Philosophy and Einstein's Discovery of the Theories of Relativity

1
Philosophyand Einstein's Discovery of
theTheories of Relativity

• John D. Norton
• Center for Philosophy of Science and
• Department of History and Philosophy of Science
• University of Pittsburgh

CARL FRIEDRICH VON WEIZSÄCKER LECTURES UNIVERSITY
OF HAMBURG June 2010
2
Carl Friedrich von Weizsäcker, The Structure of
Phyics (Aufbau der Physik). From Preface, 1985.
the apparent distractions in my life due to
politics and philosophy only slightly slowed the
pace of this work. Philosophy was indispensable
for a philosophically oriented analysis of
physics attempting to understand Plato,
Aristotle, Descartes, Kant, Frege, Heidegger was
no distraction at all from the main topic and
hence entailed no loss of time
3
Carl Friedrich von Weizsäcker, The Structure of
Phyics (Aufbau der Physik). From Preface, 1985.
When I was nineteen years old, Bohr revealed to
me the philosophical dimensions of physics. He
gave me what I had been looking for in physics.
From him I learned to understand the influence
that Socrates must have exerted of his followers
4
Carl Friedrich von Weizsäcker, The Structure of
Phyics (Aufbau der Physik). From Preface, 1985.
I have placed the three names Albert Einstein,
Niels Bohr, Werner Heisenberg at the head of of
the book. Einstein was the genius of the
century. The theory of relativity is his work,
and it was on his account that quantum got under
way. All younger workers remain under the spell
cast by his insights
5
Carl Friedrich von Weizsäcker, The Structure of
Phyics (Aufbau der Physik). From Preface, 1985.
For me, the mention of these three names also
carries the personal significance of admiring and
affectionate remembrance. I unfortunately never
met Einstein, but his name was familiar to me by
time if was a schoolboy, and from decade to
decade I learned better to understand his
greatness.
6
I unfortunately never met Einstein
7
To Einstein
8
Overview
Einstein
Philosophy
9
This Talk
I
Einsteins discovery of special relativity is
decisively advanced by his reading of philosophy.
1905
II
Einsteins discovery of general relativity
converts him to an advocate of an ancient
epistemology.
1915
10
Einsteins Discovery of Special Relativity 1905
I
11

12
The Final CrisisReconcile the Apparently
Incompatible
13
A later recollection
Today everyone knows, of course, that all
attempts to clarify this paradox of chasing the
beam of light satisfactorily were condemned to
failure as long as the axiom of the absolute
character of time, or of simultaneity, was rooted
unrecognized in the unconscious. To recognize
clearly this axiom and its arbitrary character
already implies the essentials of the solution of
the problem. The type of critical reasoning
required for the discovery of this central point
was decisively furthered, in my case, especially
by the reading of David Humes and Ernst Machs
philosophical writings.
Albert Einstein, Autobiographical Notes
! Einstein did not mean Hume and Machs analysis
of the notions of space and time specifically
14
Einsteins analysis in his 1905 On the
Electrodynamics of Moving Bodies (simplified)
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Inertial Observers Find the Same Speed for Light
An observer measures the speed of a light signal
with a rod and two synchronized clocks, A and B.
Finds light moves at c.
16
The central insightA view about how concepts
should be used in physical theories.
17
Concepts must be properly grounded in
experience...
After seven years of reflection in vain
(1898-1905), the solution came to me suddenly
with the thought that our concepts and laws of
space and time can only claim validity insofar as
they stand in a clear relation to experiences
and that experience could very well lead to the
alteration of the concepts and laws. By a
revision of the concept of simultaneity into a
more malleable form, I thus arrived at the
special theory of relativity.
From a 1924 recording transcribed by Herneck in
1966.
The concept of simultaneity does not exist for
the physicist until he has the possibility of
discovering whether or not it is fulfilled in an
actual case.
A. Einstein, Relativity, 8
an illustration which Einstein offered in
discussion. Suppose somebody uses the word
hunchback. If this concept is to have any clear
meaning, there must be some way of finding out
whether or not a man has a hunched back. If I
could conceive of no possibility of reaching such
a decision, the word would have no real meaning
for me.
To Wertheimer in 1916 interview.
18
so we may purge a priori (absoluteness of
simultaneity) from our concepts.
The illusion which prevailed prior to the
enunciation of the theory of relativity--that,
from the point of view of experience the meaning
of simultaneity in relation to spatially distant
events and, consequently, that the meaning of
physical time is a priori clear--this illusion
had its origin in the fact that in our everyday
experience we can neglect the time of propagation
of light. We are accustomed on this account to
fail to differentiate between "simultaneously
seen" and "simultaneously happening" and, as a
result, the difference between time and local
time is blurred. The lack of definiteness
which, from the point of view of its empirical
significance, adheres to the notion of time in
classical mechanics was veiled by the axiomatic
representation of space and time as given
independently of our sense experiences. Such a
use of notions--independent of the empirical
basis to which they owe their existence--does not
necessarily damage science. One may, however,
easily be led into the error of believing that
these notions, whose origin is forgotten, are
logically necessary and therefore unalterable,
and this error may constitute a serious danger to
the progress of science.
Einstein, Physics and Reality, 1936.
19
and Einstein credits Hume and Mach
Today everyone knows, of course, that all
attempts to clarify this paradox of chasing the
beam of light satisfactorily were condemned to
failure as long as the axiom of the absolute
character of time, or of simultaneity, was rooted
unrecognized in the unconscious. To recognize
clearly this axiom and its arbitrary character
already implies the essentials of the solution of
the problem. The type of critical reasoning
required for the discovery of this central point
was decisively furthered, in my case, especially
by the reading of David Humes and Ernst Machs
philosophical writings.
Albert Einstein, Autobiographical Notes
20
Mach
21
Einstein attributes this view of concepts to Mach
from Einsteins obituary for Mach, 1916
22

