In Fix Your Timestep, they briefly address the remainder time in relation to rendering. Saying that remainder can be used to generate an interpolated rendering.
We can use this remainder value to get a blending factor between the previous and current physics state simply by dividing by dt. This gives an alpha value in the range [0,1] which is used to perform a linear interpolation between the two physics states to get the current state to render.
So let's say your last two physics updates we'll call A and B are from
00:10.066, and it is now
00:10.070 when we want to perform a render. We have a remainder of
I take "interpolation between the two physics states" to mean we compare all the objects in update A and B and slide them back from B towards A by
88% (.033-.004)/.033). This would mean I'm actually rendering the physical state at
00:10.037, correct? So my physics updates A and B are really more like previous and next and my interpolation is between the previous and the next, correct?