# Smolin: Lessons from Einstein's discovery...

• A
[...] The relational degrees have less symmetry (compared to the usual diff invariant formulation of GR) and are supposed to be fundamental. [...]
Yes -- that's pretty much the conclusion I reached in my subsequent post 10.

Demystifier
Gold Member
But I think I see it now: restricting to relational degrees of freedom is analogous to (eg) decomposing the Kepler/Hydrogen problem into CoM dof's and relative dof's. The former are essentially "background", so we forget about them. The interesting physical features emerge by analysis of the latter.
Thar's a great analogy!

haushofer
Could someone elaborate on what exactly are "relational degrees of freedom", compared to absolute degrees of freedom? Is it something like "distances between points on a manifold" vs "individual points on a manifold"?

Could someone elaborate on what exactly are "relational degrees of freedom", compared to absolute degrees of freedom? Is it something like "distances between points on a manifold" vs "individual points on a manifold"?
I guess that's one example. E.g., relative velocity between 2 observers is physically significant, whereas absolute velocity is meaningless.

Demystifier
Gold Member
Is it something like "distances between points on a manifold" vs "individual points on a manifold"?
Yes, it's something like that.

Here's a quote from his book "The Singular Universe and the Reality of Time" written with with Roberto Unger Cambridge University Press 2015

"Relationalism offers a strategy that can take over at the point that reductionism fails. The properties of the elementary particles can be understood as arising from the dynamical network of interactions with other particles and fields. A property of a particle or event that is defined or explained only by reference to the network of relations it is embedded in can be called a relational property; its opposite, a property that is defined without reference to other events or particles, is called intrinsic. The ambition of a purist relational approach would be satisfied if all properties of elementary particles and events are relational." p380

He mentions a guy named Chew and collaborators from the 1960s "bootstrap approach" to understanding the observed hadrons as kind of pioneers of the view. I am just into the chapter on this now. He's working up from Liebniz' "principle of differential sufficient reason" and "principle of the identity of the indiscernible" - I'm struggling with it to be sure (and the whole chapter). It seems like a valiant but hopeless defense against infinite regress... I'm hoping it convinces me of some new way of ignoring that.

Here's a quote from his book "The Singular Universe and the Reality of Time" written with with Roberto Unger Cambridge University Press 2015
"Relationalism offers a strategy that can take over at the point that reductionism fails." ... It seems like a valiant but hopeless defense against infinite regress.

I would say reductionism fails where there is intrinsic complexity that cannot be avoided or bypassed on the way to a theory. Then if you try to sum a quantity over terms that are more and more complicated, you may get an infinity that cannot be eliminated. Is that the idea?