# Misunderstanding something: circular time dilation loop

1. Oct 1, 2012

### MHD93

Hi..

Speedo, flying in space, is at large speed compared to c relative to his brother on earth. Therefore, after a long time meeting at rest relative to each other, Speedo aged less than did his brother from his brother perspective. But from Speedo's point of view, his brother was also moving at that same large speed, and therefore he aged more slowly. So does everybody see the other younger (provided they're twins)?

So what's wrong with me?

2. Oct 1, 2012

### ghwellsjr

It's only when both twins are inertial that you can apply an inertial frame to either of them and determine that the other one is time dilated and aging less in a reciprocal way. When one of the twins is always accelerating by being in "orbit", you cannot apply an inertial frame to him, only to the other twin that stayed home so the reciprocal nature of time dilation does not apply.

So, yes, everyone agrees that, after each orbit, Speedo ages less than the twin that stays home.

3. Oct 1, 2012

### pervect

Staff Emeritus
Nothing. You've perhaps missed seeing, or possibly interpreting, the phrase "simultaneity is not absolute', "there is no absolute time", or "the concept of now depends on the observer", or of the many other similar phrases that explain this problem.

It helps to draw a space-time diagram. Speedo's concept of "at the same time", the concept of "now" is different from his brothers. You can represent this abstract concept of "at the same time" on a space-time diagram by a line - this may be helpful.

So, in speedo's "now", his watch reads one second, while his brothers reads less, say .5 seconds. In his brother's "now", which is different from speedo's, the brother's watch reads 1 second, and speedo's watch only reads .5 seconds.

Since it seems to be difficult to get people to draw their own space-time diagrams, here's one I made a while ago. The different colored arrows (green and red) represent the differing notions of simultaneity for observers A (not moving) and B (moving).

This diagram is drawn using the Lorentz transform, with a scale factor chosen such that light always moves at a 45 degree angle on the diagram.

The solid dots on the diagraram along A's and B's worldline are spaced at equal intervals (say, 1 second) according to a clock that's co-moving with the observer in question.

4. Oct 1, 2012

### soothsayer

Google the "Twin Paradox". The twins can disagree about their respective ages while Speedo is off somewhere in space and therefore unable to communicate with his twin about his age. For there to be a paradox, there must be an exchange of information. Speedo must accelerate in order to return to his twin to compare ages, and in doing so, he changes inertial frames and the paradox is ultimately broken. When he returns, both Speedo and his twin will agree on ages.