- Reichenbach published his book "Philosophie der Raum-Zeit-Lehre" in 1927 which included an appendix discussing Weyl's unified field theory. Einstein reviewed the book positively, agreeing with Reichenbach's argument in the appendix that general relativity is not an attempt to reduce physics to geometry. - Einstein also reviewed Meyerson's book "La déduction relativiste" positively, agreeing with its emphasis on the deductive-constructive nature of relativity theory and finding the term "geometrical" meaningless in the context of unified field theories. Both reviews supported Reichenbach's view that the goal of unified field theories was unification rather than geometrization.

1. Unification vs. Geometrization
Reichenbach and Einstein’s Fernparallelismus-Field Theory
marco.giovanelli@unito.it
Philosophers and Einstein’s of Relativity
Napoli 26/11/2021
UNIVERSITÀ
DEGLI STUDI
DI TORINO
0 / 44

2. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44

3. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44

4. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44

5. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44

6. Introduction
Einstein (1949, 73-75) had always regarded his 1915 field theory of
gravitation, the general theory of relativity, as nothing but a stepping
stone toward a unified field theory which would overcome a double
dualism
• the dualism between gravitational and the electromagnetic field
• the dualism between matter and field
Einstein’s quest for the final field theory spans over most of Einstein’s
professional life from 1919 (Einstein, 1919) till his death in 1955
(Einstein and Kaufman, 1955)
in the 1920s Reichenbach was the only philosopher who possessed the
epistemological insight and mathematical savvy to find his bearings
among the intricacies of the various unification attempts.
1 / 44

7. Introduction
Reichenbach
provided the first, and possibly only, overall philosophical reflection on
the unified field theory program at that time of its peak
tried to unravel the key to Einstein’s success in formulating a field
theory of gravitation by uncovering the reasons for the failure of
subsequent attempts of a theory of the total field
theory of spacetime theories ante litteram*
*
Lehmkuhl, 2017.
2 / 44

8. Introduction
Reichenbach
provided the first, and possibly only, overall philosophical reflection on
the unified field theory program at that time of its peak
tried to unravel the key to Einstein’s success in formulating a field
theory of gravitation by uncovering the reasons for the failure of
subsequent attempts of a theory of the total field
theory of spacetime theories ante litteram*
*
Lehmkuhl, 2017.
2 / 44

9. Introduction
Reichenbach’s reflections on the unified field theory program can be
organized around three correspondences, which revolve around three
conceptual issues:
Reichenbach-Weyl correspondence*
(1920-1921)
• =⇒ coordination
Reichenbach-Einstein correspondence (1926-1927)
†
• =⇒ geometrization
Reichenbach-Einstein correspondence (1928-1929)
• =⇒ unification
*
Ryckman, 1996, Rynasiewicz, 2005.
†
Lehmkuhl, 2014, Giovanelli, 2016.
3 / 44

10. Introduction
Einstein-Reichenbach Debate on Fernparallelismus-field theory
(October 1928–January 1929)
Reichenbach’s correspondence with Einstein on Fernparallelismus
• =⇒ personal quarrel*
Reichenbach’s writings on Fernparallelismus
• =⇒ intellectual estrangement
*
Hentschel, 1990.
4 / 44

11. Table of Contents
5 / 44

12. Part I
The Philosophie der Raum-Zeit-Lehre and its
Appendix
5 / 44

13. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44

14. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44

15. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44

16. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44

17. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44

18. Setting the Stage
August of 1926: “unofficial associate professor” (nichtbeamteter
außerordentlicher Professor) at the University of Berlin
December of 1926: finished Philosophie der Raum-Zeit-Lehre
(Reichenbach to Schlick, 06-12-1926)
July of 1927: publication agreement with De Gruyter (Reichenbach to
Schlick, 02-07-1927)
October of 1927: Preface
October of 1927: Einstein read the galley proofs on his way to
Brussels (Solvay Conference)
“
I finished reading Reichenbach. To be so delighted with oneself
must be pleasing, but less so for other people
(Einstein to Elsa Einstein, 23-10-1927)
”
6 / 44

