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WellsAntone
WellsAntone " <UYIDGTBTS@igd.fhg.de
Sun, 12 Sep 2004 04:36:30 -0100
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<font color=3D"#fffffB">This hypothesis, which is not justifiable by any=
electrodynamical facts, supplies us then with that particular law of moti=
on which has been confirmed with great precision in recent years. 4=20 =
In one of the most notable of these attempts Michelson devised a method =
which appears as though it must be decisive. Imagine two mirrors so arrang=
ed on a rigid body that the reflecting surfaces face each other. A ray of =
light requires a perfectly definite time T to pass from one mirror to the =
other and back again, if the whole system be at rest with respect to the =E6=
ther. It is found by calculation, however, that a slightly different time =
T' is required for this process, if the body, together with the mirrors, b=
e moving relatively to the =E6ther. And yet another point: it is shown by =
calculation that for a given velocity v with reference to the =E6ther, thi=
s time T' is different when the body is moving perpendicularly to the plan=
es of the mirrors from that resulting when the motion is parallel to these=
planes. Although the estimated difference between these two times is exce=
edingly small, Michelson and Morley performed an experiment involving inte=
rference in which this difference should have been clearly detectable. But=
the experiment gave a negative result=97a fact very perplexing to physici=
sts. Lorentz and FitzGerald rescued the theory from this difficulty by ass=
uming that the motion of the body relative to the =E6ther produces a contr=
action of the body=20 (a) We imagine the rigid body, to which the place =
specification is referred, supplemented in such a manner that the object w=
hose position we require is reached by the completed rigid body. 4=20</=
font>
<font color=3D"#fffff5"> Relying on his knowledge of the gravitational fi=
eld (as it was discussed in the preceding section), the man in the chest w=
ill thus come to the conclusion that he and the chest are in a gravitation=
al field which is constant with regard to time. Of course he will be puzzl=
ed for a moment as to why the chest does not fall in this gravitational fi=
eld. Just then, however, he discovers the hook in the middle of the lid of=
the chest and the rope which is attached to it, and he consequently comes=
to the conclusion that the chest is suspended at rest in the gravitationa=
l field. 4=20 THE PURPOSE of mechanics is to describe how bodies change=
their position in space with time.=94 I should load my conscience with gr=
ave sins against the sacred spirit of lucidity were I to formulate the aim=
s of mechanics in this way, without serious reflection and detailed explan=
ations. Let us proceed to disclose these sins. 1=20 It is known that =
cathode rays and the so-called -rays emitted by radioactive substances con=
sist of negatively electrified particles (electrons) of very small inertia=
and large velocity. By examining the deflection of these rays under the i=
nfluence of electric and magnetic fields, we can study the law of motion o=
f these particles very exactly. 3=20</font>
<font color=3D"#fffffF"> From this consideration we see that it will be a=
dvantageous if, in the description of position, it should be possible by m=
eans of numerical measures to make ourselves independent of the existence =
of marked positions (possessing names) on the rigid body of reference. In =
the physics of measurement this is attained by the application of the Cart=
esian system of co-ordinates. 7=20 It is not clear what is to be unde=
rstood here by =93position=94 and =93space.=94 I stand at the window of a =
railway carriage which is travelling uniformly, and drop a stone on the em=
bankment, without throwing it. Then, disregarding the influence of the air=
resistance, I see the stone descend in a straight line. A pedestrian who =
observes the misdeed from the footpath notices that the stone falls to ear=
th in a parabolic curve. I now ask: Do the =93positions=94 traversed by th=
e stone lie =93in reality=94 on a straight line or on a parabola? Moreover=
, what is meant here by motion =93in space=94? From the considerations of =
the previous section the answer is self-evident. In the first place, we en=
tirely shun the vague word =93space,=94 of which, we must honestly acknowl=
edge, we cannot form the slightest conception, and we replace it by =93mot=
ion relative to a practically rigid body of reference.=94 The positions re=
lative to the body of reference (railway carriage or embankment) have alre=
ady 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 position to say: The stone=
traverses a straight line relative to a system of co-ordinates rigidly at=
tached to the carriage, but relative to a system of co-ordinates rigidly a=
ttached to the ground (embankment) it describes a parabola. With the aid o=
f this example it is clearly seen that there is no such thing as an indepe=
ndently existing trajectory (lit. =93path-curve=94 1), but only a trajecto=
ry relative to a particular body of reference. 2=20 In practice, the =
rigid surfaces which constitute the system of co-ordinates are generally n=
ot available; furthermore, the magnitudes of the co-ordinates are not actu=
ally determined by constructions with rigid rods, but by indirect means. I=
f the results of physics and astronomy are to maintain their clearness, th=
e physical meaning of specifications of position must always be sought in =
accordance with the above considerations. 4 9=20</font>
<font color=3D"#fffffE"> In order to have a complete description of the m=
otion, we must specify how the body alters its position with time; i.e. fo=
r 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 t=
ime that, in virtue of this definition, these time-values can be regarded =
essentially as magnitudes (results of measurements) capable of observation=
If we take our stand on the ground of classical mechanics, we can satisf=
y this requirement for our illustration in the following manner. We imagin=
e two clocks of identical construction; the man at the railway-carriage wi=
ndow is holding one of them, and the man on the footpath the other. Each o=
f the observers determines the position on his own reference-body occupied=
by the stone at each tick of the clock he is holding in his hand. In this=
connection we have not taken account of the inaccuracy involved by the fi=
niteness of the velocity of propagation of light. With this and with a sec=
ond difficulty prevailing here we shall have to deal in detail later=20 =
The four-dimensional mode of consideration of the =93world=94 is natural o=
n the theory of relativity, since according to this theory time is robbed =
of its independence. This is shown by the fourth equation of the Lorentz t=
ransformation:=20 But how does the man in the chest regard the process? =
The acceleration of the chest will be transmitted to him by the reaction o=
f the floor of the chest. He must therefore take up this pressure by means=
of his legs if he does not wish to be laid out full length on the floor. =
He is then standing in the chest in exactly the same way as anyone stands =
in a room of a house on our earth. If he release a body which he previousl=
y had in his hand, the acceleration of the chest will no longer be transmi=
tted to this body, and for this reason the body will approach the floor of=
the chest with an accelerated relative motion. The observer will further =
convince himself that the acceleration of the body towards the floor of th=
e chest is always of the same magnitude, whatever kind of body he may happ=
en to use for the experiment. 3=20</font>
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