OK, I think I follow.
For my own part, I would say that if we take the relevant unit of meaning to be the whole physical theory (a position I find compelling in principle, if unwieldy in practice), it follows that changing the physical theory does not preserve preexisting meanings. I would not say that the meaning of "momentum" changed, precisely, but that "momentum" acquired a new meaning in addition to its old one, and anyone talking about momentum in a relativistic context is using the new meaning, even though people talking about momentum in a non-relativistic context can go on using the old meaning. (I would also say that the intent of the first physicist to use the term is effectively irrelevant.)
This also implies that people who try to copy over assertions about momentum from non-relativistic contexts to relativistic ones are essentially confusing homophones... similar in principle to what happens if I try to copy over assertions about monarchs from lepidopterological contexts to governmental ones.
But, OK, I can understand how someone could sensibly argue that no, the meaning is preserved, because the meaning was always fuzzy in the first place, we just became aware of the fuzziness late in the game. (This seems to in turn depend on a strongly externalist account of meaning.)
Despite being (IMO) a philosophy blog, many Less Wrongers tend to disparage mainstream philosophy and emphasize the divergence between our beliefs and theirs. But, how different are we really? My intention with this post is to quantify this difference.
The questions I will post as comments to this article are from the 2009 PhilPapers Survey. If you answer "other" on any of the questions, then please reply to that comment in order to elaborate your answer. Later, I'll post another article comparing the answers I obtain from Less Wrongers with those given by the professional philosophers. This should give us some indication about the differences in belief between Less Wrong and mainstream philosophy.
Glossary
analytic-synthetic distinction, A-theory and B-theory, atheism, compatibilism, consequentialism, contextualism, correspondence theory of truth, deontology, egalitarianism, empiricism, Humeanism, libertarianism, mental content externalism, moral realism, moral motivation internalism and externalism, naturalism, nominalism, Newcomb's problem, physicalism, Platonism, rationalism, relativism, scientific realism, trolley problem, theism, virtue ethics
Note
Thanks pragmatist, for attaching short (mostly accurate) descriptions of the philosophical positions under the poll comments.
Post Script
The polls stopped rendering correctly after the migration to LW 2.0, but the raw data can be found in this repo.