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

anniversary.

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

2

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.

3

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

1

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

randomness.

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”,

http://space.mit.edu/home/tegmark/everett/

[3] M. Tegmark & J. A. Wheeler, “100 Years of the

Quantum”, Scientiﬁc American, Feb. 2001, 68-75,

http://arxiv.org/pdf/quant-ph/0101077

If we can use Einstein's theory of General Relativity to predict the physics surrounding certain objects we can not observe (internal structure of black holes for example) then we should be able to use theories of quantum mechanics to predict items we cannot see as well (such as parallel universes).
Everett's theory claimed that regardless of the size of the system, scientists will not observe a wavefunction collapsing, however, this theory will be disproven by future lab experiments. Decoherence is due to constant interactions with the environment, which are impossible to avoid. This explains that what we think of as an observation doesn’t require a human; simply interacting with the environment counts. This explains why bringing large objects into superpositions of two states is extremely difficult and the superposition fades rapidly. The heaviest object so fat that has been brought into a superposition of locations is a carbon-60 molecule. More ambitious scientists have proposed to do this experiment to viruses or even heavier creatures, such as bacteria. Thus, the paradox that Schrodinger’s cat once raised, (the transfer of a quantum superposition, the decaying atom, to a large object, the cat) has been resolved. Scientists now understand that while small things (atoms, quarks, ect) can exist in superpositions for extended amounts of time, a large object will settle extremely quickly in one particular state. That is why we never see cats that are both dead and alive.
Decoherence was Zeh's theory involving Schrodinger's cat. Zeh noticed that in the real world you could not separate the cat from the environment (air molecules, the box, cosmic rays passing through the experiment). Zeh claimed that these interactions, no matter how small, can radically affect the wave function. If the wave function is disturbed in the slightest way, then the wave function will suddenly split into two distinct wave functions of the dead cat or the live cat (which no longer interact). Zeh showed that a collision with a single air molecule was enough to collapse the wavefunction, forcing the permanent separation of the dead cat and the live cat, which no longer interact, In other words, before you even open the box, the cat has been in contact with the air molecules and hence is already dead or alive.
If you would like to learn more about parallel worlds and the science behind it, here is a short article/video http://www.dailymail.co.uk/sciencetech/article-2816039/Parallel-universes-exist-Multiple-versions-living-alternate-worlds-interact-theory-claims.html
A quantum computer can solve problems that no classical computer would be able to solve within a reasonable amount of time. They would be able to decrypt the majority of the cryptographic systems in use today. Currently, Google and NASA are working on building a quantum computer, here is a video explaining more about quantum computers as a whole, and google and nasa's involvement. http://mashable.com/2013/10/13/google-quantum-computing-video/#KW2dQZTqnsq3
I don't think that's true. In a practical sense, classical computers are still faster than quantum computers. In a theoretical sense, it hasn't been proven impossible for a classical computer to factor a number in polynomial time.
This example is supposed to prove that nothing is truly "random" when it comes to probability, even if it appears so. The underlying physics proves the card falling is not random, 16 parallel worlds would exist in which this card has every possible outcome
The theory itself was incomplete because there is no mathematical way of calculating an observation, and without math to support it, a theory is merely a postulation. Scientists could not use observations as part of this theory, there was no way to accurately test an observation without mathematics behind it, thus rendering this theory incomplete.
This paper is about Everett's theory that Schrodinger's equation applies at all times, therefore the wavefunction never collapses. The author takes Everett's theory and discusses the implications associated with the non-collapse of the wavefunction (i.e. parallel worlds). This paper is important because it discusses the probability of multiple universes, a theory that (so far) is beyond our limits of observation.
Schrodinger’s equation is the basic equation for describing quantum behavior, and is constantly used in quantum mechanics. Also known as the Schrodinger wave equation, it is a partial differential equation that describes how the wavefunctions of a physical system change over time. In the past, observation of Schrodinger’s cat was said to “collapse” the wavefunction, thus leaving only one outcome (a dead or alive cat), however, Everett’s theory postulates that the wavelength never truly collapses, instead, the wavelength transforms into a parallel universe. In this case, if we were to open Schrodinger's box and find a dead cat, a parallel universe would be created where we open the box and find an alive cat.
The wave function is the mathematical formula we use to describe quantum objects. It is a wavering quantity that mathematically describes the wave characteristics of a particle. The value of the wave function of a particular particle at a given point of space/time is related to the probability of the particles being there at that time.
Here is more information on wave functions https://www.youtube.com/watch?v=aowYf44gDRY
Everett’s thesis discussed the possibility that Schrodinger’s cat is both dead and alive, because the universe splits into two. In one universe, the cat is dead; in another, the cat is alive. Everett postulated that at each quantum juncture the universe splits in half, in an incessant sequence of splitting universes. Here is an example of Everett’s theory https://www.youtube.com/watch?v=KNwKPfOKipk
Schrodinger's cat - Imagine a cat enclosed in a box with a radioactive source. If a single atom of the radioactive source decays, a mechanism would trip a hammer, which would in turn, break the vial containing the radioactive source, and kill the cat.
Until the source emits radiation, the cat would be considered (according to quantum mechanics) to be simultaneously both dead and alive, until the box is open, and the cat is observed. When the box is open, the “wavelength” collapses, and the cat can either be one of these two things: dead OR alive.
Here is a brief video demonstrating Schrodinger’s cat and the implications behind observation
https://www.youtube.com/watch?v=IOYyCHGWJq4
Here is a video going more in depth about wave functions and decoherance https://www.youtube.com/watch?v=Zbe6ov22Nok
Everett's theory claims that decoherence explains why we don't perceive parallel universes. He claimed that perhaps the cat is dead and alive at the same time, but in different universes. The cat is both dead and alive because the universe has split into two. In one universe, the cat is dead, and in another universe, the cat is alive. If this interpretation is correct, then at this very moment, your body coexists with wave functions of dinosaurs, wave functions where the Germans won world war one, where aliens roam, where you were never born, etc. The catch is we can no longer interact with these wave functions, because they have decohered from us (the waves are no longer in phase with one another). This means the slightest contamination with the environment will prevent the various wave functions from interacting with one another, thus we are unable to perceive these parallel universes.
The wavefunction never collapses in Everett's view, they just continue to evolve, forever splitting into other wave functions in a never-ending tree, with each branch representing an entire universe. However, in our universe, we perceive the wavefunction as "collapsing" because decoherence only gives us one outcome. If in this universe the outcome is "a", we perceive the wavefunction as collapsing to "a", however, there is another universe where the wavefunction collapses to "b" and the people living in that universe perceive the wavefunction collapsing to "b". Thus, decoherence appears as if it produces an effect like a collapse separately in each parallel universe, however, on a large scale, the wavefunction never collapses.