19. Setting the Stage
7 / 44

20. Setting the Stage
7 / 44

21. Setting the Stage
8 / 44

22. Setting the Stage
8 / 44

23. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44

24. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44

25. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44

26. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44

27. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44

28. Einstein’s Reviews
Einstein’s Review of Reichenbach’s Philosophie der Raum-Zeit-Lehre
• “In the Appendix, the foundation of the Weyl-Eddington theory is treated in
a clear way and in particular the delicate question of the coordination of
these theories to reality” (Einstein, 1928c, 20).
• in the Appendix, “in my opinion quite rightly—it is argued that the claim
that general relativity is an attempt to reduce physics to geometry is
unfounded” (Einstein, 1928c, 20).
Einstein’s Review of Meyerson’s La déduction relativiste
• “the term ‘geometrical’ used in this context is entirely devoid of meaning”
(Einstein, 1928a, 165), the goal is unification*.
• Einstein very much appreciated Meyerson’s insistence on the
deductive-constructive character of relativity (Hegel) (Einstein, 1928a,
165).
*
Lehmkuhl, 2014.
9 / 44

29. reconfiguration of Einstein’s
system of philosophical
alliances
Meyerson became Einstein’s
reference philosopher, a
position once proudly held by
Schlick and Reichenbach*
*
Giovanelli, 2018.
10 / 44

30. Part II
Einstein’s Fernparallelismus-Field Theory.
Reichenbach’s Unpublished Manuscript
10 / 44

31. Einstein’s Fernparallelismus-Field theory
10 / 44

32. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
a
{
→ n-bein
Aa
*
Sauer2021.
11 / 44

33. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
aAa
gµν
{
→ metric
= hµahνa, ∆ν
µσ
{
→ affine conn. ∆
ν
µσ 6= ∆
ν
σµ
= hv
a
∂hµa
∂xσ
*
Sauer2021.
11 / 44

34. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
aAa
gµν = hµahνa, ∆ν
µσ = hv
a
∂hµa
∂xσ
Ri
k,lm
{
→ Riemann tensor
= −
∂∆i
kl
∂xm
+
∂∆i
km
∂xl
+ ∆i
αl∆α
km − ∆i
αm∆α
kl = 0
*
Sauer2021.
11 / 44

35. Einstein’s Fernparallelismus-Field theory
new geometry: Riemannian geometry with distant parallelism*
:
new formalism: set of mutually orthogonal, normal vectors (n-bein)
Aν
= hν
aAa
gµν = hµahνa, ∆ν
µσ = hv
a
∂hµa
∂xσ
Ri
k,lm = −
∂∆i
kl
∂xm
+
∂∆i
km
∂xl
+ ∆i
αl∆α
km − ∆i
αm∆α
kl = 0
“
The introduction of distant parallelism implies that, according to
this theory, there is something like a straight line; i.e., a line whose
elements are all parallel to each other; such a line is of course by
no means identical with a geodetic one.
(Einstein, 1928b)
”11 / 44

36. Einstein’s Fernparallelismus-Field theory
11 / 44

37. Einstein’s Fernparallelismus-Field theory
physical interpretation:
• hν
a 16 components whereas gµν 10 components
• the field equations from δ
Z
{Hdτ} = 0, where H depends on the hν
a field.
• variation of the action with respect to the variable hν
a, Einstein and
Maxwell field equations were recovered in first appr.
• search solutions describing elementary particles and their motion
12 / 44

38. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44

39. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44

40. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44

41. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44

42. Reichenbach’s Comments on Einstein’s theory
“
Dear Herr Einstein,
I did some serious thinking on your work on the field theory and I
found that the geometrical construction can be presented better in
a different form. I send you the ms. enclosed. Concerning the phys-
ical application of your work, frankly speaking, it did not convince
me much. If geometrical interpretation must be, then I found my
approach simply more beautiful, in which the straightest line at
least means something.
Reichenbach to Einstein, 17-10-1928
”
13 / 44

