Is General Covariance the Key to Understanding Gravity?

[wolram]

am i correct in thinking that the graviton is out of favor, along with
other "things", that could explain gravity?

 

[marcus]

am i correct in thinking that the graviton is out of favor, along with
other "things", that could explain gravity?

on the contrary, it is my impression that it is very much in favor
with string theorists (who are a numerous tribe) and doubtless many others as well
besides which, at least as an approximation to how the gravitational field behaves in common situations, it is an extremely useful analytical tool

even more can be said in its favor, but I will leave that to other posters.

the clearest posts about this that I can recall recently were by Haelfix
in a thread about does string theory provide an explanation for gravity
and Haelfix' views are reasonable and moderate (he doesn't preach one one side or the other of issues). so I will try to find them and copy them in.
what he said was generally tolerant of the graviton, although
not expressing a fanatical belief in it

 

[marcus]

... its oft argued that 'who needs background independence if your theory outputs gravitons' (the thing that makes the geometry in the first place). So what if its perturbative?

Since physics is about predicting things, and we more or less know what geometries are interesting already, if String theory could output the full particle spectrum for each background, then you're really done. Thats the big 'if'!...

this is from the "does string theory provide a quantum theory of gravity?" thread
https://www.physicsforums.com/showthread.php?p=170235#post170235


later he noted that he was restating an argument often made by others, not necessarily offering his own opinion
https://www.physicsforums.com/showthread.php?p=171750#post171750

Note, I was saying what is often argued, not what I may or may not think of the situation.

The thing is, even in General relativity, all manifolds can be taken to have a locally smooth chart.. Its hard to think of curvature entering any perturbative theory of gravitons, unless its at least 2nd order effects or higher. Now, the principle contribution to quantum curvature is precisely what belongs to the manifold itself, degenerate geometries would intuitively be small perturbations of that.

Hence, its hard to see how a perturbative theory of gravitons (string theory) will be able to feel the effects of background independence until very high orders (or probably all orders of perturbation theory).

there are some interesting points here which we might get into

 

[marcus]

am i correct in thinking that the graviton is out of favor, along with
other "things", that could explain gravity?

wolram, as far as I know the "graviton" concept doesn't explain gravity any more than the einstein equation for the gravitational field

In my view the field is at least as real a thing as a graviton!
the equation tells how matter affects the field (the geometry)
but does not provide a mechanism
it says in what manner but not by what "means" (no microscopic hooks and levers)

a "graviton" is a disturbance in the field
and no mechanism is known by which a piece matter generates gravitons
no mechanism, that is, which is any deeper than the original Einstein equations for the field

so it is a false comfort, if one feels one somehow understands better having said "gravitons"---it is not more fundamental than the field and it does not explain things in any deeper way

such is my opinion. there may be folk who passionately disagree and if so
let us hear from them.

 

[Stevo]

there are some interesting points here which we might get into

Could you please elaborate?

Is Haelfix saying that because manifolds are locally smooth, curvature will have negigible effect on the dynamics of the strings, and so background independence - while nice from a mathematical point of view - may not be strictly necessary?

 

[marcus]

...Its hard to think of curvature entering any perturbative theory of gravitons, unless its at least 2nd order effects or higher. Now, the principle contribution to quantum curvature is precisely what belongs to the manifold itself, degenerate geometries would intuitively be small perturbations of that.

Hence, its hard to see how a perturbative theory of gravitons (string theory) will be able to feel the effects of background independence until very high orders (or probably all orders of perturbation theory).
-------
...Is Haelfix saying that because manifolds are locally smooth, curvature will have negigible effect on the dynamics of the strings, and so background independence - while nice from a mathematical point of view - may not be strictly necessary?

It's something like that, I think. Better if Haelfix would elaborate than for me to try.
I think in some of this thread he is reproducing a common argument used to justify stringy approaches, rather than stating his personal opinion.

