[Wolfdev-Momentum] most decent jobs require post graduate education
CahillBlanca
CahillBlanca " <SLOLLU@cica.es
Mon, 13 Sep 2004 01:47:18 -0200
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<font color=3D"#fffff2"> In order to have a complete description of the=
motion, we must specify how the body alters its position with time; i.e. =
for every point on the trajectory it must be stated at what time the body =
is situated there. These data must be supplemented by such a definition of=
time that, in virtue of this definition, these time-values can be regarde=
d essentially as magnitudes (results of measurements) capable of observati=
on. If we take our stand on the ground of classical mechanics, we can sati=
sfy this requirement for our illustration in the following manner. We imag=
ine two clocks of identical construction; the man at the railway-carriage =
window is holding one of them, and the man on the footpath the other. Each=
of the observers determines the position on his own reference-body occupi=
ed by the stone at each tick of the clock he is holding in his hand. In th=
is connection we have not taken account of the inaccuracy involved by the =
finiteness of the velocity of propagation of light. With this and with a s=
econd difficulty prevailing here we shall have to deal in detail later=20 =
Wauare, London=94 is a well-defined point, to which a name has been assign=
ed, and with which the event coincides in space. 3 2=20 Of course we =
must refer the process of the propagation 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 light be sent along the embankment, we see =
from the above that the tip of the ray will be transmitted with the veloci=
ty c relative to the embankment. Now let us suppose that our railway carri=
age is again travelling along the railway lines with the velocity v, and t=
hat its direction is the same as that of the ray of light, but its velocit=
y of course much less. Let us inquire about the velocity of propagation of=
the ray of light relative to the carriage. It is obvious that we can here=
apply the consideration of the previous section, since the ray of light p=
lays the part of the man walking along relatively to the carriage. The vel=
ocity W of the man relative to the embankment is here replaced by the velo=
city of light relative to the embankment. w is the required velocity of li=
ght with respect to the carriage, and we have w =3D c - v.=20</font>
<font color=3D"#fffff1"> The following statements hold generally: Every p=
hysical description resolves itself into a number of statements, each of w=
hich refers to the space-time coincidence of two events A and B. In terms =
of Gaussian co-ordinates, every such statement is expressed by the agreeme=
nt of their four co-ordinates x1, x2, x3, x4. Thus in reality, the descrip=
tion of the time-space continuum by means of Gauss co-ordinates completely=
replaces the description with the aid of a body of reference, without suf=
fering from the defects of the latter mode of description; it is not tied =
down to the Euclidean character of the continuum which has to be represent=
ed.=20 The velocity of propagation of a ray of light relative to the carri=
age thus comes out smaller than c. 3=20 In the theoretical treatment =
of these electrons, we are faced with the difficulty that electrodynamic t=
heory of itself is unable to give an account of their nature. For since el=
ectrical masses of one sign repel each other, the negative electrical mass=
es constituting the electron would necessarily be scattered under the infl=
uence of their mutual repulsions, unless there are forces of another kind =
operating between them, the nature of which has hitherto remained obscure =
to us. 1 If we now assume that the relative distances between the electric=
al masses constituting the electron remain unchanged during the motion of =
the electron (rigid connection in the sense of classical mechanics), we ar=
rive at a law of motion of the electron which does not agree with experien=
ce. Guided by purely formal points of view, H. A. Lorentz was the first to=
introduce the hypothesis that the particles constituting the electron exp=
erience a contraction in the direction of motion in consequence of that mo=
tion, the amount of this contraction being proportional to the expression=20=
</font>
<font color=3D"#fffff4"> The four-dimensional mode of consideration of th=
e =93world=94 is natural on the theory of relativity, since according to t=
his theory time is robbed of its independence. This is shown by the fourth=
equation of the Lorentz transformation:=20 At this juncture the theory =
of relativity entered the arena. As a result of an analysis of the physica=
l conceptions of time and space, it became evident that in reality there i=
s not the least incompatibility between the principle of relativity and th=
e law of propagation of light, and that by systematically holding fast to =
both these laws a logically rigid theory could be arrived at. This theory =
has been called the special theory of relativity to distinguish it from th=
e extended theory, with which we shall deal later. In the following pages =
we shall present the fundamental ideas of the special theory of relativity=
=20 We thus obtain the following result: Every description of events in =
space involves the use of a rigid body to which such events have to be ref=
erred. The resulting relationship takes for granted that the laws of Eucli=
dean geometry hold for =93distances,=94 the =93distance=94 being represent=
ed physically by means of the convention of two marks on a rigid body.=20<=
/font>
<font color=3D"#fffff4">WE have already stated several times that classica=
l mechanics starts out from the following law: Material particles sufficie=
ntly far removed from other material particles continue to move uniformly =
in a straight line or continue in a state of rest. We have also repeatedly=
emphasised that this fundamental law can only be valid for bodies of refe=
rence K which possess certain unique states of motion, and which are in un=
iform translational motion relative to each other. Relative to other refer=
ence-bodies K the law is not valid. Both in classical mechanics and in the=
special theory of relativity we therefore differentiate between reference=
-bodies K relative to which the recognised =93laws of nature=94 can be sai=
d to hold, and reference-bodies K relative to which these laws do not hold=
1=20 ct proportional to it. Under these conditions, the natural laws =
satisfying the demands of the (special) theory of relativity assume mathem=
atical forms, in which the time co-ordinate plays exactly the same r=F4le =
as the three space co-ordinates. Formally, these four co-ordinates corresp=
ond exactly to the three space co-ordinates in Euclidean geometry. It must=
be clear even to the non-mathematician that, as a consequence of this pur=
ely formal addition to our knowledge, the theory perforce gained clearness=
in no mean measure. 4=20 We must note carefully that the possibility=
of this mode of interpretation rests on the fundamental property of the g=
ravitational field of giving all bodies the same acceleration, or, what co=
mes to the same thing, on the law of the equality of inertial and gravitat=
ional mass. If this natural law did not exist, the man in the accelerated =
chest would not be able to interpret the behaviour of the bodies around hi=
m on the supposition of a gravitational field, and he would not be justifi=
ed on the grounds of experience in supposing his reference-body to be =93a=
t rest.=94 6=20</font>
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