 |
Books Should Be Free Loyal Books Free Public Domain Audiobooks & eBook Downloads |
|
|
|
Books Should Be Free Loyal Books Free Public Domain Audiobooks & eBook Downloads |
|
The Meaning of Relativity Four lectures delivered at Princeton University, May, 1921 By: Albert Einstein (1879-1955) |
|---|
@u
@x fi
@uff
@xff
(for
@uff
@xff
is a scalar). For physical reasons (no slipping) it
is assumed that for symmetrical dilatations in all directions,
i.e. when
@u1
@x1
=
@u2
@x2
=
@u3
@x3
;
@u1
@x2
; etc., = 0;
there are no frictional forces present, from which it follows that
fi =
2
3
ff. If only
@u1
@x3
is different from zero, let p31 = ff
@u1
@x3
,
by which ff is determined. We then obtain for the complete
stress tensor,
p = pff@u
@x @u
@x
2
3@u1
@x1 @u2
@x2 @u3
@x3: (18)
PRE RELATIVITY PHYSICS 23
The heuristic value of the theory of invariants, which arises
from the isotropy of space (equivalence of all directions), becomes
evident from this example.
We consider, finally, Maxwell's equations in the form which
are the foundation of the electron theory of Lorentz.
@h3
@x2
@h2
@x3
=
1
c
@e1
@t 1
c
i1;
@h1
@x3
@h3
@x1
=
1
c
@e2
@t 1
c
i2;
@h2
@x1
@h1
@x2
=
1
c
@e3
@t 1
c
i3;
@e1
@x1 @e2
@x2 @e3
@x3
= ;
9>
>>>>>=>>>>>>;
(19)
@e3
@x2
@e2
@x3
=
1
c
@h1
@t
;
@e1
@x3
@e3
@x1
=
1
c
@h2
@t
;
@e2
@x1
@e1
@x2
=
1
c
@h3
@t
;
@h1
@x1 @h2
@x2 @h3
@x3
= 0:
9>>>>>>=>
>>>>>;
(20)
i is a vector, because the current density is defined as the
density of electricity multiplied by the vector velocity of the
electricity. According to the first three equations it is evident
that e is also to be regarded as a vector. Then h cannot be
regarded as a vector. The equations may, however, easily be
These considerations will make the reader familiar with tensor opera
THE MEANING OF RELATIVITY 24
interpreted if h is regarded as a skew symmetrical tensor of the
second rank. In this sense, we write h23, h31, h12, in place of
h1, h2, h3 respectively. Paying attention to the skew symmetry
of h, the first three equations of (19) and (20) may be written
in the form
@h
@x
=
1
c
@e
@t 1
c
i; (19a)
@e
@x
@e
@x
=
1
c
@h
@t
: (20a)
In contrast to e, h appears as a quantity which has the same type
of symmetry as an angular velocity. The divergence equations
then take the form
@e
@x
= ; (19b)
@h
@x @h
@x @h
@x
= 0: (20b)
The last equation is a skew symmetrical tensor equation of the
third rank (the skew symmetry of the left hand side with respect
to every pair of indices may easily be proved, if attention
is paid to the skew symmetry of h). This notation is more
natural than the usual one, because, in contrast to the latter,
it is applicable to Cartesian left handed systems as well as to
right handed systems without change of sign.
tions without the special diculties of the four dimensional treatment; cor
responding considerations in the theory of special relativity (Minkowski's
interpretation of the field) will then offer fewer diculties.
LECTURE II
THE THEORY OF SPECIAL RELATIVITY
The previous considerations concerning the configuration of
rigid bodies have been founded, irrespective of the assumption
as to the validity of the Euclidean geometry, upon the hypothesis
that all directions in space, or all configurations of Cartesian systems
of co ordinates, are physically equivalent. We may express
this as the \principle of relativity with respect to direction," and
it has been shown how equations (laws of nature) may be found,
in accord with this principle, by the aid of the calculus of tensors.
We now inquire whether there is a relativity with respect
to the state of motion of the space of reference; in other words,
whether there are spaces of reference in motion relatively to each
other which are physically equivalent... Continue reading book >>
|
| eBook Download | |
|---|---|
|
Text File eBook • Computers • Windows • Mac |
PDF eBook • Download & View PDF file |
| Review this book |
|---|