Suppose we had a universe obeying the same physical laws as our own. But it had only one spatial dimension (represented by the $x$ axis) and it was totally empty. There are just two point-like particles in this universe:
- An electron which is at rest.
- A photon which is moving away from the electron.
Yet we have two important rules that can’t be broken:
- A photon can’t slow down, its speed must always be equal to $c$.
- Gravity affects all form of matter, even photons.
So how would the gravity engendered by the electron affect the photon if it can’t slow down?
If this was in $3$-dimensional or $2$-dimensional space, there would be no problem since the photon could just be slightly deviated from its trajectory. But here the photon is moving away from the electron very precisely along the axis joining them, we’re in $1$-dimensional space, the photon can’t be deviated.
We've got a paradox over here!