Time dilation

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According to the theory of relativity, widening time is the difference in the elapsed time measured by two observers, either because of the relative velocity difference with each other, or with different positions relative to the gravitational field. As a result of the nature of the time space, the clock moving relative to the observer will be measured to tick more slowly than the resting clock within the frame of reference of the observer itself. Clocks under the influence of a gravitational field that is stronger than the observer will also be measured to tick more slowly than the observer's own clock.

Such widening times have been repeatedly pointed out, for example by a small difference in a pair of atomic clocks after one of them is sent on a space journey, or with a clock in Space Shuttle running a bit slower than the reference clock on Earth, or a clock on the GPS. and the Galileo satellite runs a little faster. The widening of time has also been the subject of science fiction, as it technically provides the means for the passage of time ahead.

Video Time dilation

Histori

Time widening by Lorentz's factor was predicted by some authors at the turn of the 20th century. Joseph Larmor (1897), at least for the orbiting electrons, writes "... each electron describes the corresponding part of its orbit in a shorter time for the break system in the ratio: ${\ displaystyle \ scriptstyle {\ sqrt {1 - {\ frac {v ^ {2}} {c ^ {2} annotations> Emil Cohn (1904) specifically associates this formula with the clock level In the context of specific relativity, this is demonstrated by Albert Einstein (1905) that this effect it concerns the nature of the time itself, and it is also the first to show reciprocal or symmetry. Furthermore, Hermann Minkowski (1907) introduces the exact timing concept that further explains the meaning of time widening.$

Maps Time dilation

Time-lapse speed

Special relativity indicates that, for the observer in terms of the inertial reference, the clock moving relative to it will be measured to tick more slowly than the resting clock in its frame of reference. This case is sometimes called the widening of special relativistic time. The faster the relative speed, the greater the widening time between each other, with the time rate reaching zero when one approaches the speed of light (299.792.458 m/s). This causes particles without mass moving at the speed of light not affected by the passage of time.

Theoretically, widening time will allow passengers in fast moving vehicles to advance further into the future in no time at their own time. For a fairly high speed, the effect is dramatic. For example, a year's journey may correspond to ten years on Earth. Indeed, a constant 1 g acceleration will allow humans to travel through the entire known universe in a single human life. Space travelers can then return to Earth billions of years in the future. The scenario based on this idea is presented in Pierre Boulle's novel Planet of the Apes , and the Orion Project has been an effort towards this idea.

With today's technology severely limiting the speed of space travel, however, the difference experienced in practice is very small: after 6 months at the International Space Station (ISS) (which orbits the Earth at a speed of about 7,700 m/s) the astronaut will have been around 0.005 seconds less than there is on Earth. Hafele and Keating experiments involve airplanes around the world with atomic clocks on the board. After the journey is over the clock compared to a static atoms ground-based clock. It was found that 273 Ã, Â ± 7 nanoseconds has been obtained on the plane clock. The current human time travel record holder is Russian cosmonaut Sergei Krikalev. He earned 22.68 milliseconds a lifetime on his way into space and therefore beat the previous record of about 20 milliseconds by cosmonaut Sergei Avdeyev.

Simple conclusion widening time speed

The widening of time can be deduced from the observed firmness of the speed of light across all reference frames determined by the second postulate of special relativity.

This firmness of light velocity means that, contrary to intuition, the speed of material things and light is not additive. It is impossible to make the speed of light appear larger by moving toward or away from the light source.

Consider then, a simple clock consisting of two mirrors A and B , where the light pulse bounces. Mirror separation is L and clock once every time the pulse of light touches one of the mirrors.

