Talk:Background independence

Bullshit
I have ever seen so much bullshitting on what concerns "active" and "passive" covariance. This article is simply false. "As both metric functions have the same functional form but belong to different coordinate systems, they impose different spacetime geometries. Thus we have generated a second distinct solution!" It is just exactly the same in a different coordinate system.... You can count known solutions of Einstein equations in the vacuum on your fingers. Too bad physicists were so stupid during one century they didn't used "active" covariance to find infinitely many different solutions ! pyc 25/04/2011 —Preceding unsigned comment added by 85.218.96.37 (talk) 16:12, 25 April 2011 (UTC)

Untitled
Article claims, "Below is given an easy argument which uses only the very basics of GR making it accessible to anyone..."

Come on. I mean, really.


 * Yes, it's incomprehensible. --88.74.131.82 (talk) 19:55, 26 October 2009 (UTC)

Does emergence itself signify a concept of time
The wording of the article "independent of the actual shape of the spacetime and the value of various fields within the spacetime, and in particular to not refer to a specific coordinate system or metric" seems to me careful and important. I contrast it with writing that seems to suggest that the idea of time is absent from the theory.

For example, in the glossary of his book "The Fabric of the Cosmos," Brain Greene gives this entry for background independence: "Property of a physical theory in which space and time emerge from a more fundamental concept, rather than being inserted axiomatically." In the text (p.487) he writes, in relation to applying this concept to string theory, "In this proposal, concepts of space and time fail to have meaning until innumerable strings weave together to produce them."

What Greene writes seems very problematic. How can we conceptualize anything to "emerge" from something else without some time-like dimension along which change takes place? How can we conceptualize the difference between before and after the "weaving together of innumerable strings" without that difference taking place over something like a dimension of time? It seems to me that such questions signify that the idea of a time-like dimension is contained in the theory ab initio, but not a specific metric. And it seems to me that the formulation in the present article takes this position. Doe this reading have merit? jjb 00:09, 11 February 2007 (UTC)

Space and Time as Emergent Properties of a Background Independent System
One could imagine a model of “reality” in which some sufficiently rich vector space could contain definitions of every possible (and impossible) state and state transition, and that this vector space, itself, would be background independent (have no attributes of space or time). For example, a complete description of the number pi requires infinite information. Yet, pi “exists” everywhere, at all times. Pi is background independent.

In such a model, one might posit that every system that can be defined and that contains an observer performing an observation “exists”. In a sense, these observers and events would spontaneously “find themselves” within this background independent vector space.

In such a model, spacetime would be an emergent property of a system that possessed no space or time (background independent).

Interestingly, Einstein's spacetime is a fixed and unchangeable entity; that which happens tomorrow is exactly as fixed and immutable as that which happened yesterday or even that which happens now. Each observer in spacetime follows a different worldline with its own, unique view of the same spacetime. Straight worldlines are inertial reference frames and curved worldlines are accelerated reference frames, embedded within the same fixed spacetime.

— Michael McGinnis (talk) 22:18, 8 February 2010 (UTC)

Neutrality disputed?
I didn't add that tag, but I agree that there is a major problem with that section as written. I also agree with the comment in the section labelled "bullshit" above. Einstein's hole argument says exactly the opposite of what is asserted in that section - it says that solutions that differ by diffeomorphisms are NOT distinct, but rather are identical. Diffeos are the gauge transformations of GR, and gauge transformations are not real symmetries - they are redundancies in the description, and performing one does NOT lead to a new, distinct solution.

There is such a thing as manifest background independence - it's just a formulation of the theory that never refers to any specific background, for instance a path integral over metrics - but I think the section as written doesn't describe and is factually wrong on a number of counts. I suggest deleting it entirely, making the article much shorter, more correct, and more comprehensible. But I'll leave this comment for a while first to see if anyone disagrees.  Waleswatcher  ( talk ) 18:09, 11 January 2012 (UTC)


 * I just read (part of) the paper of Rovelli and Gaul. It does not support what is written in that section.  Specifically, it asserts that an "active" diffeo on a metric produces a distinct metric on the SAME spacetime manifold.  That's of course correct (although the distinction between active and passive is meaningless).  Instead, the article asserts that "active" diffeos produce "different spacetime geometries" and "distinct solutions", which is completely wrong.  I'll wait a few days and then edit, drastically.  Waleswatcher  ( talk ) 18:21, 11 January 2012 (UTC)

Article reverted to old version
After some thought, I don't see any way to salvage most of the material in the article as it was prior to my edits. The introductory paragraph had nothing to do with background independence as the term is used in physics, or in any of the references. The "Principle of universality" section was pretty much nonsense - for instance, the idea that the fine-structure constant cannot change in a BI theory is absurd and totally unsupported. Again, totally uncited. Then, as discussed elsewhere on the talk page, the diffeo invariance section was simply wrong (and contradicted by its own references).

