He received his PhD from Columbia University in 1957; his advisor was J. Rainwater. He joined Brookhaven National Laboratory and worked on proton-proton elastic scattering studies at the recently completed AGS. Baker moved to CERN in 1964 before returning to the U.S. and joining the newly opened National Accelerator Laboratory (later Fermilab) in 1969; he remained at Fermilab until his retirement in 2007.
Baker worked on several Fermilab experiments using beams produced by the Main Ring and later the Tevatron; many of these were studies of hadron-hadron elastic scattering and total cross sections; on some of these he was the spokesperson or deputy spokesperson for the experiment.
A private service will be held at a later date.