We derive stringent constraints on neutrino speed, weak equivalence principle violation, Lorentz invariance violation, and dual lensing from the first high-energy astrophysical neutrino source: TXS $0506+056$. Observation of neutrino (IceCube-170922A) and photons in a similar time frame and from the same direction is used to derive these limits. We describe ways in which these constraints can be further improved by orders of magnitude.

• Received 18 July 2018
• Revised 10 April 2019

DOI:https://doi.org/10.1103/PhysRevD.100.103002