Why do we experience time flow? I had read that a photon travelling at the speed of light does not experience time flow (time stops for it) also I had read somewhere that we are travelling at the speed of light. Why do we experience flow of time then?
 A: Your confusion stems from the fact that the second statement is wrong. We are not traveling with the speed of light -- in ANY frame of reference. Special relativity teaches us that an observer traveling at $c$ is traveling with this speed in any frame of reference. Therefore, if I see you standing next to me (and not traveling at c) then you are not so in any frame of reference.
However, if you were traveling at $c$ (which you would need an infinite amount of energy to do so), you would not experience the flow of time.
A: Your question raises a common and interesting misconception.
Time does not slow down from the perspective of a moving observer. The time dilation effect means that where a moving observer passes between two stationary clocks, the time experienced by the observer is less than the time difference recorded on the clocks. From the perspective of the moving traveller, time is passing at its usual rate- it is the clocks that are out of synchronisation.
The effects of SR are entirely reciprocal. From the point of view of a reference frame moving relative to Earth at 0.9999999c, time on Earth appears to have almost stopped, yet we do not experience frozen time. Our experience of time remains constant regardless of how quickly we are moving relative to any other frames in which our time seems to be more or less dilated.
