Understanding Planck Scale Derivation: Energy, Length, and Uncertainty

[victorvmotti]

I see that Planck scale of mass-energy is related to the corresponding length scale by application of the uncertainty principle.

What is not clear for me is how we find either energy or length scale to compute the other one?

What goes wrong if we assume a higher energy level than the Planck energy scale and then find the corresponding lower length scale via the uncertainty principle.

Is it related to the gravitational constant?

Should we use the concept of a tiny black hole from general relativity?

Also, how we compute the Planck time for given energy and length scales?

 

[jtbell]

Planck units are derived via dimensional analysis so as to make various fundamental constants equal to 1.

http://en.wikipedia.org/wiki/Planck_units

 

[victorvmotti]

So, we get the Planck length by demanding a combination of constants that give a length dimension. And then based on it find other related scales, such as Planck energy scale.

But can you show what goes wrong in general relativity if we consider energy-mass scales larger than Planck energy scale?

 

[victorvmotti]

0 down vote http://physics.stackexchange.com/questions/146046/planck-scale-and-qft#
I see that we use dimensional analysis involving constants of nature to obtain the Planck length and then apply the uncertainty principle to find the corresponding Planck mass-energy.

But the energy and length scales were found by invoking a "particle" interpretation of fundamental entities of nature. Wasn't it?

This is not still clear for me, I mean, where and how we used the notion of particles to obtain Planck scales?

I am not deep into the quantum field theory yet, but if we let go of the notion of particles and introduce the fields (real or complex set of functions of spacetime) instead as the fundamental entities of nature, then can we make sense of arbitrarily large energies or small distances?

But gravity, does not still have any valid QFT, it is now a classical theory, so we say for arbitrarily small distances on space, there should be only quantum fields, and therefore we are waiting for quantum gravity?

Am I right in the above argument?