Clearly "based upon the field concept, that is on continuous structures" is a euphemism - theoretical physics, being a deductive science, is actually based on well-known assumptions, some possibly related to "the field concept" and "continuous structures". So if physics is going to crumble, as Einstein suggests, one of those assumptions must be false. But which one? Is there an assumption in modern physics which, on the one hand, is closely related to "the field concept" and "continuous structures", and, on the other, is so important and indispensable as to destroy a whole branch of science after its falsehood has been exposed? The only such assumption is Einstein's 1905 light postulate:
http://arxiv.org/ftp/physics/papers/0101/0101109.pdf "The two first articles (January and March) establish clearly a discontinuous structure of matter and light. The standard look of Einstein's SR is, on the contrary, essentially based on the continuous conception of the field."
http://www.pbs.org/wgbh/nova/einstein/genius/ "And then, in June, Einstein completes special relativity, which adds a twist to the story: Einstein's March paper treated light as particles, but special relativity sees light as a continuous field of waves."
http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768 Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."
http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305457v3.pdf Joao Magueijo: "In sharp contrast, the constancy of the speed of light has remain sacred, and the term "heresy" is occasionally used in relation to "varying speed of light theories". The reason is clear: the constancy of c, unlike the constancy of G or e, is the pillar of special relativity and thus of modern physics. Varying c theories are expected to cause much more structural damage to physics formalism than other varying constant theories."
http://bourabai.narod.ru/wallace/farce05.htm Bryan Wallace: "Einstein's special relativity theory with his second postulate that the speed of light in space is constant is the linchpin that holds the whole range of modern physics theories together. Shatter this postulate, and modern physics becomes an elaborate farce! (...) The speed of light is c+v."