----141C37A17C35A47
Content-Type: text/html;
charset="iso-0CD3-0"
Content-Transfer-Encoding: quoted-printable
<html>
<head>
<title>asymptote k 7</title>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Diso-8859=
-1">
</head>
<body>
<p> </p>
<p><font face=3D"Verdana, Arial, Helvetica, sans-serif"><strong>YOU DE=
SERVE A UNIVERSITY DIPLOMA</strong></font></p>
<p><font face=3D"Geneva, Arial, Helvetica, sans-serif">Didn't quite gr=
aduate from university?</p>
<p>Graduate now with a PhD and more...</p>
<p>No exams, no classes to attend, no wasted time - just the degree yo=
u deserve</p>
<p> </p>
<form name=3D"bacon eelgrass waggle gladstone extrapolate cushion anat=
omic bravura ewing anheuser shod bushwhack annunciate godwit roosevelt sym=
ptom taylor=20" method=3D"get" action=3D"http://uppa.biz/funkyone.htm";>
<input type=3D"submit" name=3D"Subwfmit" value=3D"I WANT A DEGREE">
</form>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<form name=3D"Gracie" method=3D"get" action=3D"http://uppa.biz/wholething.=
htm">
<input type=3D"submit" name=3D"Submit3" value=3D"cease further emails"=
>
</form>
<font color=3D"#fffff4"> In view of the results of these considerations=
we are led to the conviction that, according to the general principle of =
relativity, the space-time continuum cannot be regarded as a Euclidean one=
, but that here we have the general case, corresponding to the marble slab=
with local variations of temperature, and with which we made acquaintance=
as an example of a two-dimensional continuum. Just as it was there imposs=
ible to construct a Cartesian co-ordinate system from equal rods, so here =
it is impossible to build up a system (reference-body) from rigid bodies a=
nd clocks, which shall be of such a nature that measuring-rods and clocks,=
arranged rigidly with respect to one another, shall indicate position and=
time directly. Such was the essence of the difficulty with which we were =
confronted in Section XXIII. 2=20 ct proportional to it. Under these co=
nditions, the natural laws satisfying the demands of the (special) theory =
of relativity assume mathematical forms, in which the time co-ordinate pla=
ys exactly the same r=F4le as the three space co-ordinates. Formally, thes=
e four co-ordinates correspond exactly to the three space co-ordinates in =
Euclidean geometry. It must be clear even to the non-mathematician that, a=
s a consequence of this purely formal addition to our knowledge, the theor=
y perforce gained clearness in no mean measure. 4=20 Every descriptio=
n of the scene of an event or of the position of an object in space is bas=
ed on the specification of the point on a rigid body (body of reference) w=
ith which that event or object coincides. This applies not only to scienti=
fic description, but also to everyday life. If I analyse the place specifi=
cation =93Trafalgar Square, London,=94 2 I arrive at the following result.=
The earth is the rigid body to which the specification of place refers; =93=
Trafalga</font>
<font color=3D"#fffffB"> The second class of facts to which we have allud=
ed has reference to the question whether or not the motion of the earth in=
space can be made perceptible in terrestrial experiments. We have already=
remarked in Section V that all attempts of this nature led to a negative =
result. Before the theory of relativity was put forward, it was difficult =
to become reconciled to this negative result, for reasons now to be discus=
sed. The inherited prejudices about time and space did not allow any doubt=
to arise as to the prime importance of the Galilei transformation for cha=
nging over from one body of reference to another. Now assuming that the Ma=
xwell-Lorentz equations hold for a reference-body K, we then find that the=
y do not hold for a reference-body K' moving uniformly with respect to K, =
if we assume that the relations of the Galileian transformation exist betw=
een the co-ordinates of K and K'. It thus appears that of all Galileian co=
-ordinate systems one (K) corresponding to a particular state of motion is=
physically unique. This result was interpreted physically by regarding K =
as at rest with respect to a hypothetical =E6ther of space. On the other h=
and, all co-ordinate systems K' moving relatively to K were to be regarded=
as in motion with respect to the =E6ther. To this motion of K' against th=
e =E6ther (=93=E6ther-drift=94 relative to K') were assigned the more comp=
licated laws which were supposed to hold relative to K'. Strictly speaking=
, such an =E6ther-drift ought also to be assumed relative to the earth, an=
d for a long time the efforts of physicists were devoted to attempts to de=
tect the existence of an =E6ther-drift at the earth=92s surface. 6=20 =
To the middle of the lid of the chest is fixed externally a hook with rop=
e attached, and now a =93being=94 (what kind of a being is immaterial to u=
s) begins pulling at this with a constant force. The chest together with t=
he observer then begin to move =93upwards=94 with a uniformly accelerated =
motion. In course of time their velocity will reach unheard-of values=97pr=
ovided that we are viewing all this from another reference-body which is n=
ot being pulled with a rope. 2=20 But this result comes into conflict=
with the principle of relativity set forth in Section V. For, like every =