So I just reverted to the last sensible version, and then added back some links and references. I'll add a comment about AdS/CFT too.  Waleswatcher  ( talk ) 02:16, 14 January 2012 (UTC)

Topology change
In the section "Loop quantum gravity" the article states that "any consistent quantum theory of gravity should include topology change as a dynamical process." Is there any simple argument showing that, or could someone add references that back this statement? --bajo (talk) 14:25, 28 February 2012 (UTC)
 * Well, a background independent theory can't be restricted to a unique topology any more than it can be restricted to a unique geometry (at most, it could depend on some kind of boundary conditions). When you integrate over metrics, that automatically includes more than one topology.  So that's really part of the definition of background independence.  With that said, I agree it needs a reference - the entire article is inadequately sourced.   Waleswatcher  ( talk ) 14:38, 28 February 2012 (UTC)


 * Thank you, but I see two separate issues here. One is whether "background independence" can be defined as to include only one topology, and while this might be difficult/impossible, it is not what the article states. The other is whether a quantum theory of gravity can be consistent if restricted to a single topological sector. I am not sure if there is an argument showing that in a path-integral formulation one is forced to include all the topological sectors. For example, in the case of YM theories, one can show that you need to include all the distinct instanton sectors using the cluster decomposition principle; maybe a similar argument can be used in the case of gravity, but I am not sure. Also, even if such an argument could be found, I would be a bit wary to generalize it to "any consistent theory of quantum gravity", since the path-integral is most certainly ill-defined in the case of gravity, and it is not difficult to imagine that different formulations could accomodate a single topology in a consistent fashion. As it is stated now, the sentence under discussion seems to imply that LQG is not a consistent theory of quantum gravity because it requires a fixed topology. --bajo (talk) 10:55, 29 February 2012 (UTC)
 * I think it should simply state that this makes LQG not explicitly BG independent - or at best, BG independent only in a weak sense. Asserting or implying that it makes LQG inconsistent is too strong.  Waleswatcher  ( talk ) 12:17, 29 February 2012 (UTC)

"Depoliticizing" the article
Background independence is not a Quantum Gravity specific issue. It means something largely unambiguous in the case of General Relativity, and is uncontroversial there as well. In Quantum gravity however, it's subject to a lot of debate, with differing views about what counts as background independence, what it means, whether or not one should have it, etc. In my opinion, this page seems to be the result of these arguments, where people are trying to extol the virtues of their favorite QG theory, and so all that remains on this page is a list of features, loosely related to background independence, of the two main QG theories. This articles doesn't even explain what background independence actually is! Clearly, the contributers have lost sight of what is important.

I propose, and I have started working on this, that we focus the article mostly on classical background independence, where things are much better understood and less speculative/"political", and leave the QG subtleties to a minor mention at the end. DimReg (talk) 07:39, 30 April 2013 (UTC)

I've made some updates to the article, and I think I'm mostly done editing now. If you want to revert my changes, please try to understand my reasoning first. One, I tried to define background-independence from the viewpoint of someone who believes it is very important for physics, but without making it sound like a god given condition that must be satisfied. I provided a reference to a paper with a description of the viewpoint I put in this article, as evidence that at least some academics view background-independence that way. If you disagree with this viewpoint, you should add another paragraph describing your viewpoint, and add a reference where someone describes your point of view. Simply deleting my description is unlikely to be productive.

Two, I tried to make the quantum gravity section convey less of a conflict between the two theories. The string theory section was quite nice when I got to it, but the loop quantum gravity section had an irrelevant comment about the semi-classical limit, a direct comparison to string theory, and a criticism that applied to both theories, but was only aimed at LQG. Any comment about string theory should go under the string theory section, and any comment about LQG should go under the LQG section. Further, any comment about either should be about their background independence, otherwise you should be writing in their main articles. The article I started with was written as if it was a defense of string theory, the "manifest background independence" was clearly written to defend perturbative definitions of ST, and the LQG sections tried to negatively compare it to ST. I tried to make it an article actually about background-independence.

Three, I think we should stay away from explaining background-independence in terms of diffeomorpisms and coordinate systems. In my experience this leads to a lot of confusion when stated to naively. For example, it's easy to find a coordinate independent theory that is not background independent. Same for diffeomorphism invariance, for example you can write maxwell's equations in a diffeomorphism invariant way that is perfectly valid for any manifold, but it's still not considered background-independent because you need to metric to do so, but the metric is not fixed by any condition of the theory. But I think there is nothing confusing or controversial about calling GR background-independent because of Einsteins equations determines the metric. DimReg (talk) 12:59, 1 May 2013 (UTC)

Ask a mathematician
Ask any mathematician the difference between a diffeomorphism and a coordinate transformation...they are radically different things.

