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The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases. ↗
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Technically you need the extra dimensions. At first people didn't like them too much, but they've got a big benefit, which is that the ability of string theory to describe all the elementary particles and their forces along with gravity depends on using the extra dimensions. ↗
My present work concerns the problems connected with the theory of elementary particles, the theory of gravitation and cosmology and I shall be glad if I can manage to make some contribution to these important branches of science. ↗