NSCI 314LIFE IN THE COSMOS17 - INTERSTELLAR SPACE TRAVELDr. Karen KolehmainenDepartment of Physics, CSUSB http://physics.csusb.edu/~karen/THE PROBLEM WITH INTERSTELLAR SPACE TRAVELSTARS ARE VERY VERY FAR AWAY!–THE NEAREST STAR BEYOND THE SUN (ALPHA CENTAURI) IS ABOUT 4 LY AWAY, OR 100 MILLION TIMES FARTHER AWAY THAN THE MOON.A SPACESHIP CAN’T TRAVEL FASTER THAN THE SPEED OF LIGHT (c = 300,000 km/sec). IN FACT, NOTHING CAN TRAVEL FASTER THAN c. THIS IS AN ISSUE OF FUNDAMENTAL PHYSICS, NOT TECHNOLOGY!INTERSTELLAR TRAVELEXAMPLECONSIDER A STAR 5 LIGHT YEARS AWAY.(THIS IS A VERY NEARBY STAR!)AT THE SPEED OF LIGHT, IT WOULD TAKE 5 YEARS TO TRAVEL THIS DISTANCE.AT THE SPEED OF A SPACESHIP THAT WE CAN BUILD WITH CURRENT TECHNOLOGY (10 KM/SEC), IT WOULD TAKE 150,000 YEARS TO TRAVEL 5 LY.COMPARISON OF TRAVEL TIMESMETHOD SPEED (KM/S) TIME (IN YEARS) NEEDED TO TRAVEL A DISTANCE OF 1 LYCAR 0.03 10,000,000JET PLANE 0.3 1,000,000VOYAGER 12 25,000SPACECRAFTFUSION 3000 100SPACECRAFT(DOESN’T YET EXIST)PHOTONS 300,000 1INTERSTELLAR TRAVELBECAUSE DISTANCES ARE SO LARGE, LARGE SPEEDS ARE NEEDED TO KEEP THE TRIP TIME REASONABLE.WE MUST ACCELERATE TO REACH LARGE SPEEDS.ACCELERATION: A CHANGE IN SPEED (OR DIRECTION OF MOTION) OVER TIMEHOW QUICKLY CAN WE PICK UP (OR LOSE) SPEED, i.e., HOW LARGE CAN OUR ACCELERATION BE?ACCELERATIONTYPICAL CAR ACCELERATES AT 1 OR 2 m/s2(PICKS UP 1 OR 2 m/s OF SPEED PER SECOND)GRAVITY ACCELERATES A FALLING OBJECT AT ABOUT 10 m/s2 = 1 g (g = ACCELERATION DUE TO GRAVITY)A COMFORTABLE ACCELERATION FOR HUMANS IN A SPACESHIP IS 1 g = 10 m/s2(THIS WILL “FEEL” LIKE EARTH’S NORMAL GRAVITY TO TRAVELERS IN THE SHIP)EXAMPLE: ROUND TRIP TO A STAR 5 LY AWAYASSUME WE ACCELERATE AT 1 g FOR 2.5 LY (UNTIL WE’RE HALFWAY THERE), REACHING A FINAL SPEED OF 90% c.NOW WE MUST DECELERATE AT 1 g FOR 2.5 LY SO THAT WE CAN STOP AT OUR DESTINATION.THEN REPEAT THE ENTIRE PROCESS ON THE WAY BACK.ELAPSED TIME (EARTH CLOCK) = 20 YRS.ELAPSED TIME (SHIP CLOCK) = 8 YRS.WHAT HAPPENED??INTERSTELLAR TRAVELRELATIVITYRELATIVITY DOES NOT MEAN THAT “EVERYTHING IS RELATIVE.”IMAGINE TWO OBSERVERS (PEOPLE), LET'S CALL THEM A AND B, WHO ARE MOVING RELATIVE TO EACH OTHER. (FOR EXAMPLE, A IS ON EARTH, AND B IS ON A SPACESHIP PASSING BY.) BOTH A AND B MEASURE A CERTAIN PHYSICAL QUANTITY (e.g., LENGTH OF AN OBJECT, TIME INTERVAL BETWEEN TWO EVENTS, VELOCITY OF A MOVING OBJECT, ETC.). HOW ARE THE VALUES THAT OBSERVERS A AND B MEASURE RELATED TO EACH OTHER? (ARE THEY NUMERICALLY EQUAL, RELATED BY A CERTAIN MATHEMATICAL EQUATION, ETC.?)RELATIVITYTHE ANSWER DEPENDS ON:1. WHICH PHYSICAL QUANTITY IT IS:(a) OBSERVERS A AND B WILL MEASURE THE SAME NUMERICAL VALUE (300,000 KM/SEC) FOR THE SPEED OF LIGHT IN A VACUUM.(b) OBSERVERS A AND B WILL MEASURE DIFFERENT ANSWERS FOR THE LENGTH OF AN OBJECT, THE TIME INTERVAL BETWEEN TWO EVENTS, OR THE SPEED OF A MOVING OBJECT (OTHER THAN A PHOTON).2. HOW A AND B ARE MOVING RELATIVE TO EACH OTHER: (a) IF A IS MOVING AT A CONSTANT VELOCITY RELATIVE TO B (OR VICE VERSA), THEN THE RULES RELATING WHAT A MEASURES AND WHAT B MEASURES ARE GIVEN BY SPECIAL RELATIVITY.