The Ritz-Einstein Agreement to Disagree
Robert S. Fritzius
During 1908 and 1909 Ritz and Einstein battled over what we now call the
time arrows of electrodynamics and entropy. Ritz argued that electrodynamic
irreversibility was one of the roots of the second law of thermodynamics,
while Einstein defended Maxwell-Lorentz electromagnetic time symmetry.
Microscopic reversibility remains a cornerstone of our current paradigm,
yet we are finding more and more evidence that experimentally discerned
time arrows are asymmetrical and that they all point from past to future.
This paper furnishes some comments about events leading up to the
Ritz-Einstein confrontation, some subsequent developments, and an English
translation of their agreement to disagree. A side by side comparison of
two recent summaries of their battle communiques is included to provide an
overview of what they had to say about this current issue.
Key words: arrow of time, reversibility, electrodynamics, entropy,
emission theory, elementary actions, ultraviolet catastrophe
Maxwell built his electromagnetic field theory on ideas derived from
classical mechanics, which was considered to be time reversible, but
Poincaré, mentor to Swiss physicist Walther Ritz, observed that "...treatises
on mechanics do not clearly distinguish between what is experiment, what is
mathematical reasoning, what is convention, and what is hypothesis."(1)
This paper is written from the viewpoint that microscopic time symmetry
is an unproven convention that is still accepted as established fact
and that we might find it beneficial to look under some old stones, one of
which seems to have been buried.
In 1908 Ritz, who is well known for his work in spectral physics (the
Rayleigh-Ritz perturbation theory and the Ritz combination principle) and
his still widely referenced works on the mechanical vibrations of plates,
produced a monumental, but not nearly as well known, criticism of
electromagnetic field theory.(2a) Even though
Ritz acknowledged that the Maxwell-Lorentz equations are elegant and are
here to stay, his blockbuster conclusion (which was based, largely, on the
inseparable ties of electromagnetic field theory to the discredited
solid ether continuum), was this: "The partial differential equations
and the notion of ether are fundamentally inappropriate to express the
comprehensive laws for the propagation of electrodynamic interactions."
Ritz then enunciated his own preliminary time-asymmetric emission
theory of electrodynamics (Part II of his work). He hypothesized that
charged bodies continuously emit fluxes of fictitious particles, which
travel at the speed of light with respect to their emission sources. These
emission particles constituted a kinetic electrodynamic intermediate for
retarded elementary interactions. He did not address absorption or
scattering of his emission particles by other charged bodies, or even
specify if he considered there to be more than one type of them, but he
did indicate the need to account for their interactions with ponderable
matter. For example, he admitted that this preliminary hypothesis was
not compatible with Fizeau's experiment on the entrainment of
electromagnetic waves.(2c) According to
Ritz, the Coulomb field is not a static state of space, but rather a kinetic
particulate process, taking place in an otherwise empty space that has no
properties of its own. His coulomb "interaction" could be characterized as
a revised form of the vector potential.
The incompatibility of Ritz's theory with the
entrainment of waves was probably due to Ritz's strict observance of
the superposition principle (a problem which he intended to remedy). The
bottom line to superposition seems to be action without reaction.
My personal conviction is that our adherence to the superposition principle,
in electrodynamics, is what prevents the merger of gravitation and
electrodynamics. The idea that charges can exert limitless coulomb forces
on remote charges (where the field's flux of virtual photons is not thinned
out by interactions with intervening charges) is what creates the need for
gravity, as a different kind of interaction, with different kinds of
particles (gravitons) to balance the books.
Ritz does have his present-day proponents but his theory is
outside the vale of the geometrodynamic paradigm and is not always
in the English speaking world. This is due, in part, to his works being
generally inaccessible in English. For example, Waldron keeps the fire
going, but his one-time claim that if you have a high enough potential,
particles can be accelerated to any speed(3) is not compatible with Ritz's
theory. Ritz hypothesized that electrodynamic accelerating influences
approach zero, rather than masses increasing to infinity, as bodies
approach the speed of light with respect to any given accelerator.
Waldron acknowledges (in private correspondence) that his "unlimited
speed" proposition is his own and not Ritz's.
In Ritz's day Einstein was a staunch defender of the time
symmetry of the space-time continuum. Indeed he should have been. In 1921
he stated, "The space-time theory and the kinetics of the special theory
of relativity were modelled on the Maxwell-Lorentz theory of the
The world of science has become polarized on the speed of light
issue, and the dividing line has been Einstein versus Ritz. Ritz's theory
held to Galilean relativity, i.e., c + v for electrodynamic
processes, including optics, whereas Einstein assumed the velocity of
light is independent of the motion of the source.
