Tag Archives: Copenhagen

Flash Forward: Many-Worlds Interpretation (Hugh Everett)

Many-worlds is an interpretation of quantum mechanics that asserts the objective reality of the wavefunction, but denies the reality of wavefunction collapse. It is also known as MWI, the relative state formulation, theory of the universal wavefunction, parallel universes, many-universes interpretation or just many worlds.

The original relative state formulation is due to Hugh Everett who formulated it in 1957. Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and ’70s.

Proponents argue that many-worlds reconciles how we can perceive non-deterministic events, such as the random decay of a radioactive atom, with the deterministic equations of quantum physics. Prior to many-worlds, reality had been viewed as a single “world-line”. Many-worlds, rather, views reality as a many-branched tree where every possible quantum outcome is realised.

In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence. By decoherence, many-worlds claims to resolve all of the correlation paradoxes of quantum theory, such as the EPR paradox and Schrödinger’s cat, since every possible outcome of every event defines or exists in its own “history” or “world”. In layman’s terms, there is a very large—perhaps infinite—number of universes, and everything that could possibly have happened in our past, but didn’t, has occurred in the past of some other universe or universes.

The decoherence approach to interpreting quantum theory has been further explored and developed becoming quite popular, taken as a class overall. MWI is one of many Multiverse hypotheses in physics and philosophy. It is currently considered a mainstream interpretation along with the other decoherence interpretations and the Copenhagen interpretation.

Outline

Although several versions of many-worlds have been proposed since Hugh Everett’s original work, they all contain one key idea: the equations of physics that model the time evolution of systems without embedded observers are sufficient for modelling systems which do contain observers; in particular there is no observation-triggered wavefunction collapse which the Copenhagen interpretation proposes. Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics. MWI’s main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of very many, possibly even a non-denumerablely infinitely many, increasingly divergent, non-communicating parallel universes or quantum worlds.

The idea of MWI originated in Everett’s Princeton Ph.D. thesis “The Theory of the Universal Wavefunction”, developed under his thesis advisor John Archibald Wheeler, a shorter summary of which was published in 1957 entitled “Relative State Formulation of Quantum Mechanics” (Wheeler contributed the title “relative state”; Everett originally called his approach the “Correlation Interpretation”, where “correlation” refers to quantum entanglement). The phrase “many-worlds” is due to Bryce DeWitt, who was responsible for the wider popularisation of Everett’s theory, which had been largely ignored for the first decade after publication. DeWitt’s phrase “many-worlds” has become so much more popular than Everett’s “Universal Wavefunction” or Everett-Wheeler’s “Relative State Formulation” that many forget that this is only a difference of terminology; the content of all three papers is the same.

The many-worlds interpretation shares many similarities with later, other “post-Everett” interpretations of quantum mechanics which also use decoherence to explain the process of measurement or wavefunction collapse. MWI treats the other histories or worlds as real since it regards the universal wavefunction as the “basic physical entity” or “the fundamental entity, obeying at all times a deterministic wave equation”. The other decoherent interpretations, such as many histories, consistent histories, the Existential Interpretation etc, either regard the extra quantum worlds as metaphorical in some sense, or are agnostic about their reality; it is sometimes hard to distinguish between the different varieties. MWI is distinguished by two qualities: it assumes realism, which it assigns to the wavefunction, and it has the minimal formal structure possible, rejecting any hidden variables, quantum potential, any form of a collapse postulate (i.e. Copenhagenism) or mental postulates (such as the many-minds interpretation makes).

Decoherent interpretations of many-worlds use einselection to explain how a small number of classical pointer states can emerge from the enormous Hilbert space of superpositions have been proposed by Wojciech H. Zurek. “Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected.” These ideas complement MWI and bring the interpretation in line with our perception of reality.

Many-worlds is often referred to as a theory, rather than just an interpretation, by those who propose that many-worlds can make testable predictions (such as David Deutsch) or is falsifiable (such as Everett) or that all the other, non-MWI, are inconsistent, illogical or unscientific in their handling of measurements; Hugh Everett argued that his formulation was a metatheory, since it made statements about other interpretations of quantum theory; that it was the “only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world.”

Interpreting wavefunction collapse

As with the other interpretations of quantum mechanics, the many-worlds interpretation is motivated by behavior that can be illustrated by the double-slit experiment. When particles of light (or anything else) are passed through the double slit, a calculation assuming wave-like behavior of light can be used to identify where the particles are likely to be observed. Yet when the particles are observed in this experiment, they appear as particles (i.e. at definite places) and not as non-localized waves.

Some versions of the Copenhagen interpretation of quantum mechanics proposed a process of “collapse” in which an indeterminate quantum system would probabilistically collapse down onto, or select, just one determinate outcome to “explain” this phenomenon of observation. Wavefunction collapse was widely regarded as artificial and ad-hoc, so an alternative interpretation in which the behavior of measurement could be understood from more fundamental physical principles was considered desirable.

