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Natural Units … Unnatural Science? Jim Grozier Dept of Physics & Astronomy

Natural Units … Unnatural Science? Jim Grozier Dept of Physics & Astronomy University College London. Eddington , 1924. Welcome to the world of Natural Units!. Natural Units: What are they? Where did they come from? Should we use them? Units and Fundamental Constants:

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Natural Units … Unnatural Science? Jim Grozier Dept of Physics & Astronomy

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  1. Natural Units … Unnatural Science? Jim Grozier Dept of Physics & Astronomy University College London

  2. Eddington, 1924 Welcome to the world of Natural Units!

  3. Natural Units: • What are they? • Where did they come from? • Should we use them? • Units and Fundamental Constants: • What are the current issues? • Should philosophers of science get involved? • Why integrated HPS?

  4. Eddington’s derivation M r v m (c = G = 1)

  5. Let’s try that again … M r  m v (c = 1 ???; G= 1 ???) (c = 1 einstein; G = 1 eddington)

  6. Eddington’sphilosophical argument Eddington (1924) p87 Eddington (1924) p2

  7. Parallax  Distance? θ d r

  8. Parallax Distance? θ' d r'

  9. Parallax Distance? d

  10. “Measure-numbers in different codes” X The statement Msun = 1.5 km is true only in Eddington’s system of Natural Units. Not to be confused with ….. The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. CGPM 1983 / Nadine de Courtenay 2013 The metre is the length of the path travelled by light in vacuum during a time interval of 1 light-metre  c = 1 X The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second  c = 299 792 458 metres per second  The metre is the length of the path travelled by light in vacuum during a time interval of 1 light-metre  c = 1 metre per light-metre 

  11. 25 years later … - Eddington (1946) p14 - Feynman, PhysRev74 (10) 1948

  12. “Fourier: Relations expressing physical relations should be independent of our choice of units” [Nadine de Courtenay, 2013] “The equations at which we arrive must be such that a person of any nation, by substituting the numerical values of the quantities as measured by his own national units, would obtain a true result” [Thomson 1872, quoted in Schaffer p136]

  13. - Halzen & Martin (1984) p12 - Mandl & Shaw (1984) p98

  14. Mandl& Shaw (1984) p96 - ibid. p6

  15. - ibid. p2

  16. Electrical Units: Coulomb’s Law for some k. Gaussian units: k = 1 dyne statcoulomb-2 cm2 q has dimensions Mechanical model of EM  “absolute” units, Gaussian units retained & form basis of QFT

  17. So, why should we worry about this? Generality Rigour Generality Rigour Comprehensibility Generality Rigour Comprehensibility Aesthetics Generality Rigour Comprehensibility Aesthetics Current issues: (a) Debate on the no. of fundamental constants Generality Rigour Comprehensibility Aesthetics Current issues: (a) Debate on the no. of fundamental constants (b) Redefinition of the kilogram Generality

  18. How Many Fundamental Dimensional Constants? Fundamental Constants as Pure Numbers: “The Cult of Alpha” - G, Veneziano, Trialogue on the Number of Fundamental Constants (2002) - M. Duff (2004)

  19. Redefinition of the kilogram: h = 6.62606X  10-34 J sec h = 6.62606X  10-34 kg m2 sec-1 - Sally Riordan, IHPS 2012 0 = 4  107 henry metre1 The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. CGPM 1983 / Nadine de Courtenay 2013

  20. Conclusion Natural units introduced to simplify calculations cgs units of electricity provided a precedent Technology has now rendered these factors obsolete Now is a good time to engage in the debate But we need to be properly informed! Historical perspective important  IHPS

  21. References de Courtenay, N., presentation at Dimensions of Measurement conference (Bielefeld 2013) Duff, M.J., Okun, L.B., and Veneziano, G., Trialogue on the Number of Fundamental Constants, (IOP 2002). Duff, M.J., Comment on Time-Variation of Fundamental Constants, arXiv:hep-th/0208093v3, 2004 Eddington, Sir Arthur, The Mathematical Theory of Relativity, (CUP, 1923) Eddington, Sir Arthur, Fundamental Theory (CUP, 1946) Feynman, R., Relativistic Cut-Off for Quantum Electrodynamics, Physical Review74 (10) 1430-8 (1948) Halzen, F. & Martin, A. Quarks and Leptons (Wiley 1984) Mandl, F., & Shaw, G. Quantum Field Theory (Wiley 1984) Moon, P., and Spencer, D.E., The Dimensions of Physical Concepts. Am. J. Phys.17, 171 (1949) Schaffer, S., Accurate Measurement is an English Science, inWise, M. (ed), The Values of Precision(Princeton UP, 1995) Acknowledgements Thanks to Jacqueline Edge, Sophie Osiecki, Brendan Clarke, Phyllis Illari, Toby Friend and Erman Sozudogru for feedback!

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