Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.gao.spb.ru/russian/psas/ffk2013/tfiles/tomilin2013pulkovo.pdf Äàòà èçìåíåíèÿ: Mon Nov 25 12:35:25 2013 Äàòà èíäåêñèðîâàíèÿ: Fri Feb 28 03:19:17 2014 Êîäèðîâêà: koi8-r Ïîèñêîâûå ñëîâà: transit

Workshop on Precision Physics and Fundamental Physical Constants
(FFK 2013, Pulkovo, 7-11 October)

Fundamental constants and transition to unity of system of physical quantities and units in electrodynamics
K. Tomilin
S.I.Vavilov Institute for the History of Science and Technology RAS tomilin@ihst.ru
FFK2013, CPO 11 October 2013


Be careful! Check the system of units when you open a new book about electricity! Ja.A. Smorodinsky


Outline
1. Systems of Natural Units 2. Problems caused by Gaussian system of units 3. Fundamental constants in electrodynamics 4. Systems of units in main textbooks (Landau-Lifshits and others) 5. Electrodynamics: physical quantities and laws 6. Relations between physical quantities in CGS and SI. 7. CGS systems should be replaced to the system which is equivalent to new (quantum) SI for c=1, h=1, e=1. 8. Laws of electrodynamics in CGS(Gaussian) and CGS(Quantum) Conclusion


1. Systems of Natural Units (NatÝrliche Einheiten)
in theoretical physics:
Maxwell J.C. (c and G), (e) Stoney G. (c, e, G) Planck M. (c, h, k and G) Hartree D. (, e and me) Ruark A. (c, and me) Stille U. (c, h, e, k and mp, B) 1873 1874/81 1899/06, 1950s 1928 1931 1949
GR, Quantum gravity Atomic physics

(c, and eV) High energy physics
Modern quantum metrology

in metrology:
Z.Bay et al.: c ( , h, e, k ) exact from 20 ctober 1983 exact ~2014

motivation:
1) creating of universal units for any civilizations, 2) simplification of physical formulas

reviews: Dolinsky E., Pilipchuk B. (in Russian,
Tomilin K. (1999) wikipaedia (~2004)

1965)


2. Problems caused by Gaussian system of units
Applying of these systems of units is the source a number of groundless speculations: 1. one from three constants ­ c, or e is not fundamental constant (J.Jeans, M.Born, P.Dirac et al.) 2. some physical principles can be non-fundamental (as uncertainty principle ­ P.Dirac) 3. applying of system of units where =1, =1 and e=1 simultaneously is impossible (P.Bridgeman, D.Hartree, F.Wilczek et al.) 4. physical theories with variable constants (as cosmology with variable speed of light ­ Moffat et al.) ............... But really this is not laws, but definitions of elementary charge e in mechanical units in systems: CGS(Gaussian): e2=c CGS(Heaviside): e2=4c
2

e2 CGS(Gaussian): = hc (Sommerfeld, 1915) e2 CGS(Heaviside): = 4hc

In SI (nowadays): = 4 hc 0

e

(Sommerfeld, 1935)
2

2 SI (nowadays): e 4 0hc -1 new SI (quantum): 0 4hc / e


3. Fundamental constants in electrodynamics
one dimensionless constant: fine-structure constant - dimensionless coupling constant dimensional constants: velocity of light elementary charge e Planck constant electric constant 0 magnetic constant 0 impedance of free space Z0

basic constants secondary constants defined by combinations of basic constants, fine-structure constant and mathematical constants

dimensional constants have different physical meanings in different systems of units: 2 CGS(Gaussian): e hc 2 CGS(Heaviside): e 4hc dimensional coupling constants 2 SI (nowadays): e 4 0hc new SI (quantum): c, , e ­ basic constants 0-1 4hc / e 2 - Z 0 0 1 -1 0 c 4h / e 2 dimensional coupling constants 0 0-1 -2 4h / ce 2
in new SI for =1, =1, e=1:



-1 0

= 0 = Z 0 = 4


4. Systems of units in main textbooks
Textbooks Landau L.D., Lifshits E.M. Theory of field. QED Electrodynamics of Continuous Media Sommerfeld A. Elektrodynamik. Leipzig, 1949. System of units CGS(Gaussian) Fields (E, H) Fik (E, H) E, B, D, H LTMQ (E, B), (D, H) Fik, fik E, D, B, H , f


Dimension Constants 3D 4D

3D 3D 4D 3D 4D 3D

0 and

0

SI (but without Tonnelat M.-A. Les rationanization) principÈs de la thÈorie ÈlectromagnÈtique et de la relativitÈ, 1959 Jackson J.D. Classical electodynamics. N.Y.-L.: J. Wiley&sons. 1962. CGS(Gaussian)

0 and

0

E, B, D, H


SI (but only with Feynman, R.P., R.B. 0) Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II: the Electromagnetic Field, Addison-Wesley, Reading, Mass. 1965. Purcell E. Electricity and Magnetism (Berkeley Physics Course, Vol. 2). 1965. Sivukhin D. Electricity. 2 ed. 1977 Tamm I.E. Principles of theory of electricity. Ugarov V.A. The theory of relativity. 2 ed. 1977 CGS(Gaussian)

E, B

3D



0

(E, B)

3D

CGS(Gaussian) SI (one §) CGS(Gaussian) SI

(E, B), (D, H) (E, H), (E, B, D, H) (E, B), (D, H) Fik, fik (E, H)

3D 0 and 3D 3D 3D 4D 0 and
0 0

Akhiezer A.I., Berestetsky CGS(Heaviside) V.B., QED. 1981.


