A Lattice with No Inside or Outside: Quantum Mechanics as a Description of Entanglement ✛ ✎

Original: "On the Quantum Structure"
· Dong-Sheng Wang
arXiv:1101.0503 · 2011-01-03 · arXiv non-exclusive · independent analysis · 3 min
Quantum mechanics describes not isolated objects but correlations and information in a new space called tangnet, where a universal inside-outside symmetry operates.

A woven basket holds its shape not because it has a rigid frame, but because each strand is interlaced with its neighbors. Pull one out, and the pattern unravels, leaving a heap of twigs. Quantum mechanics, according to a new paper, works the same way: its elementary objects do not exist independently, but only in interweaving with each other.

For a long time, physicists described quantum particles as isolated waves, and their interactions as something secondary that could be added later. But any real experiment shows that a particle always bathes in its environment, like a fish in water, and this environment is not just noise; it becomes part of the particle itself. The author of the paper flips the picture: it is not that the environment interferes with pure quantum life, but rather that quantumness is possible only because of openness. A wave function without an environment is a basket without strands.

Usually, a mixed state of a quantum system is represented as a mixture of pure states, as if the system is in one of them at any given moment and we just do not know which. The author shows that this view is physically incorrect: a mixed state is not a mixture but a part of a larger whole, and the difference is visible in correlations.

To make this idea rigorous, the author constructs a new space, the tangnet. It is a lattice where nodes are states and threads between them are entanglement. In ordinary space, two particles can be far apart, but in the tangnet they are neighbors if their quantum fates are intertwined. Distance here is measured not in meters but in degree of correlation. The elementary cell of such a lattice is a qubit: two subsystems so tightly linked that they have neither inside nor outside. Like a Möbius strip: one side smoothly transitions into the other, and you cannot tell where the system ends and the environment begins.

The author formulates a theorem about the inside-outside symmetry: an entangled structure remains unchanged whether you transform each subsystem individually or swap them. It is as if the basket's pattern stayed the same whether you rearrange the strands or flip the whole basket.

Previously, entanglement was considered a fragile resource that needed protection from the environment, like a rare flower from a draft. The new picture says: entanglement is not a resource but the very fabric of reality. The environment does not destroy it; it weaves into it. There are no practical applications of this idea yet, and the author honestly says so. But if the tangnet can be formalized, it could become a new language for discussing quantum gravity and why the classical world appears so stable even though it is made of quantum bricks.

The basket with which this text began has no distinguished center and no distinguished edge. So too with the tangnet: it has neither inside nor outside, only nodes and threads. Perhaps this is how the world is at its deepest level: not as a collection of separate things, but as one great interweaving.

The author calls the new space "tangnet" (from the English word tangle), emphasizing that the links between lattice nodes reflect entanglement, not geometric distance.

I = S_S + S_E - S_{SE} = 2S_E
The mutual information equals twice the entropy of the environment, reflecting the complete correlation between system and environment.
I = I(S_1E_1:S_2E_2) - I(E_1:E_2) - I(E_1:S_2|E_2) - I(E_2:S_1|E_1)
The mutual information between systems is obtained by subtracting the correlations of the environments from the total correlation, which accounts for the openness of each subsystem.
|\psi\rangle_{AB} = \frac{1}{\sqrt{2}}(|0_A1_B\rangle - i|1_A0_B\rangle)
An entangled state of two subsystems with a relative phase, which is invariant under local transformations and permutations.
Scientists
William WoottersJohn Stewart BellErwin SchrödingerAlain AspectDavid DeutschSatyendra Nath Bose
Concepts
quantum mechanics quantum wave function state work momentum classical physics trajectory physics correlation Hamiltonian mechanics momentum space coupling chemistry network time qubit matter wave curvature