INFINITY CHILLS ME -
I MEAN THAT LITERALLY.
MY BODY WEAKENS MY BALANCE
WAIVERS WHEN I TRY TO ENVISION A
COSMOS OF INFINITE SIZE.
I TRY TO PROJECT MY MIND'S EYE
TO SEE STARS AND SPACES GOING ON
AND ON AND ON AND ON.
THE UNIVERSE OR MULTIPLE
UNIVERSES VERY SIMILAR OR VERY
DIFFERENT ON AND
ON AND ON AND ON.
I CAN CONCEIVE OF A
COSMOS WHOSE SIZE IS INFINITE.
I CAN EXPLAIN IT BUT
I CANNOT FATHOM IT.
YET I WONDER WHAT AN
INFINITE COSMOS WOULD MEAN.
WHAT DO I MEAN BY MEAN?
I'M ROBERT LAWRENCE KUHN
AND IF CLOSER TO TRUTH IS MY
DESIRE TO DISCERN AN
INFINITE COSMOS I AM
ALREADY GETTING DIZZY.
WHAT WOULD AN
INFINITE COSMOS MEAN?
CLUES OF ORIGINS AND
ENDS NATURE OF EXISTENCE,
PLACE OF HUMAN BEINGS TO
ASK IS TO PROBE THE SPECIAL
NATURE OF INFINITY.
IMAGINE THE LARGEST
NUMBER YOU CAN.
INFINITY IS LARGER STILL;
INFINITELY LARGER.
INFINITY IS NOT A NUMBER
IT'S MORE A PROCESS
INFINITY NEVER ENDS.
CONTEMPLATING AN INFINITE
COSMOS IS SO DISORIENTING.
THAT'S WHY I BEGAN WITH A
COSMOLOGICAL VISIONARY OF
IMPECCABLE GOOD SENSE.
AN EXPERT ON GALAXY FORMATION
BLACK HOLES AND MULTIPLE
UNIVERSES THE UK ASTRONOMER
ROYAL, MARTIN REES.
WHAT WOULD AN INFINITE
UNIVERSE OR INFINITE
MULTIVERSE REALLY MEAN?
WELL THERE NOTHING NEW AT
ALL ABOUT THE CONCEPT
OF INFINITE SPACE.
IT WAS SPECULATED ABOUT IN
THE 18TH CENTURY AND EVEN BY THE
GREEKS BUT WHAT IS NEW IS THE
REALIZATION THAT'S A THIS MAY
NOT JUST BE A DREARY ON AND ON
IT MIGHT INDEED BE AN INFINITE
SPACE WITH A
COMPLICATED STRUCTURE.
THE PROBLEM WITH INFINITE OF
COURSE IS THAT UM UH IT DOESN'T
OBEY THE NORMAL
RULES OF ARITHMETIC.
AND SO IT RAISES PROBLEMS
WITH ISSUES LIKE PROBABILITY.
AND WHEN WE COME TO THE
QUESTION OF ASKING ARE WE IN A
TYPICAL OR PROBABLE, PART
OF THIS INFINITE UNIVERSE.
THAT'S A RATHER DIFFICULT
QUESTION BECAUSE THE WAY YOU PUT
A MEASURE IN A TACTICAL SENSE ON
THE UNIVERSE IS SOMETHING WHICH
IS RATHER ARBITRARY AND
DIFFICULT WHEN IT'S INFINITE.
IF YOU ASSUME THAT THE UNIVERSE
GOES ON INFINITELY ONE WAY OR
ANOTHER THEN YOU WILL ASSUME
THAT EVERY STATE OF AFFAIRS
OCCURS AND YOU HAVE TO
ASSUME EVERY STATE OF
AFFAIRS OCCURS INFINITELY.
AND SO PEOPLE TALK ABOUT THERE
ARE OTHER MARTINE REES'S
AND ROBERT KUHN'S
SITTING HERE TALKING TO
EACH OTHER AN
INFINITE NUMBER OF
TIMES AS YOU GO OUT
FURTHER AND FURTHER.
IT SEEMS TO ME AT
TIMES A BIT SILLY.
WELL, I THINK THAT'S AN OBVIOUS
CONSEQUENCE IF YOU ASSUME THAT
ALL COGNITIVE OPTIONS ARE
FULFILLED AND IF YOU GO THROUGH
INFINITY AND HAVE ENOUGH SPACE
TO REALIZE ALL THE OPTIONS OF
COURSE ANY SUCH COMBINATION IS
GOING TO BE FAR, FAR, FAR BEYOND
OUR HORIZON AND SO CARRYING THAT
CONCEPT FURTHER YOU HAVE TO HAVE
REALLY, REALLY VAST UNIVERSE
BEFORE YOU CAN HAVE A OBJECTS
LIKE OURSELVES BEING DUPLICATED.
BUT, I DON'T SEE WHY YOU WANT
YOU TO BE DISTURBED BY THIS I
THINK IT'S A NATURAL CONSEQUENCE
OF AN INFINITE UNIVERSE.
