The view that Heisenberg advocates—reductionism had reached a limit, and a new paradigm was needed—was a highly influential school of thought in the 1960s. In particle physics, there is a mathematical object called the S-matrix (scattering matrix), which tabulates scattering amplitudes (the quasiprobability that if these N particles enter a collision, these other M particles will be what comes out). Quantum electrodynamics (a theory with electrons and photons, let’s say) is a prototypical quantum field theory in which the S-matrix can be calculated from the stipulation that electrons and photons are fundamental. For the weak interactions (later unified with electromagnetism), this reductionist method also works.
But for the strong interactions, field theory looked intractable, and a new philosophy was advanced that the S-matrix itself should be the central mathematical object in the theory. Remember that quarks were never seen by themselves, only protons, neutrons, and a hundred other types of “hadron”. The idea of nuclear democracy was that the S-matrix for these hundred seemingly equi-fundamental particle species, would be derived from postulates about the properties of the S-matrix, rather than from an underlying field theory. This was called the bootstrap program, it is how the basic formulae of string theory were discovered (before they had even been identified as arising from strings), and it’s still used to study the S-matrix of computationally intractable theories.
These days, the philosophy that the S-matrix is primary, still has some credibility in quantum gravity. Here the problem is not that we can’t identify ultimate constituents, but rather that the very idea of points of space-time seems problematic, because of quantum fluctuations in the metric. The counterpart of the 1960s skepticism about quarks, would be that the holographic boundary of space-time is fundamental. For example, in the AdS/CFT correspondence, scattering events in Anti de Sitter space (in which particles approach each other “from the boundary”, interact, and then head back to the boundary) can be calculated entirely within the boundary CFT, without any reference to AdS space at all, which is regarded as emergent from the boundary space. The research program of celestial holography is an attempt to develop the same perspective within the physically relevant case of flat space-time. The whole universe that we see, would be a hologram built nonlocally from entanglement within a lower-dimensional space…
The eventual validation of quarks as particles might seem like a sign that this radical version of the holographic philosophy will also be wrong in the end, and perhaps it will be. But it really shows the extent to which the late thoughts of Heisenberg are still relevant. Holographic boundaries are the new S-matrix, they are a construct which has made quantum gravity uniquely tractable, and it’s reasonable to ask if they should be treated as fundamental, just as it was indeed entirely reasonable for Heisenberg and the other S-matrix theorists to ask whether the S-matrix itself is the final word.
I see, thanks again for the context! The book doesn’t mention S-matrices (at least not by name), and it wasn’t clear to me from reading it whether Heisenberg was particularly active scientifically by the 60′s/70′s or whether he was just some old guy ranting in the corner. I guess that’s the risk of reading primary sources without the proper context.
The view that Heisenberg advocates—reductionism had reached a limit, and a new paradigm was needed—was a highly influential school of thought in the 1960s. In particle physics, there is a mathematical object called the S-matrix (scattering matrix), which tabulates scattering amplitudes (the quasiprobability that if these N particles enter a collision, these other M particles will be what comes out). Quantum electrodynamics (a theory with electrons and photons, let’s say) is a prototypical quantum field theory in which the S-matrix can be calculated from the stipulation that electrons and photons are fundamental. For the weak interactions (later unified with electromagnetism), this reductionist method also works.
But for the strong interactions, field theory looked intractable, and a new philosophy was advanced that the S-matrix itself should be the central mathematical object in the theory. Remember that quarks were never seen by themselves, only protons, neutrons, and a hundred other types of “hadron”. The idea of nuclear democracy was that the S-matrix for these hundred seemingly equi-fundamental particle species, would be derived from postulates about the properties of the S-matrix, rather than from an underlying field theory. This was called the bootstrap program, it is how the basic formulae of string theory were discovered (before they had even been identified as arising from strings), and it’s still used to study the S-matrix of computationally intractable theories.
These days, the philosophy that the S-matrix is primary, still has some credibility in quantum gravity. Here the problem is not that we can’t identify ultimate constituents, but rather that the very idea of points of space-time seems problematic, because of quantum fluctuations in the metric. The counterpart of the 1960s skepticism about quarks, would be that the holographic boundary of space-time is fundamental. For example, in the AdS/CFT correspondence, scattering events in Anti de Sitter space (in which particles approach each other “from the boundary”, interact, and then head back to the boundary) can be calculated entirely within the boundary CFT, without any reference to AdS space at all, which is regarded as emergent from the boundary space. The research program of celestial holography is an attempt to develop the same perspective within the physically relevant case of flat space-time. The whole universe that we see, would be a hologram built nonlocally from entanglement within a lower-dimensional space…
The eventual validation of quarks as particles might seem like a sign that this radical version of the holographic philosophy will also be wrong in the end, and perhaps it will be. But it really shows the extent to which the late thoughts of Heisenberg are still relevant. Holographic boundaries are the new S-matrix, they are a construct which has made quantum gravity uniquely tractable, and it’s reasonable to ask if they should be treated as fundamental, just as it was indeed entirely reasonable for Heisenberg and the other S-matrix theorists to ask whether the S-matrix itself is the final word.
I see, thanks again for the context! The book doesn’t mention S-matrices (at least not by name), and it wasn’t clear to me from reading it whether Heisenberg was particularly active scientifically by the 60′s/70′s or whether he was just some old guy ranting in the corner. I guess that’s the risk of reading primary sources without the proper context.