Evening star. [volume] (Washington, D.C.) 1854-1972, 1929-01-31
PHYSICIST EXPLAINS
|. E|NSTE|N'STHEORY
Hamiltonian GeometricaI
System Discarded by Ger.
man Scientist.

man Scientist.
By the Associated Press.
BERLIN, January 3i.-Prof Albert
Einstein, originator of the famous
theory II relatively. yesterday pub
Ashed his latest work, q six-page
pamphlet Of mathematical formulate.
for which scientists throughout the
world have been waiting eagerly.
The Associated Press asked DR..
Edward Stowe Akeley, American
physicist of Chicago. now at the
Institute for Theoretical Physics in
the University Of Berlin, to present
comprehensive summary of this
latest contribution Of Prof. Einstein
to scientific thought. His summary
is given below:
BY DIR. EDWARD STOWE AKELEY.
In 1905. Prof Einstein in his SENEGAL
theory OF relatively showed that many
OF the previous difficulties in physical
theory disappeared If certain inter
relationships Of time and space were
recognized. Minkowski pointed out
that EinStein's theory OF the inter-
dependence Of space and time could be
simply stated In terms OF four dinen-
sion geometry, in which three dinen-
sionS OF space and one of time were
used.
In hts generalized theory Of relativ-
ity OF 1915 Einstein replaced this four
dimension. semi-Euclidean geometry by
the Rlemannian one. BY so doing he
fused the geometry and mechanics Of
gravltation IN such way that the laws
OF mechanics were Ceduced as geomet-
rical Identities, gravitation appeared as
fictitious force. while the proportion
atty OF intertial and gravitational mass
followed as consequence.
The Rieniannian geometry Is devel-
oped out OF the expression Of the square
Ok the approximate distance between
two points as a quadratic form In the
dlfferences OF the co-ordinates Of these
points-the approximation being the
more exact~the closer the points are
together--a very natural generalization
OF the Euclidean geometry
Original Direction Is Lost.
But in this Riemannian geometry
many OF the concepts of the Euclidean,
either partly or wholly, break down.
Thus while the paralleiisrn Of two in
finttely neighhoring lines has a definite
meaning, one cannot say that two sepa-
raote line elements are parallel or not
parallel, for the reason that II q line
element be moved continuously parallel
TO itself. on returning to its starting
point 1t viii no longer possess its origi-
nal direction.
Since 1925 there have been nnany at
temptS to add the ELECTROMAGNETIC phe-
nomena to such a scheme and number
OF theories have been developed In this
connection particularly by Weyl, Edo
lngton and Einstein himself.
The new theory Is distinguished from
al previous ones In that ii achieves the
FUSION OF geometry. mechanics and cleo
tro-magnetism, not by introducing q
more generalized geometry than RE
mannian, but rather by a Riemannian
geometry enriched by an additional con-
cept-an integrable parallelism In the
sense that II any two line elements are
given they are either parallel or nom
parallel We have new geometry,
therefor, with both the non-integrable
parallelism OF Riemann and the integ-
rable parallelism of Euclid.
After having developed a geometry,
the next step In problems of this kind
Is to seek possible geometrical relation
ships between the geometrical magni-
tudes. relationships which might repre-
sent fundamental physical laws.
Tensor Analysis Employed.
Relationships TO be geometrical or
physical are required to be invariant
under definite class Of TRANSFORMED
tons, and therefore In this connection
branch OF mathematics known as
tensor analysis Is used wherein the laws
are expressed as relationships between
certain concepts called tensors. One Of
the commonest methods Of deducing
such laws Is through a so-called Hamil-
tonian principle. Einstein. in fact. de-
veloped through principle Of this type
set OF equations Of which, as a first
approximation. came the equation of
his generalized relatively on the one
hand and the Maxwell equation of cleo
tro-magnetism on the other.
IN MS latest paper. however, he dis
carded this mode OF attack. as IL did not
give him the sort Of fusion he desired
"a FUSION that also will include a large
group OF new experimental data. the
so-called quantum phenomena, which
40 not appear to obey the previously
HnoWn Jaws OF .physics-phenomen
OF radiation. vacuum tube phenonnsna
radloactivity and X-rays.
For this reason he seeks ftlndamen-
tai laws In the form of relationshins
between sets Of fundamental qusntities
OF such type that the field Is over
determined. For instance, such over
determination might have as a result
partial determination of the boundary
conditions themselves out Of the equa-
tons. Einstein. therefore, in his latest
paper studies the tensors occurring in
his new geometry with particular at
tention to the identical relationships ex.
sting between them.
AS a result, he has obtained a theory
representing the fusion OF geometry.
mechanics and INSTRUMENTATION In the
form Of 20 independent field equations
connecting l6 fundamental quantities,
while between the equations identical
relationships exist. To determine
whether this is the theory sought for,
much difficult investigation still viii
be necessary.
(Copyr!ght, 1879, by the Associated PYeasl