This is an exercise in some rather gruesome metaphysics of parthood. If you don't like gruesome examples, stop reading. There will be a payoff, though--a defense of animalism.
Imagine a long snake, all stretched out, and for simplicity assume uniform linear mass distribution. Let's say the length of the snake is 10 meters and its diameter is 0.1 meters. Suppose that something cuts off the rear 1/4 of the snake, and the cut happens at near-light speed--maybe a blade descends on the poor snake at 90% of the speed of light. Suppose that almost instantaneously before the blade touches the unfortunate snake, a butterfly almost instantaneously brushes its wing against the tip of the snake's tail and never has any other contact with the snake or its bits. (Let's say "almost instantaneously" means "in the amount of time during which light travels 0.01 meters.) Then, it seems, butterfly touched the snake. Call the reference frame in which the above description takes place "frame A". But, it is a fact that then there is a reference frame, call it "frame B", in which when the butterfly touched the snake, the tail was already cut off. It seems that in this reference frame, the butterfly did not touch a (or the) snake--he merely touched a cut-off tail.
It follows that the following propositions cannot all be true:
- In frame A, the butterfly touched the snake.
- In frame B, the butterfly did not touch the snake.
- Whether two substances touch does not depend on the reference frame.
So we must deny at least one of (1), (2) or (3). Note that affirming (1) and (2) and discarding (3) would have the interesting consequence that whether battery has been committed depends on the reference frame. For suppose that an accident cuts off my leg at near light speed. Then there can be a situation where you very quickly mutilate the "foot" at the end of that leg (I put it in quotation marks, because there is an issue whether a disconnected foot is a foot) just before the leg is cut off. By exactly the same reasoning, then, in one reference frame it seems you've committed battery--you've mutilated a part of me--and in another you haven't. (In neither reference frame do I feel the mutilation, because the leg is cut off before the nerve signals come from the "foot" to my central nervous system.) I don't think whether battery has been committed should differ between reference frames. (Would you be guilty in one frame and innocent in another?)
So, I need to reject either (1) or (2) or both. It seems to me that (1) is harder to deny than (2). To deny (1) we would have to allow that the tail is fully connected to the snake, and yet not a part of it because it is about to be cut. So, we should deny (2). Hence, something can be a part of a body even though it is already severed from the body.
How long can this weird state of affairs go on? I don't really know. We could say that it goes on until the part is severed in all reference frames. But while that is an attractive idea, it neglects the fact that we are talking about organic parts, and what matters here is organic connections, not relativistic connections. The relevant scale of velocities is the speed of the fastest organic signals, not the speed of light. Suppose that the snake's brain sent a nerve signal to the tip of the tail, and the nerve signal passed the cut-point just before the cutting began. Because nerve signals move much slower than light, before the nerve signal arrives at the tip of the tail, it will already be the case that in all reference frames the tail is severed. Still, I think the tail might count as part of the snake, as long as the signal is traveling there. Let's say the signal tells the tip of the tail to wiggle. Maybe we can say that while the tail yet wiggles under the influence of that nerve signal, the tail is a part of the snake.
Does any of this matter, except as abstruse metaphysics? Maybe. Take animalism, the theory that you and I are animals. A standard objection to animalism is that we can survive as brains in a vat, but a brain in a vat is not an animal. However, the above considerations suggest that, at least for more complex beasts like snakes and humans, connection to the nervous system has a relevance to determining what still is and what no longer is a part of the body. The nervous system, then, has a kind of centrality in more complex animals from the organic point of view. And this makes it plausible the animal could survive as an organism when pared down to just a nervous system, assuming appropriate life-support mechanisms. And it is not a far leap from that to suppose that we can survive as organisms with just central nervous systems, and maybe even with just the central part of the central nervous system, namely the brain (in a vat, of course).
Now, if animalism is true, then we were all once fetuses--I was the numerically same organism as a fetus. Thus, a human fetus is one of us, and presumably killing it is wrong. Thus, we have here a loose line of argumentation from Relativity Theory to the wrongness of abortion. Isn't philosophy fun?