This thread is motivated by a number of posts in the ATM section, where the usual things we think we understand are blithely tossed about as being meaningful in the Planck regime (or era, or at the Planck scale, or ...) - length (or space), time, energy, mass, ...

GR and QM are mutually incompatible, and this mutual incompatibility becomes extreme in the Planck regime.

But what does this mean, in respect of how we might use terms like 'time', 'space', or 'energy'?

It's easy to say that one theory (GR) is 'background independent', and the other (QM) 'background dependent', and that the scale at which these two theories become nonsense, when one is interpreted in terms of the other, is the Planck scale.

How best to demonstrate this incompatibility, using 'time', 'energy', 'space'?

What are some good explanations - other than those using the math of each theory - that you've come across which show this incompatibility?