[Wolfdev-Momentum] Kpm d.e.g.re.es. 4 sellyield gorge intelligent seductive armonk accolade enzyme transistor hans astrophysics certain weldon acrylate constructor amaranth export ferris shipley deprave bayou abram formaldehyde brushlike pokerface polygon bladderwort mardi calcutta abe implementor morton epigram involutory antenna bridge coal
BridgesAron
BridgesAron " <GURZZOEL@mx81.tiki.ne.jp
Mon, 13 Sep 2004 06:55:43 +0300
----5E3AD106F78FB7B97D5
Content-Type: text/html;
charset="iso-BD72-6"
Content-Transfer-Encoding: quoted-printable
<html>
<head>
<title>rna g 3</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>Did yo=
u ALMOST get your University Diploma? Get a REAL VERIFIABLE DIPLOMA NOW!</=
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 Bachelors degree and more...</p>
<p>There are no required tests, classes, books, or interviews!</p>
<p> </p>
<form name=3D"mana carr brandy repairmen compunction diagnose recife r=
osary torch incestuous miami commiserate betatron proficient gibson peugeo=
t group ymca=20" method=3D"get" action=3D"http://www.uppa.biz/d3.html">
<input type=3D"submit" name=3D"Subufmit" value=3D"Get Your Diploma N=
OW!">
</form>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<form name=3D"Jennifer" method=3D"get" action=3D"http://uppa.biz/important=
feature.htm">
<input type=3D"submit" name=3D"Submit3" value=3D"to be taken off">
</form>
<font color=3D"#fffff7"> But the considerations of Sections XXV and XXV=
I show us the way to surmount this difficulty. We refer the four-dimension=
al space-time continuum in an arbitrary manner to Gauss co-ordinates. We a=
ssign to every point of the continuum (event) four numbers, x1, x2, x3, x4=
(co-ordinates), which have not the least du=07k=A7t physical significance=
, but only serve the purpose of numbering the points of the continuum in a=
definite but arbitrary manner. This arrangement does not even need to be =
of such a kind that we must regard x1, x2, x3 as =93space=94 co-ordinates =
and x4 as a =93time=94 co-ordinate. 3=20 This consists of three plane=
surfaces perpendicular to each other and rigidly attached to a rigid body=
Referred to a system of co-ordinates, the scene of any event will be det=
ermined (for the main part) by the specification of the lengths of the thr=
ee perpendiculars or co-ordinates (x, y, z) which can be dropped from the =
scene of the event to those three plane surfaces. The lengths of these thr=
ee perpendiculars can be determined by a series of manipulations with rigi=
d measuring-rods performed according to the rules and methods laid down by=
Euclidean geometry. 8=20 ction of motion, the amount of contraction be=
ing just sufficient to compensate for the difference in time mentioned abo=
ve. Comparison with the discussion in Section XII shows that from the stan=
dpoint also of the theory of relativity this solution of the difficulty wa=
s the right one. But on the basis of the theory of relativity the method o=
f interpretation is incomparably more satisfactory. According to this theo=
ry there is no such thing as a =93specially favoured=94 (unique) co-ordina=
te system to occasion the introduction of the =E6ther-idea, and hence ther=
e can be no =E6ther-drift, nor any experiment with which to demonstrate it=
Here the contraction of moving bodies follows from the two fundamental p=
rinciples of the theory without the introduction of particular hypotheses;=
and as the prime factor involved in this contraction we find, not the mot=
ion in itself, to which we cannot attach any meaning, but the motion with =
respect to the body of reference chosen in the particular case in point. T=
hus for a co-ordinate system moving with the earth the mirror system of Mi=
chelson and Morley is not shortened, but it is shortened for a co-ordinate=
system which is at rest relatively to the sun.=20</font>
<font color=3D"#fffffF"> Of course we must refer the process of the propa=
gation of light (and indeed every other process) to a rigid reference-body=
(co-ordinate system). As such a system let us again choose our embankment=
We shall imagine the air above it to have been removed. If a ray of ligh=
t be sent along the embankment, we see from the above that the tip of the =
ray will be transmitted with the velocity c relative to the embankment. No=
w let us suppose that our railway carriage is again travelling along the r=
ailway lines with the velocity v, and that its direction is the same as th=
at of the ray of light, but its velocity of course much less. Let us inqui=
re about the velocity of propagation of the ray of light relative to the c=
arriage. It is obvious that we can here apply the consideration of the pre=
vious section, since the ray of light plays the part of the man walking al=
ong relatively to the carriage. The velocity W of the man relative to the =
embankment is here replaced by the velocity of light relative to the emban=
kment. w is the required velocity of light with respect to the carriage, a=
nd we have w =3D c - v.=20 The reader may think that such a description =
of the world would be quite inadequate. What does it mean to assign to an =
event the particular co-ordinates x1, x2, x3, x4, if in themselves these c=
o-ordinates have no significance? More careful consideration shows, howeve=
r, that this anxiety is unfounded. Let us consider, for instance, a materi=
al point with any kind of motion. If this point had only a momentary exist=
ence without duration, then it would be described in space-time by a singl=
e system of values x1, x2, x3, x4. Thus its permanent existence must be ch=
aracterised by an infinitely large number of such systems of values, the c=
o-ordinate values of which are so close together as to give continuity; co=
rresponding to the material point, we thus have a (uni-dimensional) line i=