In 1963 Fox added Tolman's extinction theorem to Ritz's
electrodynamic theory. (Charges in a transparent medium absorb and
reradiate transient oscillatory electromagnetic energy. The secondary
radiation travels at the speed of light with respect to the medium. The
incident energy becomes absorbed and extinguished in the process.)
Fox reckons one extinction length , i.e., the distance into a medium
for the incident energy to be attenuated to 1/e times its original
amplitude, at sea level conditions in the Earth's atmosphere, is 0.2 cm.
In interstellar space, removed from regions of appreciable stellar gases
as in that surrounding binary stars, it is calculated to be one light-year.
By making this adjustment to Ritz's theory (which is a superposition
principle fix), Fox claims to have invalidated the majority, if not
all, of the speed-of-light experiments (including binary star
observations) that have been conducted to help us choose between Ritz
and Einstein. Based on the long lifetimes of fast muons (which are
taken as evidence for time dilation) and the speed-of-light gamma rays
from rapidly moving sources,
Fox gave a decision in favor of Einstein, but did so in a manner that
seems to suggest that the final verdict is not in.(5a) In private
correspondence Fox says:
...it is of interest for the general philosophy of science that Ritz's
theory, so different in structure from that of Maxwell, Lorentz
and Einstein, could come so close to describing correctly the
vast quantity of phenomena described today by relativistic
2. THE LORD GIVETH, THE LORD TAKETH AWAY
It may be ironic that Eddington played such a central role in the solar
eclipse expeditions of 1919, the results of which brought world acclaim to
Einstein's general theory of relativity. Eddington was also the first to
coin the phrase "time arrow"(7) and is known as the father of the time
arrow concept. Actually, he popularized Helmholtz's earlier ideas about
monotonically increasing entropy in a universe that was considered to be
According to Roger Penrose, we now have up to seven perceivable, or
deducible, arrows of time, all asymmetrical, and all pointing from
past to future.(8) Arrow No. 2 on Penrose's list is none other that Ritz's
restriction to retarded electrodynamic actions. Cramer(9) ponders which
comes first, the electromagnetic arrow or the entropy arrow, which is No.
7 on Penrose's list. According to Ritz, the electromagnetic arrow has
priority. He has a finite (flat space) universe in which electrodynamic
emissions escape at the periphery, so that the universe has to be running
3. THE WAR
During 1908 and 1909 Ritz and Einstein had a war that started over
the failure of Maxwell-Lorentz electromagnetic theory to handle blackbody
radiation, i.e., the ultraviolet catastrophe.(10),(11) Ritz took to the offensive,
arguing from his 1908 theory, which he claimed allowed us to hold on to our
hard-won ideas about space and time, while Einstein defended the new ideas
that eventually overthrew classical physics and banished physical intuition
in the relativistic arena. Ritz claimed in the third paper of the series,(12)
that by mathematically reversing the direction of time, i.e., by switching to
the advanced potential, you actually invoke a different kind of physical
process and do not simply arrive at the equivalent of the retarded potential
acting in reverse time sequence. The same argument, in quantum mechanical
notation, has been recently revoiced by Leiter.(13)
Ritz and Einstein's final written communication in this battle was a joint
that has the appearance of having been forced upon them by the
editorial staff of Physikalische Zeitschrift. The paper is their
agreement to disagree.
The appendix to the present paper is a translation of the Ritz-Einstein
paper so English-speaking readers can study a unique memento from a
critical turning point in the world of science. One point of ambiguity in the
paper needs comment. It is not clear, based on the terse German text, to
which case Einstein is saying one can restrict oneself. It appears to be either:
using both retarded and advanced potentials on equal footing or restricting
our considerations to electromagnetic processes confined to a finite space.
My sketchy peek at the earlier papers (through a translator) favors the first
The series of exchanges, including this paper, has been
summarized by Fox(5b) and Lanczos.(15) Table 1 shows, side
by side, their thumbnail abstracts of the series. Note that [... ]
Lanczos curiously misrepresents the import of the joint paper.
