On the issue of relative motion

For another thing, McGinn argues, there are difficulties with the thesis itself, never mind the argument for it First of all, on analysis it appears to be incoherent. Consider a universe with just two objects, A and B. Suppose that from A’s frame of reference, A is stationary and B is moving toward A, whereas from B’s frame of reference, B is stationary and A is moving toward B. According to the relationalist, there is no fact of the matter about which is really moving. Relative to A, B is moving and A is not, and relative to B, A is moving and B is not, and that is all that can be said. But remember that local motion is change with respect to place or location. For B to move, then, is for it to be at location L1 at one moment and at a different location L2 at the next. Now, since B is indeed moving from A’s frame of reference, the locations L1 and L2 that B is at at each movement must be different locations. But since B is not moving from B’s frame of reference, the locations L1 and L2 that B is at at each moment must not be different locations. So L1 and L2 are both identical and not identical. But that is absurd. (Edward Feser, Aristotle's Revenge, p. 213)

Second, McGinn argues that the relativity of motion becomes implausible once we factor in considerations other than motion. If we are only considering only their motion, we could say either that the sun is at rest and that the earth is moving relative to the earth, or that the earth is at rest and the sun is moving relative to the earth. However, when we factor in the different masses of the sun and the earth, this is no longer the case. … The motions considered in the abstract may be symmetrical, but the causal factors are not, so that there is a fact of the matter about which is really moving relative to which. (p. 214)

A major paradigmatic shift in science has been the shift from an absolute frame of reference to a relative frame of reference. This is especially evident when one considers the theories of relativity. Depending on the frame of reference, an object can be considered to be in motion, or be stationary. Superficially, we take the Earth to be stationary when calculating motion on Earth, although we understand the Earth to be in motion around the Sun. But relative frames of reference mean more than considering something to be a stationary point of reference. It means that the frame of reference can be swapped such that if one object X is seen as stationary, the other, Y, is seen as in motion. But if Y is seen as stationary, then X is seen to be in motion. Therefore, the very concept of "motion" is relative. It is this concept that Edward Feser, citing McGinn's argument, disputes.

McGinn's argument seems valid enough. If B is seen as moving, which is true from A's perspective, it moves from point L1 to point L2. However, if B is seen as stationary (B's perspective) and A is moving, then surely B is at point L1 and remains at point L1, never moving to point L2. Such an argument however misunderstands how relative frames of reference works. In relative frames of reference, there is no such thing as absolute points of space, and it is this error that McGinn commits.

To perceive the nature of the error, let us place a marker at point L1 and a marker at point L2, and name them M1 and M2 respectively. In A's frame of reference, B is moving towards A and it moves from L1 to L2. Thus, B would have moved past M1 and M2, as M1 and M2 are both stationary in A's frame of reference. Consider however what would be the case in B's frame of reference. If B is considered stationary, then A is moving towards B. The markers M1 and M2 would also move towards B, since they are in the same situation as A. Since M1 and M2 supposedly mark L1 and L2 respectively, then it could be said that L1 and L2 move towards B. In other words, in B's point of reference, to the extent that points L1 and L2 are supposed to be points in space, they "move" towards B if B is taken to be the frame of reference. This is seen in the diagram below:

McGinn's error therefore is in assuming that L1 and L2 mean anything at all in relative frames of motion. The entire concept of frames of reference is precisely to assert that just as there is no such thing as a fixed frame to consider motion, so there is no fixed frame to consider location. L1 and L2 only make sense in A's frame of reference, not in B's.

Feser's next paragraph deals with gravitational rotation, which is the realm of the general theory of relativity. Unfortunately, I have not really learned the General Theory of Relativity, but from my limited understanding, it is false to assert that rotation of the earth around the sun disproves relative frames of motion. First of all, the earth does not technically revolves around the sun. Rather, it revolves around the center of gravity of the entire solar system. The sun "wobbles" so to speak since it makes up most but not all of the mass of the solar system. This shows that it is not the sun as an object that is considered stationary, but rather motion under the force of gravity follows the curvature of space-time. Since space-time curvature is asymmetrical in the case of the solar system, so we do say that the earth revolves around the sun and not the other way around.

Relative frames of motion are apparent however when the space-time curvature is symmetrical, as in the case of a binary star system with stars of equal masses. In this case, it is true that star C revolves around star D, and star D revolves around star C, and also that both stars revolve around their common center of gravity, as seen in the figure below:

As it can be seen, where space-time curvature is symmetrical, relative frames of motion are present. The fact that the earth revolves around the sun, and not the sun revolves around the earth, is due to the asymmetrical nature of the space-time curvature caused by the sun, and therefore this example is not a valid one in disproving relative frames of motion.

Having examined the arguments put forward by McGinn and repeated by Feser, it is evident that their arguments against relative frames of reference betrays an ignorance of the science involved. While one can legitimately ask whether an absolute point of reference with regards to space, motion, or even time is or should be present, it is fallacious to claim that relative frames of references make no sense and are self-contradictory. They are certainly counter-intuitive, but self-contradictory nonsense they are not. Feser would certainly benefit from some science education, as the arguments he has put forward here betray an ignorance of science as a subject.