BUT IT HAS REALLY NO
RELATIONSHIP TO US IT'S JUST A
RANDOM EXPRESSION OF EVERYTHING,
SO THAT EVERYTHING THAT CAN
EXIST WILL EXIST.
AND SO, IF THERE IS SOMETHING
LIKE YOU VERY FAR FROM HERE IT'S
NOT YOU IT DOESN'T
REALLY MEAN ANYTHING.
THAT'S RIGHT AND THERE WILL BE
COMBINATIONS OF US AND IN THE
NEXT TEN SECONDS THEY WILL
ALL DIVERGE; SOME MAY STAND
UP SOME MAY SIT
DOWN, AND THEY WILL
DO DIFFERENT THINGS.
SO, ALL OPTIONS ARE CARRIED OUT
SOMEWHERE IN THE FUTURE AS WELL
AS IN THE PAST.
DO YOU HAVE AN INTUITION
WHETHER OUR UNIVERSE THAT CAME
FROM OUR BIG BANG IS OR
WILL BE INFINITE OR FINITE?
AND WHETHER A MULTIVERSE
WHICH LIKELY EXISTS IS
INFINITE OR FINITE.
WELL I THINK THIS IS NOT A
MATTER FOR INTUITION IT'S A
SCIENTIFIC QUESTION TO WHICH WE
CAN SEEK THE ANSWER ALTHOUGH WE
MAY NOT FIND IT.
I THINK I TRY AND AVOID HAVING
THE INTUITION BUT THE ONLY
RATIONAL RESPONSE IS TO SAY WE
JUST DON'T KNOW ENOUGH TO SAY
WHETHER IT'S LIKELY OR UNLIKELY.
AND WHATEVER OUR PREFERENCES
ARE WE SHOULD ACCEPT IF WE JUST
DON'T KNOW BUT WILL
EVENTUALLY COME WITHIN
THE SCOPE OF SCIENCE.
SO, I THINK THAT WE SHOULD BE
OPENED MINDED AND REMEMBER THAT
OUR PREFERENCES
COUNT FOR NOTHING.
WE'VE ACCEPTED THE
UNIVERSE AS IT IS.
GOT IT, MARTIN - 
I ACCEPT THAT WE DON'T
KNOW WHETHER OUR
UNIVERSE IS INFINITE OR FINITE.
OR EVEN WHETHER THERE IS
VARIETY AND STRANGE STRUCTURE,
NOT JUST UNENDING UNIFORMITY.
AND I APPRECIATE THAT
REALITY NEED NOT CONFORM TO OUR
INTUITIONS OR PREFERENCES
THAT ONLY SCIENCE
CAN PROVIDE ANSWERS.
YET, I AM IMPATIENT,
I'D LIKE TO KNOW NOW,
HOW TO DEEP DIVE INTO THE
INFINITE OCEAN OF SPACE AND TIME
MATTER AND ENERGY.
SCIENTIST FRIENDS INVITE ME TO
JOIN THE FOUNDATION QUESTIONS
INSTITUTE - FQXI - WHICH
LOOKS BEYOND TODAY'S
PHYSICS AND COSMOLOGY.
SO, WHEN I LEARN OF THEIR
CONFERENCE ON THE NATURE OF
TIME, ON BOARD A SHIP CRUISING
FROM NORWAY TO DENMARK I JUMP AT
THE CHANCE TO INQUIRE
ABOUT AN INFINITE UNIVERSE.
I START WITH THE FQXI
ASSOCIATES SCIENTIFIC DIRECTOR,
ANTHONY AGUIRRE.
WHEN WE ASK WHETHER THE
UNIVERSE IS INFINITE OR FINITE,
WE HAVE TO BE REALLY CAREFUL
ABOUT THE QUESTION WE ARE ASKING
BECAUSE WHAT EINSTEIN HAS TAUGHT
US IS THAT WHAT WE SHOULD REALLY
THINK ABOUT IS SPACE -TIME,
SPACE AND TIME ARE ONE THING AND
WE CAN DIVIDE THEM
UP IN DIFFERENT WAYS.
NOW WHAT IT TURNS OUT TO HAPPEN
IS THAT IF YOU DIVIDE SPACE AND
TIME UP IN ONE WAY IT COULD BE
THAT SPACE IS INFINITE BUT IF
YOU DIVIDE THE VERY SAME
SPACE-TIME UP IN A DIFFERENT
WAY ITS FINITE.
THAT SOUNDS REALLY INCREDIBLE.
IT IS, AND IT LEADS TO ONE OF
THE MOST AMAZING THINGS WHICH IS
THAT YOU CAN TAKE SOME REGION
SAY HERE IT IS I'M GOING TO
CREATE SOMETHING HERE AND THIS
IS GOING TO TURN INTO A UNIVERSE
THAT IS INFINITE IN SPACE
THAT HAS INFINITE VOLUME
AT EACH TIME.
