# Why planck scale? let me explain before kill me

1. Jan 21, 2009

### luxxio

Why we are searching quantum gravity effect at the planck scale?
The question seems very stupid (and may be) but let me explain.
I define a quantum object when his action is of the order of planck constant \bar h.
namely A~E \delta t~\bar h. So if i take a small amount of energy E i can take \delta t big.
Applied to gravity i can say that if i take a small (in terms of energy) gravitational system, i can see quantum effect at macroscopic level. In the case of electromagnetism i can have photon of macroscopic length.
In my opinion this claim is true, but is very very difficult to find or to build such object, like in the case of photon is very difficult create only one photon of macroscopic length.
Is this true?

2. Jan 22, 2009

### BenTheMan

Just look at the units. The Newton's constant can be related to a mass scale by setting hbar = c = 1. You find

$$G_N = \frac{1}{8\pi M^2}$$.

M is the planck mass, 10^19 GeV. This is the natural scale for gravitational interactions.

There is precedent for this sort of hand-wavy estimation. In Fermi Theory, we can calculate the scattering of electrons off of neutrinos. The coupling constant in that theory, with hbar = c = 1 is given by

$$G_F \sim \frac{1}{M_W}$$

where M_W is the mass of the W boson, about 80 GeV or so. It is well established that this is the scale where the Fermi Theory fails to be valid, and we have to use a different theory.

So we expect GR to be valid up to the Planck mass, and beyond that we need a new theory.

3. Jan 22, 2009

### BenTheMan

Of course, there could be some new theory which we don;t know about, which makes these estimations wrong. But, according to all we know, this is our best guess.

4. Jan 22, 2009

### luxxio

Yes i konw this argumentation, but let me explain better the question.
Is always true that appling the quantum condition to a gravitational system leads to the planck scale?