When you say maxwell's equations can be written in a diffeomnorphism invariant way what you actually mean is that they can be written in a coordinate invariant way - you are getting the two notions mixed up from the very beginning...

Any theory is invariant under coordinate transformations, only GR is invariant under diffeomorphisms (see mathematical definition!!!)

Response to "Bullshit"
Einstein got stuck of this problem for 4 years. The argument I gave was actually Hilbert's version of the Hole argument (Hilbert being the world's most brilliant mathematician at the time). Bullshit is the folk law idea that Einstein, a world class genius, got confused about coordinate transformations for 4 years...Grow a brain...

You said

"You can count known solutions of Einstein equations in the vacuum on your fingers. Too bad physicists were so stupid during one century they didn't used "active" covariance to find infinitely many different solutions !"

There's active and passive diffeomorphisms, where passive diffeomorphims are coordinate transformations and active diffeomorphisms are what mathematicians call diffeomorphisms. The class of solutions related under active diffeomorphisms all give the same predictions of say cosmological experiments (see Rovell's book for more details). A representative of this equivalence class (your "know solution") is `selected' out of all the other representatives because it is easier to derive this particular representative, but if you did the use a different representative you would get the same predictions for experiments.

Additional Response to "Bullshit"
Additional to comment made about counting solutions on one hand...Smolin's paper "The case for background independence" http://arxiv.org/pdf/hep-th/0507235:

"More generally, this assertion misses completely the key point that general relativity is itself a background independent theory. Although we sometimes use the Einstein’s equations as if they were a machine for generating solutions, within which we then study the motion of particles of fields, this way of seeing the theory is inadequate as soon as we want to ask questions about the gravitational degrees of freedom, themselves. Once we ask about the actual local dynamics of the gravitational field, we have to adopt the viewpoint which understands general relativity to be a background independent theory within which the geometry is completely dynamical, on an equal footing with the other degrees of freedom. The correct arena for this physics is not a particular spacetime, or even the linearized perturbations of a particular spacetime. It is the infinite dimensional phase space of gravitational degrees of freedom. From this viewpoint, individual spacetimes are just trajectories in the infinite dimensional phase or configuration space; they can play no more of a role in a quantization of spacetime than a particular classical orbit can play in the quantization of an electron."

about merging with general covariance
70.247.175.236 has proposed this article to merge with "General covariance." But "General covariance" is of the view point of orthogonal coordinates, i.e. General relativity. I think "background independence" is rather of the coordinate itself.--Enyokoyama (talk) 11:12, 31 December 2013 (UTC)

Not clear
Parts of the article are far from being clear, or sometimes incomprehensible. Sure that background independence at least means that it must be possible to not refer to a specific coordinate system., but what is the meaning of the defining equations of a theory to be independent of the actual shape of the spacetime? So in a 5-dimensional spacetime we should have the same (number of) Einstein equations?

Sure, Background-independence is a loosely defined property of a theory of physics, but this should appear at the beginning.

Next, the main trouble arises in the section "Manifest background-independence". Background-independence is loosely defined, so we know what it means in particular instances only; anyway, whatever background-independence means, a theory is background-independent exactly in case it (admits a formalism which) is manifest background-independence. Thus I do not understand the section at all: making a property manifest is not only aesthetic, or a useful tool: it is the only way to check that some theory is actually background-independent! PS: Of course, maybe one does not care to check that a theory is background independent, that's fine, but if someone wants to check, the only way is finding manifest independence! — Preceding unsigned comment added by 78.15.203.91 (talk) 19:05, 19 September 2014 (UTC)

Moreover, Michael McGinnis above has good reasons. In principle, mathematically, one could make every theory background-independent by making every point(/particle/observer or whatever) carry with him some state which describes the whole universe. This might look unnatural, unconvenient and tricky, but formally there is no difference (and, yep, much current phisics is attaching more and more complicated states to each point of space time). 78.15.203.91 (talk) 19:17, 19 September 2014 (UTC)

What is as "shape of the spacetime"?
near the emptyness of intension or sth. of good & bad shapes?

But, by the way, what is spacetime, if it has different shapes? Why not different flavors, colours or versions?

If the world of talking would be not limited (actually by the time humans are able to think about), mankind would talk and talk about that without coming to an end. The grandsons of the grandsons of Lee could find a newly flavored style of spacetime that currently is unknown. What I want to point out is:

If someone is not able to conclude from his assumptions that his proposal is sound and complete, we should wait until they are und just avoid to waste life time. — Preceding unsigned comment added by 84.59.227.47 (talk) 14:34, 19 December 2015 (UTC)

quantum gravity has no local degrees of freedom in 3D - why?
In the quantum gravity section... "in 3D, quantum gravity has no local degrees of freedom"

I don't see how that is intuitively obvious. Any chance further explanation could be included? — Preceding unsigned comment added by DarkSky7 (talk • contribs) 01:15, 18 May 2022 (UTC)