He has Einstein apparently admitting that he had been wrong
to defend the use of advanced potentials. Actually, although
neither author admitted any mistake, many present-day
authors are expressing the idea that the viewpoint that
Einstein defended is becoming untenable.(13), (16) -
Table 1: Ritz-Einstein Exchanges of the Ultraviolet Catastrophe
J.G. Fox C. Lanzcos
Phys. Z. 9, 903 (1908)
Ritz claimed that the ultraviolet Ritz argued that the solution of the
catastrophe in the classical Rayleigh- wave equation in terms of the re-
Jeans law had as its fundamental tarded (versus advanced) potential
reason the implicit and improper use established a genuine difference be-
of advanced potentials. tween past and future and may be
the real source of the irreversibility
of the radiation phenomenoa and the
second law of thermodynamics.
Phys. Z. 10, 185 (1909)
Einstein disagreed. Einstein maintains that instead of
solving the wave equation in terms
of intial state, one can, in principle,
equally as well use the end state and
operate with the help of the advanced
Phys. Z. 10, 224 (1909)
Ritz replied. Ritz took strong exception to this view.
Phys. Z. 10, 323 (1909)
and the series ended with the appear- and Einstein admitted his mistake.
ance of a brief, joint publication in
which each stated his position.
4. SECOND THOUGHTS?
Einstein, in later years, may have had second thoughts about
irreversiblity, but because of his revered position with respect to
the geometrodynamic paradigm was probably prevented from
expressing them publicly. We do have three glimpses into his
private leanings on the subject. In 1941 he called Wheeler and
Feynman's attention to Ritz's (1908) and Tetrode's (1921) time
asymmetric electrodynamic theories. [This was while Wheeler
and Feynman were laying the groundwork for their less than
successful (1945) time-symmetric absorber theory,
which was really emission/absorber theory, with a lot of
help from the future. They could not embrace time asymmetry,
but Gill(24) now proposes to revitalize absorber theory by
creating a generalized version without advanced
interactions.] Two pieces of Einstein's private correspondence
touch indirectly on the subject of time asymmetry.(25) In these
letters Einstein expresses his growing doubts about the
validity of the field theory space continuum hypothesis and all
that goes with it.
Since time symmetry is intimately tied to the space continuum,
if the latter falls, the former may well follow. Lanczos's slip of
the pen may be accidental but, nevertheless, could be indicative
of Einstein's feelings on this subject in his final years.
Except for the growing consensus about the asymmetry of the
arrows of time, we might have concluded that the battle between
Ritz and Einstein was a moot point and should be forgotten. The
current paradigm says that Einstein prevailed, but many of us
never heard of the battle, nor of Ritz's electrodynamics. If an
earlier court gave the decision to Einstein, it did so by default.
Ritz, at age 31, died 7 July 1909, two months after the joint
paper was published.
The world of science of Ritz's day seems to have been so
grateful to Maxwell, Lorentz and Hertz for rescuing it from the
clutches of instantaneous action-at-a-distance (through empty
space) that it couldn't bring itself to entertain any hypothesis
that sounded even remotely like the "old" action-at-a-distance.
Thus Ritz's electrodynamic theory was bundled up and tucked
away after a short but respectful period following his death.
If science cannot prove the existence of a microscopic
symmetrical time arrow (Heisenberg's uncertainty principle
says we cannot do it), then we may eventually find ourselves
using more and more of Ritz's conceptions and giving credit
where credit is due. As a minimum, Ritz's (1908) criticism of
electromagnetic field theory needs to be subjected to a modern
My thanks to Bryan G. Wallace
of St. Petersburg, Florida, for calling my attention to the Einstein letters
in Pais's book, Subtle is the Lord ... [The Science and the Life of Albert Einstein]
APPENDIX: ENGLISH TRANSLATION OF AGREEMENT TO
In order to clarify the difference in opinion that has arisen in our
separate publications (26) we present the following.
In the special cases in which an electromagnetic process stays
confined in a finite space, it is possible to represent the
process not only in the form
but likewise in the form
and in other forms.
While Einstein believes it to be possible to restrict oneself to this
case [both forms] without essentially limiting the generality
of the consideration, Ritz considers this restriction as in
principle not allowed. If one takes the position that experience
compels the representation with aid of the retarded potential as the
only possibility to consider, and supposing one is inclined to the
view that the fact of irreversibility of the radiation process is already
in the basic laws, its expression has to be found. Ritz considers the
restriction to the form of the retarded potential as one of the roots of
the second law [of thermodynamics] while Einstein believes that
irreversibility depends exclusively upon reasons of probability.
Zurich, April 1909
Received on 10 August 1989.
