### Why Theoretical Physics is Hard…

#### Posted by Urs Schreiber

… while mathematical physics is easy, but much slower? Because for the former you need an oracle, without being able to strictly confirm what counts as an oracle.

In his latest piece #, E. Witten comments on the role of these oracles as follows:

We make at each stage the most optimistic possible assumption. Decisive arguments in favor of the proposals made here are still lacking. The literature on three-dimensional gravity is filled with claims (including some by the present author) that in hindsight seem less than fully satisfactory. Hopefully, future work will clarify things.

The proposal in question is about

[…] the problem of identifying the [2-dimensional quantum field theories] that may be dual to pure gravity in three dimensions with negative cosmological constant.

Jacques Distler has a summary here.

It is hard to find a precise definition even of what the word “*dual*” here – meant is holographic duality – is supposed to refer to.

Last time somebody guessed what the axiomatics behind this might be, he was told that this is the wrong axiomatics for what physicsists had in mind. Which may be true. But then it would be good to try to find the right axiomatics.

So I have my own proposal for what the holographic principle *really* is.

*If a $d$-dimensional QFT is a $d$-functor from $d$-dimensional extended cobordisms to $d$-vector spaces, then a $(d-1)$-dimensional QFT $\mathrm{tra}$ and a $d$-dimensional QFT $\mathrm{curv}$ are “holographically related” if the former is the component map of a pseudonatural transformation “trivializing” the latter *:
$$I\stackrel{\mathrm{tra}}{\to}\mathrm{curv}\phantom{\rule{thinmathspace}{0ex}}.$$

Looks pretty through the binocular like this, but turns out to be an intimidating mountain height as one approaches it.

With a little luck Jens Fjelstad will be vising Hamburg in a month, and we’ll continue to scale that rock.

Posted at June 25, 2007 9:01 PM UTC
## Re: Why theoretical physics is hard…

That principle is maths, not physics.