Dalam frame di mana jam sedang beristirahat (diagram di sebelah kiri), pulsa cahaya menelusuri jalur panjang 2 L dan periode jam adalah < span> 2 L dibagi dengan kecepatan cahaya:

${\ displaystyle \ Delta t = {\ frac {2L} {c}}.}  ÂÂ$

From the moving observer reference frame traveling at a velocity of v

Total waktu untuk pulsa cahaya untuk melacak jalurnya diberikan oleh

${\ displaystyle \ Delta t '= {\ frac {2D} {c}}.}  ÂÂ$

Panjang setengah jalan dapat dihitung sebagai fungsi dari kuantitas yang dikenal sebagai

${\ displaystyle D = {\ sqrt {\ left ({\ frac {1} {2}} v \ Delta t '\ right) ^ {2} L ^ { 2}}}.}  ÂÂ$

Eliminasi variabel D dan L dari ketiga persamaan ini menghasilkan

${\ displaystyle \ Delta t '= {\ frac {\ Delta t} {\ sqrt {1 - {\ frac {v ^ {2}} {c ^ {2} }}}}},}  ÂÂ$

yang mengungkapkan fakta bahwa periode pengamat yang bergerak dari jam ${\ displaystyle \ Delta t '}  ÂÂ$ lebih panjang dari periode ${\ displaystyle \ Delta t}  ÂÂ$ dalam bingkai jam itu sendiri.

Timbal balik

Given the particular frame of reference, and the "stationary" observer described earlier, if the second observer is accompanied by a "moving" clock, each observer will see the other clock as ticking at a slower rate of their own local clock , as they both feel the other to be one that moves relative to their own stationary reference frame.

Common sense will dictate that, if the passage of time has slowed to a moving object, the object mentioned will observe the time of the external world to be accelerated. Controversially, special relativity predicts otherwise. When two observers move relative to each other, each one will measure another slowing clock, corresponding to those in motion relative to the reference frame of the observer.

While this seems to contradict yourself, similar peculiarities occur in everyday life. If two people A and B look at each other from a distance, B will appear small for A, but at the same time A will appear small for B. Being familiar with the effects of perspective, there is no contradiction or paradox in this situation.

In the Minkowski diagram of the second image on the right, clock C rests in the inertial frame S? meet hour A on d and clock B in f (both based on S). All three clocks simultaneously start ticking in S. The line of world A is the ct axis, the world line B intersected f parallel to the c-axis, and the world line C is ct? -axis. All simultaneous events with d in S are on the x axis, in S? on x? -axis.

The exact time between two events is indicated by the hours present in both events. It is invariant, that is, in all frames of inertia it is agreed that this time is indicated by that clock. The interval df is the exact time of the clock C, and shorter by observing the coordinate time ef = dg of clock B and A in S. Conversely, also the exact time > ef B is shorter than the time if in S?, since event e is measured in S? it is in due course i because of the relativity of the simultaneity, long before C starts ticking.

It can be seen, therefore, that the exact time between two events represented by the immeasurable clock is present in both events, compared to the synchronized coordinate time measured in all other inertia frames, always at least the time interval in between these events. However, the interval between two events can also match the exact time of the accelerated hour present in both events. Below all possible precise time between two events, the exact time of the immeasurable hour is maximum , which is the solution to the twin paradox.

Derivation and Formulation

Karena jam tetap diam dalam bingkai inersia, ia akan mengikuti ${\ displaystyle x_ {a} = x_ {b}}  ÂÂ$ , sehingga interval ${\ displaystyle \ Delta t ^ {\ prime} = t_ {b} ^ {\ prime} -t_ {a} ^ {\ prime}}  ÂÂ$ diberikan oleh

${\ displaystyle \ Delta t '= \ gamma \, \ Delta t = {\ frac {\ Delta t} {\ sqrt {1 - {\ frac {v ^ {2 }} {c ^ {2}}}}}} \,}  ÂÂ$

Where? t is the time interval between two co-local events (ie occurs in the same place) for the observer in some inertial framework (eg ticks on the watch), known as the right time ,? t? is the time interval between the same events, as measured by other observers, moves inertia with the velocity v in respect of the former observer, v is the relative velocity between observer and clock move, c is the speed of light, and the Lorentz factor (usually symbolized by Greek or gamma letters) is

${\ displaystyle \ gamma = {\ frac {1} {\ sqrt {1 - {\ frac {v ^ {2}} {c ^ {2} }}}}} \,.}$

Thus the clock cycle duration of the moving clock is found to increase: it is measured to be "slow running". The range of such variants in ordinary life, where v << c , even considering space travel, is not large enough to produce detectable time with easy dilatation effects and very small effects can be safely ignored for most purposes. Only when an object approaches a speed in the order of 30,000 km/s (1/10 the speed of light) that widening time becomes important.

Hyperbolic movements

In special relativity, the simplest time width is explained in circumstances where the relative velocity does not change. Nevertheless, the Lorentz equation allows one to calculate the exact time and movement in space for simple cases of spacecraft applied in force per unit mass, relative to some reference objects in uniform motion (ie constant speed), equal to g during the measurement period.

Let t be the time in the inertia frame which is then called the resting frame. Let x be the spatial coordinate, and let the constant acceleration and spacecraft speed (relative to the break frames) parallel to x -axis. Assuming the spacecraft's position at t = 0 becomes x = 0 and the velocity becomes v ₀ and defines the following abbreviations

_{          ?                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,                          =                     Â 1      Â         <Â>     Â 1      Â     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ...    Â  <Â>}                                 0        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,                                2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ/                             /        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ...         ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï mi½ <Â>                                2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       Â                          ,               {\ displaystyle \ gamma _ {0} = {\ frac {1} {\ sqrt {1-v_ {0} ^ {2}/c ^ { 2}}}},}  Â

the following formula applies:

Posisi:

${\ displaystyle x (t) = {\ frac {c ^ {2}} {g}} \ kiri ({\ sqrt {1 {\ frac {\ left ( gt v_ {0} \ gamma _ {0} \ right) ^ {2}} {c ^ {2}}}}} - \ gamma _ {0} \ kanan).}  ÂÂ$

Kecepatan:

${\ displaystyle v (t) = {\ frac {gt v_ {0} \ gamma _ {0}} {\ sqrt {1 {\ frac {\ left ( gt v_ {0} \ gamma _ {0} \ right) ^ {2}} {c ^ {2}}}}}}.}  ÂÂ$

Waktu yang tepat:

${\ displaystyle \ tau (t) = \ tau _ {0} \ int _ {0} ^ {t} {\ sqrt {1- \ left ({\ frac {v (t ')} {c}} \ right) ^ {2}}} dt'.}  ÂÂ$

Dalam kasus di mana v (0) = v ₀ = 0 dan ? (0) = ? ₀ = 0 integral dapat dinyatakan sebagai fungsi logaritmik atau, ekuivalen, sebagai fungsi hiperbolik inverse:

${\ displaystyle \ tau (t) = {\ frac {c} {g}} \ ln \ kiri ({\ frac {gt} {c}} {\ sqrt {1 \ left ({\ frac {gt} {c}} \ right) ^ {2}}} \ right) = {\ frac {c} {g}} \ operatorname {arsinh} \ left ({\ frac {gt} {c}} \ right).}  ÂÂ$

Hipotesis jam

The clock hypothesis is the assumption that the rate at which the clock is affected by the widening of time is independent of its acceleration but only at its instantaneous speed. This is equivalent to stating that the clock is moving along the path ${\ displaystyle P}$ measure the exact time, determined by:

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂdÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â?Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â=Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{          ?                 Â¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯                                          Â     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,              t                             2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>      ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÃ, -      Â     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,              x                             2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>                       Â /                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                             2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>      ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÃ, -      Â     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,    Â  <                             2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>                       Â /                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                             2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>      ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÃ, -      Â     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       Â                              2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>                       Â /                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                             2        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,         Â  <Â>                                 {\ displaystyle d \ tau = \ int _ {P} {\ sqrt {dt ^ {2} -dx ^ {2}/c ^ {2} -dy ^ {2}/c ^ {2} -dz ^ {2}/c ^ {2}}}}  Â} .

The clock hypothesis is implicitly (but not explicitly) included in the formulation of Einstein's original special relativity of 1905. Since then, it has become a standard assumption and is usually included in the special axiom of relativity, especially in the light of experimental verification to very high acceleration in particle accelerators.

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The widening of gravity time

The widening of gravity time is experienced by observers that, under the influence of the gravitational field, will measure its own clock to slow down, compared to others under the weaker gravitational field.

The widening of gravity time is being played for example for ISS astronauts. While the relative speed of astronauts slows down their time, the effect of reduced gravity at their location accelerates, albeit to a lesser extent. Also, the climber's time theoretically

Source of the article : Wikipedia