En 1908 et 1909 Ritz et Einstein se querellaient sure ce que nous appelons
maintenant les flèches de temps d'électrodynamique et entropie. Ritz
soutenait que l'rréresibilitié électrodynamique était à la racine de la
deuxième loi de la thermodynamique tandis qu'Einstein defendait
la symmetrie de temps de l'électromagnetisme de Maxwell-Lorentz. La
microréversibilité demeure un fondement de notre paradigme courant,
toutefois nous trouvons de plus en plus des preuves que les flèches de temps
mises en évidence expérimentalement sont asymmetriques et toujours du
passé vers le futur. Cet article fournit quelques commentaires sure les
évenements qui menèrent à la querelle susdite, quelques développements
ultérieures et une traduction en anglais de leur accord sur le désaccord. Une
comparaison directe de deux sommaires récents de leur bulletins de bataille
est inclus afin que le lecteur puisse avoir un aperçu de ce qu'ils avaient à dire
à ce sujet toujours actuel.
1. H. Poincaré, Science and Hypothesis (1905)
(Dover, 1952) p. 89.
2. (a) W. Ritz, Ann. Chim. Phys. 13, 145 (1908). [For an
English translation of Part I of this paper, see W. Ritz,
Critical Researches on General Electrodynamics, Introduction and
First part (R.S. Fritzius, Starkville, MS 1980)]
(b) ibid. 172;
(c) ibid. 151;
(d) ibid. 194.
3. R.A. Waldron, Spec. Sci. Tech. 3, 399 (1980).
4. A. Einstein, Sidelights on Relativity, G.B. Jeffery and W.
Perrett, translators (Methuen & Co., London, 1922). p. 11.
J.G. Fox, Am J. Phys. 33, 1, 16 (1965);
Idem, private correspondence.
7. A.S. Eddington, The Nature of the Physical World (MacMillan,
NY, Cambridge, 1929), p.68.
8. T. Rothman, Discover 1987 (Feb) 62.
9. J.G. Cramer, Found. Phys. 18, 1205 (1988).
10. H.A. Lorentz, Phys. Z. 9, 562 (1908).
11. J.H. Jeans, ibid. 853.
12. W. Ritz, ibid. 10, 224 (1909).
13. D. Leiter, Found. Phys. 14, 857 (1983).
14. W. Ritz and A. Einstein, Phys. Z. 10, 323 (1909).
15. C. Lanczos, The Einstein Decade (1905-1915) Academic,
NY, London, 1974) p. 161.
16. B. Gal-Or, Found. Phys. 5, 50 (1977).
17. D. Leiter, Nuovo Cimento 44, 665 (1985).
18. L.D. Landau and E.M. Lifshitz, Statistical Physics
(Addison-Wesley, Reading, MA, 1969), pp. 13, 29.
19. T. Futamase and T. Matsuda, Nuovo Cimento B 100,
20. E. Joos, J. Non-Equilibrium Thermodyn. 12, 27 (1987).
21. W. Schommers, Int. J. Mod. Phys. B (Singapore) 3, 1
22. D. Leiter, Nucl. Phys. B. Proc. Suppl. 6, 337 (1989).
23. J.A. Wheeler and R.P. Feynman, Rev. Mod. Phys. 17,
24. T.L. Gill, Hadronic J. 7, 1224 (1984).
25. A. Pais, Subtle is the Lord ... The Science and the Life of
Albert Einstein, Oxford, 1982), p.467.
26. W. Ritz, Phys. Z. 9, 903 (1908); A. Einstein,
ibid. 10, 185 (1909).
Robert S. Fritzius
305 Hillside Drive
Starkville, Mississippi 39759 U.S.A.
Links to related articles:
Kevin Brown, Advanced and
Retarded Potential - Math Pages: Physics
John D. Norton,
Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905 [PDF]
The Arrow of Electromagnetic Time and Generalized Absorber Theory -
Das Prinzip der
Relativität in der Optik, (Antrittsrede zur Habilitation am 5. Mai 1908)
Entnommen aus dem Buch: Theorien über Äther, Gravitation, Relativität und
Elektrodynamik - Herausgegeben und mit einem Nachwort versehen von Dr. Karl Dürr,
Schritt-Verlag, Bern und Badisch-Rheinfelden 2. Auflg. (1965), S. 5 - 14. Courtesy,
Mathias Frisch, Wolfgang Pietsch,
Ritz-Einstein debate on the radiation asymmetry in classical electrodynamics,
Studies in History and Philosophy of Science - Part B: Studies in History and Philosophy
of Modern Physics. 55, 13-23, (2016). [Added 19 Sep 2017.]