Does Time Dilation Apply to Objects Moving at Sub-Light Speeds?

[Jake]

I'm trying to understand the mechanics of time dilation. Mabye some of the SR/GR Gurus can help me with this one

So an often used example that helps to visualize time dilation is a light click. A person moving in a vehicle WITH the light click just sees the light moving up and down, wheares someone in a rest frame relative to the vehicle sees the light moving up and down, AND forward, in a zigzag. Since light moves at a constant speed regardless of speed, the longer distance == more time thus time dilation.

But would that same example work for massive objects moving at less than C? Example, someone onboard the vehicle bounces a ball up and down, to him it just bonced up 3 feet, but to someone on land it moved 3 ft + the 10 feet the vehicle moved in that period of time. Thus, since in a given area of road, the ball moved different amounts to different frames of refrence, time was slow for the frame of refrence moving?

I'm not sure, let me know what you think :)

 

[Doc Al]

The reason that "light clocks" are used is that the behavior of light is easy to describe in SR: its speed is the same for all observers. So, just using the basic postulates of SR, the light clock allows you to derive the time dilation effect.

Would a "rubber ball clock" work? Sure, but it would be harder to analyze. You'd have to use the relativistic velocity addition formula to find the speed of the ball as seen from the moving frame. So the ball clock is not a useful "thought experiment" for deriving SR effects.

The bottom line: time dilation is exhibited by any moving clock, but some clocks are easier to analyze than others.

 

[Gonzolo]

But would that same example work for massive objects moving at less than C? Example, someone onboard the vehicle bounces a ball up and down, to him it just bonced up 3 feet, but to someone on land it moved 3 ft + the 10 feet the vehicle moved in that period of time. Thus, since in a given area of road, the ball moved different amounts to different frames of refrence, time was slow for the frame of refrence moving?

I'm not sure, let me know what you think :)

The key difference in the light and the ball is from your own quote :

"Since light moves at a constant speed regardless of speed, the longer distance == more time thus time dilation."

The first part is the 2nd postulate. The ball, however, does not move at the same constant speed for both observers. So to derive the relativity relations the first time, you practically must use light. Using the relativistic velocity addition formula would work, but it would be a rather bizarre postulate. I believe it was known in Einstein's time, but rather empirically. The constancy of c, however is noticeable from Maxwell's equations, and thus makes a better postulate, allowing simple continuity from 1 theory to another.

 

[Jake]

Thanks guys for the explanation.

So am I correct in saying that time dilation is in essence the fact that one person sees the ball moving more distance than the other person?

Also what about the 'relativistic velocity addition formula' that you both spoke of. How does it factor into time dilation?

I just find visuallizing a ball much easier, because everytime I think of the light clock example, I get sidetracked into wondering about the nature of why C is the same for everyone...Heh, if you know the answer let me know

Thanks again guys!

 

[Gonzolo]

Either you think of the light clock or you think of both the ball and the rel. addition formula. But not the ball alone.

Get used to the fact that light is the same for everyone. If it wasn't, then even more bizarre things would happen.

Such as a room being gradually lit from one side of the room to another when you turn on a single light bulb in the middle of the room on a moving earth. And the direction of the flow would depend on whether it is day or night... and summer or winter, or ... then again the sun itself is moving around the galaxy... and the galaxy itself moves... so ...in effect, you'd get some freaky gradual lighting that would depend on what time of day it is. Of course, nothing of this happens, a room lit by a single bulb in the middle is indeed lit symetrically, irrespective of the room's velocity .

 

[ostren]

So am I correct in saying that time dilation is in essence the fact that one person sees the ball moving more distance than the other person?

Also what about the 'relativistic velocity addition formula' that you both spoke of. How does it factor into time dilation?

I just find visuallizing a ball much easier, because everytime I think of the light clock example, I get sidetracked into wondering about the nature of why C is the same for everyone...Heh, if you know the answer let me know

Aye, "one person sees the ball moving more distance than the other person", yet over the same time elapsed. So for any normal object, such as a ball, that simply means that the object's journey was made at greater velocity. But it was found that light is special and its speed would be perceived as c regardless, so the clocks and rulers had to be adjusted instead, the result being the Lorentz group of transformations. Time dilation is just one of several distortions implied. The "Addition of Velocities" formula is just another ramification from the same Lorentz transform. You are hovering motionless in deep space with two other sister crafts. One sister takes off at .75c, and the other sister does likewise but in the opposite direction. Are your two fellow crafts moving faster than light with respect to one another, such that they won't be able to SEE each other? No, because velocity .75c plus .75c equals velocity .96c according to that same Lorentz transformation formulae.

As for WHY c is constant, it works well into the scheme of things, in Nature. For example, some distant galaxies are moving away from us at relativistic speeds. What of the hypotheitical aliens that might populate all those places? Their VISIONS of their SURROUNDINGS would be all awry if light instead moved at fixed speed relative to some cosmic background space/grid, a grid with respect to which Earth would then need to be assessed as stock still (based on how we observe light behaving here).

Satisfied?