NOW THAT SEEMS JUST TOTALLY
LUDACRIS RIGHT BUT IT'S GOT
FINITE VOLUME HOW'S IT GOING
TO TURN INTO SOMETHING WITH
INFINITE VOLUME, BUT THE
DECOMPOSING SPACE-TIME INTO
SPACE AND TIME IS THE KEY.
SO THE WAY IT WORKS IN SOME
SENSE IS THAT SUPPOSE I TAKE
SOME NUGGET OF STUFF AND IT
STARTS GROWING AND I LET IT GROW
FOR AN INFINITE
AMOUNT OF TIME OKAY.
THEN YOU'LL AGREE THAT THIS
THING HAS GROWN INTO SOMETHING
WITH INFINITE
SPACE-TIME, VOLUME.
WELL IT GOES ON FOREVER BUT IF
IT STARTS FINITE IT IS ALWAYS
SOME NUMBER, WHATEVER NUMBER YOU
WANT IT'LL EVENTUALLY GET THERE
AND EXCEED IT BUT AT ANY GIVEN
TIME IT IS STILL FINITE THAT'S
WHAT YOU MIGHT THINK BUT IF YOU
THINK ABOUT IT THIS WAY SO IF I
TAKE THIS THING THEN A MOMENT
LATER MAYBE IT'S THIS BIG AND A
MOMENT LATER IT'S THIS BIG, SO
AT EACH TIME IT HAS A FINITE
SIZE JUST AS YOU SAID.
BUT THAT'S ACCORDING TO WHEN I
SAY THIS MOMENT A MOMENT LATER
A MOMENT LATER.
THAT'S A DEFINITION OF WHAT A
MOMENT IS AND WHAT IS EXISTING
AT ONE TIME.
NOW I CAN TAKE THAT SAME THING
AND SLICE AND DICE IT INTO SPACE
AND TIME IN A SLIGHTLY DIFFERENT
WAY SUCH THAT WHEN YOU LOOK AT
THAT AT EVERY MOMENT IT LOOKS
LIKE IT IS SPATIALLY INFINITE.
THE REGION YOU ARE ALLOWED
TO LOOK AT IS ONLY THE REGION
INSIDE THIS BLOB.
YEAH YEAH YEAH.
SO YOU CAN FIND YOURSELF INSIDE
THE BLOB BUT YOU CUT IT UP IN
SUCH A WAY THAT INSIDE
THAT BLOB IT LOOKS LIKE
AN INFINITE UNIVERSE.
AND THAT CUT IS AS LEGITIMATE
AS THE INTUITIVE ONE THAT
WE COME TO.
EVEN MORE SO ONCE YOU GO INSIDE
THE BLOB WHEN YOU CUT IT THAT
WAY THAT I DESCRIBED IT
ACTUALLY LOOKS UNIFORM,
IT LOOKS HOMOGENOUS IN FACT
JUST LIKE THE BIG BANG COSMOLOGY
WHICH IS HOMOGENOUS THAT IS
UNIFORMED AND IS THE SAME
IN EVERY DIRECTION.
AND THIS IS JUST
OUR LOCAL UNIVERSE.
THAT'S RIGHT, SO OUTSIDE
THIS BLOB THERE COULD
BE OTHER STUFF.
RIGHT, AND SO, OUR UNIVERSE THAT
WE ARE IN CAN BE INFINITE CUT
THIS WAY AND YET THERE STILL
CAN BE INFINITE NUMBERS OF OTHER
UNIVERSES WITHIN WHICH
EACH ONE WOULD BE INFINITE.
EXACTLY.
IS THAT RIGHT?
THAT'S RIGHT.
WELL, I SOUNDED LIKE I KNEW
WHAT I WAS TALKING ABOUT,
BUT I CERTAINLY DON'T.
BUT ITS TRUE, WHAT IT LOOKS IF
YOU'RE IN ONE OF THESE UNIVERSES
AND YOU SAY HOW DO I GET OUT?
HOW DO I SEE OTHER STUFF?
IT GENERALLY LOOKS LIKE YOU
HAD TO TRAVEL BACK IN TIME.
BECAUSE IN SOME SENSE TO GO
OUT OF THE BLOB THAT YOU ARE IN.
YOU HAVE TO GO THROUGH EARLIER
AND EARLIER OR TRAVEL FASTER
THAN LIGHT IS ANOTHER
WAY TO THINK ABOUT IT.
WELL, BECAUSE IF YOU HAVE MORE
THAN ONE UNIVERSE EACH OF WHICH
IS INFINITE IN SPACE IT WOULD
SEEM LIKE THEY HAD TO OVERLAP.
THEY DON'T HAVE TO OVERLAP BUT
THAT IS PERMISSIBLE BECAUSE IT
CAN BE THE CASE IF THEY
START FAR ENOUGH APART,
THEY'RE IN THE EXTERNAL
DESCRIPTION IN WHICH THEY LOOK
FINITE THEY'RE EXPANDING
TOWARDS EACH OTHER.