Everett’s Ph.D. work provided such an alternative interpretation. Everett noted that for a composite system – for example a subject (the “observer” or measuring apparatus) observing an object (the “observed” system, such as a particle) – the statement that either the observer or the observed has a well-defined state is meaningless; in modern parlance the observer and the observed have become entangled; we can only specify the state of one relative to the the other, i.e. the state of the observer and the observed are correlated after the observation is made. This led Everett to derive from the unitary, deterministic dynamics alone (i.e. without assuming wavefunction collapse) the notion of a relativity of states.

Everett noticed that the unitary, deterministic dynamics alone decreed that after an observation is made each element of the quantum superposition of the combined subject-object wavefunction contains two “relative states”: a “collapsed” object state and an associated observer who has observed the same collapsed outcome; what the observer sees and the state of the object have become correlated by the act of measurement or observation. The subsequent evolution of each pair of relative subject-object states proceeds with complete indifference as to the presence or absence of the other elements, as if wavefunction collapse has occurred, which has the consequence that later observations are always consistent with the earlier observations. Thus the appearance of the object’s wavefunction’s collapse has emerged from the unitary, deterministic theory itself. (This answered Einstein’s early criticism of quantum theory, that the theory should define what is observed, not for the observables to define the theory). Since the wavefunction appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam’s razor, he removed the postulate of wavefunction collapse from the theory.

Probability

A consequence of removing wavefunction collapse from the quantum formalism is that the Born rule requires derivation, since many-worlds claims to derive its interpretation from the formalism. Attempts have been made, by many-world advocates and others, over the years to derive the Born rule, rather than just conventionally assume it, so as to reproduce all the required statistical behaviour associated with quantum mechanics. There is no consensus on whether this has been successful.

Everett, Gleason and Hartle

Everett (1957) briefly derived the Born rule by showing that the Born rule was the only possible rule, and that its derivation was as justified as the procedure for defining probability in classical mechanics. Everett stopped doing research in theoretical physics shortly after obtaining his Ph.D., but his work on probability has been extended by a number of people. Andrew Gleason (1957) and James Hartle (1965) independently reproduced Everett’s work, known as Gleason’s theorem which was later extended.

De Witt and Graham

Bryce De Witt and his doctoral student R. Neill Graham later provided alternative (and longer) derivations to Everett’s derivation of the Born rule. They demonstrated that the norm of the worlds where the usual statistical rules of quantum theory broke down vanished, in the limit where the number of measurements went to infinity.

Deutsch et al

An information-theoretic derivation of the Born rule from Everettarian assumptions, was produced by David Deutsch (1999) and refined by Wallace (2002-2009) and Saunders (2004). Deutsch’s derivation is a two-stage proof: first he shows that the number of orthonormal Everett-worlds after a branching is proportional to the conventional probability density. Then he uses game theory to shows that these are all equally likely to be observed. The last step in particular has been criticised for circularity. Other reviews have been positive, although the status of these arguments remains highly controversial. It is fair to say that some theoretical physicists have taken them as supporting the case for parallel universes. In the New Scientist article, reviewing their presentation at a September 2007 conference, Andy Albrecht, a physicist at the University of California at Davis, is quoted as saying “This work will go down as one of the most important developments in the history of science.”

Wojciech H. Zurek (2005) has produced a derivation of the Born rule, where decoherence has replaced Deutsch’s informatic assumptions. Lutz Polley (2000) has produced Born rule derivations where the informatic assumptions are replaced by symmetry arguments.

Advantages

  • MWI removes the observer-dependent role in the quantum measurement process by replacing wavefunction collapse with quantum decoherence. Since the role of the observer lies at the heart of most if not all “quantum paradoxes,” this automatically resolves a number of problems; see for example Schrödinger’s cat thought-experiment, the EPR paradox, von Neumann‘s “boundary problem” and even wave-particle duality. Quantum cosmology also becomes intelligible, since there is no need anymore for an observer outside of the universe.

  • MWI is realist, deterministic, local theory, akin to classical physics (including the theory of relativity), at the expense of losing counterfactual definiteness. MWI achieves this by removing wavefunction collapse, which is indeterministic and non-local, from the deterministic and local equations of quantum theory.

  • MWI (or other, broader multiverse considerations) provides a context for the anthropic principle which may provide an explanation for the fine-tuned universe.

  • MWI, being a decoherent formulation, is axiomatically more streamlined than the Copenhagen and other collapse interpretations; and thus favoured under certain interpretations of Ockham’s razor. Of course there are other decoherent interpretations that also possess this advantage with respect to the collapse interpretations.

Common objections and misconceptions

  • MWI states that there is no special role nor need for precise definition of measurement in MWI, yet uses the word “measurement” repeatedly through out its exposition.

MWI response: “measurements” are treated a subclass of interactions, which induce subject-object correlations in the combined wavefunction. There is nothing special about measurements (they don’t trigger any wave function collapse, for example); they are just another unitary time development process. This is why no precise definition of measurement is required in Everett’s formulation.

