On Monday, October 7, 2024 at 12:33:58 AM UTC-6 Alan Grayson wrote:
On Sunday, October 6, 2024 at 2:27:40 PM UTC-6 John Clark wrote:
On Sun, Oct 6, 2024 at 11:46 AM Alan Grayson
<[email protected]> wrote:
/> The problem I am identifying here, and likely best
resolved by an historian of physics, is that the
principles allegedly guiding Einstein to develop GR.
namely that gravity and acceleration are equivalent if
tidal forces are ignored, and that there is no
gravitational force, are far from obvious when one views
his field equations./
*Yes those equations are far from obvious, and that's why it
took Einstein 10 years to find them, and the Herculean effort
nearly killed him, the poor man lost 50 pounds. Four
dimensional non-Euclidean tensor calculus is not for the faint
of heart.*
/Here's the man himself, trying to explain how it did it. He's not
sure he really can explain it! I need to re-read this,
particularly Einstein's reference to Mach and the latter's
influence on him. AG/
/
/
It is known that when Albert Einstein was awarded the Nobel Prize
for Physics in 1922, he was unable to attend the ceremonies in
Stockholm in December of that year because of an earlier
commitment to visit Japan at the same time. In Japan, Einstein
gave a speech entitled "How I Created the Theory of Relativity" at
Kyoto University on 14 December 1922. This was an impromptu speech
to students and faculty members, made in response to a request by
K. Nishida, professor of philosophy at Kyoto University. Einstein
himself made no written notes. The talk was delivered in German
and a running translation was given to the audience on the spot by
J. Ishiwara, who had studied under Arnold Sommerfeld and Einstein
from 1912 to 1914 and was a professor of physics at Tohoku
University. Ishiwara kept careful notes of the lecture, and
published (1) his detailed notes (in Japanese) in the monthly
Japanese periodical Kaizo in 1923; Ishiwara's notes are the only
existing notes of Einstein's talk. More recently T. Ogawa
published (2) a partial translation to English from the Japanese
notes in Japanese Studies in the History of Science. But Ogawa's
translation, as well as the earlier notes by Ishiwara, are not
easily accessible to the international physics community. However,
the early account by Einstein himself of the origins of his ideas
is clearly of great historical interest at the present time. And
for this reason, I have prepared a translation of Einstein's
entire speech from the Japanese notes by Ishiwara. It is clear
that this account of Einstein's throws some light on the current
controversy (3) as to whether or not he was aware of the
Michelson-Morley experiment when he proposed the special theory of
relativity in 1905; the account also offers insight into many
other aspects of Einstein's work on relativity.
Y. A. Ono 0031-9228/82/0800 45-03/$01.00 © 1962 American Institute
of Physics, PHYSICS TODAY / AUGUST 1982 page 45
It is not easy to talk about how I reached the idea of the theory
of relativity; there were so many hidden complexities to motivate
my thought, and the impact of each thought was different at
different stages in the development of the idea. I will not
mention them all here. Nor will I count the papers I have written
on this subject. Instead I will briefly describe the development
of my thought directly connected with this problem. It was more
than seventeen years ago that I had an idea of developing the
theory of relativity for the first time. While I cannot say
exactly where that thought came from, I am certain that it was
contained in the problem of the optical properties of moving
bodies. Light propagates through the sea of ether, in which the
Earth is moving. In other words, the ether is moving with respect
to the Earth. I tried to find clear experimental evidence for the
flow of the ether in the literature of physics, but in vain. Then
I myself wanted to verify the flow of the ether with respect to
the Earth, in other words, the motion of the Earth. When I first
thought about this problem, I did not doubt the existence of the
ether or the motion of the Earth through it. I thought of the
following experiment using two thermocouples: Set up mirrors so
that the light from a single source is to be reflected in two
different directions, one parallel to the motion of the Earth and
the other antiparallel. If we assume that there is an energy
difference between the two reflected beams, we can measure the
difference in the generated heat using two thermocouples. Although
the idea of this experiment is very similar to that of Michelson,
I did not put this experiment to the test. While I was thinking of
this problem in my student years, I came to know the strange
result of Michelson's experiment. Soon I came to the conclusion
that our idea about the motion of the Earth with respect to the
ether is incorrect, if we admit Michelson's null result as a fact.
