← All parts of this equation

Equation 27 · Part 7 · The Clock That Comes Back Wrong by Exactly Its Mass

subscript

[Ki,Pj]=iℏ m δij 1,[K_i,P_j]=i\hbar\,m\,\delta_{ij}\,\mathbb 1,
subscript

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

They do not commute. The defining fact of the nonrelativistic symmetry group, established by Bargmann and sharpened by Lévy-Leblond, is that its faithful quantum representations require a centrally extended algebra in which [Ki,Pj]=iℏ m δij 1[K_i,P_j]=i\hbar\,m\,\delta_{ij}\,\mathbb 1. with mass m appearing not as an eigenvalue to be measured state by state but as a fixed number multiplying the identity operator across an entire representation [ 1 , 2 ] . This is what “central” means: the commutator commutes with everything, including K\mathbf K and P\mathbf P themselves.

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

The article lists its research sources here.