Background Indipendant or Dependant?

[madhatter106]

QM is independent right? and a classical view of dependent would be a fixed all encompassing space time. But isn't trying to unify all of physics trying to merge both of those backgrounds? If everything interacts with everything else then is it independent or dependent? I don't think there is a math calc able to handle infinite probabilities and reducing it down to deterministic outcomes doesn't makes sense either.

Taking the quantum duality it's both at the same time, why wouldn't it follow that the background of space is both dependent and independent simultaneously?

Is there a fear that such a thing would cause a large restructuring of physics as it's now known?

--If this is in the wrong area, mods feel free to move it. I couldn't determine where it fit--

 

[haael]

Taking the quantum duality it's both at the same time, why wouldn't it follow that the background of space is both dependent and independent simultaneously?

No, that's a logical contradiction.

I personally believe that the unified quantum gravity should be background-independent, that is, it must obey the translation symmetry, rotation and relativity. If it doesn't it would mean that the space (vacuum) has some structure on its own (ether?) which is unlikely IMO.

We would have to wait for fully unified theory, though.

 

[my_wan]

By background independence I presume you mean coordinate independence. Yet you seem to have tied "duality" into this in some unspecified way. Background independence is a property of coordinate systems such that a choice of scale is arbitrary, i.e., has no real physical meaning. Basically just a bookkeeping device for comparing relative scales, which are physically meaningful. Though background independent formalisms exist which do not specify scale. Any choice of scale can be added after the fact by choosing the units that define the constants.

General Relativity is fully background independent. In fact GR provides the prototype of background independence. The situation is somewhat more subtle in QM. Hilbert space is characterized by an abstract linear space, such that the inner product of vectors has definable meaning. Then by adding Lorentz covariance these vectorial components can be transformed in equivalent components under boost. Yet it is more generally accepted that Hilbert space representations are themselves a mere bookkeeping device lack real physical significance in itself. Though some people beg to differ under highly variable ontological justifications.

Now in what way "duality" or complementarity is related to coordinate independence, or what way you may have intended to imply this meaning, I do not know. As long is there is a relative scale you might define this ratio as some sort of dependence, such as in relativity where relative scales absolutes when expressed as ratios. Yet in the sense "background" in meant in terms of background independence it refers to the background coordinate system independent of any relative relation to things in that background. As such background independence cannot strictly be recovered by weakening the notion of a background to merely mean some distinct observable in that background.

<opinion>
In my opinion ontologies fall into this category of neither being right or wrong, such that you can choose ontologies as freely as you choose coordinate systems. The symmetries of nature only entail that whatever ontology you choose must impose distinct constraints on the ontologies associated with rest of the system in question. Hence there is no more one a true ontology than there is one true coordinate system. However, to date, nobody has been able to construct a completely valid ontological model based on realism. Especially the kind of realism that Newton's critiques invoked to object to his ad hoc fields.