correct me if i'm wrong... but in order for this to catch hold, we'd need to know why this distinction doesn't have a significant effect in the classical world?

correct me if i'm wrong... but in order for this to catch hold, we'd need to know why this distinction doesn't have a significant effect in the classical world? e.g. for relativity, we know that time dilation doesn't have a measurable effect because we move at very speeds. anyone have an idea why this wouldn't show up?