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Friday, December 18, 2015

G Space

The article linked in this post is proclaiming and, above all, calculating that spacetime is emerging from quantum entanglement, a concept that Mark Van Raamsdonk tantalized years ahead. But it is just a twisting the holographic Maldacena's most famous idea with the CFT. Thus it is a role model Universe, a possible Universe, but not our Universe. So far, following up this math way of making "physics" I will bet for the concept in the paper published in ArXiv some months ago and pasted at the end of this paragraphs. It is connected with the "G Space", beyond the Hilbert Space, postulated in the UNST or Nature Mechanics.
That paper has explored a starting point for quantum gravity grounded in quantum mechanics, rather than beginning with spacetime. This approach is suggested by indications that the usual locality of local quantum field theory is not a fundamental property of gravitational theory, as I showed in other posts in my page Nature Mechanics some days ago, and by difficulties of approaches that begin with spacetime and then try to quantize the metric.
If the correct framework for quantum gravity is intrinsically quantum-mechanical, an important question is what mathematical structure is needed beyond that of Hilbert space. While for finite or locally finite quantum systems important additional structure is supplied by a tensor factor structure for the Hilbert space, such a structure is problematic even in field theory both due to the type-III property (infinite entanglement), together with the presence of long range gauge fields. Instead, one focuses on the algebraic structure, and a net of subalgebras which correspond to subregions of the spacetime. Moreover, in gauge theory only certain restricted classes of operators define commuting subalgebras.
These observations prompt exploration of a possible fundamental role for the algebra of observables in quantum gravity, and indicate the importance of understanding further refinements of this algebraic structure. Given that a particle is inseparable from its gravi- tational field, and that gravity apparently cannot be screened, one finds an obstacle to even identifying a subalgebra structure associated with regions, a subtlety going beyond that of gauge theory. This is readily seen if one assumes a principle of correspondence, where the quantum structure of gravity approximately matches onto that of quantized general relativity in the long-distance/low-energy limit. Even in this limit, gravitationally-dressed operators generally fail to commute even when describing excitations which na ̈ıvely are created in spacelike-separated regions. Thus, this further confirms and quantifies the limi- tations of local quantum field theory that have been parameterized by locality bounds. One does find that commutators can be small, in the long-distance/low-energy limit, so it appears possible to recover the subalgebras of local quantum field theory approximately in the correspondence limit.
This discussion appears to have important implications for attempts to find a quantum theory of gravity. There is not a clear primary role for entanglement, given the difficulty with defining tensor factorizations, and it is difficult to see how spacetime itself could emerge from entanglement. Moreover, if one takes a quantum information perspective and thinks of particles as roughly corresponding to qubits, and asks the question “how big is a qubit?” it appears that the answer is that the qubit is arbitrarily large in the sense of having infinitely extended weak field, and moreover its strong-field region grows with the energy of the qubit. This is a qualitative difference with behavior of more familiar quantum systems.
If quantum gravity can be formulated in such an intrinsically quantum-mechanical framework, it will be very important to further characterize the structure of its algebra of observables, and possible refinement of that structure. Important guides in this include correspondence with the known long-distance/low-energy behavior of gravity. Indeed, ul- timately one might anticipate that the familiar geometric structure of spacetime emerges from a more basic quantum algebraic structure, defining such a “quantum emergent geometry.”
In conclusion, the phys-math Nature Individuality is at the very deep bottom of the reality.

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