Equation 55 · A Reference Frame Becomes Classical by Publishing Its Orientation
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol R_epsilon,delta
psilon,delta is the quantity selected or evaluated by the optimization written on the right.
Symbol g
g is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol M
M appears in the objective or constraint used by the optimization on the right.
Symbol l
l appears in the objective or constraint used by the optimization on the right.
Symbol F_1
appears in the objective or constraint used by the optimization on the right.
Symbol F_M
appears in the objective or constraint used by the optimization on the right.
Symbol p_epsilon
psilon appears in the objective or constraint used by the optimization on the right.
Symbol F_k
appears in the objective or constraint used by the optimization on the right.
Symbol delta
delta is the quantity selected or evaluated by the optimization written on the right.
Symbol k
k appears in the objective or constraint used by the optimization on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Now define . subject to 1-> and to a fixed rule for which fragment partitions are admissible. The displayed g records the physical parameter of interest; under the Haar-average convention the resulting scalar is independent of its coordinate label. A worst-case definition would retain explicit dependence until the infimum is taken.
Sources cited in the article section
- [12] Objective Properties from Subjective Quantum States: Environment as a Witness ↗
- [11] Quantum Darwinism ↗
- [13] Quantum Darwinism in an Everyday Environment: Huge Redundancy in Scattered Photons ↗
- [15] Objectivity in a Noisy Photonic Environment through Quantum State Information Broadcasting ↗
- [16] Strong Quantum Darwinism and Strong Independence Are Equivalent to Spectrum Broadcast Structure ↗
These citations give research context. Read each source to check which claims it supports.
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