Einstein attributes this view of concepts to Mach
from Einsteins obituary for Mach, 1916
23
Hume
24
and still much more Hume
Your exposition is also quite right that
positivism suggested rel. theory, without
requiring it. Also you have correctly seen that
this line of thought was of great influence on my
efforts and indeed E. Mach and still much more
Hume, whose treatise on understanding I studied
with eagerness and admiration shortly before
finding relativity theory.
Einstein to Moritz Schlick, Dec 14 1915
treatise on understanding A Treatise of
Human Nature? or An Enquiry concerning Human
Understanding?
25
Hume, A Treatise of Human Nature
26

Hume, A Treatise of Human Nature
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Why Hume more than Mach?
A conjecture Einstein thought that Mach (but not
Hume) denied the freedom of creation of concepts
exercised by Einstein when he introduced a new
definition of distant simultaneity in 1905?
28
How to Use Concepts in Physical Theories
Einstein on
Concepts must be properly grounded in experience,
else they fail to represent the physically real
and are fictional. (From Hume and Mach)
Concepts without proper physical grounding need
not be abjured (contrary to Mach and Hume). They
can be retained in a physical theory as long as
their arbitrary character is recognized and in a
way that does not unwittingly introduce false
presumptions.
The breakthrough in Einsteins discovery of
special relativity came when he applied this view
to the traditional concept of the simultaneity of
distant events.
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Einsteins Discovery of General Relativity
1907-1915
II
30
Physical versus Formal
approach
approach
Considerable overlap. Often both are the same
inferences in different guises.
31

32
Einsteins early distain for higher mathematics
in physics
Special relativity, light quantum use only
calculus of many variables. Marked reluctance to
adopt Minkowskis four-dimensional methods. He
does not use them until 1912. Quip I can
hardly understant Laues book 1911 textbook on
special relativity that used Minkowskis
methods. Four-dimensional methods disparaged as
superfluous learnedness.
33
Abrahams 1912 theory of gravity
Abrahams theory is the simplest mathematically
delivered by four-dimensional methods.
uict
where cc(F) Einsteins idea!
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General relativity begins to turn the tide
In 1912, Einstein began work on the precursor to
general relativity, the Entwurf theory of 1913
with the mathematical assistance of Marcel
Grossmann, who introduced Einstein to Ricci and
Levi-Civitas absolute differential calculus
(now called tensor calculus).
35
Einstein and Grossmanns Entwurf 1913
Complete framework of general theory of
relativity. Gravity as curvature of spacetime
geometry. One thing is missing
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The Einstein Equations are approached
Einstein and Grossman present gravitational field
equations that are not generally covariant and
have no evident geometrical meaning.
37
Einsteins Zurich Notebook
A notebook of calculation Einstein kept while he
worked on the Entwurf theory with Grossmann.
38
Inside the cover
39
Einstein connects gravity and curvature of
spacetime.
p. 39L
40
The physical approach to energy-momentum
conservation
p.5R
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and the formal approach to energy-momentum
conservation.
Is the conservation law
of the form
p.5R
42
The formal approach to the gravitational field
equations
Following pages Einstein shows how to select
coordinate systems so that they do vanish.
p. 14L
43
Failure of the formal approach
Einstein finds multiple problems with the
gravitational field equations based on the
Riemann curvature tensor.
p. 21R
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Entwurf gravitational field equations
Derived from a purely physical approach.
Energy-momentum conservation.
pp. 26L-R
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Einsteins short-lived methodological moral of
1914
The physical approach is superior to the formal
approach.
At the moment I do not especially feel like
working, for I had to struggle horribly to
discover what I described above. The general
theory of invariants was only an impediment. The
direct route proved to be the only feasible one.
It is just difficult to understand why I had to
grope around for so long before I found what was
so near at hand.
Einstein to Besso, March 1914
46
Einstein snatches triumph from near disaster
Fall 1915.

