Originally posted by Silverious
..."Hey, if there is a smallest unit of matter, then there should also be a smallest unit of energy."...
Personally I don't know of any theory that supports the idea of a
"smallest measurable amount of energy". I do not think that Loop Gravity, in particular, contains that notion. I will get back to that after making a general comment:
I think that there is a larger question that you are on to which
makes sense to ask, which is this:
There seems to be a natural system of units built into nature which are the so-called "planck" units. WHAT ROLE do these units play in what we see happening around us?
In the Planck system of units the unit speed is c, the speed of light and the unit of force is an extremely large force of around
10
40 tons.
Ooops, I have to go----OK, back again.
The thing you have to remember is that just because something is a Planck unit doesn't mean it is always "the smallest measureable whatever"
that MIGHT be the case (in the case of length, or area, or volume)
but in the case of speed or force it conceivably might be the largest and not the smallest. Or it might be neither the smallest or the largest-----like the Planck mass is 22 micrograms which is neither large compared with an elephant or small compared with an atom.
---------------------------
in 1899 Max Planck identified the pl. units and
in 1905 Einstein came up with specialrelativity in which
one of the Planck units (c) plays a central role as a universal speed limit looking the same to all observers
then in 1915 Einstein came up with generalrelativity in which the Planck force is the central constant in the main so-called "Einstein" equation relating the curvature of a region to the energy density there---in effect it models gravity and the central coefficient that relates the lefthand side of the equation to the righthand side is this force constant (which works out to about 10
40 tons.
and around 1995 the LQG people, Rovelli and Smolin, discovered that in LQG the surface area and the volume of any physically defined region is quantized in little bits and there is a smallest measureable area and a smallest measureable volume and these are some constant of order one (still not determined for sure) times the Planck area and Planck volume.
the Planck quantities are a system of quantities (some very tiny and some very large, and others just middlesized) which KEEP TURNING UP and we have no really good explanation for that, as far as I know.
They are the set of units you get if you insist on measuring length and time in such a way that the speed of light turns out to be ONE.
And beyond that, measuring mass on a scale that makes Newtons gravity constant G and Plancks hbar constant ALSO turn out to be one. If you tweak your units so all these good things turn out to be unity, then you find that your length unit is Planck length and force unit is what I said earlier and so on. There is no choice. everything is determined as soon as you say c = G = hbar = 1.
That explains how the Planck units were originally defined by Planck. But it is still a mystery why they should keep appearing in nature.
In 1905 SR and in 1915 GR and in 1995 LQG. And in various other venues along the way.
We are all free to speculate. I don't think your 100 percent energy efficiency idea will work, but the general question is a good one to be asking about now-----why is it that these natural units seem built into nature and what all things do they do and what role do they play in what is happening and the texture of space and time and so forth.
