I know this is somewhat old news, so my first question is whether there have been any recent developments in the discussion on possible variations in certain physical parameters (fine structure constant, alpha) etc.
https://www.newscientist.com/article/dn19429-laws-of-physics-may-change-across-the-universe/
https://www.newscientist.com/article/mg18324541-100-if-the-speed-of-light-can-change/
Has this idea been largely accepted or rejected? Or is it still something that is unfolding?
But then, my second question would be: If it is possible some of these parameters change, what implications does that have?
I see nothing problematic in this. being that we also are beginning to suspect none of the constants are constant.
http://news.stanford.edu/news/2010/august/sun-082310.html
The problem is people simply do not understand the speed of light. Measuring devices and all things sharing a frame of reference change with acceleration.
Time, distance and the speed of light is like kinetic energy. In a bullets frame it reads zero velocity and zero kinetic energy, even if in our frame we read both a velocity and a kinetic energy for the bullet. Likewise in our frame we read zero velocity and zero kinetic energy for us. Zero points are reset as energy is added to or subtracted from all things sharing a frame dependent upon acceleration or deceleration. Energy is lost or gained and the zero points are reset proportionally.
This is evident in that a bullet reads zero kinetic energy in its frame - and if slowed down to stationary in our frame, will still read zero kinetic energy. There is no such thing as a backwards moving clock or a bullet with negative kinetic energy. Zero points are constantly reset proportional to the energy gained or lost.
The problem is people still try to use the same times and distances from this frame and apply it to other frames. This can not be done, because the zero points in the other frame have been reset proportionally to the energy gained. This is why light will always calculate to c regardless of one's velocity. Zero points have been reset proportionally to the energy gained or lost due to that change in velocity. The speed of light is not mysterious or magical. It is simply a proportional measurement based upon the energy gained or lost due to changes in one's velocity.
Changes to those measuring devices can never be detected from within the frame - but only to frames not sharing our same relative velocity. You can never reach the speed of c using your own clocks and rulers, because they will always read your velocity as zero as the zero points are reset with changes in energy. Those changes in energy exactly compensate for the changes in velocity, so that light will always calculate to c regardless of your velocity.
Look at the second hand of a clock. A point near the hub (stationary frame) does not read the same elapsed time or distance that a point near the tip (accelerating frame) does. Like kinetic energy the zero points will reset depending on your frame of reference. The point near the tip sees the same thing as the point near the hub does, because the zero point has shifted when you shift to the other frame. Both will observe the same proportional arcs of time and distance. To the point near the tip all his measuring devices instead say he is the point near the hub. When in the tips frame, you must shift the entire zero point to that frame, not leave it in the other frame. It is this confusion that leads to thoughts of backwards moving clocks, or even clocks that stop. Both are a complete impossibility. The same impossibility of the thought of a bullet with negative kinetic energy. It will never happen.