My previous attempt at a reply didn’t make much sense. And this is deep enough into the thread that I won’t bother with rot13.
Let’s try again:
The description given by Thomas accurately models how each individual particle accelerates (towards the origin). It thus also accurately models how the center of mass accelerates in the non-limiting case.
I think Richard Kennaway’s answer is correct and it seems to me to be opposite to your original answer. The non-limiting case is not interesting. The question is whether there is a coherent extension of Newtonian mechanics to infinitely many particles. It does cover this case and the center of mass still works.
V guvax gung va gur aba-yvzvgvat pnfr, gur neenatrzrag fubjvat rirelguvat qevsgvat gbjneqf gur bevtva vf pbeerpg naq gur neenatrzrag fubjvat gur pragre bs znff fgnlvat fgvyy vf va reebe. Bs pbhefr, va gur yvzvg nf gur ahzore bs cbvag znffrf vapyhqrq tbrf gb vasvavgl, vg’f gur bgure jnl nebhaq.
bx, gung vf n ceboyrzngvp erneenatrzrag. Ohg juvpu fvqr vf pbeerpg? Lbh znqr n pynvz nobhg guvf va lbhe bevtvany pbzzrag, ohg V guvax lbh tbg vg onpxjneqf.
My previous attempt at a reply didn’t make much sense. And this is deep enough into the thread that I won’t bother with rot13.
Let’s try again: The description given by Thomas accurately models how each individual particle accelerates (towards the origin). It thus also accurately models how the center of mass accelerates in the non-limiting case.
I think Richard Kennaway’s answer is correct and it seems to me to be opposite to your original answer. The non-limiting case is not interesting. The question is whether there is a coherent extension of Newtonian mechanics to infinitely many particles. It does cover this case and the center of mass still works.
I think this paradox shows that the answer is no.
I can’t figure out what this sentence was intended to mean.
Richard Kennaway’s answer
V guvax gung va gur aba-yvzvgvat pnfr, gur neenatrzrag fubjvat rirelguvat qevsgvat gbjneqf gur bevtva vf pbeerpg naq gur neenatrzrag fubjvat gur pragre bs znff fgnlvat fgvyy vf va reebe. Bs pbhefr, va gur yvzvg nf gur ahzore bs cbvag znffrf vapyhqrq tbrf gb vasvavgl, vg’f gur bgure jnl nebhaq.