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*This conception is in itself not very satisfactory. It follows from what has
been said, that closed spaces without limitsare conceivable.
In this sense we
can imagine a sphericalspace.
Their whole universe of observationextends
exclusively over the surface of the sphere. In short, we can designate v as the
relative velocity of the twosystems. (2)Those space-time points (events) which
satisfy (x) must also satisfy(2). gifThus we have obtained the Lorentz
transformation for events on thex-axis. We require to find x and t when x and t
are given. 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.
Obviously this will be the case when the relation (x
- ct) = l (x - ct) . We start off on a consideration of a Galileian domain, i.
Under such conditions theyhave traversed the whole spherical space. We suppose
a light-signal sent out from the origin of K at the time t= 0. As regards its
space it would be infinite. ** These two deductions from the theory have
bothbeen confirmed. gifThus we have obtained the Lorentz transformation for
events on thex-axis. All the free end-points of these lengths lie on aspherical
surface.
Ourprojected audience is one hundred million readers.
Obviously this
will be the case when the relation (x - ct) = l (x - ct) .
The predicted effect
can be seen clearly from theaccompanying diagram.
It will be propagated
according to the equation eq. (2)Those space-time points (events) which satisfy
(x) must also satisfy(2).
gifThis _expression_ may also be stated in the
following form: eq. We require to find x and t when x and t are given.
These
result from the following discussion.
gifThis _expression_ may also be stated in
the following form: eq.
which have already been fitted intothe frame of the
special theory of relativity.
of experience that we can have in themovement of
rigid bodies.
This may be shown in the followingmanner.
There does arise,
however, a strange difficulty.
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