SO, THEY'RE BOTH GROWING AT
THIS HIGH RATE SO YOU CAN THINK
OF THE EDGES OF THEM
MOVING TOWARDS EACH OTHER.
BUT THE INTERVENING SPACE IS
EXPANDING EVEN FASTER SO THEY
ARE MOVING TOWARDS EACH OTHER
BUT THE SPACE IS GOING FASTER
AND SO, THEY NEVER MEET.
BUT, LOOKED AT FROM
OUTSIDE THEY BOTH LOOK FINITE.
THEY BOTH LOOK FINITE.
BUT INSIDE..?
THEY BOTH LOOK INFINITE.
AND, FUNDAMENTALLY,
WHY IS THAT THE CASE?
IT'S BECAUSE THE QUESTION OF
WHETHER ITS FINITE OR INFINITE
IS ONE THAT DEPENDS ON
YOUR DEFINITION OF TIME.
AND YOUR FREE TO MAKE ANY
DEFINITION YOU LIKE - ITS MIND
BOGGLING I KNOW.
THE FIRST TIME I LEARNED THIS I
JUST COULDN'T BELIEVE IT CAUSE
IT YOU THINK CERTAIN THINGS ARE
JUST PHILOSOPHICALLY IMPOSSIBLE.
YEA IT JUST SEEMS LIKE
LOGICAL CONTRADICTION.
RIGHT AND THEN YOU
REALIZE THAT PHYSICS HAS
TAUGHT YOU SOME WAY TO
ACTUALLY SO IT NONETHELESS.
OUR SENSE OF WHAT IS POSSIBLE
AND IMPOSSIBLE IS BASED ON THOSE
IDEAS ABOUT HOW SPACE
AND TIME ARE INTUITIVELY -
ARE ORDINARY PERCEPTIONS
RIGHT AND THOSE AREN'T CORRECT.
THOSE AREN'T CORRECT.
MULTIPLE INFINITE UNIVERSES
IT'S NOT JUST THAT OUR UNIVERSE
IS INFINITE IN SIZE BUT THAT
THERE ARE AN INFINITE NUMBER OF
UNIVERSES LIKE OURS EACH OF
WHICH ARE INFINITE IN SIZE.
INFINITIES WITHIN INFINITIES,
VIEWED FROM OUTSIDE
UNIVERSES APPEAR FINITE.
VIEWED FROM INSIDE,
UNIVERSES APPEAR INFINITE.
IMPOSSIBLE? WELL, PHYSICS
OVERRIDE HUMAN INTUITIONS.
SPACE-TIME...
CUT IT ONE WAY SPACE
IS FINITE WITH A SPECIFIC
CUT IT ANOTHER WAY SPACE IS
INFINITE GOING ON FOREVER.
ASSUMING THE COSMOS
IS INFINITE, WHY IS IT SO?
AS OUR SHIP NEARS COPENHAGEN
I RUSH TO SPEAK WITH PHYSICIST
RAPHAEL BOUSSO, WHO HAS
THEORIZED A VAST LANDSCAPE
OF POSSIBLE UNIVERSES.
THERE ARE DIFFERENT WAYS THAT
THE UNIVERSE COULD BE INFINITE.
ONE WAY IT COULD BE INFINITE
IS IF IT WERE INFINITE
TO START WITH.
IF FOR SOME REASON IT WAS
CREATED ALREADY AS INFINITE
SPACE IT MIGHT SOUND
SURPRISING BUT THEN IT COULD
BE EXPANDING ANYWAY.
AND THAT IS CERTAINLY
A MODEL THAT FITS THE
DATA REASONABLY WELL.
BUT THERE ARE A NUMBER OF
REASONS THAT WE BELIEVE NOW THAT
EVEN IF THE UNIVERSE
WAS SPATIALLY FINITE,
IT DOES BECOME
INFINITE OVER TIME.
THAT THE EXPANSION OF THE
UNIVERSE IS ACTUALLY ETERNAL AT
LEAST ON THE LARGER SCALES.
AND NEVER COMPLETELY COMES TO
A HALT EVERYWHERE, IT'S CALLED
ETERNAL INFLATION AND IT
ARISES VERY NATURALLY.
NOW, IN THAT CASE, WHAT HAPPENS
IS THAT BY THE SHEER SIZE OF THE
UNIVERSE THAT YOU GENERATE
EVERYTHING THAT CAN HAPPEN IN
THAT UNIVERSE WILL HAPPEN
OVER AND OVER AND OVER AGAIN IN
DIFFERENT ENORMOUSLY
SEPARATED REGIONS.
I MEAN, DON'T EXPECT TO FIND
ANOTHER COPY OF US TALKING IN
THE ROOM NEXT DOOR.