43. Reichenbach’s Manuscript
14 / 44

44. Reichenbach’s Manuscript
14 / 44

45. Reichenbach’s Manuscript
Riemann-Einstein approach (equality of lengths at distant points):
ds2
= gµν
{
metric←
dxµdxν
Weyl-Eddington approach (paralleism of vectors at close-by points):
dAτ
= Aµ
dxν l2
= Aµ
Aν
,
15 / 44

46. Reichenbach’s Manuscript
Riemann-Einstein approach (equality of lengths at distant points):
ds2
= gµν dxµdxν
Weyl-Eddington approach (paralleism of vectors at close-by points):
dAτ
= Γτ
µν
{
parall. displ. or affine conn. Γ
τ
µν 6= Γ
τ
νµ←
Aµ
dxν l2
= gµν
{
metric←
Aµ
Aν
,
15 / 44

47. Reichenbach’s Manuscript
Riemann-Einstein approach (equality of lengths at distant points):
ds2
= gµν dxµdxν
Weyl-Eddington approach (paralleism of vectors at close-by points):
dAτ
= Γτ
µν Aµ
dxν l2
= gµν Aµ
Aν
,
15 / 44

48. Reichenbach’s Manuscript
Riemann-Einstein approach (equality of lengths at distant points):
ds2
= gµν dxµdxν
Weyl-Eddington approach (paralleism of vectors at close-by points):
dAτ
= Γτ
µν Aµ
dxν l2
= gµν Aµ
Aν
,
d l2
= (
∂gµν
∂xσ
+ Γµσ,ν + Γνσ,µ
{
→ Kµν,σ non-metricity tensor
)Aµ
Aν
dxσ
15 / 44

49. Reichenbach’s Manuscript
balanced space (ausgeglichener Raum)
d(l2
) = l2
κσdxσ Kµν,σ = gµν κσ =⇒ general displacement space
(comparability of lengths at the same point)
• Γτ
µν = Γτ
νµ (Weyl geometry)
d(l)2
= 0 Kµν,σ = 0 =⇒ general metrical space (comparability of
lengths at distance)
• Γτ
µν = Γτ
νµ (Riemannian geometry)
16 / 44

50. Reichenbach’s Manuscript
balanced space (ausgeglichener Raum)
d(l2
) = l2
κσdxσ Kµν,σ = gµν κσ =⇒ general displacement space
(comparability of lengths at the same point)
• Γτ
µν = Γτ
νµ (Weyl geometry)
d(l)2
= 0 Kµν,σ = 0 =⇒ general metrical space (comparability of
lengths at distance)
• Γτ
µν = Γτ
νµ (Riemannian geometry)
16 / 44

51. Reichenbach’s Manuscript
balanced space (ausgeglichener Raum)
d(l2
) = l2
κσdxσ Kµν,σ = gµν κσ =⇒ general displacement space
(comparability of lengths at the same point)
• Γτ
µν = Γτ
νµ (Weyl geometry)
d(l)2
= 0 Kµν,σ = 0 =⇒ general metrical space (comparability of
lengths at distance)
• Γτ
µν = Γτ
νµ (Riemannian geometry)
16 / 44

52. Reichenbach’s Manuscript
balanced space (ausgeglichener Raum)
d(l2
) = l2
κσdxσ Kµν,σ = gµν κσ =⇒ general displacement space
(comparability of lengths at the same point)
• Γτ
µν = Γτ
νµ (Weyl geometry)
d(l)2
= 0 Kµν,σ = 0 =⇒ general metrical space (comparability of
lengths at distance)
• Γτ
µν = Γτ
νµ (Riemannian geometry)
Rτ
µνσ(Γ)
{
→ Riemann tensor
=
∂Γτ
µν
∂xσ
−
∂Γτ
µσ
∂xν
+ Γτ
αν Γα
µσ − Γτ
ασΓα
µσ= 0
{
Euclidean geometry←
16 / 44

