Relativity & the GPS

Yesterday I gave my first lecture of term, all about the Global Positioning System (GPS), and managed to cover some very interesting things with the students. For example, special (SR) and general relativity (GR), which is important for GPS satellites which are fast moving, so time slows for them (SR), and higher up in the Earth's gravity well, so time speeds up for them (GR).

To explain relativity, I talked about a couple of mirrors with light bouncing between them to form a clock: say, each bounce is a second. Now if the mirrors move sideways relative to you the light has further to travel along the diagonal, but because the speed of light is supposed to be the same in all reference frames the light can't speed up, so the mirror-clock ticks more slowly for the moving mirrors: time dilation.

As I told my students (who were healthily sceptical of all this!): you might think that the slowness of the clock is just an apparent thing because we are seeing it from afar, but no! This has been tested. Some scientists (Hafele and Keating, 1971) left one atomic clock at home and took one for a ride on a fast and high plane to slow it down and speed it up by relativity. When they brought the clocks back together the effects of relativity were still there. This is amazing, because it means that the slowing down of time, is "real" (whatever that means) and not just apparent. This has a huge implication: that reality is what you can observe. It seems that because it is impossible in our reference frame to ever perceive the clock going at the 'normal' speed, then it doesn't go at the normal speed, it goes at the only speed we can perceive it to go.

Similarly, in MiHsC, the idea is that because we can never in principle measure the longer Unruh waves that don't fit exactly within the Hubble scale, they cannot exist. It's not particularly that we as humans cannot see them (it's not subjective), but rather that they cannot be seen "in principle", a more objective view. I'm suggesting that relativity should be modified very slightly, by MiHsC, based on this kind of thinking. It may seem strange that the world works in this Wycsiwyg (What you can see is what you get) manner, but the cosmos is no stranger to strangeness (sometimes it seems about as sane as a Penrose triangle). The point is that thinking like this does make correct predictions of nature, and that's the important thing.