BUT IF YOU GO NOT JUST BILLIONS
OF LIGHT YEARS BUT EXPONENTIALLY
MORE THAN THAT FAR AWAY FROM
HERE PERHAPS THERE IS ANOTHER
YOU AND ME HAVING EXACTLY THE
SAME CONVERSATION RIGHT NOW.
IT'S PERPLEXING TO US, BECAUSE
IT TELLS US THAT WE DON'T REALLY
KNOW HOW TO COMPUTE
PROBABILITIES FOR ANYTHING.
BECAUSE EVERYTHING IS INFINITE
THERE ARE INFINITE MANY YOU'S
WHO WIN THE LOTTERY
IN THEIR LIFETIME,
EVEN THOUGH THAT IS SUPPOSED TO
BE QUITE UNLIKELY AND WE THINK
KNOW THAT'S UNLIKELY
AND TO COMPUTE THAT.
BUT ONCE YOU START ASKING
QUESTIONS ABOUT WHAT WE SHOULD
SEE IN COSMOLOGY WHEN WE
LOOK OUT INTO THE SKY WE START
REALIZING THAT YOU REALLY ARE
GETTING YOU WHOLE METHOD OF
COMPUTING PROBABILITIES
FOR ANYTHING UNDERMINED
BY THESE INFINITIES.
AND THAT IS REALLY
THE CORE OF SCIENCE,
IF WE CAN'T COMPUTE WHAT SHOULD
HAPPEN IF WE CAN'T SAY THIS IS
LIKELY AND THIS IS UNLIKELY HOW
COULD WE EVER RULE OUT A THEORY
AND SAY THAT IT IS WRONG BECAUSE
IT SAYS WHAT HAPPENS ALL THE
TIME IS UNLIKELY.
SO, HOW DO WE GET TO A SOLUTION?
WELL, THE WAY THAT WE HAVE TRIED
TO DEAL WITH THE INFINITIES IS
TO SOMEHOW FIND RULES FOR
CONSIDERING ONLY A PORTION OF
THIS INFINITE UNIVERSE
AND IGNORING THE REST,
THAT PORTION BEING FINITE.
SO THAT WE CAN COUNT HOW MANY
TIMES YOU WIN THE LOTTERY AND
HOW MANY TIMES YOU DON'T AND
THEN WE CAN SAY THE RATION OF
THOSE TWO NUMBERS IS IS
THE PROBABILITY FOR
WINNING THE LOTTERY.
THE WAY THAT ALL OF THE MOST
SUCCESSFUL MEASURE PROPOSALS
WORK THAT WE HAVE SO FAR
IS TO END THE UNIVERSE AT
A CERTAIN TIME.
THE FINITE PIECE THAT YOU KEEP
IS WHAT HAPPENED PRIOR TO THAT
TIME AND THE INFINITE PIECE
THAT YOU THROW AWAY IS
WHAT HAPPENED AFTERWARDS.
AND IT WORKS REALLY WELL THE
PREDICTIONS ARE GOOD BUT THERE'S
ONE PREDICTION WHICH IS
REALLY CRAZY SOUNDING.
AND YOU CAN SEE IMMEDIATELY
WHAT THAT PREDICTION IS WE ARE
COMPUTING PROBABILITIES AT THE
END OF THE DAY IN A UNIVERSE
THAT ENDS AT A CERTAIN TIME.
AND THE PROBABILITIES
REFLECT THAT.
SO, THE PROBABILITIES IN
PARTICULAR TELL YOU THAT THERE
IS A CERTAIN PROBABILITY PER
UNIT TIME FOR THE WORLD TO END.
NOW THAT PROBABILITY
IS NOT VERY HIGH,
YOU KNOW, THE CHANCES ARE THE
UNIVERSE IS GONNA LAST FOR
ANOTHER SEVERAL BILLION
YEARS BEFORE IT ENDS.
BUT, JUST CONCEPTUALLY IT IS
A VERY PUZZLING PREDICTION.
AND WHAT DO YOU MEAN BY END?
THAT THE UNIVERSE REALLY
BEHAVES AS IF ALL OF A
SUDDEN IT STOPPED.
LIKE YOU REACH A CERTAIN
TIME AND IT DOESN'T GO ON,
LIKE EVERYTHING
JUST DISAPPEARS NOW,
YOU'RE RIGHT IN BEING PUZZLED,
THIS RUNS COMPLETELY COUNTER TO
OUR INTUITION AS PHYSICISTS.
IT'S A PREDIICTION THAT DOESN'T
CONFLICT WITH EXPERIMENT AND SO
WE SHOULD CONSIDER
THE POSSIBILITY THAT
IT'S ACTUALLY CORRECT.
THERE IS A FINITE PROBABILITY
THAT WITHIN THE NEXT SEVERAL
BILLION YEARS, THE UNIVERSE
IS GOING TO COME TO AN
END RIGHT HERE.
