Hi I was having after thoughts after learning about time dilation in relativity and had some questions. I was initially taught if there were two space ships traveling relative to each other, the time of the clock in spaceship 1 that person in space ship 1 sees will differ from the time of the clock in space ship 1 that a person in the spaceship 2 sees. To me, it sounds like the cause of it is the observer's relative speed to the light that delivers information about clock. So this got me wondering if the time dilation occurs in an isotropic manner or if it only occurs in the direction of travel in space.
Here is an example that relates to my question: I travel down a road towards North from the starting point A, so that there was a time dilation between myself and stationary people along side the road, because of the relative speed of light that reaches from myself to the people and the relative speed of light that reaches from the people to myself. Then if there were bunch of people from somewhere down the road east from the starting point A, so that the light that reflects off them cannot reach me, obstructed by buildings, would there still be time dilation between those people and me?
Thanks
Best Answer
Hi I think this is answered in the math surrounding this answer (Relativity tangential light clock, in which I do a basic derivation of Lorentz contraction [lots of ways to do it, btw])
In summary, then, the initial impact of relative velocity is indeed directional. Of course it would be, relative velocity is a vector. Light and therefore the rate of interaction of all things takes longer in that relative direction.
The next step is to consider that time is perceived by us as scalar. I mean, intuitively you just wouldn't build a physics in which the rate time elapsed varied with direction. (Now I'm sure there's a theorist or two out there who's tried it, of course ) In terms of the "equivalence principle", the founding assumption of relativity, we are looking for scalar [directionally homogeneous] time in each equivalent frame. This so that the same physics works in these frames.
Our perception/measurement of the universe has to cope with this? We perceive that, in essence, everything in the direction of travel outside our own frame appears shorter, the famous "length contraction" phenomena. Things are shorter by exactly the right amount to achieve our perception of scalar time in those other frames. Shorter by exactly the right amount to make our laws of physis apply so that frame is equivalent to our own.