53. Reichenbach’s Manuscript
exchange of specialization
Diagram of Reichenbach’s classification of geometries Reichenbach, 1928b, 5
17 / 44

54. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44

55. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44

56. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44

57. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44

58. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44

59. Reichenbach’s Manuscript
from a geometrical point of view Einstein’s Fernparallelismus not new:
• Einstein’s Fernparallelismus geometry was simply one of the possibilities
implicit in the Weyl-Eddington classification.
• Einstein uses a new formalism in which the Γτ
µν and the gµν are
considered as functions of a parameter hν
α
gµν = hµαhνα Γτ
µν = −hτ
α
∂hµα
∂xν
from a physical point of view Einstein’s Fernparallelismus not
convincing:
• “[t]he derivation of the Maxwellian and gravitational equation from a
variational principle was already achieved by other approaches”
(Reichenbach, 1928b, 6),
• a “real physical achievement is obtained only if, in addition, the operation
of displacement is filled with physical content” (Reichenbach, 1928b, 7).
18 / 44

60. Reichenbach’s Manuscript
“
. . . that this is possible has been show previously by the author
(Reichenbach, 1928b, 8)
”
Reichenbach’s theory
d(l2
) = 0
Γτ
µν 6= Γτ
νµ
Rτ
µνσ(g) 6= 0
charged mass points move along
the straightest lines, uncharged
along the shortest line
Einstein’s theory
d(l2
) = 0
Rτ
µνσ(g) = 0
Γτ
µν 6= Γτ
νµ
straightest lines different from the
shortest line, but without physical
meaning
19 / 44

61. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44

62. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44

63. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44

64. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44

65. Einstein’s Comments on Reichenbach’s Manuscript
“
Dear Mr. Reichenbach,
[Your presentation] is possible, but is not the simplest [. . .]. The
best logical classification according to me seems to be the follow-
ing: One consider theories in which the local comparison of vector
length is given as meaningful [. . .]. For manifolds of this type, fur-
ther specializations are possible.
1. Neither the comparison of length at distance nor of direction
is meaningful (Weyl)
2. Comparison at distance of length but of direction is
meaningful (Riemann)
3. Comparison at distance of directions but of lengths (not
considered yet)
4. Comparison at distance of length and of direction is
meaningful (Einstein)
Of course one can also start with the displacement law, and spe-
cialize it [. . .] as you have done. But this is less simple and natural.
Einstein to Reichenbach, 19-10-1928
”20 / 44

66. Einstein’s Comments on Reichenbach’s Manuscript
Invitation for a tea with Schr̈odinger on December 5, 1928
Einstein and Reichenbach probably discussed:
further developments of Fernparallelismus-theory
not simply recovering Maxwell and Einstein equations, but new results
philosophical differences
21 / 44

67. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

68. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

69. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

70. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

71. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

72. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

73. Stodola-Festschrift
The only hope is to construct a theory “in a speculative way” (Einstein,
1929c, 128).
only motivation the deep conviction of the “formal simplicity of the
structure of reality” (Einstein, 1929c, 127).
the belief in the fundamental simplicity of the real is “so to speak, the
religious basis of the scientific endeavor” (Einstein, 1929c, 127).
“Meyerson’s comparison with Hegel’s program [Zielsetzung] lluminates
clearly the danger that one here has to fear” (Einstein, 1929c, 127)
search for the mathematical structure of the field (the gµν , Γτ
µν , hν
a, ,
etc..) =⇒ no physical interpretation needed
search for simplest generally covariant field equations which can be
obeyed by the field structure =⇒ variational or other approaches
22 / 44

