- #1

kith

Science Advisor

- 1,332

- 442

## Main Question or Discussion Point

I just stumbled upon the well-written 1972 paper "Missed Opportunities" by Freeman Dyson. It can be found here.

Dyson argues that over time, people have become worse in following the mathematical hints inherent in the structure of physical theories. As an example, he compares the developments in both mathematics and physics following Newtonian physics with the "failure" to discover special relativity based purely on the transformation properties of the Maxwell equations and other things. Both hindsight bias as well as selection bias might be involved here but I think it is an interesting thesis.

He goes on to identify three things he considers missed opportunities as of 1972 and thus proposes:

1) ... to create a mathematical structure preserving the main features of the Haag-Kastler axioms but possessing E-invariance instead of P-invariance.

2) ... to construct a conceptual scheme which will legalize the use of Feynman sums [...] with suitable Iagrangians which are not quadratic.

3) ... to try to achieve a rigorous definition of Feynman sums which are invariant under general coordinate transformation.

(Check the paper for details.)

Now I'm not very familiar with QFT and much less BtSM physics. Has there been considerable progress or effort in these directions? How do renormalization and contemporary QG efforts like String theory and LQG tie in with what he writes?

Dyson argues that over time, people have become worse in following the mathematical hints inherent in the structure of physical theories. As an example, he compares the developments in both mathematics and physics following Newtonian physics with the "failure" to discover special relativity based purely on the transformation properties of the Maxwell equations and other things. Both hindsight bias as well as selection bias might be involved here but I think it is an interesting thesis.

He goes on to identify three things he considers missed opportunities as of 1972 and thus proposes:

1) ... to create a mathematical structure preserving the main features of the Haag-Kastler axioms but possessing E-invariance instead of P-invariance.

2) ... to construct a conceptual scheme which will legalize the use of Feynman sums [...] with suitable Iagrangians which are not quadratic.

3) ... to try to achieve a rigorous definition of Feynman sums which are invariant under general coordinate transformation.

(Check the paper for details.)

Now I'm not very familiar with QFT and much less BtSM physics. Has there been considerable progress or effort in these directions? How do renormalization and contemporary QG efforts like String theory and LQG tie in with what he writes?