Planck time

In quantum mechanics, the Planck time (tP) is the unit of time in the system of natural units known as Planck units. A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 5.39 × 10 −44 s.[1] The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:[2]

where:

ħ = ​h2π is the reduced Planck constant (sometimes h is used instead of ħ in the definition[1])
G = gravitational constant
c = speed of light in vacuum

Using the known values of the constants, the approximate equivalent value in terms of the SI unit, the second, is

where the two digits between parentheses denote the standard error of the approximated value.

History

The Planck time (also known as Planck second) was first suggested by Max Planck[3] in 1899. He suggested that there existed some fundamental natural units for length, mass, time and energy. Planck derived these using dimensional analysis only using what he considered the most fundamental universal constants: the speed of light, the Newton gravitational constant and the Planck constant. The Planck time is by many physicists considered to be the shortest possible measurable time interval; however, this is still a matter of debate.

Physical significance

The Planck time is the unique combination of the gravitational constant G, the special-relativistic constant c, and the quantum constant ħ, to produce a constant with dimension of time. Because the Planck time comes from dimensional analysis, which ignores constant factors, there is no reason to believe that exactly one unit of Planck time has any special physical significance. Rather, the Planck time represents a rough time scale at which quantum gravitational effects are likely to become important. This essentially means that while smaller units of time can exist, they are so small their effect on our existence is negligible. The nature of those effects, and the exact time scale at which they would occur, would need to be derived from an actual theory of quantum gravity.

The reciprocal of the Planck time, which is Planck frequency, can be interpreted as an upper bound on the frequency of a wave. This follows from the interpretation of the Planck length as a minimal length, and hence a lower bound on the wavelength.

All scientific experiments and human experiences occur over time scales that are many orders of magnitude longer than the Planck time,[4] making any events happening at the Planck scale undetectable with current scientific knowledge. As of November 2016, the smallest time interval uncertainty in direct measurements is on the order of 850 zeptoseconds (8.50 × 10−19 seconds)[5]

See also

References

  1. ^ a b "Big Bang models back to Planck time". Georgia State University. 19 June 2005.
  2. ^ CODATA Value: Planck Time – The NIST Reference on Constants, Units, and Uncertainty.
  3. ^ M. Planck. Naturlische Masseinheiten. Der Koniglich Preussischen Akademie Der Wissenschaften, p. 479, 1899
  4. ^ "First Second of the Big Bang". How The Universe Works 3. 2014. Discovery Science.
  5. ^ "Scientists have measured the smallest fragment of time ever". 12 May 2010. Retrieved 19 April 2012.

External links

Astrarium

An astrarium, also called a planetarium, is the mechanical representation of the cyclic nature of astronomical objects in one timepiece. It is an astronomical clock.

Chronometry

Chronometry (from Greek χρόνος chronos, "time" and μέτρον metron, "measure") is the science of the measurement of time, or timekeeping. Chronometry applies to electronic devices, while horology refers to mechanical devices.

It should not to be confused with chronology, the science of locating events in time, which often relies upon it.

Chronon

A chronon is a proposed quantum of time, that is, a discrete and indivisible "unit" of time as part of a hypothesis that proposes that time is not continuous.

Common year

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar, (like the earlier Julian calendar), employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

The common year of 365 days has 52 weeks and one day, hence a common year always begins and ends on the same day of the week (for example, January 1 and December 31 fell on a Sunday in 2017) and the year following a common year will start on the subsequent day of the week. In common years, February has four weeks, so March will begin on the same day of the week. November will also begin on this day.

In the Gregorian calendar, 303 of every 400 years are common years. By comparison, in the Julian calendar, 300 out of every 400 years are common years, and in the Revised Julian calendar (used by Greece) 682 out of every 900 years are common years.

Cosmological decade

A cosmological decade (CÐ) is a division of the lifetime of the cosmos. The divisions are logarithmic in size, with base 10. Each successive cosmological decade represents a ten-fold increase in the total age of the universe.

HD2IOA

HD2IOA is the callsign of a time signal radio station operated by the Navy of Ecuador. The station is located at Guayaquil, Ecuador and transmits in the HF band on 3.81 and 7.6 MHz.The transmission is in AM mode with only the lower sideband (part of the time H3E and the rest H2B/H2D) and consists of 780 Hz tone pulses repeated every ten seconds and voice announcements in Spanish.

While sometimes this station is described as defunct, reception reports of this station on 3.81 MHz appear regularly at the Utility DX Forum.

Instant

An instant is an infinitesimal moment in time, a moment whose passage is instantaneous.

