Metallic cylinder tracks parallel with commercial jet near restricted MOAsI am a pilot and have been flying for over 30 years, so I am familiar with all types of aircraft and weather conditions. While on commercial flights I typically follow the flight progress by looking for airports below and trying to figure out our position. My wife and I were flying out of San Diego on a commercial flight on 16 April that departed about 3 pm local time. We were seated a few rows in front of the wing of the MD-80. About fifteen minutes out of San Diego we passed over three very remote airports at an altitude I would estimate as between 12,000 and 15,000 AGL. The area is desert mountains and is very rugged. The last airport I saw was marked "US NAVY" on the approach end of the northwest-facing runway (about 320 degrees). From referring back to aviation sectional maps I believe we were just south of El Centro, AZ, which is located in an area of highly restricted MOAs (Military Operational areas). I have noted that the sectional maps warn that there is a tethered surveillance aerostat (blimp) north of El Centro at between 5,000 and 15,000 ft MSL. What we observed was clearly not a blimp. About a minute after we passed over the US Navy landing strip, which was situated between two small mountain ranges we both observed a large, extremely bright and shiny metallic cylindrical object below us, on the opposite side of the eastern range about 20 miles from the airfield. The cylinder was oriented north/south. Based on its relative size, I initially I assumed it was another commercial jet traveling about 2 miles to the north of our track and a few thousand feet below us, but I could see no wings or tail or markings. As our jet flew eastward we observed the ground gradually disappear beneath our wing and as the Navy landing strip disappeared we noted that the metallic cylinder was not moving away from us but was nearly keeping pace with our aircraft, although we were moving slightly faster. What was most interesting was that the cylinder was oriented perpendicular to us but traveling parallel to us. The craft did not move northward; it was flying perpendicular to how a normal aircraft would move. Realizing that this was highly unusual, I now spent some time trying to calculate the size and distance of the craft, based on my experience with visual cues at altitude. Based on the ground detail and runway appearance, I would guess that we were at 15,000 ft AGL. By comparing the observable detail on the cylinder, which consisted of two parallel lines running almost the full length of the craft as well as some slight variations of surface texture on the highly polished surface, I would guess that the craft was three to four hundred feet in length and traveling eastward at about 7,000 AGL. The craft continued to travel in an eastward direction, running parallel with our jet, until it disappeared from view beneath our wing.