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 group $$G_{c}$$ in the limit for $$c = \infty$$, i.e. as group $$G_{\infty}$$, exactly becomes the full group belonging to ian Mechanics. In this state of affairs, and since $$G_{c}$$ is mathematically more intelligible than $$G_{\infty}$$, a mathematician may, by a free play of imagination, hit upon the thought that natural phenomena actually possess an invariance, not for the group $$G_{\infty}$$, but rather for a group $$G_{c}$$, where c is definitely finite, and only exceedingly large using the ordinary measuring units. Such a preconception would have been an extraordinary triumph for pure mathematics. Now, although mathematics only shows irony at this place, still the satisfaction remains for it, that thanks to its fortunate antecedents by its senses sharpened in free remote-view, it is instantly able to grasp the deep consequences of such a modification of our view of nature.

At the same time I shall remark about which value of c we eventually will arrive. For c, we shall substitute the propagation velocity of light in free space. In order to avoid speaking either of space or of vacuum, we again may take this quantity as the ratio between the electrostatic and electromagnetic units of the quantity of electricity.

We could form an idea of the invariant character of natural laws for the corresponding group $$G_{c}$$ in the following manner:

Out of the totality of natural phenomena, we can, by successive higher approximations, deduce with increased precision a coordinate system x, y, z, and t, space and time, by means of which we can represent the phenomena according to definite laws. This system of reference, however, is by no means uniquely determined by the phenomena. ''We can change the system of reference in any possible manner corresponding to the transformation of the above mentioned group $$G_{c}$$, but the expressions for natural laws will not be changed thereby. ''

For example, corresponding to the figure described above, we also can denote $$t'$$ as time, but in connection with this, we must necessarily define the space by the manifoldness of the three parameters x' y z. The physical laws are now expressed by means of x', y, z, t', — and the expressions are exactly the same as in the case of x, y, z, t. According to this, we shall have, not one space, but an infinite number of spaces in the world, — analogous to the case that the three-dimensional space consists of an infinite number of planes. The three-dimensional geometry becomes a chapter of four-dimensional physics. Now you perceive, why I said in the beginning that time and space shall reduce to mere shadows and we shall have only one world itself.