If there is curiosity, grow for a season in a glass bowl/pot. cover the edges so the suns rays do not affect the roots, and observe the changes that occur.
I did give this a try. I potted some trees in clear plastic orchid pots and made grids that I glued to them, intending to count root crossings of grid lines as a measure. I did this with 8 Dougleas firs, 8 lodgepole pines, 4 zelkova serratas, 4 Eastern redbuds, and 4 cork oaks. I diligently counted root crossings of grid lines every two weeks. I even attempted recounting as many as three times every time I did counts, in order to asses my repeatability with counting.
My personal issues were overwhelming. I had huge problems with repeatability. I had intended to just count new white roots, but I could not consistently decide if this was the extent of 'white' or if it was 'over there'. Unfortunately roots don't abruptly change from white to brown. Then, lighting conditions when I made the counts also had an influence. Sometimes I could see darkish roots on bright sunny days that I couldn't/didn't see on overcast ones. In brief, I came to appreciate why academic researchers use cameras and digital image analyzers to accomplish this.
I could have given this another try last year, but frankly, I've lost interest. I've found a number of scholarly papers that detail there being a strong surge in root growth in the spring. After the summer solstice, roots again grow, but more steadily.
So, currently I think there is a surge in root growth in advance of the rapid growth above ground - roots powered up to support the impending top-side growth. Hence, roots will recover quickly from pruning damage (I've certainly overdone spring root pruning and either killed the tree or spent most of the season nursing it along). Just after the summer solstice, the rate of bole thickening of all species I tested peaks. I believe that this means auxin and photosynthates are now available so that roots are able to recover from pruning. As far as my experiment material is concerned, I continue to repot half of each in spring and half in July/Aug and can see no difference in the two groups.
Otherwise, I continue to repot my maples and other deciduous species (angiosperms) in spring and my conifers (gymnosperms) in Aug/Sep. It nicely balances my work load (a strange term to be attached to a hobby, huh?). I remain curious about the topic, but my aims are to make bonsai. It is my hobby. I'm not really interested in finding funding for my one-man horticultural research institute