R.F Streater Critiques Diff M Gauge Group

[arivero]

The use of Diff M as a sort of gauge group is critiquised here by R.F Streater, of Streater-Wightman book.

http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XXII

 

[marcus]

the passage by Streater seems to date back to 1997 at the time when a paper by Kauffman and Smolin appeared (which he cites at the outset and focuses on discussing)

http://www.edge.org/3rd_culture/smolin/smolin_p1.html

and so, in a way, Streater's comments are his contribution to the Edge 12 conversation about this paper, which Streater gives a link to.

http://www.edge.org/documents/archive/edge12.html

BTW Streater could have made things clearer if he had clearly distinguished between spatial diffeos and general one. He just says "Diff M" without specifying whether M is 4D or 3D. I assume he means 4D.
But I don't believe the 4D continuum has physical existence, any more than the particle's WHOLE TRAJECTORY exists. one can't specify where it was at each instant, but only that it got from here to there, and one tries to consider all the ways that might have happened. So in a "path integral" theory of spacetime one considers all the ways the 3D manifold might have evolved from one shape to another. And two diffeomorphic 3D manifolds describe the same reality so spatial diffeos are gauge.
Well this is a digression which doesn't engage very well with Streater's remarks because he is talking about 4D diffeomorphisms (I think) and has a very different picture in mind.

I got the impression that Streater would have been happy to be included in that 1997 conversation at Edge, which indeed was quite interesting. John Baez made some remarks---explaining "the problem of time" as it arises in a background independent theory, for lay audience----which are so helpful I want to quote them.

 

[selfAdjoint]

Excellent discussion, to be borne in mind. LQG, in the Ashtekar-Thiemann form I am familiar with, does not use diff M as a gauge group. Rather diff invariance is imposed as a constraint.

 

[marcus]

What John Baez said at Edge 12 about the problem of time

http://www.edge.org/documents/archive/edge12.html

----quote from Baez at Edge 12, reviewing a 1997 paper by Kauffman and Smolin---

I won't try to define a "background-independent theory" here. It's easier to start with the main example of such a theory, namely general relativity. Normally we imagine running an experiment and timing it with a clock on the wall that ticks along merrily regardless of what's going on in the experiment. In general relativity it's known that this is not strictly true. This has to do with how gravity affects spacetime. Very roughly speaking, if you move an object, you change the gravitational field in the room and inevitably affect the rate of ticking of the clock. So if you run an experiment and ask "what did the voltage meter read when the clock said it was 5:30 pm?" you have to recognize that the experimental setup has affected not only the oscilloscope but also the clock. To put it rather floridly, you can't treat the spacetime measured by clocks and rulers as some sort of fixed grid upon which events play out while remainingly loftily unaffected by these events; instead, it interacts with them.


For most purposes these effects are small enough that we can either ignore them or treat them as small corrections. The fun starts when we try to figure out how to do physics while taking them seriously. In one approach, one decides to treat everything relationally. In particular, one treats clocks as just another part of the physical world with no privileged status: instead of asking what the voltage meter reads when the clock says it's 5:30, one could equally well ask "what did the clock say when the voltage meter read 217 V?".


Taking this viewpoint to the extreme, one can argue that the laws of physics don't describe how things change "as time passes": instead, they just express correlations between various observed quantities, like meter readings. This is what's meant by the "disappearance of time" in background-independent theories.


Julian Barbour is a strong proponent of this sort of purely relational view — though I'm surely oversimplifying his thoughts. Kauffman and Smolin seem to want a way out of this view. I'm not sure how clearly it comes through in their paper, but in conversations Smolin has made it clear that he wants to keep some notion of time in order to preserve the concept of NOVELTY. In the purely relational view, there is no fundamental notion of the passage of time; there is simply a fixed set of ways the world can be, and laws describing correlations, like: "if X holds, then Y holds with probability P". As Barbour noted, Smolin finds this idea "scary". Personally I don't find it scary, and I am also rather suspicious about pursuing a course of research to avoid some conclusion one finds scary — though I have no quarrel with striving to reach a conclusion one finds attractive.


Anyway, Kauffman and Smolin suggest the following way out: perhaps it doesn't really matter if there is a fixed set of ways the world can be, because we cannot tell what this set is! Here they are taking advantage of the work of Gödel, Turing and others. These folks showed that there are lots of mathematical...

-----end quote----
It doesn't really matter what Kauffman and Smolin said about the problem of time back in 1997. many resolutions have been tried over decades and theirs is just one attempt in a long struggle which is still going on. So I will stop quoting here. What I like is how Baez describes the problem, not what he says about this one attempt to solve it.

[edit: hey selfAdjoint! glad you're commenting too]