In our world where 'c' is large, most people intuitively understand Galilean addition of velocities at everyday speeds i.e. if someone stands 40m behind me and rolls a ball towards me at 10m/s (assuming we are not moving relative to each other) it takes 4s to reach me. If we repeat the experiment while I'm walking away from them at 2m/s, the ball would take 5s to reach me by which time I would have moved to be 50m away from the person rolling the ball. In this latter case I am effectively reducing the relative speed at which the ball approaches me meaning it takes longer to reach me.(adsbygoogle = window.adsbygoogle || []).push({});

For simplicity, imagine repeating the above experiment in a universe where 'c', the universal speed limit is 10m/s. If I am standing still, there is no difference to the above case and the ball would still reach me at 10m/s after 4 seconds as before. Using the Relativity equation for addition of velocities S = v+u/1+(vu/c2) I can calculate that if as before I repeat the experiment while I move away from the ball roller at 2m/s, I am unable to change the relative speed of the ball in my direction at all, and it approaches me at 10m/s however fast I travel away from the ball roller.

What I can't quite understand is what this means in practice. i.e. I can grasp what happens in the Galilean view of things where I can reduce the relative velocity of the ball coming towards me (and therefore increase the time it takes to reach me) by moving away from the ball roller, but I can't quite grasp what NOT being able to affect the relative speed of the ball towards me means. Does it still take longer to reach me as in the Galilean view, or does it take 4s no matter how fast I move away from the ball roller?

Although I'm tempted to interpret things to mean that no matter how fast I move away from the ball thrower (in this low-c universe, or from a light source in ours) it always reaches me after the same amount of time, I know this cannot be the case because if in our universe a new star started to shine and during the time it took for it's light to reach Earth I travelled in the opposite direction away from Earth in a spaceship, I would expect to see the new star well after those I left behind on Earth saw it...and yet this seems like a Galilean way of looking at things i.e. it seems I DID then affect the relative velocity of light in my direction by moving away from its source.

I'm confused (clearly!) and would welcome any constructive pointers in the right direction to understand this more clearly. If it helps this all comes from my attempt to understand Relativity of Simultaneity, part of which states that a person on a train sees a lightning flash in the direction their train is travelling before one that happens at an equal distance behind the train, which seems to me as an assumption at odds with invariant 'c' (the relative velocity of the light you are moving towards has been increased and that of the light you are moving away from has been decreased) but clearly I'm missing something.

Regards,

OBL

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# Difficulty understanding invariant 'c' implications

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