Question about how Time varies with Velocity

[rsclafani]

I'm posting this in order to better understand the relationship between the rate at which time passes and an object's velocity. As I currently understand it, as the velocity of an object increases, time, or the rate at which time passes, slows in order to keep the speed of light a constant for that object. So, an object, with mass, moving at a certain velocity will have a certain time rate specific to that object at that velocity. Now my question is two fold. First, what is the rate of time of the earth? I would like to be specific about this. Because, as I understand it, while I feel no motion I am actually moving at an incredible speed through space. For example the Earth is spinning, which gives me, on its surface, some velocity. Next, the Earth is also traveling around the sun in its orbital path which again gives me added velocity. Also, the solar system is traveling about the galactic center with some velocity, and lastly, the galaxy itself is flying through space with its own velocity. So, I'm wondering, how fast does time move for me in comparison to let's say an area of empty space? Which brings me to the second part of the question. How fast does time move in an area of no mass? For example the area between stars or maybe the area between galaxies. Along this line of reasoning to seems to me that time might move at different rates in different parts of the universe corresponding to objects which have higher or lower velocities. Also, I'd like to know how does time flow when there is no mass around?

I'm very curious about this so if someone could please clarify this for me I'd greatly appreciate it.

 

[ghwellsjr]

Just like velocity is relative, the rate of a time is also relative. No matter how fast we are moving on the surface of the Earth relative to the sun or the galactic center or anything else, we can consider ourselves to be stationary and the sun or the galactic center to be what's moving which means time for us is perfectly normal and it is the sun and the galactic center that has slower rates of time. Of course, the sun or the galactic center can consider themselves to be stationary and we are the one that is moving. So we will see the sun's time as being slower by one rate and the galactic center to be slower by a different rate. The faster they are moving relative to us, the slower the rate of time we will consider them to be experiencing, and vice versa, by exactly the same amount.

It's just like relative velocity, if I see you going by me at some speed, you will see me going by you at exactly the same speed. And that speed will determine the rate of time slowing down that I will observe in you and you will observe in me.

 

[rsclafani]

I see, that answers the first part of the question. So you're saying that the rate of time passing is relative depending on the observer.

I'm still a little confused about one thing. Let's say there was no object that can be observed. For example if I'm looking at an area of space through a telescope that is empty. How is that time rate, the time within that empty region of space, passing with respect to me?

I may be asking the wrong question here, something like if the tree falls in the forest and there is no one to hear it, does it make a sound?

Would the answer be, if I fix a reference frame to that region of space, then the time within that frame be slowed by our relative velocity or my velocity with respect to that empty region of space?

 

[ghwellsjr]

If there is no physical object traveling at a speed relative to you, the observer, then there is no sense in which you can talk about time slowing down in that region of empty space. Your question about the tree in the forest would be more analogous to: if there is no forest, would there be a sound when a tree fell?

When you fix a reference frame, it extends out in all directions from wherever you consider the origin to be. Time also extends out from time zero to infinity past and future. In other words, there is no place and there is no time that is not covered by the reference frame (how could there be, it's just a coordinate system?). There aren't separate reference frames for you over here and the empty space over there. So if you fix a reference frame at your present location and time, then you can talk about where and when this empty region of space is. Or you could image the origin (when and where all four coordinates of the reference frame are zero) to be at an empty region of space and you are located some very large distance away.

You can also use the Lorentz Transform to change all four of the coordinates of events in one reference frame to other sets of coordinates in a second reference frame moving at some speed with respect to the first one. So in these two reference frames the same clock could be ticking away at different rates, as defined by each reference frame, but an observer located with that clock would not be aware that according to a different reference frame, he and his clock are experiencing time at a different rate, just like he cannot be aware of any change in the coordinates of his location when it is considered from two different reference frames.

 

[yoron]

You can also define it as you never will find a time dilation in your own 'frame of reference'. They (time dilations) only exist relative other 'frames of reference'. And as gravity is the 'metric of space', according to Einstein, that will mean that all clocks should be 'time dilated' relative your own 'local clock'. That as gravity creates 'time dilations' relative your local clock too. Well, it might mean that there are possible 'patches' too, having the same 'gravity' etc, as you, possible to define as a same 'frame of reference'. But how do you find them?

Even here on Earth.

You can define it as if sending a light signal (from the exact middle) between two uniformly moving (identical) objects/clocks, being at rest relative each other, could be used to synchronise those clocks, defining a same 'frame of reference' for both, but only if ignoring gravity.

A 'flat space' is a theoretical definition as all objects of mass, coupled to gravity, are in 'relative motion' and so should be redefining the space/clocks/gravity between them constantly. For my type of definition you have to consider ideal clocks though, able to measure 'Planck time'.