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Time dilation

From Simple English Wikipedia, the free encyclopedia
Two clocks will show different times inouter space and onEarth.

Gravitational time dilation is aphysics concept about changes in the passage oftime, caused bygeneral relativity. Aclock inouter space moves quicker than a clock onEarth.Heavy things likeplanets create agravitational field that slows down time nearby. An example of gravity causing time dilation is that if an object is near ablack hole its time will slow relative to that of time on earth. This means that a clock on a spaceship far away from any planet would move faster than a clock near Earth.

This is different from time dilation explained byspecial relativity, which says fast objects move more slowly through time. Closesatellites like theInternational Space Station move very quickly toorbit the Earth, so they are slowed down. Because the ISS is inlow Earth orbit (LEO), time dilation due to gravity is not as strong as time dilation due to its speed, so a clock on it is slowed down more than it is sped up. An object inGeostationary orbit moves less quickly and is farther away from Earth, so gravitational time dilation is stronger, and clocks move quicker than in LEO. This means thatengineers need to pick different clocks for different orbits.GPS satellites work because they know about both kinds of time dilation.[1]

Case #1: Inspecial relativity, clocks that are moving run slower, according to a stationary observer's clock.This effect does not come from workings of the clocks, but from the nature ofspacetime.

Case #2: the observers may be in positions with differentgravitational masses. Ingeneral relativity, clocks that are near a strong gravitational field run slower than clocks in a weaker gravitational field.

If you were to have a rotor, or motor, moving at a very fast speed (any measurement of speed will cause time dilation just in varying amounts) and have a beam of sorts with a capsule, the faster it spins the more time changes.

This could theoretically make atime machine although it could only go forward and would be very dangerous.

Evidence

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Experiments support both aspects of time dilation.[2][3][4][5]

Time dilation due to relative velocity

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The formula for determining time dilation in special relativity is:

Δt=Δt1v2/c2{\displaystyle \Delta t'={\frac {\Delta t}{\sqrt {1-v^{2}/c^{2}}}}\,}

where

Δt{\displaystyle \Delta t\,} is the time interval for an observer (e.g. ticks on his clock) – this is known as theproper time,
Δt{\displaystyle \Delta t'\,} is the time interval for the person moving with velocityv with respect to the observer,
v{\displaystyle v\,} is the relative velocity between the observer and the moving clock,
c{\displaystyle c\,} is thespeed of light.

It could also be written as:

Δt=γΔt{\displaystyle \Delta t'=\gamma \Delta t\,}

where

γ=11v2/c2{\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}\,} is theLorentz factor.

A simple summary is that more time is measured on the clock at rest than the moving clock, therefore, the moving clock is "running slow".

When both clocks are not moving, relative to each other, the two times measured are the same. This can be proven mathematically by

Δt=Δt10/c2=Δt{\displaystyle \Delta t'={\frac {\Delta t}{\sqrt {1-0/c^{2}}}}={\Delta t}\,}

For example:In a spaceship moving at 99% of the speed of light, a year passes. How much time will pass on earth?

v=0.99c{\displaystyle v=0.99c\,}
Δt=1{\displaystyle \Delta t=1\,} year
Δt=?{\displaystyle \Delta t'=?\,}

Substituting into :Δt=Δt1v2/c2{\displaystyle \Delta t'={\frac {\Delta t}{\sqrt {1-v^{2}/c^{2}}}}\,}

Δt=11(.99c)2/c2=11(.99)2(c)2c2=11(.99)2{\displaystyle \Delta t'={\frac {1}{\sqrt {1-(.99c)^{2}/c^{2}}}}={\frac {1}{\sqrt {1-{\frac {(.99)^{2}(c)^{2}}{c^{2}}}}}}={\frac {1}{\sqrt {1-(.99)^{2}}}}}
=110.9801=10.0199=7.08881205{\displaystyle ={\frac {1}{\sqrt {1-0.9801}}}={\frac {1}{\sqrt {0.0199}}}=7.08881205}years

So approximately 7.09 years will pass on earth, for each year in the spaceship.

In ordinary life today, time dilation had not been a factor, where people move at speeds much less than thespeed of light, the speeds are not great enough to produce any detectable time dilation effects. Such vanishingly small effects can be safely ignored. It is only when an object approaches speeds on the order of 30,000kilometres per second (67,000,000 mph) (10% the speed of light) that time dilation becomes important.

However, there are practical uses of time dilation. A big example is with keeping the clocks onGPS satellites accurate. Without accounting for time dilation, the GPS result would be useless, because time runs faster onsatellites so far from Earth'sgravity. GPS devices would calculate the wrong position due to the time difference if the space clocks were not set to run slower on Earth to offset the quicker time in highEarth orbit (geostationary orbit).

References

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  1. Ashby, Neil (2003)."Relativity in the Global Positioning System"(PDF).Living Reviews in Relativity.6 (1): 16.Bibcode:2003LRR.....6....1A.doi:10.12942/lrr-2003-1.PMC 5253894.PMID 28163638. Archived fromthe original(PDF) on 2015-11-05. Retrieved2019-07-08.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  2. Blaszczak Z. 2007 (15 April 2010).Laser 2006. Springer. p. 59.ISBN 978-3540711131.{{cite book}}: CS1 maint: numeric names: authors list (link)
  3. Hasselkamp D; Mondry E. & Scharmann A. 1979 (1979). "Direct observation of the transversal Doppler-shift".Zeitschrift für Physik A.289 (2):151–155.Bibcode:1979ZPhyA.289..151H.doi:10.1007/BF01435932.S2CID 120963034.{{cite journal}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
  4. Chou C.W.et al 2010 (2010)."Optical clocks and relativity".Science.329 (5999):1630–1633.Bibcode:2010Sci...329.1630C.doi:10.1126/science.1192720.PMID 20929843.S2CID 206527813.{{cite journal}}: CS1 maint: numeric names: authors list (link)
  5. Pound R.V. & Snider J.L. 1964 (1964)."Effect of gravity on nuclear resonance".Physical Review Letters.13 (18):539–540.Bibcode:1964PhRvL..13..539P.doi:10.1103/PhysRevLett.13.539.{{cite journal}}: CS1 maint: numeric names: authors list (link)
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