PERHAPS, THE UNIVERSE WAS
ALWAYS INFINITE, WHATEVER THAT
MAY MEAN, OR PERHAPS THE
UNIVERSE BECAME INFINITE OVER
TIME, BUT COULD SOMETHING
FINITE BECOME INFINITE?
NO MATTER HOW FAST
AND LONG IT GROWS.
THEN THAT MEASURE PROBLEM, AN
INFINITE UNIVERSE UNDERMINES ALL
PROBABILITIES BECAUSE WHEN
EVERYTHING HAPPENS AN INFINITE
NUMBER OF TIMES, NOTHING
IS MORE OR LESS LIKELY.
A SOLUTION?
SAMPLE A SMALL
SEGMENT OF THE UNIVERSE.
IGNORE THE INFINITE REST,
BUT THEN THE UNEXPECTED.
A FINITE PROBABILITY
THAT THE UNIVERSE WILL
END; ABRUPTLY END.
AND IF TIME IS INFINITE,
ANYTHING WITH A FINITE
PROBABILITY MUST HAPPEN.
SO THE UNIVERSE MUST END.
I KNEW INFINITY WAS
WEIRD, WHAT TO DO?
ARE THERE DIFFERENT WAYS
IN WHICH SPACE AND TIME
CAN BE INFINITE?
AS THE FQXI CONFERENCE
CONTINUES IN COPENHAGEN,
I SPEAK WITH SEAN CARROLL,
A COSMOLOGIST AT CALTECH.
A THOUSAND YEARS FROM NOW, WHEN
WE HAVE A PERFECT UNDERSTANDING
OF COSMOLOGY, IT WILL INVOLVE
EITHER AN INFINITE UNIVERSE
OR A FINITE ONE.
ALL OF THE ATTEMPTS SO FAR, TO
SERIOUSLY COME UP WITH TRUE LAWS
OF PHYSICS HAVE INVOLVED
INFINITY IN ONE WAY OR ANOTHER.
IT DOESN'T MEAN THE
UNIVERSE IS PHYSICALLY,
INFINITELY BIG, BUT IT MIGHT
MEAN THAT BETWEEN MY FINGERS
THERE ARE INFINITE
NUMBERS OF POINTS.
OR, THERE ARE AN INFINITE NUMBER
OF POSSIBILITIES FOR THE QUANTUM
STATE OF A SINGLE PARTICLE, MUCH
LESS A WHOLE BUNCH OF PARTICLES.
SO, I DON'T THINK WE
SHOULD BE AFRAID OF INFINITY,
IT PLAYS A ROLE IN
OUR THEORIES RIGHT NOW,
WE MIGHT END UP BEING
ABLE TO DO WITHOUT IT,
BUT, WE SHOULD
KEEP IT ON THE TABLE.
IS THE UNIVERSE INFINITE, OR
IS IT ALWAYS A VERY BIG NUMBER,
BUT IT'S NEVER REALLY INFINITY?
SO, THERE'S SORT OF
TWO VERSIONS OF THAT,
IS THE UNIVERSE
INFINITE IN SPACE,
IS IT INFINITELY BIG,
AND IS IT INFINITE IN TIME,
DOES IT LAST FOREVER, EITHER TO
THE FUTURE OR THE PAST OR BOTH?
SO, YOU CAN IMAGINE, YOU
KNOW, FOUR POSSIBILITIES,
FINITE IN SPACE,
FINITE IN TIME, ET CETERA,
THE UNIVERSE COULD BE FINITE
IN SPACE OR INFINITE IN SPACE,
IT COULD BE FINITE IN
TIME AND INFINITE IN TIME.
PERSONALLY, I THINK IT CAN'T
BE BOTH FINITE IN SPACE AND
INFINITE IN TIME AND THE REASON
WHY IS BECAUSE THAT WOULD MEAN
THERE'S AN ONLY, A FINITE NUMBER
OF THINGS THAT CAN HAPPEN
AND INFINITELY LONG
FOR THEM ALL TO HAPPEN.
SO, YOU JUST GET INTO A NEECHAN
REOCCURRENCE WHERE EVERYTHING
HAPPENS AN INFINITE NUMBER OF
TIMES AND IT DOESN'T MAKE SENSE
HOW TO DO IT.
IF BOTH ARE INFINITE, THEN
WE HAVE A DIFFERENT KIND OF
PROBLEM, THAT WE
CAN'T CALCULATE ANYTHING.
IT'S AN OFFICIAL PROBLEM
IN COSMOLOGY KNOWN AS
THE MEASURE PROBLEM.
WHEN AN INFINITE NUMBER OF
THINGS HAPPEN FOR AN INFINITE
LONG PERIOD OF TIME, HOW CAN YOU
MAKE SENSE OF A QUESTION LIKE
WHAT IS THE PROBABILITY
THAT SOMETHING HAPPENED?