Anyway, I would paraphrase it much the same way you did. I would say, why bother with background independence? because it is difficult to implement and doesn't make much difference to the graviton [!]

The picture I associate with this argument is that the graviton is bunched up in one place and small compared to the geometry, so the place where the graviton is imagined to be localized is approximately flat. It's not a terribly realistic or persuasive picture, to me, but the message it projects is that all gravitons are pretty much the same animal and can't tell the difference between one space and another, so let's just calculate everything in Minkowski space.

 

[marcus]

BTW Stevo we should put in a link to your thread
discussing the essay you are writing about this

https://www.physicsforums.com/showthread.php?t=18780

hope its going well

 

[wolram]

the thing i don't understand is that, if gravity can be created by any form
of energy, or condenced energy in the form of mass, these gravitons
would have to be everywhere at, some constant density throghout the
universe to give us consistent laws of gravity.

 

[kurious]

Could gravitons give the universe most of its mass in the way that gluons give quarks most of theirs? A spin 2 graviton splitting into 2 spin 1 particles would be analagous to what gluons can do.

 

[selfAdjoint]

One difference between gluons and gravitons is that gluons are charged (with the charges of the strong force) and gravitons are not (the "charge" of gravity is mass, and gravitons are massless). So the energy in gluon-gloun interactions is much greater than that in graviton-graviton interactions. It is of course true that "gravity gravitates" but the contribution is relatively smal.

 

[kurious]

If current gravity laws are wrong over big distances then it is possible in principle that the gravitational potential energy could be associated with a lot of mass -perhaps the missing mass of the universe?

 

[Haelfix]

One has to be a little careful, there are some really subtle technicalities in quantum gravity that can throw your perturbation series to hell. (I think String theory has these problems too).

You really need a metric that is asymptotically flat, and has enough killing vectors to be manageable.

there's a notion of in and out states, that underlies how we actually count particles in fock space (b/c the notion of a particle is very ambiguous in quantum gravity).

What I don't know about, is how String theory's renormalizability transfers over to the graviton perturbation series (I asked that question on SpS recently). I don't know if geometry contributions are subject to these laws or not. If they are, indeed its a whole different ballgame.

 

[Stevo]

hope its going well

Yeah, it's almost done. I've had to revise my plan a little, basically to keep within the word limit and to keep it more in line with the course content. It's more about the ontology of spacetime described in quantum gravity, but a lot of that has links to the background (in)dependence of the various theories.

 

[marcus]

Yeah, it's almost done. I've had to revise my plan a little, basically to keep within the word limit and to keep it more in line with the course content. It's more about the ontology of spacetime described in quantum gravity,...

speaking of ontology
there is this piquant quote from Einstein (1916)

"...the requirement of general covariance takes away from space and time
the last remnant of physical objectivity..."

from "Grundlage der allgemeinen Relativitaetstheorie" Annalen der Physik vol 49 page 769 ff.

My experience of you is you often have a completely different take on things from me so that I would be interested to know if you touch on this (kind of ontological) saying of A.E. in your paper and what you make of it and do you have a way of deflecting it or disposing of it or keeping it at bay.

maybe we have discussed this quote before but if so I don't remember how you handled it. it is a bit radical, how he puts it.

-------------------
added when I saw your response:

What you say in following post seems to me soundly reasoned, concise and clear.
So rather than complicate things by replying to it I am simply
applauding "in advance"----the paper you are writing about this should
be a good one, perhaps you will post it and give us a link in case others
want to have a look

 

[Stevo]

I take general covariance to remove any ontological significance from the manifold. If the values with physical meaning do not depend on which smooth manifold we take (up to diffeomorphism) then the points on the smooth manifold have no intrinsic identity. I think that we can only ascribe physical meaning to points when there is a metric describing them, since this metric represents relations that are supervenient upon a real physical entity - the gravitational field.

So I would say that general covariance removes physical objectivity from space and time in that we can't remove space and time from matter. There is no clear distinction between the two, as there is in, say, Newtonian physics.