72
J. Maruani
interpreted as a quantized curvature involving an additional dimension, then this
dissymmetry means that a single sign is privileged for this curvature, charge
conjugation amounting to its reversal. Mass arises from the confined motion of
the extra-dimension curvature over usual space-time.
3. By relating rest mass to spin motion, quantum theory brings an insight into such
relativistic concepts as the proper interval x 0 , which is the residual interval when
the space coordinates r 2 are subtracted from the time coordinate c 2 t 2 . The velocity of light c is not simply that of electromagnetic waves, but also that of
basic motions at the heart of matter. Time is deeply related to the inner clock:
τ 0 = x 0 /c, spin momentum: s = p 0 r C , and rest mass: m 0 = p 0 /c, of the matter
particles.
4. If the electron is regarded as the ground state of a subsystem analogous to the
Bohr atom, then a regular series of excited states, with decreasing Compton
wavelength, may occur, starting with the parent muon and tau leptons and ending
at the Planck limit. Being charged fermions, the two quark families could follow
a similar pattern.
Acknowledgements I wish to thank Erkki Brändas, Roland Lefebvre, John Macken, and Francis
Sanchez for useful discussions and critical comments.
References
1. de Broglie L (1925) Recherches sur la théorie des quanta. Ann Phys 10(III):22–128. (Thesis,
Sorbonne, Paris, 1924)
2. Dirac PAM (1928) Quantum theory of the electron. Proc R Soc Lond A 117:610–624
3. Dirac PAM (1931) Quantised singularities in the electromagnetic field. Proc R Soc Lond A
133:60–72
4. Dirac PAM (1933) Theory of electrons and positrons. Nobel lectures 320–325
5. Dirac PAM (1930) The principles of quantum mechanics, 1st edn. Clarendon Press, Oxford.
4th edn (1958), Chaps 11–12
6. de Broglie L (1934) L’électron magnétique: théorie de Dirac. Hermann, Paris. Chaps 9–22
7. Feymann RP (1998) Quantum electrodynamics. Addison-Wesley, Reading
8. Cottingham WN, Greenwood DA (1998) Introduction to the standard model of particle physics. Cambridge University Press, Cambridge
9. Weinberg S (1995) The quantum theory of fields. Cambridge University Press, Cambridge
10. Compton AH (1923) A quantum theory of the scattering of x-rays by light elements. Phys Rev
21:483–502
11. Schrödinger E (1930) Über die kräftefreie Bewegung in der relativistischen Quantenmechanik.
Sitzungsber Preuss Akad Wiss Berlin, Phys Math Kl 24:418–428
12. Schrödinger E (1931) Zur Quantendynamik des Elecktrons. Sitzungsber Preuss Akad Wiss
Berlin, Phys Math Kl 25:63–72
13. Hönl H (1938) Ann Phys (V) 33:565
14. Hönl H, Papapetrou A (1939) Über die innere Bewegung des Elecktrons. Z Phys 112:512
15. Hönl H, Papapetrou A (1939) Über die innere Bewegung des Elecktrons. Z Phys 114:478
16. Hönl H, Papapetrou A (1940) Über die innere Bewegung des Elecktrons. Z Phys 116:153
17. Huang K (1952) On Zitterbewegung of the Dirac electron. Am J Phys 20:479–484
18. Barut AO, Bracken AJ (1981) Zitterbewegung and the internal geometry of the electron. Phys
Rev D 23:2454–2463
J. Maruani
interpreted as a quantized curvature involving an additional dimension, then this
dissymmetry means that a single sign is privileged for this curvature, charge
conjugation amounting to its reversal. Mass arises from the confined motion of
the extra-dimension curvature over usual space-time.
3. By relating rest mass to spin motion, quantum theory brings an insight into such
relativistic concepts as the proper interval x 0 , which is the residual interval when
the space coordinates r 2 are subtracted from the time coordinate c 2 t 2 . The velocity of light c is not simply that of electromagnetic waves, but also that of
basic motions at the heart of matter. Time is deeply related to the inner clock:
τ 0 = x 0 /c, spin momentum: s = p 0 r C , and rest mass: m 0 = p 0 /c, of the matter
particles.
4. If the electron is regarded as the ground state of a subsystem analogous to the
Bohr atom, then a regular series of excited states, with decreasing Compton
wavelength, may occur, starting with the parent muon and tau leptons and ending
at the Planck limit. Being charged fermions, the two quark families could follow
a similar pattern.
Acknowledgements I wish to thank Erkki Brändas, Roland Lefebvre, John Macken, and Francis
Sanchez for useful discussions and critical comments.
References
1. de Broglie L (1925) Recherches sur la théorie des quanta. Ann Phys 10(III):22–128. (Thesis,
Sorbonne, Paris, 1924)
2. Dirac PAM (1928) Quantum theory of the electron. Proc R Soc Lond A 117:610–624
3. Dirac PAM (1931) Quantised singularities in the electromagnetic field. Proc R Soc Lond A
133:60–72
4. Dirac PAM (1933) Theory of electrons and positrons. Nobel lectures 320–325
5. Dirac PAM (1930) The principles of quantum mechanics, 1st edn. Clarendon Press, Oxford.
4th edn (1958), Chaps 11–12
6. de Broglie L (1934) L’électron magnétique: théorie de Dirac. Hermann, Paris. Chaps 9–22
7. Feymann RP (1998) Quantum electrodynamics. Addison-Wesley, Reading
8. Cottingham WN, Greenwood DA (1998) Introduction to the standard model of particle physics. Cambridge University Press, Cambridge
9. Weinberg S (1995) The quantum theory of fields. Cambridge University Press, Cambridge
10. Compton AH (1923) A quantum theory of the scattering of x-rays by light elements. Phys Rev
21:483–502
11. Schrödinger E (1930) Über die kräftefreie Bewegung in der relativistischen Quantenmechanik.
Sitzungsber Preuss Akad Wiss Berlin, Phys Math Kl 24:418–428
12. Schrödinger E (1931) Zur Quantendynamik des Elecktrons. Sitzungsber Preuss Akad Wiss
Berlin, Phys Math Kl 25:63–72
13. Hönl H (1938) Ann Phys (V) 33:565
14. Hönl H, Papapetrou A (1939) Über die innere Bewegung des Elecktrons. Z Phys 112:512
15. Hönl H, Papapetrou A (1939) Über die innere Bewegung des Elecktrons. Z Phys 114:478
16. Hönl H, Papapetrou A (1940) Über die innere Bewegung des Elecktrons. Z Phys 116:153
17. Huang K (1952) On Zitterbewegung of the Dirac electron. Am J Phys 20:479–484
18. Barut AO, Bracken AJ (1981) Zitterbewegung and the internal geometry of the electron. Phys
Rev D 23:2454–2463