(b) IF ONE OBSERVER IS ACCELERATING (CHANGING VELOCITY) RELATIVE TO THE OTHER, THEN THE RULES RELATING WHAT A MEASURES AND WHAT B MEASURES ARE GIVEN BY GENERAL RELATIVITY.RELATIVITYCONSIDER THE CASE OF MEASURING TIME .OBSERVERS A (ON EARTH) AND B (ON SPACESHIP) BOTH MEASURE THE INTERVAL OF TIME BETWEEN TWO CERTAIN EVENTS .EXAMPLES OF TIME INTERVAL BETWEEN TWO EVENTS:- TIME BETWEEN PERSON B’S DEPARTURE FROM EARTH AND PERSON B’S ARRIVAL AT A DISTANT STAR- TIME BETWEEN TWO “TICKS” OF A CLOCK LOCATED ON THE SPACESHIP (B’S CLOCK)- TIME BETWEEN TWO “TICKS” OF A CLOCK LOCATED ON THE EARTH (A’S CLOCK)SPECIAL RELATIVITY TIME DILATION: CONSIDER TWO OBSERVERS MOVING AT A CONSTANT VELOCITY RELATIVE TO EACH OTHER. THE TWO OBSERVERS WILL MEASURE DIFFERENT ANSWERS FOR THE INTERVAL OF TIME BETWEEN TWO EVENTS, i.e., TIME PASSES AT DIFFERENT RATES ON CLOCKS MOVING AT DIFFERENT SPEEDS.EXAMPLE: A SPACESHIP FLIES BY THE EARTH AT A CONSTANT VELOCITY CLOSE TO THE SPEED OF LIGHT. THERE ARE CLOCKS ON EARTH AND ON BOARD THE SHIP. BOTH THE PERSON ON THE SHIP (B) AND THE PERSON ON EARTH (A) CAN WATCH EACH OTHER’S CLOCKS (e.g., THROUGH TELESCOPES). WHAT DO THEY FIND?SPECIAL RELATIVITYTIME DILATION:EACH OBSERVER SEES THE OTHER OBSERVER’S CLOCK AS RUNNING SLOW COMPARED TO HIS/HER OWN, e.g., THE OTHER PERSON’S CLOCK MOVES FORWARD ONLY 3 MINUTES WHILE YOUR OWN MOVES FORWARD 5 MINUTES. OBSERVER A SEES HIS OWN CLOCK AS “NORMAL” AND OBSERVER B’S CLOCK AS “SLOW.” OBSERVER B SEES HER OWN CLOCK AS “NORMAL” AND OBSERVER A’S CLOCK AS “SLOW.” EACH OF THEM SEES HIS/HER OWN CLOCK AS NORMAL AND THE OTHER PERSON’S CLOCK AS RUNNING SLOW, i.e., THEY DON’T AGREE ON WHICH CLOCK IS FAST AND WHICH CLOCK IS SLOW!SPECIAL RELATIVITY – TIME DILATIONWHICH OF THE OBSERVERS IS “CORRECT?” BOTH!TIME IS NOT AN “ABSOLUTE” UPON WHICH ALL OBSERVERS CAN AGREE!THIS IS A REAL EFFECT. - IT IS NOT SOME SORT OF OPTICAL ILLUSION! - IT CAN’T BE EXPLAINED BY THE FACT THAT THE LIGHT FROM A CLOCK TAKES A CERTAIN AMOUNT OF TIME TO REACH A DISTANT OBSERVER!SPECIAL RELATIVITY – TIME DILATIONTIME DILATION WORKS FOR ALL “CLOCKS” - MECHANICAL, ELECTRONIC, ATOMIC, BIOLOGICAL, ETC.THIS MEANS THAT PERSON A (ON THE EARTH) SEES ALL OF PERSON B’S BIOLOGICAL PROCESSES (INCLUDING AGING) OCCURRING IN “SLOW MOTION”. SIMILARLY, PERSON B SEES PERSON A’S BIOLOGICAL PROCESSES OCCURRING IN SLOW MOTION.SPECIAL RELATIVITY – TIME DILATIONTHE FASTER THE RELATIVE SPEED OF THE SHIP AND THE EARTH, THE BIGGER THE DIFFERENCE IN THE TIME INTERVALS MEASURED BY THE TWO OBSERVERS. THE EFECT ISN’T DRAMATIC UNLESS THE RELATIVE SPEED IS NEAR THE SPEED OF LIGHT.INTERSTELLAR TRAVELBUT SPECIAL RELATIVITY (AND THEREFORE TIME DILATION) ONLY ADDRESSES THE CASE WHERE THE SPACESHIP MOVES RELATIVE TO EARTH AT A CONSTANT VELOCITY.IN ORDER TO COMPLETE A VOYAGE TO A DISTANT STAR, THE SHIP MUST ACCELERATE AND DECELERATE ALONG ITS WAY (ACCELERATION UPON TAKE-OFF FROM EARTH, CHANGING DIRECTION AND PERHAPS SPEED WHILE TURNING AROUND, AND DECELERATION UPON RETURN TO EARTH)THEREFORE WE NEED GENERAL RELATIVITY!THE TWIN PARADOXJANE AND JOE ARE TWINS.JANE TAKES OFF ON A ROUND TRIP INTERSTELLAR SPACE VOYAGE AT HIGH SPEED.JOE REMAINS ON EARTH.WHEN JANE RETURNS TO EARTH, WHICH TWIN IS OLDER?–TIME DILATION  EACH WOULD SAY