IT, Fundamental Constants, Related Quantities

Title of this meeting isNMIJ-BIPM Workshop on the Impact of Information Technology

in MetrologyGoal of talk is to describe theImportance of information technology (IT) to the determination and distribution of recommended values of the fundamental constants and related quantities.

Presentation based mainly on

CODATA recommended values of the fundamental physical constants: 2002

P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005)(http://physics.nist.gov/cuu)

Importance of accurate values of constants

Critical comparisons of theory and experiment– Test QED

Advances in metrology– Determining next decimal place never trivial!Reproducible and invariant system of measurement units

c, KJ = 2e/h, RK = h/e2

Calculations– Atomic and molecular energy levels– Important industrial materials and processes

IT, Fundamental Constants, Related Quantities

We shall see thatInformation technology has led to a paradigm shift in1. how least-squares adjustments (LSAs) of the values of the

constants are carried out;2. how the resulting recommended values are distributed;3. how frequently adjustments are done

– now every 4 years instead of every 13 years;

4. how, in general, IT has altered the way databases containing numerical results are obtained and presented to users.

Determination of Best Values of the Fundamental Constants

Turn to the back of a physics textbook, or browse the CRC Handbook of Chemistry and Physics, and one finds a list of best values of fundamental constants and energy conversion factors:

– c, h, e, G, me, α, or even KJ, RK, ae, gn, µp, c1

– kg → Hz : {c2/h} eV → m–1 : {e/hc}

How are such values obtained and what is role of IT?

Basic Tasks

1. Awareness of literature and current research: CONTINUOUS

2. Identify, critically review data

3. Analyze data

Leads to selection of final set of data and calculation of

adjusted constants (unknowns) from final LSA

4. Calculate other constants from adjusted constants

5. Disseminate new recommended values

6. Use new values for new database(s)

Task 1. Gather information

Keep up-to-date with fundamental constants literatureKeep up-to-date with current research

Must know what relevant theoretical calculations and experiments have been published and are currently underway

IT crucial to this task– New online search tools such as Web of Science from ISI– Electronic versions of relevant journals: download papers – Email authors, other libraries when necessary– arXiv.org preprint server at Cornell– Email researchers for research status updates

NIST online bibliographic data base on fundamental constants– Each paper has code, for example, 2000105

Task 2. Review data

Identify, critically review all relevant input data

Uncertainty assignment crucial, since w = 1/u2

– Reevaluate uncertainties so all on equal footing

Possibly uncover errors in experiment and theory

Benefits of “common place” email incalculable– Over 1000 email exchanges for both 1998 and 2002 LSAs– Infinite improvement over “old fashion” letter, telephone

Exchanges stimulate new experimental and theoretical work– Colleagues published five papers as a direct result of

questions asked for 1998 LSA

Task 3. Analyze data

Carried out in three stages

1. Compare measured quantities of same type

2. Compare measured quantities of different types via inferred value of a third quantity

3. Investigate data via multivariate LS analysis: statistical tools

▪ Based on analysis, select final input data and uncertainties

▪ Carry out final LSA, obtain adjusted constants (unknowns)

▪ Computer critical but nothing fancy: quadruple precision Fortran, invert 61 by 61 matrix, computer algebra software

Task 4. Calculate other constants

Output of final LSA is best values of 61 adjusted constants and their variances and covariances

All 2002 CODATA recommended values and their uncertainties essentially obtained from these

A number of the 300+ recommended values are adjusted

constants: α, h, R∞, Ar(e), Ar(p), me/mµ, Rp, d220, ROthers obtained from equations such as the following, but although computer critical, nothing fancy

2r u

2(e)R hRk

cA M α∞=

1/ 2

0

2 hec

αμ

⎛ ⎞= ⎜ ⎟⎝ ⎠

Task 5. Dissemination

Prepare written text for Rev. Mod. Phys. using Latex– Detailed description of data and its analysis (107 pp.)– Tables of recommended values of constants– Hundreds of references—clearly, a formidable task!

Prepare wallet cards and wall charts and distributeMake numbers available for handbooks and text books

BUT MOST IMPORTANTPut new values on NIST interactive Web site: The NIST Reference on Constants, Units, and Uncertainty

– More timely: 9 Dec. 2003 vs.18 March 2005 (RMP Web site)

– Wider audience: 150 000 per month

Task 5. Dissemination, cont’d

Key to everything is error avoidance

– All numbers and references generated by computer and automatically entered into text and Web (includes formatting and two digit uncertainty)

NO PROOF READING Of NUMBERS NECESSARY

Similar procedure for references

– References entered into RMP text automatically from fundamental constants bibliographical database using seven digit code: 2000105

There is a long history of determinations of the proton radius basedon the analysis of electron scattering data.Recent work that takes into account Coulomband recoil corrections has yielded \numcitep{2003222}\begin{eqnarray}R_{\rm p} &=& 0.895(18) \ {\rm fm} \ .\elabel{eq:rp}\end{eqnarray}

There is a long history of determinations of the proton radius basedon the analysis of electron scattering data.Recent work that takes into account Coulomband recoil corrections has yielded \numcitep{2003222}\begin{eqnarray}R_{\rm p} &=& \Eqns{rpes03} \ {\rm fm} \ .\elabel{eq:rp}\end{eqnarray}

\def\Eqns#1{\input{/u/fundadj/LSA2002/Text/Eqns/#1} {\tt #1}}

\def\Eqns#1{\input{/u/fundadj/LSA2002/Text/Eqns/#1}}

Task 6. New database(s):http://physics.nist.gov/hdel

Hydrogen and deuterium transition frequencies for n ≤ 200– Based on a generalized least-squares analysis– Number of different frequencies is so large must calculate

them online in real time– Fortunately, can avoid inverting large matrices and thus do

calculation quickly• Required least-squares analysis is generalization of

2002 CODATA final LSA• Can be expressed explicitly in terms of the results of the

2002 LSA by two successive applications of the Schur-Banachiewicz inverse formula

Conclusion

Overwhelmingly clear:During last decade, IT has allowed quantum leaps forward in the

determination of values of the fundamental constants;distribution of values of the fundamental constants;creation of data bases, their accessibility, and ease of use.A Paradigm shift in the way science and technology are done!

Researchers now expect to find the information they need just a mouse click away!

But what of the future?▪ We are just beginning!

– Eventually, all journals, handbooks, data sources online– Eventually, online, real-time calculations will be the norm