[nyc111]

I think what you did is standard. But what I question is, if we can solve our problem without assuming spacetime, why do we need the abstraction called spacetime? Spacetime looks like a historical quirk that physicists feel obligated to carry.

For instance, bending of the light experiment is not done in spacetime but in space and time.

[kryptiskt]

But you can't rip them apart in our physical theories, in relativity different observers will have different ideas about space and time, but will agree about certain invariants if you take both space and time into account. Then a few years later, Minkowski formulated special relativity very elegantly using a four dimensional space-time. That view is basic to general relativity, where the foundation is the spacetime metric and the energy-momentum tensor.