# Baez says what if area is more fundamental than length

• marcus
In summary, Baez suggests that an area could be considered a fundamental constant, and that this area might be more fundamental than the Planck length. He also suggests that this area could be found in all the light around us, and that to get our hands on it we would need the other constant, F, which is pervasive in gravity.

#### marcus

Gold Member
Dearly Missed
This is an intriguing suggestion from John Baez in the Usenet
archive at cornell

http://www.lns.cornell.edu/spr/1999-12/msg0020466.html

I've been fascinated by this idea and have never been sure how to take it. Is it serious or just a passing fancy? what do you think? Have you heard other people besides Baez propose that area might be more fundamental in some sense?

Exerpt from Baez post:

[[...To understand why, note first that
in the usual Planck units, the Planck length is sqrt(G hbar / c^3)
When you see a square root, it's often a hint that some simpler
idea without a square root is lurking around the corner! This
suggests that perhaps more fundamental than the Planck length is
the "Planck area" G hbar / c^3
And, lo and behold: in loop quantum gravity, area turns out to be
more fundamental than length! Spin network edges give area to
surfaces they poke through, and area is quantized. A spin network
edge labelled by the spin j gives an area equal to sqrt(j(j+1)) times
8 pi G hbar / c^3 to any surface it pokes through...]]

He seems to be suggesting that a certain area could be considered a fundamental constant, namely the area

Ghbar/c^3

or else the area which is 8pi times that, hardly matters which
I should think.

Has anyone come across this area in coursework or research and formed any impression of it? Apparently it is prevalent in loopquantumgravity. But that is only one context and it would be nice to know of it surfacing in others.

There is one nice thing that impresses me about it. It is an algebraically simple combination of those 3 constants G, hbar, c.
Other Planck quantities tend to be comparatively more complicated to write----involving square root or else higher powers. Like the force unit involves the fourth power and the time unit involves the square root and the fifth power. So G hbar/c^3 is really pretty simple and easy to remember by comparison, if you care about conceptual ease and stuff like that.

It's a common idea among the 'classical' quantum gravity (Penrose etc) and all the quantum geometry (aka loop quantum gravity aka nonperturbative quanutm gravity) people. cf Penrose, spin foams, Lee Smolin, Abhay Ashtekar...

I'm still learing GR/QFT, so all the quantum gravity stuff is a bunch of gobbeldygook to me.

let's avoid the quagmires of gobblegook, damgo,
but let's also try to find some broadly accessible path to seeing that this area (Ghbar/c^3)
is a good one to know.

Someone who studies GR very likely knows the force F = c^4/G. It is the central constant in the Einstein equation

G_mn = (8pi/F) T_mn

This force is what relates energy density to curvature, and for that matter also relates pressure to curvature.
(If you divide a pressure or an energy density by a force you get the reciprocal of area. In GR it is energy density and pressure that cause curvature, so the constant relating them must be a force) This is not news to you, damgo, but someone else might be reading.

And it is basic that, with any photon of light, its energy multiplied by its (vacuum, angular) wavelength is a constant energy*length or force*area product----hbar*c.

F is basic to gravity and hbar*c is a force*area quantity basic to light. And dividing the latter by F gives this area.

If we abbreviate A = Ghbar/c^3, for the area, then AF is equal to hbar*c.

So this area is on the surface of things, in all the light around us. Its quantum energy*wavelength is one of the few things that is the same for each bit of light. And this all-pervasive constant is AF.

But to get our hands on the area it seems we need this other constant F, which is pervasive too, but in gravity. F is central to how gravity behaves, and AF is central to light. But to get the area out we have to divide AF by F.

I am looking for support for viewing A as a fundamental pervasive constant without invoking anything arcane like "loop quantum gravity" and the other things you mentioned. BTW thanks for the suggestions and ultimately if an appeal to gobbledegook must be made then so be it. Also BTW the parody was a masterpiece, where did you learn to write like that or is it easy?

That was the first time I tried it, wasn't hard really. Having read a lot of Gibbon and other stuff from that era I'd heard the style a bunch. Legacy of a misspent youth. The only thing I can think of right now along these lines is that the idea of using loops turns out to be very very powerful in topology and geometry -- homotopies, holonomies, etc -- even in high-dimensional manifolds. In many of the proofs I've seen, the exact length or dimensions of the loop is irrelevant; what's shows up is the area. Explicit example:

You can get the Riemann tensor -- contains all the curvature information of the manifold and manipulated gives you the left side of the GR field equations -- by considering the effect of parallel transporting a vector around an infinitesimal loop (its holonomy). You find something like

dV_u = area * X_r * Y_s * R_rsuv * V_v

where X and Y are unit vectors that roughly define the 'plane' the loop is in.

In sci.physics.whatever... I started a small thread on this, but not very deep.

Let me point out that an area appears also in any situation of symmetry breaking. While/if the unifyed coupling is dimension less, the efective broken theory gets a coupling corrected by inverse mass square. So, for instance, Fermi constant for weak interactions.

Originally posted by arivero
In sci.physics.whatever... I started a small thread on this, but not very deep.

Let me point out that an area appears also in any situation of symmetry breaking. While/if the unifyed coupling is dimension less, the efective broken theory gets a coupling corrected by inverse mass square. So, for instance, Fermi constant for weak interactions.

Here's a Feb 2003 article in Nature by Baez about "quantizing area"

http://math.ucr.edu/home/baez/q.html

Might interest you, if you haven't seen it.

I liked several of your posts and the context of discussion very much. But don't think I actually found the thread you refer to.
There is a lot to sift through.

Originally posted by damgo
It's a common idea among the 'classical' quantum gravity (Penrose etc) and all the quantum geometry (aka loop quantum gravity aka nonperturbative quanutm gravity) people. cf Penrose, spin foams, Lee Smolin, Abhay Ashtekar...

I'm still learing GR/QFT, so all the quantum gravity stuff is a bunch of gobbeldygook to me.

damgo you gave me a really good bunch of leads here, it turns out

I happened onto some usenet conversation that touched on LQG and led to papers by all those guys and their like, and I see Planck area all over the place.

just by itself the Baez article in Nature magazine, which was written in non-technical style for general readers, had a lot
of links to online articles that related to this

http://math.ucr.edu/home/baez/q.html

Including the Bekenstein-Hawking formula for the entropy
of a (normal, i.e. uncharged nonrotating) black hole.

It is the surface area divided by (4 times Planck area).

Probably familiar to you and not dependent on loops or anything, the underlying reasoning being described as "classical".

then there is this quantizing of the area of a BH which the Baez
paper talks about where the area comes in steps of

(4 times log(3) times Planck area).

this I found completely amazing. the natural logarithm of 3?
yes.

well thanks for the pointers. will try to steer clear of gobbledegook while appreciating some of the simpler results