Lecture Notes on Scattering and Memory Effect

Overview

• The lecture discusses scattering events and memory effects in the context of gravitational waves.
• Focus on the relationship between incoming and outgoing measurements and the physical implications.

Key Concepts

Memory Effect

• The memory effect is defined as the difference between measurements at different times (e.g., at time u=0 and u=10).
• Measurements are taken at future null infinity (scry+) to analyze the effect of incoming data.
• Important to consider assumptions about initial data from scry-.

Setup of the Problem

• Observations made by far away observers in a static frame where galaxies have relatively slow motion.
• Observers boost to a highly accelerated frame, measure gravitational waves, and return to compare results.
• Defined a suitable coordinate system near scry+ for analysis.

Coordinate System

• Introduced affine coordinates along null generators of scry+ and defined further coordinates for the neighborhood.
• The metric in this system resembles familiar forms used in gravitational waves analysis.

Asymptotic Flatness

• Definition of asymptotic flatness presented, highlighting guiding principles for falloff conditions.
• Conditions necessary for finite charges and the validity of equations of motion at leading order discussed.

Observations and Measurements

• BMS (Bondi-Metzner-Sachs) observers' methodologies to measure gravitational waves and memory effects outlined.
• BMS observers operate under fixed trajectories with respect to the cosmic background.
• Measurements involve distances between mirrors and synchronization of clocks to determine changes induced by gravitational waves.

Soft Theorems and Memory Effects

• The relationship between soft theorems and memory effects is emphasized.
• Clarification that gravitational wave memories are measurable and existentially linked to energy and momentum.
• The impact of gravitational waves on clocks and distances in various observational setups is crucial for understanding the memory effect.

Conclusions

• The discussion concludes with the implications of the findings for current and future gravitational wave observations, including LIGO.
• Recognition of the delicate interplay between classical and quantum mechanical frameworks in understanding gravitational phenomena.

Future Directions

• Further exploration of super translations and their relation to memory effects.
• Investigation into the implications of found results for experimental observables in gravitational wave astronomy.