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Our experience is far from beingsufficient to enable us to answer this
question. Itpossesses a finite volume, which is determined by its
radius(2p2R3).
Here the Gaussian coordinates are samply Cartesian
ones.
TheGaussian coordinate system is a logical generalisation of theCartesian
co-ordinate system.
I shall prepare the reader for this in thefollowing
paragraphs. Under such conditions theyhave traversed the whole spherical
space.
Let us consider, forinstance, a material point with any kind of motion.
More careful consideration shows,however, that this anxiety is unfounded. What
will be his experience in this enterprise ? The sole exception is Mercury,
theplanet which lies nearest the sun.
a domainin which there is no
gravitational field relative to the Galileianreference-body K.
What will be his
experience in this enterprise ?
The Gauss co-ordinate system has to take the
place of thebody of reference.
The stellar universe ought to be afinite island
in the infinite ocean of space.
the lattice construction,considered in Section
24.
We shall suppose that the rods expand by in amount proportional to the
increase of temperature. Butaccording to Section 21 the general theory of
relativity cannotretain this law. This view is not in harmony with the theory
of Newton. We call themagnitude ds the distance apart of the two events
orfour-dimensional points.
The form there used, All bodies of reference K,
K1,etc.
Their whole universe of observationextends exclusively over the surface
of the sphere. Notes*) First observed by Eddington and others in 1919.
Our
experience is far from beingsufficient to enable us to answer this
question.
Itpossesses a finite volume, which is determined by its
radius(2p2R3).
It may be mentioned that there is yet another kind of curved
space: elliptical space. However, the Gauss treatment for ds2 which we have
given above is notalways possible.
To imagine aspace means nothing else than
that we imagine an epitome of our space experience, i. Thus all our previous
conclusions based on general relativity wouldappear to be called in
question.
They willcall the line joining the free ends of these lines a
circle.
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