Kinematics is basically the study of how energy and momentum conservation laws constrain and affect physical interactions. The two basic predictions of SR in this regard are that massive objects will have a limiting velocity of c (the speed of light), and that their “relativistic mass” will increase with velocity. This latter property implies that the newtonian equations for conservation of energy and momentum will be violated by enormous factors for objects with velocities approaching c, and that the corresponding formulas of SR must be used. This has become so obvious in particle experiments that few experiments test the SR equations, and virtually all particle experiments rely upon SR in their analysis. The exceptions are primarily early experiments measuring energy as a function of velocity for electrons and protons.
Note that the nomenclature has changed over the past century, and current literature focusses more on rest mass than relativistic mass because rest mass is an invariant property of an object. In this article, use of the word "mass" means rest mass. See also this FAQ page.
- Champion, Proc. R. Soc. A136 (1932), pg 630.: Electron-electron elastic scattering
- Foley et al., “Experimental Test of the Pion-Nucleon Forward Dispersion Relation at High Energies”, Phys. Rev. Lett. 19 no. 4 (1967), pg 193.: The dispersion relation basically expresses conservation of probability, and its validity at different energies is related to relativistic kinematics.
- Akerlof et al., “Elastic Proton-Proton Scattering at 90° and Structure within the Proton”, Phys. Rev. 159, no. 9, pg 1138 (1967).: In newtonian mechanics, when two equal-mass objects scatter elastically, in the rest frame of one initial particle the two outgoing particles always travel at right angles to each other. In SR, that angle can be much less than a right angle, and in this experiment it is strikingly less than 90° (see their Fig. 3).
Experiments that Show the Limiting Velocity c
- Alspector et al., Phys. Rev. Lett. 36, pg 837 (1976).: A comparison of neutrino and muon velocities, at Fermilab.
- Kalbfleisch et al., Physics Review Letters 43, pg 1361 (1979).: A comparison of muon, neutrino, and antineutrino velocities over a range of energies, at Fermilab.
- Guiragosian et al., Phys. Rev. Lett. 34 no. 6 (1975), pg 335.: Relative velocity measurements of 15 GeV electrons and gammas. No significant difference was observed within ~2 parts in 107. See also Brown et al.
- G.L. Greene et al.,”Test of special relativity by a determination of the Lorentz limiting velocity: Does E=mc2?” Physical Review D 44 (1991) R2216.: An analysis combining the results of several experiments gives the result that the Lorentz limiting velocity must be equal to the speed of light to within 12 parts per million.
- Stodolsky, “The Speed of Light and the Speed of Neutrinos”, Phys. Lett. B201 no. 3 (1988), pg 353.: A comparison of neutrino and photon speeds from supernova SN1987A puts a limit of about 1 part in 108 on their speed difference.
Electron Relativistic Mass Variations
In the early 20th century there was an alternative theory by Abraham that is now little known, because these experiments rejected it in favor of SR. A critical review of the experimental evidence concerning the Lorentz model compared to the Abraham model was given in: Farago and Jannossy, Il Nuovo Cim. Vol5, No 6, pg 1411 (1957).
- W. Kaufmann, Nachr. K. Ges. Wiss. Goettingen 2, pg 143 (1901)W. Kaufmann, Nachr. K. Ges. Wiss. Goettingen 3, pg 291 (1902);W. Kaufmann “Die elektromagnetische Masse des Elektrons”, Phys. Zeitschr. 4, pg 54 (1902)W. Kaufmann, Nachr. K. Ges. Wiss. Goettingen 4, pg 90 (1903)W. Kaufmann, “Uber die Konstitution des Elektrons”, Ann. Physik 19 ,495 (1906) and Nachtrag 20, 639–640 (1906);W. Kaufmann, “Uber die Konstitution des Elektrons”, Sitzungsberichte der preussichen Akademie der Wissenschaften, 1905, Part 2.W. Kaufmann, “Uber die Konstitution des Elektrons” Ann. Physik 19 ,495 (1906);W. Kaufmann, “Uber die Konstitution des Elektrons”, Sitzungsberichte der preussichen Akademie der Wissenschaften, 1915, Part 2.: There were several discussions about the conclusions from Kaufmann's experiments and his data analysis. See for instance: M. Planck, “Die Kaufmannschen Messungen der Ablenkbarkeit der beta-Strahlen in ihrer Bedeutung fur die Dynamik der Electron”, Verhandlungen der Deutschen Physikalischen Gesellschaft, 8, 1906; and M. Planck, “Nachtrag zu der Besprechung der Kaufmannschen Ablenkungsmessungen”, Verhandlungen der Deutschen Physikalischen Gesellschaft, 9, 1907.
- A.H. Bucherer, Phyz. Zeitschr. 9 (1908), pg 755; Ber. d. deutschen Phys. Ges. 6 (1908), pg 688.A. Bucherer, “Die experimentelle Bestatigung des Relativitatsprinzips”, Annalen der Physik, 28, 1909.: -
- E. Hupka, Ann. Phys. 31 (1910), pg 169.: -
- Cl. Schaefer and G. Neumann, Phys. Zeitschr. 14 (1913), pg 1117.G. Neumann, “Die trдge Masse schnell bewegter Elektronen”, Ann. Phys. 45, pg 529 (1914).: -
- Ch.E. Guye and Ch. Lavanchy, Comptes rendus 161 (1915), pg 52.: -
- Zahn and Spees, Phys. Rev. 53 (1938), pg 511.: -
- Rogers et al., Physical Review 57 (1940), pg 379.: Measurement of m/e and v for three beta-particles (electrons) from Radium. Supports the Lorentz model over the Abraham model by > 10 σ.
- Meyer et al., Helv. Physica Acta 36 , pg 981 (1963).: -
- W. Bertozzi, Am. J. Phys. 32, 551 (1964).: Measurements of speed vs. energy for 0.5–15 MeV electrons.
- Geller and Kollarits, Am. J. Phys. 40 (1972), pg 1125.: -
Proton Relativistic Mass Variations
- Zrelov, Tiapkin, Farago Soviet Physics JETP, Vol. 34, pg 384 (1958).: -
Calorimetric Test of Special Relativity
- D.R. Walz, H.P. Noyes and R.L. Carezani, Physical Review A29 (1984), pg 2110.: The beam power at SLAC is measured using temperature rise in a calorimeter, for electrons of ~17 and 20 GeV and beam currents up to ~15 microamperes. Their results confirm SR with a resolution of about 30%, and are “many orders of magnitude larger than predicted by the theory of autodynamics”, of which Carezani is the author (and also member of this experimental group).