Instructions: To add a question/comment to a specific line, equation, table or graph simply click on it.
Click on the annotations on the left side of the paper to read and reply to the questions and comments.
This paper is about Everett's theory that Schrodinger's equation ap...
Everett’s thesis discussed the possibility that Schrodinger’s cat i...
Schrodinger's cat - Imagine a cat enclosed in a box with a radioact...
The wave function is the mathematical formula we use to describe qu...
Schrodinger’s equation is the basic equation for describing quantum...
Decoherence was Zeh's theory involving Schrodinger's cat. Zeh notic...
The wavefunction never collapses in Everett's view, they just conti...
This example is supposed to prove that nothing is truly "random" wh...
If we can use Einstein's theory of General Relativity to predict th...
Everett's theory claims that decoherence explains why we don't perc...
Everett's theory claimed that regardless of the size of the system,...
A quantum computer can solve problems that no classical computer wo...
If you would like to learn more about parallel worlds and the scien...
arXiv:0707.2593v1 [quant-ph] 18 Jul 2007
Many lives in many worlds
Max Tegmark
(In this universe:) Dept. of Physics & MIT Kavli Institute,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
(Dated: Published in Nature, 448, 23, July 2007)
I argue that accepting quantum mechanics to be universally tru e means that you should also
believe in parallel universes. I give my assessment of Everett’s th eory as it celebrates its 50th
Almost all of my colleagues have an opinion about it,
but almost none of them have read it. The first draft of
Hugh Everett’s PhD thesis, the shortened official version
of which celebrates its 50th birthday this year, is buried
in the out-of-pr int book The Many-Worlds Interpretation
of Quantum Mechanics [1]. I remember my excitement
on finding it in a small Be rkeley book store back in grad
school, and still view it as one of the most brilliant texts
I’ve ever read.
By the time Everett started his graduate work with
John Archibald Wheeler at Princeton University, q uan-
tum mechanics had chalked up stunning successes in ex-
plaining the atomic realm, yet a debate raged on as to
what its mathematical formalism really meant. I was for-
tunate to get to discuss q uantum mechanics with Wheeler
during my postdoctorate years in Princeton, but never
had the chance to meet Everett.
Quantum mechanics specifies the state of the univer se
not in classical terms, such as the positions and veloci-
ties of all particles, but in terms of a mathematical ob-
ject called a wavefunction. According to the Schr¨odinger
equation, this wavefunction evolves over time in a de-
FIG. 1: Is it only in fiction that we can experience parallel
lives? If atoms can be in two places at once, so can you.
terministic fashion that mathematicians term “unitary ”.
Although quantum mechanics is often described as inher-
ently random and uncertain, there is nothing random or
uncertain abo ut the way the wavefunction evolves.
The sticky part is how to connect this wavefunc-
tion w ith what we observe. Many legitimate wavefunc-
tions correspond to counterintuitive situations, such as
Schr¨odinger’s cat being dead-and-alive at the same time
in a “superpo sition” of states. In the 1920s, physicists
explained away this weirdness by postulating that the
wavefunction “collapsed” into some random but definite
classical outcome whenever s omeone made an obs e rva-
tion. This add-on had the virtue of explaining observa-
tions, but rendered the theor y incomplete, be c ause there
was no mathematics specifying what constituted an ob-
servation that is, when the wavefunction was supposed
to collapse.
Everett’s theory is simple to state but has complicated
implications, including par allel universes. The theory can
be summed up by saying that the Schr¨odinger equation
applies at all times; in other words, that the wavefunction
never collapses. That’s it no mention of parallel uni-
verses or splitting worlds, which are implications of the
theory rather than po stulates. His brilliant insight was
that this collapse- free quantum theory is, in fact, consis-
tent with observation. Although it predicts that a wave-
function describing one classical reality gradually evolves
into a wavefunction des cribing a superposition of ma ny
such realities the many worlds observers subjectively
exp erience this splitting merely as a slig ht randomness
(see Figure 2), w ith probabilities consistent with those
calculated using the wavefunction-collapse recipe.
