Re: Energizing spin networks in LQG & Background Independence inq.

quant wrote:
Hi,

In Superstrings. Brian Greene said that If you use high energy or
momentum (for low wavelength as it is inversely proportional) to probe
into the planck length, the superstring would get larger in size.
No black holes would be formed unlike in standard model
(without GR/QM unification).

Now in Loop Quantum Gravity. What would happen to the spin
networks if you'd use similar high momentum energy probe into
the planck length? Would the spin networks just vibrate
violently.. like boiling or would it be magnify too like strings?

No, this won't happen. The simple reason is that in string theory
strings are dynamical objects, while spin networks in LQG label states
of geometry. In other words, since strings propagate in some fixed
space-time, one can describe their motion as vibration and talk about
their size approaching or receding from the Planck scale. On the other
hand, spin networks are determined entirely by their topology and their
edge and vertex labels. Thus, it is impossible to speak of any sort of
vibration, dynamics can only take form of transitions between states
labeled by different spin networks. Lastly, spin networks describe the
geometry of space itself, which you can think of as *setting* the
Planck scale instead of probing it. However, one must not foget that
spin networks describe quantum geometry, which is to classical geometry
(say specifying the metric or the connection everywhere) as momentum
eigenstates are to position eigenstates for a free particle.

Another question. Lee Smolin keeps repeating again and again in
his book "Three Roads to Quantum Gravity" that superstrings is
not background independent unlike LQG. How significant is
this background independence state.

Obviously, it depends on who you ask. But I think everyone will agree
that whatever fundamental quantum theory is developed, it must give
back general relativity with matter on it. The latter theory is
background independent (which simply means that the space-time geometry
is dynamical and not fixed in advance). This is the importance of
background independence. Most of the differences appear when it is
assigned different priorities, e.g. foremost in LQG and secondary in
string theory.

How would you intend to make superstrings background independent?

Wouldn't everyone like to know. :-)

Hope this helps.

Igor

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