The continuous nature of time and its infinite divisibility was addressed by Aristotle in his Physics, where he wrote on Zeno's paradoxes. The philosopher and mathematician Bertrand Russell was still seeking to define the exact nature of an instant thousands of years later.In physics, a theoretical lower-bound unit of time called the Planck time has been proposed, that being the time required for light to travel a distance of 1 Planck length. The Planck time is theorized to be the smallest time measurement that will ever be possible, roughly 10−43 seconds. Within the framework of the laws of physics as they are understood today, for times less than one Planck time apart, one can neither measure nor detect any change. It is therefore physically impossible, with current technology, to determine if any action exists that causes a reaction in "an instant", rather than a reaction occurring after an interval of time too short to observe or measure.

As of November 2016, the smallest time interval uncertainty in direct measurements is on the order of 850 zeptoseconds (850 × 10−21 seconds).

Intercalation (timekeeping)

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

Kugelblitz (astrophysics)

In theoretical physics, a kugelblitz (German: "ball lightning") is a concentration of heat, light or radiation so intense that its energy forms an event horizon and becomes self-trapped: according to general relativity and the equivalence of mass and energy, if enough radiation is aimed into a region, the concentration of energy can warp spacetime enough for the region to become a black hole, although this would be a black hole whose original mass-energy had been in the form of radiant energy rather than matter. In simpler terms, a kugelblitz is a black hole formed from radiation as opposed to matter. (Such a black hole would notheless have properties identical to one of equivalent mass and angular momentum formed in a more conventional way, in accordance with the no-hair theorem.) A kugelblitz would be so hot it would surpass the Planck temperature, the temperature of the universe 5.4×10−44 seconds (one Planck time) after The Big Bang.

The best-known reference to the kugelblitz idea in English is probably John Archibald Wheeler's 1955 paper "Geons", which explored the idea of creating particles (or toy models of particles) from spacetime curvature. Wheeler's paper on geons also introduced the idea that lines of electric charge trapped in a wormhole throat might be used to model the properties of a charged particle-pair.

Kugelblitz drives have been considered as possible future black hole starship engines.

Minute

The minute is a unit of time or angle. As a unit of time, the minute is most of times equal to ​1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to ​1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time.

Orders of magnitude (time)

An order of magnitude of time is (usually) a decimal prefix or decimal order-of-magnitude quantity together with a base unit of time, like a microsecond or a million years. In some cases, the order of magnitude may be implied (usually 1), like a "second" or "year". In other cases, the quantity name implies the base unit, like "century". In most cases, the base unit is seconds or years. Prefixes are not usually used with a base unit of years, so we say "a million years", not "a megayear". Clock time and calendar time have duodecimal or sexagesimal orders of magnitude rather than decimal, i.e. a year is 12 months, and a minute is 60 seconds.

The smallest meaningful increment of time is the Planck time, the time light takes to traverse the Planck distance, many decimal orders of magnitude smaller than a second. The largest realized amount of time, given known scientific data, is the age of the universe, about 13.8 billion years - the time since the Big Bang as measured in the cosmic microwave background rest frame. Those amounts of time together span 60 decimal orders of magnitude. Metric prefixes are defined spanning 10−24 to 1024, 48 decimal orders of magnitude which may be used in conjunction with the metric base unit of second. Metric units of time larger than the second are most commonly seen only in a few scientific contexts such as observational astronomy and materials science although this depends on author; for everyday usage and most other scientific contexts the common units of minutes (60 s), hours (3600 s or 3.6 ks), days (86 400 s), weeks, months, and years (of which there are a number of variations) are commonly used. Weeks, months and years are significantly variable units whose length crucially depends on the choice of calendar and is often not regular even with a calendar, e.g. leap years versus regular years in the Gregorian calendar. This makes them problematic for use against a linear and regular time scale such as that defined by the SI since it is not clear as to which version of these units we are to be using. Because of this, in the table below we will not use weeks and months and the year we will use is the Julian year of astronomy, or 365.25 days of 86 400 s exactly, also called an annum and denoted with the symbol a, whose definition is based on the average length of a year of the Julian calendar which had one leap year every and always every 4 years against common years of 365 days each. This unit is used, following the convention of geological science, to form larger units of time by the application of SI prefixes to it at least up to giga-annum, or Ga, equal to 1 000 000 000 a (short scale: one billion years, long scale: one milliard years).

Planck length

In physics, the Planck length, denoted ℓP, is a unit of length that is the distance light travels in one unit of Planck time. It is equal to 1.616229(38)×10−35 m. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.

Planck units

In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units.

Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of several systems of natural units, but Planck units are not based on properties of any prototype object or particle (that would be arbitrarily chosen), but rather on only the properties of free space. Planck units have significance for theoretical physics since they simplify several recurring algebraic expressions of physical law by nondimensionalization. They are relevant in research on unified theories such as quantum gravity.