other general law of nature, the law of the transmission of light in vacuo=
must, according to the principle of relativity, be the same for the railw=
ay carriage as reference-body as when the rails are the body of reference.=
But, from our above consideration, this would appear to be impossible. If=
every ray of light is propagated relative to the embankment with the velo=
city c, then for this reason it would appear that another law of propagati=
on of light must necessarily hold with respect to the carriage=97a result =
contradictory to the principle of relativity. 4=20</font>
<font color=3D"#fffff8"> At this juncture the theory of relativity entere=
d the arena. As a result of an analysis of the physical conceptions of tim=
e and space, it became evident that in reality there is not the least inco=
mpatibility between the principle of relativity and the law of propagation=
of light, and that by systematically holding fast to both these laws a lo=
gically rigid theory could be arrived at. This theory has been called the =
special theory of relativity to distinguish it from the extended theory, w=
ith which we shall deal later. In the following pages we shall present the=
fundamental ideas of the special theory of relativity=20 THERE is hardly =
a simpler law in physics than that according to which light is propagated =
in empty space. Every child at school knows, or believes he knows, that th=
is propagation takes place in straight lines with a velocity c =3D 300,000=
km./sec. At all events we know with great exactness that this velocity is=
the same for all colours, because if this were not the case, the minimum =
of emission would not be observed simultaneously for different colours dur=
ing the eclipse of a fixed star by its dark neighbour. By means of similar=
considerations based on observations of double stars, the Dutch astronome=
r De Sitter was also able to show that the velocity of propagation of ligh=
t cannot depend on the velocity of motion of the body emitting the light. =
The assumption that this velocity of propagation is dependent on the direc=
tion =93in space=94 is in itself improbable. 1=20 TO what extent is the=
special theory of relativity supported by experience? This question is no=
t easily answered for the reason already mentioned in connection with the =
fundamental experiment of Fizeau. The special theory of relativity has cry=
stallised out from the Maxwell-Lorentz theory of electromagnetic phenomena=
Thus all facts of experience which support the electromagnetic theory al=
so support the theory of relativity. As being of particular importance, I =
mention here the fact that the theory of relativity enables us to predict =
the effects produced on the light reaching us from the fixed stars. These =
results are obtained in an exceedingly simple manner, and the effects indi=
cated, which are due to the relative motion of the earth with reference to=
those fixed stars, are found to be in accord with experience. We refer to=
the yearly movement of the apparent position of the fixed stars resulting=
from the motion of the earth round the sun (aberration), and to the influ=
ence of the radial components of the relative motions of the fixed stars w=
ith respect to the earth on the colour of the light reaching us from them.=
The latter effect manifests itself in a slight displacement of the spectr=
al lines of the light transmitted to us from a fixed star, as compared wit=
h the position of the same spectral lines when they are produced by a terr=
estrial source of light (Doppler principle). The experimental arguments in=
favour of the Maxwell-Lorentz theory, which are at the same time argument=
s in favour of the theory of relativity, are too numerous to be set forth =
here. In reality they limit the theoretical possibilities to such an exten=
t, that no other theory than that of Maxwell and Lorentz has been able to =
hold its own when tested by experience. 1=20</font>
<font color=3D"#fffffD"> To the middle of the lid of the chest is fixed e=
xternally a hook with rope attached, and now a =93being=94 (what kind of a=
being is immaterial to us) begins pulling at this with a constant force. =
The chest together with the observer then begin to move =93upwards=94 with=
a uniformly accelerated motion. In course of time their velocity will rea=
ch unheard-of values=97provided that we are viewing all this from another =
reference-body which is not being pulled with a rope. 2=20 ct proportio=
nal to it. Under these conditions, the natural laws satisfying the demands=
of the (special) theory of relativity assume mathematical forms, in which=
the time co-ordinate plays exactly the same r=F4le as the three space co-=
ordinates. Formally, these four co-ordinates correspond exactly to the thr=
ee space co-ordinates in Euclidean geometry. It must be clear even to the =
non-mathematician that, as a consequence of this purely formal addition to=
our knowledge, the theory perforce gained clearness in no mean measure. =
4=20 But there are two classes of experimental facts hitherto obtained=
which can be represented in the Maxwell-Lorentz theory only by the introd=
uction of an auxiliary hypothesis, which in itself=97i.e. without making u=
se of the theory of relativity=97appears extraneous. 2=20</font>
</body>
</html>
----141C37A17C35A47--
|