Suppose one took our universe and divided everything in half; mass, space, time and so on - would we notice? And if we don't doesn't this mean that there is no intrinsic notion of length - despite appearances?
Or should I say absolute?
I don't think you can choose a way to do this that would allow the speed of light 'c', the Planck constant 'h-bar' and the gravitational constant 'G' to all remain the same.
It has always seemed to me that the balance of these three is what sets the scale of the universe. The ratio of the first two vaguely governs how mass and speed are related in one way, and the other determines how mass and speed are related in another way. The odds of these balancing out at multiple points seems vanishingly small.
So let's try:
If we divide both length and time in half we have maintained c.
You have divided times in half, so h-bar, which limits the product of energy and time, would go down to half of its original value unless you double energies, which requires you double masses (given E=mc^2).
Then what happens to the gravitational constant? Everything weighs twice as much and is half as far apart, so the force between two things will be (M + m)G/r^2, which has increased eightfold if you double M and m, and halve r (which doubles the value, twice). So G would have to change significantly.
If the arithmetic is correct, I think this implies that however you pulled this off, we would notice -- one of the three values would change.