> According to the generalized uncertainty principle (a concept from speculative models of quantum gravity), the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that.

At least according to Wikipedia, it seems it is indeed the smallest observable distance. Although it has never been proven and follows from the theoretical generalized uncertainty principle. https://en.m.wikipedia.org/wiki/Planck_length#Theoretical_si...

If you have some time to spare, watch this talk "The astonishing simplicity of everything" by Neil Turok. He explains all this so beautifully.

https://www.youtube.com/watch?v=f1x9lgX8GaE

From what I understand the particles you need to probe distances on the order of the Planck length are so energetic that their own gravity would start interfering. Their Swarzschild radius would become bigger than the distance you're trying to measure.