IF THE UNIVERSE IS FINITE
IN SPACE AND FINITE IN TIME,
THEN ALL OF THE CALCULATIONAL
PROBLEMS GO AWAY,
BUT YOU HAVE A
REALLY BIZARRE UNIVERSE,
LIKE, IF THERE'S ONLY ONE
UNIVERSE THAT LASTS A FINITE
TIME AND IT'S NOT THAT BIG,
WHY DOES IT LOOK AS WEIRD AS
OUR UNIVERSE DOES?
SO, EVERY POSSIBILITY THAT IS
VIABLE HAS WHAT LOOKS A SERIOUS
PROBLEM AND THAT MEANS THAT
WE DON'T YET KNOW WHAT WE
ARE DOING REALLY.
SO, TELL ME RIGHT
NOW, YOUR OPINION,
TELL ME THE SECRET,
UNIVERSE INFINITE OR FINITE
TIME AND SPACE?
I THINK THE UNIVERSE
INFINITE IN BOTH TIME AND SPACE.
I THINK THAT THAT
IS OUR BEST HOPE,
FOR COMING UP WITH A NATURAL AND
COMPELLING EXPLANATION FOR THE
LITTLE PART OF THE UNIVERSE
THAT WE CAN ACTUALLY SEE.
IT DOESN'T LOOK TYPICAL, IT
DOESN'T LOOK LIKE YOU WOULD
EXPECT AND I THINK THE
RIGHT WAY TO ACCOUNT FOR THAT,
IS TO SAY WELL IT'S AN
OUTGROWTH OF A MUCH,
MUCH BIGGER PROCESS, A PROCESS
THAT GOES ON FOREVER AND
WILL NEVER END.
I LIKE CREATING
THE COMBINATIONS,
ARRAYING FINITE AND
INFINITE IN SPACE AND IN TIME.
BUT WHEN EVERY POSSIBILITY
HAS A SERIOUS PROBLEM,
I AGREE WITH SEAN.
WE DON'T YET KNOW,
WHAT WE'RE REALLY DOING.
COULD SPACE AND
TIME BE A REAL INFINITY?
I PRESS FOR
MEANING, SIGNIFICANCE,
IMPLICATIONS, RAMIFICATIONS,
CLUES ABOUT THE DEEP
NATURE OF EXISTENCE.
I DON'T EXPECT REAL MEANING,
JUST IDEAS ON POSSIBLE MEANING.
I HEAR OF AN EXPERIMENTAL
PHILOSOPHER AT YALE WHO WONDERS
HOW AN INFINITE UNIVERSE WOULD
AFFECT OUR MORAL IMPERATIVES:
MORALITY, INFINITY, THE
COUPLING SEEMS, WELL, ODD.
BUT THAT'S THE MYSTICAL
POWER OF INFINITY.
I SPEAK WITH JOSHUA KNOBE.
JOSH, IF INDEED
THERE IS AN INFINITY,
IN THE UNIVERSE, IN TERMS
OF NUMBERS OF GALAXY,
STARS, PLANETS, WHAT WOULD
THAT MEAN AS A PHILOSOPHER?
WELL, FOR PHILOSOPHERS, IT POSES
A REALLY DIFFICULT QUESTION.
ONE THING THAT WE'VE OFTEN
THOUGHT IS THAT WHAT WE ARE
REQUIRED TO DO MORALLY IS
TO MAKE THINGS BE BETTER
ON THE WHOLE.
SO, WE HAVE TO
INCREASE THE TOTAL SAY,
OF HAPPINESS IN THE UNIVERSE,
DECREASE THE TOTAL AMOUNT OF
DEATH AND SO FORTH.
BUT WHAT WE SEEM TO BE SEEING
IS THAT THE TOTAL IN ALL OF
THESE CASES IS INFINITE.
THERE'S INFINITE
HAPPINESS IN THE UNIVERSE,
THERE'S AN INFINITE AMOUNT OF
PEOPLE BEING TORTURED TO DEATH
AT THIS MOMENT.
SO, NOTHING I DO THEN, CAN
HAVE ANY EFFECT ON THE TOTAL.
REGARDLESS OF WHAT I DO, THE
TOTAL AMOUNT OF HAPPINESS IN THE
UNIVERSE IS STILL
GOING TO BE INFINITE.
WHAT'S THE IMPLICATION OF THAT?
WELL, IT SEEMS LIKE TO THE
EXTENT THAT YOU THINK LIFE HAS
ANY MEANING AT ALL, IT CAN'T
HAVE TO DO WITH SOMETHING ABOUT
THE TOTAL NUMBER OF PEOPLE, IT
MUST BE SOMETHING THAT HAS TO
DO WITH, CERTAIN
PARTICULAR PEOPLE.
SO RIGHT NOW FOR EXAMPLE, I
COULD SAY SOMETHING REALLY NICE
TO YOU OR I COULD SAY
SOMETHING MEAN TO YOU.
