost if it has not been preserved in memory or in a work of art,
    • the memories or imaginations that names or objects evoke.
  • "Time heals everything, I thought, except the truth." ( Carlos Ruiz Zafón )
  • Martin Amis published in 1991 his novel Arrow of Time (Engl. Time's Arrow ), in which the time - with all the interesting consequences - runs backwards.
  • Alan Lightman undertook further thought experiments in his 1992 novel Und immer wieder die Zeit ( Einstein's Dreams ); there the time does not run evenly, but drives capers like jumps, delays or reversals.

Tense

The tense in grammar is called tense . In different languages ​​there are different tenses that are formed differently. In the standard German language, time is represented in three ways.

  • The tense of the verb allows a distinction to be made between the present ( present tense ) and the past ( past tense ). Example: I go and I went.
  • The specification of auxiliary verbs (have to be) allowed the distinction between past tenses as perfect and pluperfect . Example: I went and I was gone. In addition, auxiliary verbs (here: become ) are used to represent the future ( future tense ). Examples: I will go. I will be gone.
  • An explicit specification of the time or period is possible . Examples: Now I'm going to school. Tomorrow I go to school. I will go to school tomorrow. It was yesterday: I am walking down the street and I see a twenty euro note.

You can also use the participle to indicate a chronological progression . Example: the flowing water.

An extreme case is the controversial claim by Benjamin Lee Whorf , who claims to have established in an investigation into the language of the Hopi that the Hopi language had no concept for the concept of time. This led to the linguistic relativity principle alias the Sapir-Whorf hypothesis , according to which thinking depends on the languages ​​spoken.

Tempus is also a basic concept in music theory .

Music as a medium in time

As music , time is to be understood not only through the meter , for example tense , but through the vibration itself and every conceivable practical involvement. In this way, time appears as an elementary prerequisite for music. Music is closest to the arts of the time, which is emphasized by appropriate statements that music is particularly fleeting and a “medium in time”. Music beyond time, however, is often controlled by musicians and thus forms its own theoretical horizon.

literature

classic

History of science

  • Arno Borst : Computus  : time and number in the history of Europe . dtv, Munich 1999. ISBN 3-423-30746-3 .
  • Trude Ehlert (Ed.): Time Concepts, Time Experience, Time Measurement. Paderborn / Vienna / Zurich 1997.
  • Hans Jörg Fahr : Time and Cosmic Order. Carl Hanser Verlag, Munich, Vienna 1995. ISBN 3-446-18055-9 .
  • Roland Färber, Rita Gautschy (ed.): Time in the cultures of antiquity . Böhlau Verlag, Cologne 2020. ISBN 978-3-412-51816-5 .
  • Kurt Flasch : What is time? Augustine of Hippo. The XI. Book of Confessiones. Text - translation - comment . Vittorio Klostermann GmbH, Frankfurt / M., 2nd edition 2004.
  • David Landes : Revolution in Time. Clocks and the Making of the Modern World . Cambridge Mass. and London 1983. (New edition Viking, London 2000, ISBN 0-670-88967-9 )
  • Hans Lenz: Universal history of the time. 3rd, revised edition. Marix Verlag, Wiesbaden 2017, ISBN 978-3-86539-050-9 .
  • Hans Maier : The Christian calendar . Herder, Freiburg i.Br. 1991. ISBN 3-451-04018-2 .
  • Richard Sorabji : Time, Creation and the Continuum. Duckworth, London 1983. Comprehensive presentation of theories of time from antiquity to the Middle Ages, standard work
  • Kristen Lippincott: The Story of Time . London 1999.
  • Mike Sandbothe : The temporalization of time. Basic tendencies of the modern contemporary debate in philosophy and science. Scientific Book Society, Darmstadt 1998.
  • Karen Gloy : Philosophical History of Time. Fink Verlag, Munich 2008, ISBN 978-3-7705-4671-8 .
  • Klaus Mainzer : Time - from primeval times to computer times. CH Beck, Munich 2005, ISBN 978-3-406-44911-6 .
  • Thomas de Padova : Leibniz, Newton and the invention of time. Piper, Munich 2013, ISBN 978-3-492-05483-6 .

