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"Here is a picture of (I think) Maru the cat playing in a bag. He loves bags.
Here is the same picture of Maru, at half the size:
Now imagine that Maru is a physicist and the pictures are not pictures but instead windows into the universe he occupies, separate from ours with (possibly) its own unique set of physical laws. The only difference between the two universes is that one has the lengths of everything reduced by a factor of 2.
Can the parallel versions of Maru tell which universe they're in - the smaller or the larger? "
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Yeah, good catch and for some reason I love to see cats nosing into bags. (Note the smooth video repeat.) I'll repeat the comment I left there with tiny changes, it's food for thought (and apparently none of the typos I've been leaving in many comments all over lately, jumping around too much):
I accept the basic point about the relational nature of dimension-holding constants in general. However: it is pretty clear that G can be decoupled from other factors and could reasonably and observably vary with respect to other constants. Think: if "G were half the current value" we can indeed imagine other things, all of atomic physics etc. just being the same, but for example gravity at Earth's surface (well, supposing it kept it's same diameter given slight relaxing effect) would be half of current value, and so on. So the purist approach to the idea is misleading, isn't it?