Originally posted by wolram
sorry I am not sure if this is the correct pigeon hole to use.
planck dimentions are well known but why are they the
smalest possible units?
i think it was wheeler that used Planck units in his
quantum foam theory, would we have this theory without
planck units?
this is a fine pigeonhole
the process of quantizing GR tends to bring Planck units to the fore
Physicists tend to be vague about factors of "order one"----like factors of 2pi and 1/2. So be alert to the fact that someone might say that the Planck area is the smallest possible non-zero surface area something can have and what he really means is that the smallest area is 8pi times Planck area
or "some factor of order one" times Planck area, and 8 pi is not
even strictly speaking of order unity but anyway there's room for a bit of fudge here
There are several variants of Planck units----that differ from each other by small numbers, small factors.
Most commonly people say the Planck area is (hbar G)/c
3
But
John Baez has written advocating using 8pi G instead of plain G. So his Planck area would be 8 pi (hbar G)/c
3.
Thats only a sample. A lot of this goes on. You can't nail theorists down to one official system of anything.
In the main system for quantizing GR the area and volume operators turn out to have discrete spectrums----discrete sets of values. So for any given surface or region there is a smallest area or volume it can have, in any quantum state.
These are something like Planck area and volume----but there are some factors of order unity or anyway some small numbers that get into the picture.
Baez and another guy published a paper proving that the smallest length one might reasonably expect to be able to ever measure is on the order of the Planck length-----some small number times Plancklength-----"around" Plancklength.
somebody else here may feel more confident than I do and may wish to lay it out in an assured tone of voice and make it seem simple.
But I don't think the situation is simple.
Some people seem to think that LQG, for instance, quantizes space and time using a regular uniform cubical lattice with every link the same length---Plancklength. I don't think it does.
I haven't seen any evidence that the people actually doing the research and getting the results have everything tied up in neat packages and think of space as all granular with the same size grains or foamy with the same size bubbles.
the Planck length plays a major major role in the formulas of Quantum Gravity and DSR (doubly special relativity) and the Planck scale is emerging clearly as the threshold of new physics.
But I have a feeling that people are still making up their minds about how Plancklength (area, volume, mass, energy...etc)
occurs in nature and why it is so important.
Wheeler is an example of incredible intuition and hunches turning out right---and risk-taking. You don't need Planck length to theorize foam. He said if you keep jacking up the magnification and look closer and closer then eventually when you get down to a certain scale it looks foamy. And he conjectured that would happen at around Planck scale.
My feeling is that we would still have this theory even if we lived on a different planet with a different culture and used slightly different constants----like maybe
John Baez 8pi G, instead of G---or something else besides Planck's hbar----and had slightly different Planck units called something else.
My feeling is there has to be some scale which if you get down to around there then flat ("Minkowski") space disappears and the usual ("Lorentz" or "Poincare") symmetries and conversion formulas break down.
To put it in a non-name-dropping way: flat space disappears and the usual symmetries fail----at some scale.
A lot of people guess, for reasons that sound sensible to me anyway, that it happens at around Planck scale.
Wolram, I've been reading a recent paper about this!
Giovanni Amelino-Camelia et al
"Quantum Symmetry, the Cosmological Constant, and Planck Scale Phenomenology"
http://arxiv.org/hep-th/0306134
Here's the start of their abstract:
"We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant,
not under the Poincare group but under a deformation of it parametrized by a dimensional parameter proportional to the Planck mass..."
In other words the symmetries start getting unusual when you get down near Planck scale----the threshold may not be exactly Planck mass itself but something "proportional" to Planck mass. They always leave themselves wiggle-room with factors of order unity
