Just chanced upon this site and wow, what an interesting proposition this one. Lots of math thrown around but sometimes a little randomly, I think, without really getting to the bones of the argument.
(After all, math and numbers are totally abstract systems - I’ll flesh that out a little later).
And sometimes we are all answering a different question - so what should the question be?
Irishman, I like your thinking here (last post), but it’s a teeny bit flawed. If we leave in the effect of the air (which is dragged around by the earth), and gravity, and fire in a random direction, we are truly lost in space. This complicates matters enormously from a mathematical point of view.
So a more sensible question might be: ‘What happens if a rifle is fired in a vacuum, at the equator on a massless rotating sphere the size of the earth, both with and against the direction of rotation (E-W then W-E)?’
And the answer to this question is - NOTHING. It wouldn’t make the slightest bit of difference if we fired E-W or W-E. Why? Because the Earth’s motion is added to or subtracted from the bullet’s. Exactly as it is with the target.
Think about the classic ‘fly in a railroad carriage’ (or a person) the fly can’t tell that the carriage is moving (at constant velocity). And nor would YOU if the visual and auditory etc. cues are taken away. If you were on the top of the carriage in a vacuum (ok so you’re wearing a spacesuit) and you fired end to end at a target in either direction there would be no difference RELATIVE TO YOU at all. This is what got Einstein so excited when he thought about light.
We can even throw in gravity. No difference. The projectile necessarily describes a parabolic curve as it travels but that doesn’t change the argument.
If the rifle is fired in a random direction we then have 2 vectors to consider so it gets interesting. Someone may want to work out an example.
Anyway thats enough of that for now. What about the expanding / contracting barrel?
When heated, all points in a material move away from each other and the centre point, even if it doesn’t exist because it’s been hollowed out, as in the gun barrel. I just don’t see the i.d. contracting on a thermal differential because it’s ‘held’ by the outer part.
Interestingly, going back to the math part, any calculation here, like so many, could never be absolutely correct. Why? Because considering a section of the barrel, we would have to imagine an infinite number of infinitely thin concentric rings. And every time we use math with infinities (like integration and differentiation) we can never have an absolute answer.
I can’t remember which greek philoshopher said that we can have 1 of something but never 2 of anything because 1 apple (or whatever) can never be the same as the next. He had a very good point.
Anyway I’ve digressed a little here but I hope it’s got people thinking and ready to challenge!