5. Electrodynamics: physical quantities and laws

E = F /q
force [E ] = charge

divD =

[ ]
-1 0

force length 2 hc = = 2 2 charge e

charge [D] = length 2

F = (cB, - iE )
"intensive" quantities (IntensitÄtsgrÆúen)

f = ( H , - icD )
"extensive" quantities (QuantitÄtsgrÆúen)

0 Fik = f ik = Z0 f 0
- Fik = 0 1 f ik

ik

(Sommerfeld A.)

(Ugarov V.A.)

Fik = 4f

ik

(for c=1, =1, e=1)


6. Relations between physical quantities in CGS and SI.
CGS(Gaussian) E D B H q, SI

4 0 E
4



D B

0

4



0

40 H
1 (q, ) 4 0
-1 / 2

Thus electric charge q ()= ( 4 0 ) where
-1 0

(Table from Jackson J.D., 1962) 1/ 2 q (Gaussian), field E (SI)= ( 4 0 ) E (Gaussian),

hc e 2 . However, between six-vectors and tensors in these systems there is noone correspondence (this is is possible only when c=1): = 4
F = ( E , B ) (Gaussian)


F= 4 0 (E, cB)

(SI) (SI)

f=(D, H) (Gaussian)



f= 4 0 (cD, H)


7. CGS system should be replaced to system which equivalent to quantum SI for c=1, h=1, e=1.
Gaussian system 1870s Heaviside system 1894 Classical electrodynamics QED ` MKS, Giorgi MKSQ, Sommerfeld MKSA SI 1903 1933/34 1950s 1960

Classical electrodynamics

new SI (quantum SI) 2014

CGS(Quantum) quantum SI for c=1, =1, e=1 Should be recommended to go over in new textbooks from Gaussian or Heaviside systems to QSI (quantum SI) or system which is equivalent QSI for c =1, =1, e =1. It requires transition to other physical quantities: -1 / 2 1/ 2 charges q 1 / 2 q and field ( E , B ) ( E , B ) and ( D, H ) 4 ( D, H ) .


8. Laws of electrodynamics in CGS(Gaussian) and CGS(Quantum)
CGS(Gaussian):

1 L = - Fik F 4

ik

Maxwell equations:

Div F* = 0 Div f = 4J F=f
q1q F= 2 r

1 2 2 L= (E - H ) 8

1 1 ik L = - Fik f = - Fik F 4 16 1 L = (ED- BH) 2

ik

Coulomb law:

F* = ( -iE , cB) f = ( H , - icD )

Div F* = 0 Div f = J F = 4f ,

and

2

q1q F = 2 r

2


Conclusion
1. A variety of systems of units in electromagnetism is unacceptable, because it is a source of errors and produces a variety of unfounded speculations. 2. The basis for the unity of the system of units in electromagnetism is provided by new (quantum) SI. 3. What should be changed in the textbooks (which uses SI) (1) providing definitions of the secondary dimensional constant 0, 0, Z0 through more fundamental constants c, and e. (2 ) it is desirable to transit from three dimensional constants 0, 0 and Z0 to one (also taking into account the speed of light) 4 . What should be changed in the textbooks (which uses the Gaussian system and a Heaviside) (1 ) In those books and articles that use the fields E, H ( as in the Landau-Lifshitz textbook), use E and B.


(2 ) to introduce the fine-structure constant explicitly in the laws of electromagnetism, so that such system of units was completely equivalent to new (quantum) system SI with the choice of c=1, =1, e=1. This is due to the transition to a different system physical quantities. (3 ) two tensor (six-vectors) Fik = (E, B), fik = (D, H) should be distinguished even in vacuum, since the fine-structure constant is in relation between them. Thus, the "material equation" as it is considered in Gaussian system becomes the fundamental equation of electromagnetism. It is no accidentally Sommerfeld wrote it even in the preface of his book. This will ensure the unity of the system quantities and units in electrodynamics, both classical and quantum electrodynamics. 5. Should be used and 4-dimensional quantities (tensors), and 3-dimensional, but not only 3-dimensional. 6. It is need to change the terminology in accordance with the physical meaning, since the terminology is formed in the XIX century, and does not reflect modern electrodynamics.


Thank you for attention!