Connections between the ScientificErrorAnalysis and ScientificConstants Packages
Relationship of ScientificConstants to ScientificErrorAnalysis
Relationship of ScientificErrorAnalysis to ScientificConstants
Relevance of Systems of Units in ScientificConstants to ScientificErrorAnalysis
Although ScientificErrorAnalysis and ScientificConstants are separate packages, there are many connections between them.
The Constant() and Element() objects of ScientificConstants represent quantities with associated uncertainties. The method to access the uncertainties (that is, the ScientificConstants[GetError] command) is available to ScientificErrorAnalysis because it has been added using ScientificErrorAnalysis[AddStructure].
Hence, to ScientificErrorAnalysis, the Constant() and Element() objects of ScientificConstants are quantities-with-error, and can be included in error analysis calculations, for example, with combine/errors.
Furthermore, the derivations of the derived physical constants of ScientificConstants are also available to ScientificErrorAnalysis (because they have been added using ScientificErrorAnalysis[AddStructure]), allowing the derived constants to be treated as quantities-with-error with functional dependence.
ScientificErrorAnalysis has defined a correlation matrix between 18 of the nonderived physical constants of ScientificConstants (using ScientificErrorAnalysis[SetCorrelation]). This reflects the statistical dependence of their uncertainties as determined by the CODATA 1998 Adjustment. See Initial Physical Constants for an overview of the CODATA 1998 Adjustment.
If ScientificErrorAnalysis[Variance] or ScientificErrorAnalysis[Covariance] is called with derived physical constant arguments (for example, from combine/errors or ScientificConstants[GetError]), the usual formula of error analysis involving a first-order expansion is used to calculate the covariance or variance, which uses the correlation matrix. This is essentially the method of extending the covariance matrix for the duration of the calculation.
ScientificConstants uses ScientificErrorAnalysis to calculate the errors of derived physical constants (using ScientificErrorAnalysis[Variance]).
See Initial Physical Constants for an overview of the constant derivations, as determined by the CODATA 1998 Adjustment.
The ScientificConstants[GetError] command accepts only ScientificConstants objects.
However, the ScientificErrorAnalysis[GetError] command accepts any quantity-with-error because the methods used to access them have been made available with ScientificErrorAnalysis[AddStructure]).
Therefore, it is recommended that if short form command calling sequences are used for both packages, with(ScientificErrorAnalysis) be performed after with(ScientificConstants).
Because ScientificErrorAnalysis stores correlation coefficients, it neither has nor requires explicit recognition of systems of units.
Of course, variances and covariances involving physical constants are not scale-free, but these are calculated naturally and correctly by ScientificErrorAnalysis in the implied system of units because central values and errors are obtained from the interface to ScientificConstants.
Unusual cases are possible involving the covariance between the same physical constant in different systems, but expected results are obtained. See Covariance.
Initial Physical Constants
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