I was reading through some blogs/articles and watching youtube videos that explained to non-physicists such as myself – how time warping or a gradient in time flow around any object can create gravity. I am able to understand the mechanics (minus the math, I'm not a physicist) of gravity according to this theory, but, a question bugs me:
What creates the time gradient in the first place? Why would the infinitesimally small clocks (or connected particles that move through time at different rates) have the the different tick rates in the first place?
(Kindly be gentle on the math – I am not a mathematician either!)
A follow up question: if an object in space-time is massive enough, such as a black hole, can it stop moving through time… in a way bending time over itself and never letting it go, like light?
Best Answer
There is a subtle but important distinction you might want to consider which may help you form a better conceptual picture of what happens.
When we talk of time dilation, it is a geometric effect- it means that the length of paths between two points in time can vary. To explain what I mean by analogy, imagine that you and I are standing at a corner of a large square. You walk diagonally across to the opposite corner while I walk around the edge of the square to meet you there. The distances we each walk are quite different because we have followed different paths. If we were carrying pedometers, they would show we had walked different distances, and you would consider that entirely natural- you would not feel you had to make up an explanation about your pedometer being 'pace dilated' relative to mine.
Now, carry that idea over into special relativity and consider time dilation in that context. If you move between two clocks in my frame of reference, and during your journey 4 second pass on your watch, while my clocks show a time difference of 5 seconds between the start and end of your journey, it is not because something has caused your watch to run slow, but that the path through time you have taken between the two points was only 4 seconds long, and your watch has correctly recorded it as such, running at its usual rate to tick off the seconds faithfully.
In general relativity, the mathematics are much more complicated, but the conceptual idea still applies. If you follow one curved path through time its length (in seconds) can be more or less than another curved path through time, so clocks taking the different paths will show different elapsed times. It is not because they are somehow running slow or fast, in the sense of not faithfully recording a true time, but because they are accurately showing real differences in the lengths of their paths through time.