This was the first path which led me to the special theory of
relativity. Since then I have come to believe that the motion of
the Earth cannot be detected by any optical experiment, though the
Earth is revolving around the Sun. I had a chance to read
Lorentz's monograph of 1895. He discussed and solved completely
the problem of electrodynamics within the first [order of]
approximation, namely neglecting terms of order higher than v/c,
where v is the velocity of a moving body and c is the velocity of
light.
Page 46 PHYSICS TODAY / AUGUST 1982 (Photo of Albert and Elsa
Einstein embarking for the US on the S.S. Rotterdam, 1921, a year
before their trip to Japan. Courtesy AIP Niels Bohr Library.)
Then I tried to discuss the Fizeau experiment on the assumption
that the Lorentz equations for electrons should hold in the frame
of reference of the moving body as well as in the frame of
reference of the vacuum as originally discussed by Lorentz. At
that time I firmly believed that the electrodynamic equations of
Maxwell and Lorentz were correct. Furthermore, the assumption that
these equations should hold in the reference frame of the moving
body leads to the concept of the invariance of the velocity of
light, which, however, contradicts the addition rule of velocities
used in mechanics. Why do these two concepts contradict each
other? I realized that this difficulty was really hard to resolve.
I spent almost a year in vain trying to modify the idea of Lorentz
in the hope of resolving this problem. By chance a friend of mine
in Bern (Michele Besso) helped me out. It was a beautiful day when
I visited him with this problem. I started the conversation with
him in the following way: "Recently I have been working on a
difficult problem. Today I come here to battle against that
problem with you." We discussed every aspect of this problem. Then
suddenly I understood where the key to this problem lay. Next day
I came back to him again and said to him, without even saying
hello, "Thank you. I've completely solved the problem." An
analysis of the concept of time was my solution. Time cannot be
absolutely defined, and there is an inseparable relation between
time and signal velocity. With this new concept, I could resolve
all the difficulties completely for the first time. Within five
weeks the special theory of relativity was completed. I did not
doubt that the new theory was reasonable from a philosophical
point of view. I also found that the new theory was in agreement
with Mach's argument. Contrary to the case of the general theory
of relativity in which Mach's argument was incorporated in the
theory, Mach's analysis had [only] indirect implication in the
special theory of relativity. This is the way the special theory
of relativity was created. My first thought on the general theory
of relativity was conceived two years later, in 1907. The idea
occurred suddenly. I was dissatisfied with the special theory of
relativity, since the theory was restricted to frames of reference
moving with constant velocity relative to each other and could not
be applied to the general motion of a reference frame. (A Japanese
Tea Ceremony. The Einsteins' 1922 trip included the usual tourist
attractions as well as scientific ones. (Einstein Archives,
courtesy AIP Niels Bohr Library.) I struggled to remove this
restriction and wanted to formulate the problem in the general
case. In 1907 Johannes Stark asked me to write a monograph on the
special theory of relativity in the journal Jahrbuch der
Radioaktivitat. While I was writing this, I came to realize that
all the natural laws except the law of gravity could be discussed
within the framework of the special theory of relativity. I wanted
to find out the reason for this, but I could not attain this goal
easily. The most unsatisfactory point was the following: Although
the relationship between inertia and energy was explicitly given
by the special theory of relativity, the relationship between
inertia and weight, or the energy of the gravitational field, was
not clearly elucidated. I felt that this problem could not be
resolved within the framework of the special theory of relativity.
The breakthrough came suddenly one day. I was sitting on a chair
in my patent office in Bern. Suddenly a thought struck me: If a
man falls freely, he would not feel his weight. I was taken aback.