Gaining acceptance
It is often said that important scientific discoveries go
though three phases: first they are completely ignored,
then they are violently attacked, a nd finally they are
brushed aside as well-known. Everett’s discovery was no
exception: it took over a decade until it started getting
noticed. But it was too late for Everett who left academia
disillusioned [2].
Everett’s no-collapse idea is not yet at stage three, but
after being widely dismissed as too crazy during the 1970s
and 1980s, it ha s gradually gained more acceptance. At
an informal poll taken at a conference on the foundations
of quantum theory in 1999 physicists rated the idea more
highly than the alternatives, although there were still
100%0% 25% 50% 75%
Fraction of queens face up
FIG. 2: According to quantum theory, a card perfectly b al-
anced on its edge will fall down in what is known as a “su-
perposition” the card really is in two places at once. If a
gambler bets money on the queen landing face up, her own
state changes to become a superposition of two possible out-
comes winning or losing the bet. In either of these parallel
worlds, the gambler is unaware of the other outcome and feels
as if the card fell randomly. If the gambler repeats this game
four times in a row, there will be 16 (2 × 2 × 2 × 2) possible
outcomes, or parallel worlds. In most of these worlds, it will
seem that q ueens occur randomly, with about 50% probabil-
ity. Only in two worlds will all four cards land the same way
up. If the game is continued many more times, almost every
gambler in each of the worlds will conclude that the laws of
probability apply even though th e underlying physics is not
random and, as Einstein would have put it, “God does not
play dice”.
many more ”undecided” [3]. I believe the upwards trend
is clear.
Why the change? I think there are several reasons.
Predictions of other types of para llel universes from co s-
mological inflation and string theory have increased tol-
erance for weird-sounding ideas. New experiments have
demonstrated quantum weirdness in ever larg er systems.
Finally, the discovery of a process known as decoherence
has a nswered crucial questions that Everett’s work had
left dang ling.
For example, if these parallel universes exist, then why
don’t we perceive them? Quantum superpositions can-
not be confined as most quantum experiments are to
the microworld. Beca use you are made o f atoms , then if
atoms can be in two places at once in superposition, so
can you (Figure 1).
The breakthrough came in 1970 with a seminal paper
by H. Dieter Zeh, who showed that the Schr¨odinger equa-
tion itself gives rise to a type of censorship. This effect
became known as “decoherence ”, and was worked out in
great detail by Wojciech Zurek, Zeh and others over the
following decades. Quantum superpositions were found
to remain observable only as long as they were kept secret
from the rest of the world. The quantum card in Figure 2
is constantly bumping into air molecules, photons, and
so on, which thereby find out whether it has fallen to
the left or to the right, destroying the coherence of the
supe rp osition and making it unobservable. Decoherence
also explains why states resembling classical physics have
sp e c ial status: they are the most robust to decoherence.
Science of philosophy?
The main motivation for introducing the no tion of ran-
dom wavefunction collapse into quantum physics had
been to e xplain why we perceive probabilities and not
strange macroscopic superpositions . After Everett had
shown that things wo uld appear rando m anyway (Fig-
ure 2) and decoherence had b e en found to explain why
we never perceived anything strange, much of this moti-
vation was gone. Even though the wavefunction techni-
cally never collapses in the Everett view, it is generally
agreed that decoherence produces an effect that looks like
a co llapse and smells like a collapse .
In my opinion, it is time to update the many quantum
textbooks that introduce wavefunction collapse as a fun-
damental postulate of quantum mechanics. The notion
of collapse still has utility as a calculational recipe, but
students should be told that it is probably not a funda-
mental proces s violating the Schr¨odinge r equation so as
to avoid any subsequent confusion. If you are consider-
ing a quantum textbook that does not mention “Everett”
and “decoherence” in the index, I recommend buying a
more modern one.
After 50 years we can c e le brate the fact that Everett’s
interpretation is still consistent with quantum observa-
tions, but we face another pressing question: is it science
or mere philosophy? The key point is that parallel uni-
verses are not a theory in themselves, but a prediction of
certain theories. For a theory to be falsifiable, we need
not observe and test all its predictions one will do.