Natural philosophy

  • Hans Michael Baumgartner (Ed.): Concepts of time and experience of time. (Frontier Questions (Science, Philosophy, Theology), Volume 21). Alber, Freiburg / Munich 1994, ISBN 3-495-47799-3 .
  • Antje Gimmler, Mike Sandbothe , Walther Ch. Zimmerli (eds.): The rediscovery of time. Reflections Analysis Concepts. Primus, Darmstadt 1997.
  • Adolf Grünbaum : Philosophical Problems of Space and Time. Reidel, Dordrecht / Boston 1963, second a. expanded edition 1974, ISBN 978-90-277-0357-6 .
  • Gottfried Heinemann (Ed.): Concepts of time. Results of the interdisciplinary symposium "Concept of time in the natural sciences, time experience and time consciousness". (Kassel 1983). Alber, Freiburg / Munich 1986, ISBN 3-495-47596-6 .
  • Kurt Hübner : On the variety of time concepts . Eichstätter University Speeches, 2001.
  • Olaf Georg Klein : Time as the Art of Living. (Paperback edition WAT632). Verlag Klaus Wagenbach, Berlin 2010, ISBN 978-3-8031-2632-0 .
  • Hans Reichenbach : Philosophy of space-time teaching. de Gruyter, Berlin / Leipzig 1928. (New edition: Braunschweig 1977, ISBN 3-528-08362-X )
  • Ewald Richter : Original and physical time. Duncker & Humblot, Berlin 1996, ISBN 3-428-08522-1 .
  • Craig Callender: The Oxford handbook of philosophy of time. Oxford University Press, Oxford 2011, ISBN 978-0-19-929820-4 .
  • Horst Völz : Description of the world. Space, time, temperature and information - aspects, positions, debates. Shaker Verlag, Aachen 2018, ISBN 978-3-8440-6323-3 .

Cultural studies

Popular literature on modern physics

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Individual evidence

  1. ^ Harold Spencer Jones : The rotation of the earth, and the secular accelerations of the sun, moon and planets . In: Monthly Notices of the Royal Astronomical Society . tape 99 , 1939, pp. 541–558 , bibcode : 1939MNRAS..99..541S (English, summary on the last page).
  2. ^ The International System of Units (SI). (PDF) BIPM , 2019, pp. 206–207 , accessed on January 17, 2020 (English, 9th edition of “SI Brochure”).
  3. ↑ IERS Bulletin B. IERS, January 1, 2020, accessed on January 17, 2020 (English, In November 2019 the measurement error was between 5.0 and 7.5 μs.).
  4. ↑ The energy-time indeterminacy relation, https://www.tu-braunschweig.de/Medien-DB/ifdn-physik/quant7.pdf
  5. ↑ Martin Bojowald: Back to the Big Bang. The whole history of the universe. , u. a. P. 127f, 131f, 260f S. Fischer, Frankfurt am Main 2009, ISBN 978-3-10-003910-1 .
  6. ↑ Hans-Georg Gadamer: The beginning of knowledge . Stuttgart 1999.
  7. ^ Margot Fleischer: Beginnings of European Philosophizing. Heraclitus - Parmenides - Plato's Timaeus . Wuerzburg 2001.
  8. ↑ Aurelius Augustine: What is time? (Confessiones XI / Confessions 11). Ingl., Translated u. annotated by Norbert Fischer, Lat.-dt., Felix Meiner Verlag, Hamburg, 2000.
  9. ↑ The quote comes from Gottfried Wilhelm Leibniz: The metaphysical beginnings of mathematics. In: Manuscripts on the basis of philosophy. II, p. 35 ff. Quoted from: Annette Antoine, Annette von Boetticher : Leibniz Quotes. Matrix Media Verlag, Göttingen 2007.
  10. ↑ Stella Schalamon: Time researcher on the internal clock: "It must be in the brain" . In: The daily newspaper: taz . March 28, 2020, ISSN  0931-9085 ( taz.de [accessed on March 29, 2020]).
  11. ^ Philippe Ariès: Time and History. Translated from the French by Perdita Duttke. Athenäum Verlag, Frankfurt / M., 1988. Otto Hansmann: From time management in school lessons. Münster u. a., Waxmann, 2009.
  12. ^ Freiburg, Munich: Alber, 1985, ISBN 3-495-47548-6
  13. ↑ Das Spiel des Engels, Reinbek 2009, p. 408 ISBN 3-10-095400-9