# Special Relativity, Question on C and Time Dilation

1. Dec 16, 2008

### iRish_waKe

I've searched around and I keep getting various answers, explanations, and examples for Time Dilation and The Lorentz Transformation, but it isn't what I'm looking for.

I was watching "The Universe" last week and the episode dealt with The Speed of Light and it's properties.

They had an example where a scientist was riding his bike, we'll call him the cyclist, in a circle around another scientist who is stationary.

The track the cyclist was on was circular and for this example we'll say 1/4 of a mile, not that it matters. As theorized by Einstein, as the cyclist approaches the speed of light (.99c), time for him slows down and he ages must more slowly than the stationary scientist. When he stops, he is younger than the scientist who did not move. Now, many times throughout my life I've heard the expression, time slows down as you approach the speed of light, but now I question why? I've Googled and searched and sat and thought about it but the more and more I think about it the more and more I'm getting confused.

It seems to me this is backwards, even though I know it's not, and because I know it's not, it's bothering me.

The way I think about it is:

Let's just say that the cyclist can actually watch the stationary scientist as he travels around him. Ignoring the fact that his view would be distorted because he's traveling so fast, everything around him would appear to be almost stationary. (I think about the scene in "Over the Hedge" when the squirrel or whatever drinks the energy drink, if anyone has seen this movie you know what I'm referring to).

Am I right to assume this much? I'll continue:

If the cyclist is moving that fast, everything around him appears to be almost stationary, this is what I imagine when I think about "time slowing down". If the cyclist were able to look at a clock that was being held up by the stationary scientist, it would take a REALLY long time for one second on that clock to pass, whereby if he were to look at his wristwatch, time would be moving along just as it normally does, right?

This is my problem: If everything above is looked at from the point of the cyclist, if he spent 30 minutes cycling at .99c, watching everything around him barely move, when he slowed back down to 20km/h, wouldn't everything only be like 1 second ahead of where it was? Instead of the stationary scientist aging faster, it's the cyclist.

This makes sense to me. The opposite, which is the accepted way of thought and a proven fact, does not make sense.

Can someone break this particular experiment down and tell me why what seems like the obvious answer is wrong?

2. Dec 16, 2008

### JesseM

No, you've got it backwards. The stationary scientist would see the clock of the cyclist running slow, while the cyclist would see the clock of the stationary scientist running fast--that's why, when he stops, he's aged less than the scientist. The reason for this asymmetry is that the normal rules of time dilation (clocks which are moving from your point of view run slow) only work for inertial observers, i.e. observers moving at constant velocity (which means both unchanging speed and unchanging direction, so moving in a circle doesn't qualify). An observer who is moving non-inertially in special relativity will know they're moving non-inertially because they feel G-forces, like the centrifugal force you feel when you spin in a circle, or the G-forces you feel when you accelerate in a straight line.

3. Dec 16, 2008

### iRish_waKe

I know I have it backwards I'm just trying to understand WHY the obvious is wrong, and no offense but your answer doesn't really help. I don't understand if moving in a circle negates time dilation, why would they say that on "The Science Channel"? I mean I know this is a theory, but time dilation is REAL and works like Einstein said it does, I'm just trying to figure out what part of this whole thing is backwards.

Looking for some more takes on this...

4. Dec 16, 2008

### JesseM

Did you understand about the difference between inertial and non-inertial frames? The usual time dilation equation doesn't work in non-inertial frames, are you asking why that's true? I don't think there's any "why", it's just a symmetry of the laws of physics that they work the same in inertial frames but not non-inertial ones, you might as well ask "why" gravity is attractive rather than repulsive. As an analogy, if you have a 2D Euclidean plane and you draw a Cartesian x-y coordinate system on it, then the distance between two points with coordinates (x1,y1) and (x2,y2) will always be given by the Pythagorean formula $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$, regardless of how your axes are oriented; but if you draw a distorted non-Cartesian coordinate system where the x-y axes aren't at right angles to one another or aren't even straight lines, then this formula will no longer correctly give the distance between points with coordinates (x1,y1) and (x2,y2).

5. Dec 16, 2008

### iRish_waKe

Haha, okay your bit about gravity made me laugh. I guess, because thats what happens when this set of variables are in place, is going to have to do. I was just trying to "visualize" what traveling that fast would look like, when in reality, it would be horribly distorted because light wouldn't be getting to my eyes at the same speed. I guess I was taking too much out of the equation and still trying to solve it.

I had accepted it for so many years, and then that show came on and I was like wait a sec, that makes no sense. Now when I go back and think about it, it can only make sense when certain criteria are met. Stupid television.

Thank you.