Spinning a rigid object cannot affect its shape.
If four-dimensionalism is true, spinning a rigid object can affect its shape.
So, four-dimensionalism is not true.
The easiest way to see that 2 is true is to imagine that space is two-dimensional. Then if objects are considered to be extended in time, as the four-dimensionalist says, an object intuitively thought of as a rectangle that stays still is really a rectangular prism, while if that rectangle is spun by 90 degrees, it looks like a twisty thing.
I don’t think it’s too costly to deny 2. And perhaps one can make sense of some notion of internal shape that doesn’t change no matter how a rigid object moves around.
Rigid objects don’t make much sense in relativistic physics (and hence in this world as we currently understand it). If you start with a rod at rest and push one end, the ‘push’ travels along the rod as a wave with a finite speed. You can ‘choreograph’ rigidity, but you can’t make it work causally - “No action at a distance.” Of course, relativistic physics is not the only possible physics. But this line of thought does give a reason not to worry about problems with rigidity.
ReplyDeleteTake the argument in its own terms, and take time and space as independent. Can’t we define rigidity something like this: every time slice of a rigid object is a Euclidean transformation of every other?
Yeah, but even with relativity it should be true that an object does not change its shape much if you spin it slowly.
ReplyDeleteThe suggested redefinition makes sense.
I think the point of my little argument is that when we think of shape, we think of 3D shape.
An argument against four-dimensionalism from dualism:
ReplyDelete1. If four-dimensionalism is true, then anything that is located in time is located in space.
2. Souls exist in time.
3. Souls do not exist in space.
4. Therefore, something exists in time but not in space. (2,3)
5. Therefore, four-dimensionalism is false. (1,4)
It makes sense that if time is a dimension, then anything located in time is in space. In a cartesian coordinate plane graph, any point with an x value also has a y value.
Interesting. But just as there can be multiple parallel spacetimes with different spatial dimensions (e.g., two spatial dimensions and one time dimension), there could be, parallel to us, a spaceless time (i.e., zero spatial dimensions and one time dimensions). And there could be causal interactions between us and that spaceless time, which causal interactions could induce enough correlations between the two that it would make sense to talk about what is happening "there" "now".
ReplyDelete