Time Dilation Definition: What is Time Dilation?

In summary, time dilation is the phenomenon in which the closer a body travels to the speed of light, the more its clock slows down. This is described by the Lorentz' Equation and can be seen in practical examples such as particle accelerators. However, time dilation is not affected by the acceleration of the clock, only by its velocity. Gravity also plays a role in time dilation, as seen in the gravitational time dilation factor. It is important to note that time dilation does not apply to photons, as there is no reference frame for them.
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Definition/Summary

Time dilation is the factor by which an inertial observer measures another observer's clock as going slow.

Time dilation is composed of two factors:
1) a relative factor of [itex]\sqrt{1\ -\ v^2/c^2}[/itex] for Lorentz time dilation, which depends only on the velocity of the clock
2) an absolute factor of [itex]\sqrt{-g\,_{0\,0}}[/itex] for gravitational time dilation, which depends only on the position of the clock.

Time dilation does not depend on the acceleration of the clock.

Lorentz time dilation is mutual for two inertial observers, in the sense that they will each regard the other's clock as running slow by the same factor.

Gravitational time dilation is greater (the clock is slower) where gravity is stronger (and gravitational potential is higher).

Equations

Lorentz (special relativity) time dilation:

[tex]\sqrt{1\ -\ v^2/c^2}[/tex]

Static metric, with gravitational potential U:

[tex]ds^2\ =\ g_{00}dt^2\ +\ g_{ij}dx^idx^j\ \simeq\ - (1\ -\ 2U)dt^2\ +\ g_{ij}dx^idx^j[/tex]

Gravitational time dilation in static metric:

[tex]\sqrt{\frac{g_{00}(clock)}{g_{00}(observer)}}\ \simeq\ \sqrt{\frac{1\ -\ 2U(clock)}{1\ -\ 2U(observer)}}\ \simeq\ 1\ -\ U(clock)\ +\ U(observer)\ =\ 1\ -\ \Delta\,U[/tex]

Schwarzschild (static metric) gravitational potential at distance r from mass M:

[tex]U\ =\ \frac{2GM}{rc^2}\ =\ \frac{2gr}{c^2}[/tex]

Extended explanation

Accelerating observers:

These formulas are not intended to apply when an accelerating observer measures another observer's clock.

But they do apply when only the clock is accelerating: for example, when an observer on Earth measures a satellite clock.

Time dilation and red-shift:

The Lorentz red-shift or blue-shift for movement directly away from or toward the observer is [itex]\sqrt{(1\ -\ v/c)(1\ +\ v/c)}[/itex]

Gravitational red-shift (for any velocity) is the same as gravitational time dilation.

Static metric:

A static metric is stationary (the coefficients do not depend on t), and has [itex]g_{i\,0}\ =\ g_{0\,i}\ =\ 0,\ \ i\ =\ 1,2,3[/itex] (so there are are no "space-and-time" terms such as dxdt dydt or dzdt).

Simultaneity:

For gravitational time dilation to be meaningful, the spacetime metric must … time coordinate … simultaneity … [hmm … still thinking about this … see p100, Ciufolini & Wheeler … anyone wanting to jump in and finish this, or add anything else, be my guest! :biggrin:]

Approximations:

At low speeds, [itex]\sqrt{1\,-\,v^2/c^2}[/itex] is approximately [itex]1\ -\ (1/2)(v/c)^2[/itex]

For example, the Earth orbits the Sun at about 18 miles per second (about 64,000 mph), which is about 1/10,000 of the speed of light, and so time dilation, as seen by a non-orbiting observer, would be about 1 - 1/200,000,000.

Near the speed of light, [itex]\sqrt{1\,-\,v^2/c^2},\ =\ \sqrt{(1\,+\,v/c)(1\,-\,v/c)}[/itex] is approximately [itex]\sqrt{2(1\,-\,v/c)}[/itex]

Orbits:

A clock on a satellite in orbit goes slower than a stationary clock on the planet: it has a "slowing-down" SR time dilation depending on its speed, and a smaller "speeding-up" GR time dilation depending on its distance from the planet.

There is no "clock paradox" since the satellite clock is the clock of an accelerating observer, not of an inertial observer (the instantaneous inertial frame of the satellite clock keeps changing).

Circular orbits:

Between two satellites on circular orbits of the same radius, only their relative speed matters.

If they're on the same orbit, in the same direction, then their relative speed will be constant, and there will be no time dilation between them (though both will be slower than a clock on the planet).

On different orbits (of the same radius), there will be time dilation between them (though that dilation will cancel out once every orbit, as can be seen by comparison with any planetary clock).

* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
 
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  • #2
Time dilation is a very interesting phenomenon. The closer a body travels to c, the more its clock slows down, according to the Lorentz' Equation. That means for light, the entire universe has contracted into absolute zero length and the time it takes for going from source to anything is zero (for itself). For us, light takes about 8 mins. to reach us from the Sun. But for light, its clock is completely dilated and w.r.t light frame, the time taken is zero. IF a spaceship travels at relativistic speeds, the thoughts, pulse rate,etc. of the astronaut inside will slow down w.r.t the people on Earth. There is even a practical proof for this. Radioactive isotopes which are accelerated to speeds near c in Particle Physics Laboratories have comparatively longer lives than their at-rest counterparts.
 
  • #3
Amey said:
Time dilation is a very interesting phenomenon. The closer a body travels to c, the more its clock slows down, according to the Lorentz' Equation. That means for light, the entire universe has contracted into absolute zero length and the time it takes for going from source to anything is zero (for itself). For us, light takes about 8 mins. to reach us from the Sun. But for light, its clock is completely dilated and w.r.t light frame, the time taken is zero. IF a spaceship travels at relativistic speeds, the thoughts, pulse rate,etc. of the astronaut inside will slow down w.r.t the people on Earth. There is even a practical proof for this. Radioactive isotopes which are accelerated to speeds near c in Particle Physics Laboratories have comparatively longer lives than their at-rest counterparts.
You are making the common mistake of believing that there is such a thing as a reference frame for a photon. There is not.
 
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  • #4
I am new in this forum.
I read at Wikipedia About Time dilation and:
1)Understood that gravity bends the space and hence time.
But, does velocity in any manner do alter space/time ?
 
  • #5
The universe tends to ignore misperceptions about the way reality works
 
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What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for an object or person that is moving at high speeds or in a strong gravitational field, compared to an observer who is at rest.

How does time dilation occur?

Time dilation occurs due to the principles of special and general relativity, which state that the laws of physics are the same for all observers and that the speed of light is constant. This means that time and space are relative and can be affected by an object's velocity and the strength of local gravity.

Can time dilation be observed?

Yes, time dilation can be observed and has been verified through numerous experiments and observations. For example, atomic clocks on airplanes and satellites have been found to run slightly slower than clocks on the ground due to the difference in velocity and gravitational pull.

What are the practical applications of time dilation?

Time dilation has practical applications in fields such as space travel, satellite navigation, and particle accelerators. Without accounting for time dilation, these technologies would not be as accurate or effective as they are today.

Is time dilation just a theory?

No, time dilation is a well-established phenomenon that has been extensively studied and verified through experiments and observations. It is a fundamental aspect of modern physics and is crucial for understanding the nature of time and space.

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