Because Einstein’s theory of General Relativity has
successfully predicted many things that we can observe,
we also take s eriously its predictions for things we can-
not, like the internal structure of black holes. Analo-
gously, successful pre dictio ns by unitary quantum me-
chanics have made scientists take more seriously its other
predictions, including parallel universes
Moreover, Everett’s theory is falsifiable by future lab
exp eriments: no matter how large a system they probe,
it s ays, they will not observe the wavefunction collapsing.
Indeed, collapse-free superpositions have been demon-
strated in, for example, carbon-60 molecules. Several
groups are now attempting to create quantum super po-
sitions of objects involving 10
7 ato ms or more, tanta-
lizingly close to o ur human macroscopic s cale. There is
also a g lobal effort to build quantum computers which,
if successful, will be able to factor numbers exponen-
tially faster than classical computers, effectively perfor m-
ing parallel computations in Everett’s parallel worlds.
The bird perspective
So Everett’s theory is testable and so far ag rees with
observation. But should you really believe it? When
thinking about the ultimate nature of reality, I find it
useful to distinguish between two ways of viewing a phys-
ical theory: the outside view of a physicist studying its
mathematical equations, like a bird surveying a land-
scape from high above, and the ins ide view of an observer
living in the world described by the equations, like a frog
being watched by the bird.
From the bird perspec tive, Everett’s multiverse is sim-
ple. There is only one wavefunction, and it evolves
smoothly and deterministically over time without a ny
kind of splitting or parallelism. The abs tract quantum
world des c rib e d by this evolving wavefunction contains
within it a vast number of class ic al parallel storylines
(“worlds”), continuously splitting and merging, as well
as a number of quantum phenomena that lack a classi-
cal description. From their frog perspective, observers
perceive only a tiny fraction of this full rea lity, and they
perceive the splitting of classical storylines as quantum
What is more fundamental the frog pers pective or
the bird perspective? In other words, what is more ba-
sic to you: human languag e or mathematical la nguage?
If you opt for the former, you would pro bably prefer
a “many words” interpretation of quantum mechanics,
where mathematical simplicity is sacrificed to collapse
the wavefunction and eliminate parallel universes.
But if you pre fer a simple and purely ma thematical
theory, then you like me are stuck with the many
worlds interpretation. If you struggle with this you are
in good company: in general, it has proven extremely
difficult to formulate a mathematical theory that predicts
everything we can observe and nothing else and not just
for quantum physics.
Moreover, we should expect quantum mechanics to feel
counterintuitive because evolution endowed us with intu-
ition only for thos e aspects of physics that had survival
value for our distant ancestors, such as the trajectories
of flying rocks.
The choice is yours. But I worry that if we dismiss
theories like Everett’s b ecause we can’t observe every-
thing or because they seem weird, we risk missing true
breakthroughs, perpetuating our instinctive reluctance to
expand our horizons. To modern ears the Shapley- Curtis
debate of 1920 about whether there were really a multi-
tude of galaxies (parallel universes by the standards of
the time) sounds positively quaint.
Everett asked us to acknowledge that our physical
world is grander than we had imagined, a humble sug-
gestion that is probably easier to accept after the recent
breakthroughs in cosmology than it was 50 years ago.
I think Everett’s only mistake was to be born ahead of
his time. In another 50 years, I believe we will be more
used to the weird ways of o ur cosmos, and even find its
strangeness to be part of its charm.
Acknowledgments: This work was supported by
NASA grant and NNG06GC55G, NSF grants AST-
0134999 and 0607597, the Kavli Foundation, and fellow-
ships from the David and Lucile Packard Foundation and
the Research Corporation.
[1] H. Everett, in “The Many-Worlds Interpretation of Quan-
tum Mechanics”, B. S. DeWitt & N. Graham (eds.),
Princeton Univ. Press, Princeton (1973)
[2] E. Shikhovtsev, “Biography of Hugh Everett, III”,
[3] M. Tegmark & J. A. Wheeler, “100 Years of the
Quantum”, Scientific American, Feb. 2001, 68-75,