74. Part III
The Einstein-Reichenbach Falling-Out.
Einstein’s Popular Article on
Fernparallelismus
22 / 44

75. Einstein in the Daily Press
November 4, 1928: the New York Times
announced the prospect of another epoch-making
breakthrough
December of 1928: difficulties with the theory
had started to become apparent by the end of
1928.
January 10, 1929: paper submitted for
publication in the Sitzungsberichte Prussian
Academy (Einstein, 1929d).
January 11, 1929: Einstein issued a brief
statement to the press
January 12, 1929: New York Times’s
sensationalistic article
January 16, 1929: leaks of some friends (Einstein
to Kerkhof, 16-01-1929)
23 / 44

76. Reichenbach’s Papers on Fernparallelismus
January 22, 1929: non-technical paper for the Zeitschrift für
Angewandte Chemie
January 22, 1929: technical paper for Zeitschrift für Physik
January 25, 1929: popular article for the Vossische Zeitung
(Reichenbach, 1929b).
24 / 44

77. Reichenbach’s Article for the Vossische Zeitung
“[T]wo vast bodies of laws stood at the pinnacle of physics,” Einstein’s
gravitational field equations and Maxwell’s electromagnetic field
equations (Reichenbach, 1929b; tr. 1978, 1:261).
These two sets of equations had “nothing to do with each other; the
world of physics was divided into two kingdoms, one ruled by Einstein,
and the other by Maxwell” (Reichenbach, 1929b; tr. 1978, 1:261).
“The temptation to attempt a supreme union was irresistible: however,
nature proved to be more stubborn than had been anticipated”
(Reichenbach, 1929b; tr. 1978, 1:261)
25 / 44

78. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44

79. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44

80. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44

81. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44

82. Reichenbach’s Article for the Vossische Zeitung
“
But today Einstein has taken a new step [. . .] And indeed, the new
theory succeeds in uniting the fundamental laws of relativity me-
chanics and the fundamental laws of electricity into a single for-
mula. [. . .] Einstein is able to show that the previously known
laws can be derived from this formula [. . .] Yet the new formula
achieves still more; it represents the older theory of two systems
as a special case and makes new assertions concerning the relation
between gravitation and electricity in relatively complicated fields.
Thus, the new theory is of more than merely formal significance,
for it asserts the existence of an effect of gravitation upon electri-
cal events and vice versa
(Reichenbach, 1929b; tr. 1978, 1:262)
”
26 / 44

83. Einstein’s Reaction
January 25, 1929: Einstein complained to the Vossische Zeitung
(Einstein to Vossische Zeitung, 25-01-1929).
January 26, 1929: Jacobs apologizes but defended the newspaper
(Jacobs to Einstein, 26-01-1929)
January 21, 1929: Reichenbach complained behavior (Reichenbach
to Jacobs, 21-01-1929)
January 27, 1929 Reichenbach felt betrayed by Einstein’s behavior
(Reichenbach to Einstein, 27-01-1929)
January 30, 1929: Einstein was somewhat pleased by Reichenbach’s
reaction (Einstein to Reichenbach, 30-01-1929)
January 31, 1929: Reichenbach closed the incident (Reichenbach to
Einstein, 31-01-1929)
Hentschel, 1990.
27 / 44

84. Part IV
Geometrization vs. Unification.
Reichenbach’s Academic Papers on
Fernparallelismus
27 / 44

85. Geometrization vs. Unification
history of the unified field theory program
progressive downfall of the geometrization program
and the concurrent rise of the unification program
28 / 44

86. Geometrization vs. Unification
Einstein: geometrical interpretation of the gravitational field via the
gµν
Weyl: geometrical interpretation of the electromagnetic field via the κσ
d(l2
) = l2
κσ
{
change of length←
dxσ Kµν,σ = gµν κσ
{
→ electromagnetic four-potential
Weyl1: coordinative definition of displacement: “an influence of the
electric field on transported rods and clocks” (Reichenbach, 1929a,
122).
• measuring rod objection (no second clock effect)
Weyl2: no coordinative definition of the process of displacement in
terms of rods-and-clocks readings
• purely formal theory
29 / 44

87. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44

88. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44

89. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44

90. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44

91. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44

92. Geometrization vs. Unification
“
However, mathematicians did not give up on the new idea. If a
direct physical interpretation of Weylean space was not possible,
they tried an indirect approach. They regarded Weyl’s space as a
type a mathematical apparatus [. . .] [that] opened the possibility
for a unification of the electrical and gravitational equations. The
actual geometrical sense of Weyl’s approach was therefore com-
pletely abandoned, and the extended type of space was only used,
so to speak, in the sense of a calculating machine, [to find the field
equations]. [. . .] In this sense, several influential researchers have
tried to develop Weyl mathematics into a physical theory, in ad-
dition to Weyl, above all [. . .] Eddington [. . .] and also Einstein
himself.
(Reichenbach, 1929a, 122)
”
30 / 44

93. Geometrization vs. Unification
sacrifice the geometrical interpretation (no coordinative definition of
Γτ
µν , κσ and so on)
use the field structures (Γτ
µν , κσ and so on) as calculation device for
finding the field equations
“
The last stage on this path is the new work that [Einstein] recently
presented to the Academy
(Reichenbach, 1929a, 123)
”
31 / 44

94. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44

95. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44

96. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44

97. Geometrization vs. Unification
The field variables hν
a do not receive a geometrical interpretation.
• “Einstein was guided” by abstract mathematical considerations “about
invariants in Weylean space and the possibilities of deriving equations
from them” (Reichenbach, 1929a, 123).
Electromagnetic field and gravitational field are unified.
• “a certain concatenation of both systems of equations occurs in such a
way that a physical dependence between electricity and gravity is
asserted” (Reichenbach, 1929a)
32 / 44

98. The Duality of Unifications
33 / 44

99. The Duality of Unifications
unification?
formal unification: the new system does not claim more than the other
two combined;
• empirically equivalent theories (Einstein vs. Minkowski)
inductive unification: the new theories claim more than the other two
combined;
• empirically nonequivalent theories (Newton vs. Einstein)
34 / 44

100. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44

101. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44

102. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44

103. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44

104. The Duality of Unifications
Reichenbach: proper geometrical interpretation without proper
unification
“
The author [Reichenbach] has shown that the first way can be re-
alized in the sense of a combination of gravitation and electricity
to one field, which determines the geometry of an extended Rie-
mannian space; it is remarkable that thereby the operation of dis-
placement receives an immediate geometrical interpretation, via
the law of motion of electrically charged mass points. The straight-
est line is identified with the path of electrically charged mass
points, whereas the shortest line remains that of uncharged mass
points. [. . .] By the way [the theory introduces] a space which
is cognate to the one used by Einstein, i.e., a metrical space with
non-symmetrical Γτ
µν . The aim was to show that the geometrical in-
terpretation of electricity does not mean a physical value of knowl-
edge per se
(Reichenbach, 1929c, 688)
”35 / 44

105. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44

106. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44

107. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44

108. The Duality of Unifications
Einstein: proper unification without proper geometrical interpretation
“
On the contrary, Einstein’s approach, of course, uses the second
way since it is a matter of increasing physical knowledge; it is the
goal of Einstein’s new theory to find such a concatenation of gravi-
tation and electricity, that only in first approximation it is split in the
different equations of the present theory, while is in higher approx-
imation reveals a reciprocal influence of both fields, which could
possibly lead to the understanding of unsolved questions, like the
quantum puzzle. However, it seems that this goal can be achieved
only if one dispenses with an immediate interpretation of the dis-
placement, and even of the field quantities themselves. From a
geometrical point of view, this approach looks very unsatisfying.
Its justification lies only on the fact that the above-mentioned con-
catenation implies more physical facts that those that were needed
to establish it
(Reichenbach, 1929c, 688)
”36 / 44

