Equation 47 · 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 p_blind
lind is part of the quantity the equation computes from the expression on the right.
Symbol epsilon
epsilon occurs above the fraction bar. The numerator is divided by the entire denominator below it.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
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
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
There is a trap. Even an orientation-blind fragment can sometimes satisfy a loose threshold by guessing from the prior. For uniform SO(3) , the probability that a blind estimate lies within geodesic angle of the true rotation is . This expression follows from the Haar distribution of rotation angle, whose density on [0,] is 2/ . It passes the limiting checks: at =0 , blind success is zero; at = , it is one. The redundancy definition is informative only when 1-> . Otherwise an empty box can qualify as a witness.
Sources cited in the article section
- [5] Aligning Reference Frames with Quantum States ↗
- [6] Optimal Estimation of Group Transformations Using Entanglement ↗
These citations give research context. Read each source to check which claims it supports.
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