BUT, THERE ARE INFINITELY MANY
PEOPLE WHO ARE EXACTLY LIKE YOU
THROUGHOUT THE UNIVERSE,
INFINITELY MANY OF WHOM,
SOMETHING NICE WILL HAPPEN
TO YOU AND INFINITELY MANY OF
WHOM SOMETHING MEAN
WILL HAPPEN TO.
SO THE ONLY WAY THAT I COULD
JUSTIFY TRYING TO BE NICE TO YOU
IS IN TERMS OF SOMETHING THAT
WILL HAPPEN TO YOU IN PARTICULAR
AND NOT TO SORT OF THE TOTAL OF
- NUMBER OF PEOPLE QUALITATIVELY
IDENTICAL TO YOU.
AS A PHILOSOPHER,
DOES THAT BOTHER YOU?
YOU KNOW, I THINK
THERE'S SOMETHING ABOUT US,
ABOUT THE IDEA THAT NOTHING THAT
WE DO CAN BE UNIQUE IN THE WAY
THAT WE THOUGHT IT WAS.
WHENEVER YOU'RE COMING UP
WITH SOME IDEA IS ORIGINAL,
NOT ONLY IS NOT UNIQUE, IT'S AN
EXPERIENCE THAT INFINITELY MANY
PEOPLE HAVE HAD.
SO, THIS CONVERSATION,
WHICH WE'RE HAVING RIGHT NOW,
IS OCCURRING IN INFINITELY
MANY REGIONS OF OUR UNIVERSE AT
THIS ONE MOMENT.
THERE'S SOMETHING A LITTLE BIT
DEPRESSING ABOUT KNOWING THAT
WE'RE SO NOT SPECIAL.
WELL, THERE MAY BE
SOMETHING INCOHERENT ABOUT IT,
DO YOU THINK?
IT CERTAINLY, IT'S NOT
MATHEMATICALLY INCOHERENT,
BUT THERE'S SOMETHING TROUBLING
EXISTENTIALLY ABOUT IT.
DON'T YOU THINK THIS THOUGH,
MAY BE A CHARACTERISTIC OF THE
CONCEPT OF INFINITY WHICH IS NOT
JUST THE LARGEST NUMBER BUT IT'S
NOT A NUMBER, IT'S JUST A
DEFINITIONAL KIND OF THING AND
MAYBE INVESTED IN THAT TERM
IS MORE THAN REALLY EXISTS.
YOU MIGHT THINK THAT THERE ARE
CERTAIN KINDS OF CONFUSIONS WE
FACE, WHEN WE REACH UP TO
THIS CONCEPT OF THE INFINITE BUT
IT CERTAINLY SEEMS AS THOUGH,
IF I'M INTERESTED IN MAKING YOUR
LIFE BETTER, THERE'S NO SENSE IN
WHICH THAT COULD BE INCREASING
THE TOTAL AMOUNT OF HAPPINESS
THAT THERE IS IN THE UNIVERSE.
IF THAT TOTAL IS INFINITE THERE
IS NOTHING I CAN DO ABOUT IT IN
MY ACTIONS RIGHT NOW.
SO IT REALLY DOES SEEM TO RAISE
SOME VERY PERPLEXING QUESTIONS
FOR THE MORAL PHILOSOPHY THAT
WE'VE HAD AT EARLIER DECADES.
ARE INFINITES AND
THE COSMOS REAL?
TO DISCERN MEANING,
CONSIDER THE POSSIBILITIES.
ONE: A UNIVERSE FINITE
IN TIME, FINITE IN SPACE.
THE COSMOS CAME INTO
BEING AND CONTINUES TO EXPAND.
THIS IS THE OLD MODEL OF
SCIENCE AND THE UNCHANGING MODEL
OF WESTERN RELIGION.
TWO: A UNIVERSE FINITE
IN TIME, INFINITE IN SPACE.
THE COSMOS CAME INTO BEING
AND HAS BECOME INFINITE IN SIZE,
THIS IS THE NEW MODEL OF
INFLATIONARY COSMOLOGY.
THREE: A UNIVERSE INFINITE
IN TIME, FINITE IN SPACE.
THE COSMOS HAS ALWAYS
EXISTED IN A LIMITED SPACE,
AN ODD WAY FOR THINGS TO BE.
FOUR: A UNIVERSE INFINITE
IN TIME, INFINITE IN SPACE.
THE COSMOS HAS ALWAYS
EXISTED IN UNLIMITED SPACE,
THIS IS COHERENT,
HOWEVER, MIND BOGGLING.
ARE WE APPROACHING A
MAXIMUM EXPLICATION OF REALITY?
AN INFINITE NUMBER OF
UNIVERSES, INFINITE IN SIZE,
INFINITE IN TIME,
NESTING INFINITIES,
TOWERS OF INFINITIES, ENOUGH;
I PLEAD FOR COMMON SENSE.
IS GENERAL RELATIVITY,
COMMON SENSE?
NO.
QUANTUM PHYSICS?
DOUBLE NO.
AM I ANY CLOSER TO TRUTH?