109. Success of General Relativity
general relativity
the theory provided a proper geometrical interpretation of the
gravitational field, since it introduced a coordinative definition of the
field variables gµν , in terms of the behavior of those that were
traditionally considered geometrical measuring instruments, like rods
and clocks
the theory provided a proper unification by predicting that the
gravitational field had certain effects on such measuring instruments
that were not implied by previous theories of gravitation—like
gravitational time dilation
physical hypothesis =⇒ equivalence principle
37 / 44

110. Two strategies
after general relativity
geometrization strategy: general relativity was a successful theory
because it had provided a geometrical interpretation of the
gravitational field
• Weyl
unification strategy: general relativity was a successful theory because
it had achieved the unification of two different fields, gravitational and
inertial field
• Einstein
physical hypothesis =⇒ mathematical simplicity of nature
38 / 44

111. Two strategies
after general relativity
geometrization strategy: general relativity was a successful theory
because it had provided a geometrical interpretation of the
gravitational field
• Weyl
unification strategy: general relativity was a successful theory because
it had achieved the unification of two different fields, gravitational and
inertial field
• Einstein
physical hypothesis =⇒ mathematical simplicity of nature
38 / 44

112. Two strategies
after general relativity
geometrization strategy: general relativity was a successful theory
because it had provided a geometrical interpretation of the
gravitational field
• Weyl
unification strategy: general relativity was a successful theory because
it had achieved the unification of two different fields, gravitational and
inertial field
• Einstein
physical hypothesis =⇒ mathematical simplicity of nature
38 / 44

113. Two strategies
the core of Reichenbach’s philosophy was the separation of
mathematical necessity and physical reality.
in the search of a unified field theory, Einstein had come implicitly to
question this very distinction, ultimately pleading for a reduction of
physical reality to mathematical necessity
“
. . . even God could not have established these connections other-
wise than they actually are, just as little as it would have been in
his power to make the number 4 a prime number
Einstein, 1929c
”
39 / 44

114. Conclusion
39 / 44

115. Conclusion
January 30, 1929: Einstein’s new derivation of the
Fernparallelismus-field equations was published (Einstein, 1929d).
February 3, 1929: popular writing in the The Times of London
February 4 and February 5, 1929: popular writing in the New York
Times (Einstein, 1929a,b)
40 / 44

116. Conclusion
40 / 44

117. Conclusion
Einstein insisted on “the degree of formal speculation, the slender
empirical basis, [. . .] [t]he fundamental reliance on the unity and
comprehensibility of the secrets of [nature]” (Einstein, 1930, 114).
Einstein was not afraid to side with “Meyerson in his brilliant studies on
the theory of knowledge” who had emphasized the ‘Hegelian’ nature of
physics’ enterprise, “without thereby implying the censure which a
physicist would read into this” (Einstein, 1930, 115).
Reichenbach (or Schlick) =⇒ Meyerson
41 / 44

118. Conclusion
metaphysical-realist interpretation positivist-operational interpretation
unified field theory
quantum mechanics
“
Not long afterward I believe it was in 1932 I was visiting Einstein in
Berlin . . .
(Frank, 1947)
42 / 44

119. Conclusion
metaphysical-realist interpretation positivist-operational interpretation
unified field theory
quantum mechanics
“
Not long afterward I believe it was in 1932 I was visiting Einstein in
Berlin . . .
(Frank, 1947)
42 / 44

120. Conclusion
43 / 44

121. Conclusion
“The problem of gravitation made me to a believing rationalist [zu
einem gläubigen Rationalisten], that is, one who seeks the only
trustworthy source of truth in mathematical simplicity” (Lanczos to
Einstein, 01-03-1938)
“However, I think that there was no point in asking that [the
mathematical structure] should be of a geometrical nature; we all
agree that this is just a way of speaking, without a clear meaning”
(Lanczos to Einstein, 01-03-1938)
44 / 44

122. Thanks!
Acknowledgements:
Marco Giovanelli
Università degli Studi di Torino
Dipartimento di Filosofia e Scienze
dell’Educazione
marco.giovanelli@unito.it
44 / 44