The Impact of Gravity on Time: Exploring the Maximum Speed of Time Flow

[strangemuon]

Hello All,

I am new here and I have been searching for answers to some questions I have. Please excuse me if what I am asking has previously been answered here, I did try to search but didn't have much luck. If you can direct me to the thread where it has been previously discussed then that would be great. Alright, here goes.

As I understand it gravity affects the rate of time flow. For example, time of an atomic clock located on the surface of Earth would run slower than an identical atomic clock located on a satellite orbiting Earth. I believe this is a real-world problem that had to be solved for the GPS system to work correctly. Given this information I would have the following questions:

1. If two identical twins were available for an experiment and one stayed on the surface of Earth while the other lived on the international space station (or even in a shuttle) for a period of time, let's say 1 year. At the end of the 1 year would it be true that the twin in space would actually be older than the twin that stayed on Earth? I don't know the actual rate difference between time on Earth and time in space (I would like to find out) but to put some numbers to my example I will assume that time moves 5 times faster in space than on Earth. I know this is not an exact model but I just wanted to put the numbers to it so I can relate my example. According to what I have written, is it true that after 1 year the space twin would be 5 years older than the Earth twin, assume what I have for the example?

2. Since the effects of gravity dissipate inversely proportionally to the distance from an object, I do realize that the effects of gravity are always able to be calculated regardless of how far away from an object you are however there is a point where it would become negligible. At this point, where the effects of gravity from an object are negligible, what is that rate of flow of time? I guess maybe I am asking how much faster would time flow in deep space where gravity is non-existent in comparison to Earth time? Or maybe a better question is what would be the maximum speed of time flow?

If anything requires further explanation, please let me know. Thanks in advance for everyone's input. Also, I think it is very possible I am misunderstanding something and/or not factoring in something important. If this is the case, please steer me in the correct direction.

 

[schroder]

There are several relativistic effects regarding an orbiting satellite in the GPS network, but the two most prevalent are the gravitational blue shift and the time dilation due to relative motion. The blue shift means the orbiting clock is running faster than one on the earth’s surface, while the time dilation effect makes the orbiting clock run slower. If the orbital radius is approximately 9550 Km, the two effects cancel each other. At the orbital height of the GPS satellite, 20,000 Km, the gravitational blue shift is predominant and it must be taken into account to keep the clocks synchronized. However, a satellite orbiting the Earth is not going to create a significant “twin paradox” as even over a span of five years the difference will be less than one second!

 

[strangemuon]

Thank you for the great feedback! As a follow-up question, would there be a point outward from Earth, maybe just theoretical, where the time difference would become significant? Assuming that point away would not have the added effect of additional gravity from other celestial objects. If so, what would the maximum time difference value become as the distance away goes to infinity?

Thanks again for all the help.

 

[russ_watters]

It does depend a little on what you consider significant, but there is no distance from Earth where the gravitational time dilation would be noticeable to human perception.

 

[strangemuon]

What if the one twin lived a lifespan of 100 years all being lived within the zero gravity region as compared to the other twin living all those 100 years on Earth? What would the time difference be then? 1 day? 1 year? more? less?

 

[russ_watters]

A fraction of a second would be my guess, but you can calculate it easily enough from this equation: http://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere