I include here a comment on this issue I received from John
Baez: ``I believe there
is
a deep reason why area is more fundamental than length in loop
quantum gravity. One way to say it is that the basic field is not
the tetrad
e
but the 2-form
. Another way to say it is that the loop representation is based
on the theory of quantized angular momentum. Angular momentum is
not a vector but a bivector, so it corresponds not to an arrow
but to an oriented area element.'' On this, see Baez's [33]. On the relation between
E
field and area see in particular [170].