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An Introduction To Non-aristotelian Systems And General Semantics.

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electron or proton or light quantum or what not, has energy W, there must be in the system a periodic phenomenon of frequency v, defined by W=hv. From this point of view all forms of energy, radiation included, must have an atomic structure and the atoms of energy must be grouped around certain points, forming what we call 'electrons', 'light quanta',.
Applying the Lorentz-Einstein transformation, he finds a rather startling fact - that the frequency associated with any assumed mass mo; namely,
ft--------, represents no more and no less than a periodic phenomenon, analogous
to a stationary wave, which spreads around the point of which the mass is a
In other words, a 'mass particle' at rest is the centre of a pulsation throughout the spread, or otherwise it is a singularity of the pulsation. The quantity
\j/ and \f$ is interpreted as the electric density, where $
which pulsates is called
is the conjugate of the complex quantity
In the Minkowski representation, the above astonishing result becomes quite simple, and we can see clearly how simultaneous pulsations become travelling waves. In Fig. 2, we give a two-dimensional diagram of space-time. OXo is the 'space' co-ordinate, OTq the 'time' (icto) co-ordi
1^1, ifo, 4>t, represent the traces of the sur-
faces of constant phase which are perpendicular to OTo. The Lorentz-Einstein transformation is equivalent to the transformation from rectangular
XoOTo to the rectangular system XOT,
forming an angle 8. In the new system the lines l^i. \^2, fa , are no longer parallel to the X axis and so represent a moving wave front. In this new system the ^-lines represent the moving wave front for different points, P, P'. , on one phase line and have different values of t. The smaller the velocity (») of the particle, the smaller the angle 0 and the greater the distance PQ travelled by the phase in a given 'time',
P'Q or At, which means the greater the phase velocity «.
The frequency of these pulsations or waves is the 'total energy of the particle' divided by Planck's constant, h. in symbols, hvtnc2-(-potential energy, where
Vl-/32 c
The problem before us is to connect structurally, the waves with two ob. servations, one of the radiations, the other of what we call the 'material particles'.
Our interest at present lies only in the connection with the latter. According to this theory, the 'region occupied by the particle' is only a region