CAPT OF AN MLG INSTRUCTED THE FLYING FO TO DO TURNS OVER THE GRAND CANYON NATIONAL PARK DURING DSCNT RESULTING IN ATC INTERVENTION.

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WHILE ON VECTORS FROM ZLA FOR THE CROWE 6 ARR TO LAS VEGAS; WE PASSED OVER THE GRAND CANYON. THE ZLA HAD CLRED US TO DSND TO FL220. PASSING 25000 FT; THE CAPT SUGGESTED THAT I PUT THE ACFT INTO A TURN TO GIVE THE PAX A BETTER VIEW. THINKING HE WAS CLRING OUR MANEUVER WITH ATC; I BECAME INTENT ON GIVING OUR PAX THE BEST VIEW. AFTER ABOUT A 30 DEG TURN AND AS I WAS BEGINNING A TURN IN THE OPPOSITE DIRECTION; THE LAX CTLR SUDDENLY ASKED WHERE WE WERE GOING AND TO IMMEDIATELY LEVEL AT FL240 AS HE HAD AREA TFC AT FL230. WE COMPLIED AND THE CAPT APOLOGIZED PROFUSELY FOR NOT ASKING PERMISSION FIRST. THAT WE DID NOT CLR OUR DEV FIRST IS INEXCUSABLE AND I WILL MAKE CERTAIN THAT ANY FUTURE EXCURSIONS ARE CLRED BY A CTLR BEFORE I DO IT OR ALLOW IT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT HE REALIZED THAT THEY DID NOT HAVE THE TURNS COORDINATED WITH THE CTR (ATC) WHEN THE CTLR ASKED THEM WHERE THEY WERE GOING AND TO STOP THEIR DSCNT AT ONCE. HE SAID THAT THE CAPT CALLED THE CTR BY TELEPHONE AFTER LNDG TO APOLOGIZE FOR THEIR ACTIONS. THE CTR SUPVR ADVISED THAT IF THEY HAD CONTINUED IT WOULD HAVE CAUSED LESS THAN THEIR STANDARD SEPARATION. AS IT WAS THEY WERE STOPPED SOON ENOUGH AND A CONFLICT WAS AVOIDED. THE RPTR HAS APPROX 5000 HRS IN B737 TYPE ACFT AND THE ACFT FLOWN DURING THIS INCIDENT WAS A B737-400.