I HAVE NEVER BEEN ABLE TO QUITE FIGURE THIS ONE OUT……

A train is running along a straight railway line, doesn’t matter how fast but let’s pretend it’s really, really fast just for the fun of it. It’s an old fashioned engine with flat vertical forward facing windows, not the most aerodynamic of designs but functional. Ahead of the train a small fly is busy flying along minding its own business, it is heading straight for the train window and…. Well you can imagine the result.
Or can you?
Let’s analyse what happens in a bit more detail……….

The fly impacts the window and its remains rapidly find themselves moving in exactly the opposite direction. Something quite remarkable has happened in fact. The fly has reversed direction without ever being stationary because the window that it hit was already moving. But how can this be? Think carefully about the last few moments of the flies life, one moment it is moving in one direction, the next instant it is moving in the opposite direction but at no time did it actually stop.
Can you imagine reversing a car and then putting it into a forward gear without stopping in between?
OK so let’s imagine a car on a long trailer being towed by a lorry. Start the car at the front of the trailer, reverse it down the trailer and then stop and drive forwards again. Is this situation analogous to the fly on the train window? Maybe it is. The car clearly stops relative to the trailer before proceeding to move forwards again but in truth the car is only stationary relative to the universal reference frame when it is moving backwards at the same speed as the trailer is moving forwards. Once it starts to slow down it is in fact moving forwards. Hmmm, does this help with the fly /train quandary? I’m guessing this is a ‘reference frame situation’, that is, viewed from one frame of reference something impossible appears to be happening whereas viewed from another it is not so it is the use of a false reference frame that is the problem. Consider. From the point of view of the fly’s vector firstly it has velocity in one direction and then it under goes a very short period of extremely strong deceleration followed by a movement at a constant velocity in the opposite direction, it does not appear to go through an acceleration phase for if that were the case it would imply that the train were accelerating which it is not. Agreed the train is slowed very (very) slightly by the impact of the fly but the fly after decelerating strong is somehow instantly moving at a constant velocity in the opposite direction and without passing through a stationary phase for, if the fly were to be stationary then that would imply that the train were also stationary, if only for an instant……
So lets try and develop and alternative reference frame. This time we take the train as the reference, relative to the train in fact the fly decelerates to a dead stop. Indeed, the fly is no longer moving once it has spread itself out on the window. So that’s it, problem solved… I guess, but I still come back to what I see as an observer of the fly’s vector. First it has a constant velocity in one direction and then it has a constant velocity in the opposite direction. In fact, if we replace the fly by a mathematical point then there is not even a period of deceleration merely an instantaneous change of direction with no period of being stationary.
My head hurts…… Ideas on a postcard please….