Time Dilation; Twins Paradox

[PFC]

I'm not a science major person but I've a question :

 

Time is slower with gravity.

 

So why a person traveling closed to speed of light in space can return to earth to be younger than her twin? Gravity is stronger on earth than in space right? If so, the time in space is faster than on the earth? How the space traveler twin be younger?

[A-wal]

Two different causes (well not really).

 

Galilean relativity is the basic premise that all inertial motion is relative.

 

Special relativity describes relative motion free from gravitation, and includes the twin paradox that isn't actually a paradox at all. The twin that accelerated will be younger once they're back in the same inertial frame of reference.

 

General relativity describes gravitation and includes gravitational time dilation.

 

Either ways, it's acceleration that causes time dilation.

 

Length contraction is equally important. To keep the speed of light constant in all possible inertial frames, length contraction shortens the distance and time dilation reduces that amount of time it takes to cover that shorter distance.

[CraigD]

So why a person traveling closed to speed of light in space can return to earth to be younger than her twin? Gravity is stronger on earth than in space right? If so, the time in space is faster than on the earth? How the space traveler twin be younger?

Due to gravitational time dilation, a person far from Earth or another planet (and, more importantly, the Sun or another star) does age faster than one on Earth, but only by about 1 second every 3 years. Gravity is stronger on Earth than far from any planet or star, but is still weak compared to what’s needed to slow time so much it would be noticeable other than using very precise clocks.

 

The relative velocity time dilation for a speed needed to travel to nearby stars within a human lifetime – let’s say 10% the speed of light – results in the traveling person aging about 7 minutes per day less than the Earthbound one.

 

So the traveler ages a tiny amount faster due to the reduced gravity, but so much slower due to their speed that people usually ignore the effect of gravity when discussing the “twin paradox” thought experiment.

 

Here’re the formulas needed:

[math]\frac{t_0}{t} = \sqrt{1 - \frac{r_s}{r}}[/math]

[math]r_s = \frac{2 G}{c^2} M[/math]

[math]\frac{t}{t_0} = \sqrt{1 - \left( \frac{v}{c} \right)^2 }[/math]

Where [math]t_0[/math] is the Earthbound clock rate, [math]t[/math] the traveling clock rate, [math]r[/math] the distance from the main gravity-making body (the Sun and Earth), [math]G[/math] the gravitational constant, [math]M[/math] the mass of the main body, and [math]v[/math] the speed of the traveler.

 

Plug in [math]M[/math] and [math]r[/math] for the Sun and Earth, and [math]v=0.1 c[/math], do a bit of unit conversion, and you’ll get the examples I give above.

[A-wal]

Either ways, it's acceleration that causes time dilation.

I should clarify this. I think what confuses people is that the difference on clocks in the same inertial frame is usually referred to as time dilation as well as the difference in coordinate time between different inertial frames.

 

I'll call the difference in elapsed proper time 'temporal delay'. So the quote from the previous post would read: Either ways, it's acceleration that causes temporal delay, because acceleration is responsible for the difference on watches in the same inertial frame.

 

What's important (and what a lot of people get wrong) is that temporal delay is only caused by acceleration, never velocity. It's not caused by time dilation and length contraction due to a difference in velocity because that's symmetric, each is time dilated and length contracted from the other frame's point of view.

 

Gravity can be thought of as acceleration, so an object in a stronger gravitation field will experience greater acceleration and more temporal delay that one in a lower weaker gravitation, so less time passes on the watch experiencing stronger gravity.