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Equation 27 · Part 5 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol delta_ij

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

What this part means

deltaia_ij is an input to the expression that computes the quantity on the left.

Its job in the formula

deltaia_ij is an input to the expression that computes the quantity on the left.

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.

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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.

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