The term "Planck scale" refers to the magnitudes of space, time, energy and other units, below which (or beyond which) the predictions of the Standard Model, quantum field theory and general relativity are no longer reconcilable, and quantum effects of gravity are expected to dominate. This region may be characterized by energies around 1.22×1019 GeV (the Planck energy), time intervals around 5.39×10−44 s (the Planck time) and lengths around 1.62×10−35 m (the Planck length). At the Planck scale, current models are not expected to be a useful guide to the cosmos, and physicists no longer have any scientific model whatsoever to suggest how the physical universe behaves. The best known example is represented by the conditions in the first 10−43 seconds of our universe after the Big Bang, approximately 13.8 billion years ago.

The five universal constants that Planck units, by definition, normalize to 1 are:

the speed of light in a vacuum, c,

the gravitational constant, G,

the reduced Planck constant, ħ,

the Coulomb constant, ke = 1/4πε0

the Boltzmann constant, kBEach of these constants can be associated with a fundamental physical theory or concept: c with special relativity, G with general relativity, ħ with quantum mechanics, ε0 with electromagnetism, and kB with the notion of temperature/energy (statistical mechanics and thermodynamics).

Quantum cosmology

Quantum cosmology is the attempt in theoretical physics to develop a quantum theory of the Universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe.

The classical cosmology is based on Albert Einstein's general theory of relativity (GTR or simply GR). It describes the evolution of the universe very well, as long as you do not approach the Big Bang. It is the gravitational singularity and the Planck time where relativity theory fails to provide what must be demanded of a final theory of space and time. Therefore, a theory is needed that integrates relativity theory and quantum theory. Such an approach is attempted for instance with the loop quantum gravity, the string theory and the causal set theory.

Tempus fugit

Tempus fugit is a Latin phrase, usually translated into English as "time flies". The expression comes from line 284 of book 3 of Virgil's Georgics, where it appears as fugit inreparabile tempus: "it escapes, irretrievable time". The phrase is used in both its Latin and English forms as a proverb that "time's a-wasting". Tempus fugit, however, is typically employed as an admonition against sloth and procrastination (cf. carpe diem) rather than a motto in favor of licentiousness (cf. "gather ye rosebuds while ye may"); the English form is often merely descriptive: "time flies like the wind", "time flies when you're having fun".

The phrase's full appearance in the Georgics is:

The phrase is a common motto, particularly on sundials and clocks.

Tomorrow (time)

Tomorrow is a temporal construct of the relative future; literally of the day after the current day (today), or figuratively of future periods or times. Tomorrow is usually considered just beyond the present and counter to yesterday. It is important in time perception because it is the first direction the arrow of time takes humans on Earth.

Unit of time

A unit of time or midst unit is any particular time interval, used as a standard way of measuring or expressing duration. The base unit of time in the International System of Units (SI), and by extension most of the Western world, is the second, defined as about 9 billion oscillations of the caesium atom. The exact modern definition, from the National Institute of Standards and Technology is:

The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.Historically units of time were defined by the movements of astronomical objects.

Sun based: the year was the time for the earth to rotate around the sun. Year-based units include the olympiad (four years), the lustrum (five years), the indiction (15 years), the decade, the century, and the millennium.

Moon based: the month was based on the moon's orbital period around the earth.

Earth based: the time it took for the earth to rotate on its own axis, as observed on a sundial. Units originally derived from this base include the week at seven days, and the fortnight at 14 days. Subdivisions of the day include the hour (1/24th of a day) which was further subdivided into minutes and finally seconds. The second became the international standard unit (SI units) for science.

Celestial sphere based: as in sidereal time, where the apparent movement of the stars and constellations across the sky is used to calculate the length of a year.These units do not have a consistent relationship with each other and require intercalation. For example, the year cannot be divided into 12 28-day months since 12 times 28 is 336, well short of 365. The lunar month (as defined by the moon's rotation) is not 28 days but 28.3 days. The year, defined in the Gregorian calendar as 365.24 days has to be adjusted with leap days and leap seconds. Consequently, these units are now all defined as multiples of seconds.

Units of time based on orders of magnitude of the second include the nanosecond and the millisecond.

YVTO

YVTO is the callsign of the official time signal from the Juan Manuel Cagigal Naval Observatory in Caracas, Venezuela. The content of YVTO's signal, which is a continuous 1 kW amplitude modulated carrier wave at 5.000 MHz, is much simpler than that broadcast by some of the other time signal stations around the world, such as WWV.

The methods of time transmission from YVTO are very limited. The broadcast employs no form of digital time code. The time of day is given in Venezuelan Standard Time (VET), and is only sent using Spanish language voice announcements. YVTO also transmits 100 ms-long beeps of 1000 Hz every second, except for thirty seconds past the minute. The top of the minute is marked by a 0.5 second 800 Hz tone.The station previously broadcast on 6,100 MHz but appears to have changed to the current frequency by 1990.

Yesterday (time)

Yesterday is a temporal construct of the relative past; literally of the day before the current day (today), or figuratively of earlier periods or times, often but not always within living memory.

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