This is a rather old issue, but one that has recently been on my mind. We often say that gravity is the curvature of space-time, with good reason. At the same time, we also talk about the "gravity" in Einstein's elevator, as an example of the equivalence principle. This is also with good reason, and is historically important. But Einstein's elevator is set in flat space-time. There is no curvature. So if we talk about gravity in Einstein's elevator, we're talking about gravity without curvature. But we have perhaps just previously said - or some other poster has previously said - that gravity is due to the curvature of space-time. Thus we are left with what appears to be a confused message. What's the best way of resolving this issue? Are we forced to talk about connections and Christoffel symbols to adequately define what we mean by gravity in Einstein's elevator? Is there a better way of doing this, preferably one that is accessible to B and I level readers? I don't really regard either connections or Christoffel symbols as being I level, and definitely not B level. On the flips side, can we modify or qualify saying that gravity is due to the curvature of space-time , in a way that will not confuse the presentation, but also allow us to talk about the "gravity" in Einstein's elevator?