• David Hilbert in Göttingen applies formal methods
  to general field equations for Einsteins theory
• ... and Einstein knows it.
• Communications to the Göttingen Academy

Einstein realizes his Entwurf field equations
are wrong and returns to seek generally covariant
equations. Communications to the Prussian
Academy
Nov. 4 Almost generally covariant field
equations Nov. 11 Almost generally covariant
field equations Nov. 18 Explanation of Mercurys
perihelion motion Nov. 26 Einstein equations
Nov. 20 Something very close to Einsteins
equations
47
Einsteins new methodological moral
Triumph of formal methods over physical
considerations.
I had already taken into consideration the only
possible generally covariant equations, which now
prove to be the right ones, three years ago with
my friend Grossmann. Only with heavy hearts did
we detach ourselves from them, since the physical
discussion had apparently shown their
incompatibility with Newton's law.
Hardly anyone who has truly understood it can
resist the charm of this theory it signifies a
real triumph of the method of the general
differential calculus, founded by Gauss, Riemann,
Christoffel, Ricci and Levi-Civita.
Einstein to Hilbert Nov 18, 1915
This time the most obvious was correct however
Grossmann and I believed that the conservation
laws would not be satisfied and that Newton's law
would not come out in the first approximation.
Communication to Prussian Academy of Nov. 4, 1915
Einstein to Besso, Dec. 10, 1915
48
Einsteins manifesto of June 10, 1933
Herbert Spenser Lecture, "On the Methods of
Theoretical Physics," University of Oxford
49
Conclusion
50
The reciprocal relationship of epistemology and
science is of noteworthy kind. They are dependent
upon each other. Epistemology without contact
with science becomes an empty scheme. Science
without epistemology is -- insofar as it is
thinkable at all -- primitive and
muddled. Einstein, Autobiographical
Notes--Remarks Concerning the Essays Brought
together in this Co-operative Volume." p. 683
51
Read all about it
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53

www.pitt.edu/jdnorton
54

55

philsci-archive.pitt.edu
56

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Finis
58
Einstein Recalls the Decisive Moment
Why are these two things inconsistent with each
other? I felt that I was facing an extremely
difficult problem. I suspected that Lorentzs
ideas had to be modified somehow, but spent
almost a year on fruitless thoughts. And I felt
that was puzzle not to be easily solved.
But a friend of mine living in living in Bern
(Switzerland) Michele Besso helped me by
chance. One beautiful day, I visited him and said
to him I presently have a problem that I have
been totally unable to solve. Today I have
brought this struggle with me. We then had
extensive discussions, and suddenly I realized
the solution. The very next day, I visited him
again and immediately said to him Thanks to
you, I have completely solved my problem. My
solution actually concerned the concept of time.
Namely, time cannot be absolutely defined by
itself, and there is an unbreakable connection
between time and signal velocity. Using this
idea, I could now resolve the great difficulty
that I previously felt. After I had this
inspiration, it took only five weeks to complete
what is now known as the special theory of
relativity.
From a lecture given in Kyoto, Dec. 14, 1922.
Notes by Jun Ishiwara translation Akira Ukawa
revised John Stachel.
59
Physical approach illustrated
Based on Einsteins 1905 magnet-conductor thought
experiment.
Principle of relativity requires that the
electromagnetic field manifests as different
mixtures of magnetic field B and electric field E
according to motion of observer.
60
Formal approach illustrated
Write Maxwells equations using four-vector and
six-vector (now antisymmetric second rank tensor)
quantities and operators of Minkowskis 1908
spacetime, geometrical approach. Satisfaction of
the principle of relativity is automatic.
Frame dependence of decomposition of
electromagnetic field is a consequence of
spacetime geometry.
61
Evolution of Einsteins approaches
1902-1904 statistical physics 1905 Brownian
motion 1905 Light quantum 1905 Special
relativity 1906 Specific heats 1909 Wave particle
duality 1907-1915 General
relativity 1916 A and B coefficients 1917
Relativististic cosmology 1924-25
Bose-Einstein statistics 1935 EPR
Physical
62
Einsteins search for unified field theory
I have learned something else from the theory of
gravitation no collection of empirical facts
however comprehensive can ever lead to the
setting up of such complicated equations as
non-linear field equations of the unified field.
A theory can be tested by experience, but there
is no way from experience to the construction of
a theory. Equations of such complexity as are the
equations of the gravitational field can be found
only through the discovery of a logically simple
mathematical condition that determines the
equations completely or almost completely. Once
one has obtained those sufficiently strong formal
conditions, one requires only little knowledge of
facts for the construction of the theory in the
case of the equations of gravitation it is the
four-dimensionality and the symmetric tensor as
expression for the structure of space that,
together with the invariance with respect to the
continuous transformation group, determine the
equations all but completely.
Autobiographical Notes, 1946