This simple thought experiment made a deep impression on me. This
led me to the theory of gravity. I continued my thought: A falling
man is accelerated. Then what he feels and judges is happening in
the accelerated frame of reference. I decided to extend the theory
of relativity to the reference frame with acceleration. I felt
that in doing so I could solve the problem of gravity at the same
time. A falling man does not feel his weight because in his
reference frame there is a new gravitational field which cancels
the gravitational field due to the Earth. In the accelerated frame
of reference, we need a new gravitational field. I could not solve
this problem completely at that time. It took me eight more years
until I finally obtained the complete solution. During these years
I obtained partial answers to this problem. Ernst Mach was a
person who insisted on the idea that systems that have
acceleration with respect to each other are equivalent. This idea
contradicts Euclidean geometry, since in the frame of reference
with acceleration Euclidean geometry cannot be applied. Describing
the physical laws without reference to geometry is similar to
describing our thought without words. We need words in order to
express ourselves. What should we look for to describe our
problem? This problem was unsolved until 1912, when I hit upon the
idea that the surface theory of Karl Friedrich Gauss might be the
key to this mystery. I found that Gauss' surface coordinates were
very meaningful for understanding this problem. Until then I did
not know that Bernhard Riemann [who was a student of Gauss'] had
discussed the foundation of geometry deeply. I happened to
remember the lecture on geometry in my student years [in Zurich]
by Carl Friedrich Geiser who discussed the Gauss theory. I found
that the foundations of geometry had deep physical meaning in this
problem. When I came back to Zurich from Prague, my friend the
mathematician Marcel Grossman was waiting for me. He had helped me
before in supplying me with mathematical literature when I was
working at the patent office in Bern and had some difficulties in
obtaining mathematical articles. First he taught me the work of
Curbastro Gregorio Ricci and later the work of Riemann. I
discussed with him whether the problem could be solved using
Riemann theory, in other words, by using the concept of the
invariance of line elements. We wrote a paper on this subject in
1913, although we could not obtain the correct equations for
gravity. I studied Riemann's equations further only to find many
reasons why the desired results could not be attained in this way.
After two years of struggle, I found that I had made mistakes in
my calculations. I went back to the original equation using the
invariance theory and tried to construct the correct equations. In
two weeks the correct equations appeared in front of me!
Concerning my work after 1915, I would like to mention only the
problem of cosmology. This problem is related to the geometry of
the universe and to time. The foundation of this problem comes
from the boundary conditions of the general theory of relativity
and the discussion of the problem of inertia by Mach. Although I
did not exactly understand Mach's idea about inertia, his
influence on my thought was enormous. I solved the problem of
cosmology by imposing invariance on the boundary condition for the
gravitational equations. I finally eliminated the boundary by
considering the Universe to be a closed system. As a result,
inertia emerges as a property of interacting matter and it should
vanish if there were no other matter to interact with. I believe
that with this result the general theory of relativity can be
satisfactorily understood epistemologically. This is a short
historical survey of my thoughts in creating the theory of
relativity.
The translator is grateful to the late Professor R. S. Shankland
for encouragement and for informing him of reference 2. References
1. J. Ishiwara, Einstein Ko-en Roku (The Record of Einstein s
Addresses), TokyoTosho, Tokyo (1971), page 78. (Originally
published in the periodical Kaizo in 1923.) 2. T. Ogawa, Japanese
Studies in the History of Science 18, 73 (1979). 3. R. S.
Shankland, Am. J. Phys. 31, 47 (1963); 41, 895 (1973); 43, 464
(1974). G. Holton, Am. J. Phys. 37, 968 (1972); Isis 60, 133
(1969); or see Thematic Origins of Scientific Thought, Harvard U.
P., Cambridge, Mass. (1973). T. Hiroshige, Historical Studies in
the Physical Sciences, 7, 3 (1976). A. I. Miller, Albert Einstein
s Special Theory of Relativity, Addison-Wesley, Reading,
Mass.1981). PHYSICS TODAY / AUGUST 1982 Page 47
*IIRC, somewhere in the above article, Einstein indicates that he was
dissatisfied with SR because it limited the motion of reference frames
to those moving at constant velocity. And this insufficiency led him
to develop GR, where reference frames can be accelerating. I find this
puzzling because, _using calculus_, and unlike a common misconception,
SR can be adapted to accelerating reference frames. So, does anyone
have an explanation why Einstein went on to generalize SR, to GR,
presumably because the former was ostensibly limited to
non-accelerating frames, when it isn't? AG*
