Sunday, June 6, 2021

A fun little argument against four-dimensionalism

  1. Spinning a rigid object cannot affect its shape.

  2. If four-dimensionalism is true, spinning a rigid object can affect its shape.

  3. 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.


IanS said...

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.

Take 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?

Alexander R Pruss said...

Yeah, but even with relativity it should be true that an object does not change its shape much if you spin it slowly.

The suggested redefinition makes sense.

I think the point of my little argument is that when we think of shape, we think of 3D shape.