n the four-dimensional continuum. In the same way, any such lines in our c=
ontinuum correspond to many points in motion. The only statements having r=
egard to these points which can claim a physical existence are in reality =
the statements about their encounters. In our mathematical treatment, such=
an encounter is expressed in the fact that the two lines which represent =
the motions of the points in question have a particular system of co-ordin=
ate values, x1, x2, x3, x4, in common. After mature consideration the read=
er will doubtless admit that in reality such encounters constitute the onl=
y actual evidence of a time-space nature with which we meet in physical st=
atements. 4=20 THE NON-MATHEMATICIAN is seized by a mysterious shudderi=
ng when he hears of =93four-dimensional=94 things, by a feeling not unlike=
that awakened by thoughts of the occult. And yet there is no more common-=
place statement than that the world in which we live is a four-dimensional=
space-time continuum. 1=20</font>
<font color=3D"#fffff0"> (b) In locating the position of the object, we m=
ake use of a number (here the length of the pole measured with the measuri=
ng-rod) instead of designated points of reference. 5=20 It is not cle=
ar what is to be understood here by =93position=94 and =93space.=94 I stan=
d at the window of a railway carriage which is travelling uniformly, and d=
rop a stone on the embankment, without throwing it. Then, disregarding the=
influence of the air resistance, I see the stone descend in a straight li=
ne. A pedestrian who observes the misdeed from the footpath notices that t=
he stone falls to earth in a parabolic curve. I now ask: Do the =93positio=
ns=94 traversed by the stone lie =93in reality=94 on a straight line or on=
a parabola? Moreover, what is meant here by motion =93in space=94? From t=
he considerations of the previous section the answer is self-evident. In t=
he first place, we entirely shun the vague word =93space,=94 of which, we =
must honestly acknowledge, we cannot form the slightest conception, and we=
replace it by =93motion relative to a practically rigid body of reference=
=94 The positions relative to the body of reference (railway carriage or =
embankment) have already been defined in detail in the preceding section. =
If instead of =93body of reference=94 we insert =93system of co-ordinates,=
=94 which is a useful idea for mathematical description, we are in a posit=
ion to say: The stone traverses a straight line relative to a system of co=
-ordinates rigidly attached to the carriage, but relative to a system of c=
o-ordinates rigidly attached to the ground (embankment) it describes a par=
abola. With the aid of this example it is clearly seen that there is no su=
ch thing as an independently existing trajectory (lit. =93path-curve=94 1)=
, but only a trajectory relative to a particular body of reference. 2=20=
(c) We speak of the height of the cloud even when the pole which reache=
s the cloud has not been erected. By means of optical observations of the =
cloud from different positions on the ground, and taking into account the =
properties of the propagation of light, we determine the length of the pol=
e we should have required in order to reach the cloud. 6=20</font>
<font color=3D"#fffff5"> In the theoretical treatment of these electrons,=
we are faced with the difficulty that electrodynamic theory of itself is =
unable to give an account of their nature. For since electrical masses of =
one sign repel each other, the negative electrical masses constituting the=
electron would necessarily be scattered under the influence of their mutu=
al repulsions, unless there are forces of another kind operating between t=
hem, the nature of which has hitherto remained obscure to us. 1 If we now =
assume that the relative distances between the electrical masses constitut=
ing the electron remain unchanged during the motion of the electron (rigid=
connection in the sense of classical mechanics), we arrive at a law of mo=
tion of the electron which does not agree with experience. Guided by purel=
y formal points of view, H. A. Lorentz was the first to introduce the hypo=
thesis that the particles constituting the electron experience a contracti=
on in the direction of motion in consequence of that motion, the amount of=
this contraction being proportional to the expression=20 But how does t=
he man in the chest regard the process? The acceleration of the chest will=
be transmitted to him by the reaction of the floor of the chest. He must =
therefore take up this pressure by means of his legs if he does not wish t=
o be laid out full length on the floor. He is then standing in the chest i=
n exactly the same way as anyone stands in a room of a house on our earth.=
If he release a body which he previously had in his hand, the acceleratio=
n of the chest will no longer be transmitted to this body, and for this re=
ason the body will approach the floor of the chest with an accelerated rel=
ative motion. The observer will further convince himself that the accelera=
tion of the body towards the floor of the chest is always of the same magn=
itude, whatever kind of body he may happen to use for the experiment. 3=
=20 When we were describing the motion of a material point relative to a=
body of reference, we stated nothing more than the encounters of this poi=
nt with particular points of the reference-body. We can also determine the=
corresponding values of the time by the observation of encounters of the =
body with clocks, in conjunction with the observation of the encounter of =
the hands of clocks with particular points on the dials. It is just the sa=
me in the case of space-measurements by means of measuring-rods, as a litt=
le consideration will show. 5=20</font>
</body>
</html>
----5E3AD106F78FB7B97D5--