Is emergent spacetime the same as saying background independence?
Background Independence is a (heuristic) property of (so far) classical theories implying that the geometric structure is subject to the laws of physics and not put in by hand.
Emergent Spacetime is the idea that the very manifold on which this geometric structure sits (and thereby the geometry on top of it) is only an approximate description to a more fundamental theory whoes degrees of freedom have no interpretation in terms of differential structures/metric geometry.
this is off topic, but I've been noticing you have a really good English style (it is the kind of concise easy-to-read unambiguous style that sometimes goes with clear thinking)
some scientists are twice as valuable to us because they can write effectively (as well as do research) maybe you will turn out like that.
hope things going well at your new Uni
touqra, this is a really interesting question. Glad you asked
and I would like to contribute to the discussion
but I don't see anything right now to add to what f-h said
both concepts are deep and important and strategic to the ongoing shifts occuring in physics theory research
Can we have both background independence and emergent spacetime in our theory?
Do you mean that in emergent spacetime, there is fundamentally no notion of distance/ metric? Will causality be emergent?
If the degrees of freedom is not a function of metric or geometrical terms, then, what is this manifold? I mean, what's the manifold good for? I assume that this manifold means the surface that corresponds to our universe...
Or am I missing something?
The emergence of spacetime, or just space and time, can be though of as analogous to the emergence of emotions. It is usually impossible to derive or predict emergent properties from knowledge of the underlying structure(s).
If spacetime is emergent, then you could think of the spacetime manifold and its geometry as a useful way of representing properties of the (unknown) underlying structure, just as certain emotions represent properties of the physical situations that trigger them.
Background independence is a general requirement, reflecting the philosophy that a theory or model should be self-contained, with no arbitrarily imposed structure such as a metric or other field. One would expect a theory of emergent spacetime to be background independent.
Models like LQG and CDT, assume background independence, where measurable properties like time and distance [space] are emergent. GR is also considered background independent because such properties only appear after solving the metric. No such assumptions are required to solve the metric - i.e., they are emergent. Background independence is basically what separates string from non-string approaches to quantum gravity.
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