# Time Dilation on a Merry Go Round

1. Apr 17, 2010

### EebamXela

I watched a video today about time dilation and Lorenz contraction. It had Albert stationary and Henry on a moving track, both holding a photon clock, and it showed how time slows down for moving objects, relative to the stationary observer. I get all that stuff.... sorta...

I was thinking, would the same effect be observed if albert were standing at the center of a rotating merry go round, and henry is standing on the edge? I can't quite wrap my head around this one, because it seems like henry would appear to be stationary as well if albert just simply stood still and spun along with the merry go round. If he did just stand still he would observe the surroundings moving past, but if he shifted his feet so that he did not spin, he would observe Henry moving by really fast.

I'm not even sure if i'm presenting my confusion adequately. There would still be movement occurring, but all the person in the middle would have to do is change his rotation.

Someone please help.

2. Apr 17, 2010

### JesseM

The normal equations of special relativity, including the time dilation equation, only apply in inertial frames of reference (a 'frame of reference' being a coordinate system for labeling events with space and time coordinates), where any object that's at rest at a fixed position in that frame will be moving at constant velocity (constant speed and direction). Any departure from constant velocity is a form of acceleration, and an accelerating observer can always tell objectively that they're accelerating because they'll feel G-forces, like the apparent ttp://hyperphysics.phy-astr.gsu.edu/HBASE/corf.html#cent[/URL] that will be felt by someone rotating in a circle. So, the time dilation equation doesn't work in a rotating frame of reference (one where Henry is at rest), you can't assume that clocks moving relative to such a frame will be running slow.

Incidentally, when you say "it showed how time slows down for moving objects, relative to the stationary observer", keep in mind that "moving" and "stationary" can only be defined in a relative way. If Henry and Albert are moving at constant velocity relative to one another, then there will be one inertial frame where Henry is at rest and Albert is moving (and thus Albert's clock runs slow in this frame), while there'll be another inertial frame where Albert is at rest and Henry is moving (and thus Henry's clock runs slow in this frame), and both frames are considered equally valid. Different frames can also disagree about the "simultaneity" of events that happen far apart--in one frame the event Henry's clock reading 20 seconds might happen at the "same time" that Albert's clock reads 16 seconds at a different location, while in another frame the event of Henry's clock reading 20 seconds might happen at the same time that Albert's clock reads 25 seconds at a different location. However, it works out so that different frames always agree in their predictions about [i]local[/i] events which occur at a single point in space and time, like what Albert and Henry's respective clocks will read at the moment they pass right next to one another.

Last edited by a moderator: Apr 25, 2017
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