  • The many-worlds interpretation is very vague about the ways to determine when splitting happens, and nowadays usually the criterion is that the two branches have decohered. However, present day understanding of decoherence does not allow a completely precise, self contained way to say when the two branches have decohered/”do not interact”, and hence many-worlds interpretation remains arbitrary. This is the main objection opponents of this interpretation raise, saying that it is not clear what is precisely meant by branching, and point to the lack of self contained criteria specifying branching.

MWI response: the decoherence or “splitting” or “branching” is complete when the measurement is complete. In Dirac notation a measurement is complete when:

\lang O[i]|O[j]\rang = \delta_{ij}

where O[i] represents the observer having detected the object system in the i-th state. Before the measurement has started the observer states are identical; after the measurement is complete the observer states are orthonormal. Thus a measurement defines the branching process: the branching is as well- or ill- defined as the measurement is. Thus branching is complete when the measurement is complete. Since the role of the observer and measurement per se plays no special role in MWI (measurements are handled as all other interactions are) there is no need for a precise definition of what an observer or a measurement is – just as in Newtonian physics no precise definition of either an observer or a measurement was required or expected. In all circumstances the universal wavefunction is still available to give a complete description of reality.

Also, it is a common misconception to think that branches are completely separate. In Everett’s formulation, they may in principle quantum interfere (i.e. “merge” instead of “splitting”) with each other in the future, although this requires all “memory” of the earlier branching event to be lost, so no observer ever sees two branches of reality.

  • There is circularity in Everett’s measurement theory. Under the assumptions made by Everett, there are no ‘good observations’ as defined by him, and since his analysis of the observational process depends on the latter, it is void of any meaning. The concept of a ‘good observation’ is the projection postulate in disguise and Everett’s analysis simply derives this postulate by having assumed it, without any discussion.

MWI response: Everett’s treatment of observations / measurements covers both idealised good measurements and the more general bad or approximate cases. Thus it is legitimate to analyse probability in terms of measurement; no circularity is present.

  • Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic or arbitrary.

MWI response: Everett analysed branching using what we now call the “measurement basis“. It is fundamental theorem of quantum theory that nothing measurable or empirical is changed by adopting a different basis. Everett was therefore free to choose whatever basis he liked. The measurement basis was simply the simplest basis in which to analyse the measurement process.

  • We cannot be sure that the universe is a quantum multiverse until we have a theory of everything and, in particular, a successful theory of quantum gravity. If the final theory of everything is non-linear with respect to wavefunctions then many-worlds would be invalid.

MWI response: all accepted quantum theories of fundamental physics are linear with respect to the wavefunction. Whilst quantum gravity or string theory may be non-linear in this respect there is no evidence to indicate this at the moment.

  • Conservation of energy is grossly violated if at every instant near-infinite amounts of new matter are generated to create the new universes.

MWI response: Conservation of energy is not violated since the energy of each branch has to be weighted by its probability, according to the standard formula for the conservation of energy in quantum theory. This results in the total energy of the multiverse being conserved.

  • Occam’s Razor rules against a plethora of unobservable universes – Occam would prefer just one universe; i.e. any non-MWI interpretation.

MWI response: Occam’s razor actually is a constraint on the complexity of physical theory, not on the number of universes. MWI is a simpler theory since it has fewer postulates. See the “advantages” section.

  • Unphysical universes: If a state is a superposition of two states ΨA and ΨB, i.e. Ψ = (aΨA + bΨB), i.e. weighted by coefficients a and b, then if b << a, what principle allows a universe with vanishingly small probability b to be instantiated on an equal footing with the much more probable one with probability a? This seems to throw away the information in the probability amplitudes. Such a theory makes little sense.

MWI response: The magnitude of the coefficients provides the weighting that makes the branches or universes “unequal”, as Everett and others have shown, leading the emergence of the conventional probabilistic rules.

  • Violation of the principle of locality, which contradicts special relativity: MWI splitting is instant and total: this may conflict with relativity, since an alien in the Andromeda galaxy can’t know I collapse an electron over here before she collapses hers there: the relativity of simultaneity says we can’t say which electron collapsed first – so which one splits off another universe first? This leads to a hopeless muddle with everyone splitting differently. Note: EPR is not a get-out here, as the alien’s and my electrons need never have been part of the same quantum, i.e. entangled.

MWI response: the splitting can be regarded as causal, local and relativistic, spreading at, or below, the speed of light (e.g. we are not split by Schrödinger’s cat until we look in the box). For spacelike separated splitting you can’t say which occured first — but this is true of all spacelike separated events, simultaneity is not defined for them. Splitting is no exception; many-worlds is a local theory.

Brief overview

Schematic representation of pair of “smallest possible” quantum mechanical systems prior to interaction: Measured system S and measurement apparatus M. Systems such as S are referred to as 1-qubit systems.

In Everett’s formulation, a measuring apparatus M and an object system S form a composite system, each of which prior to measurement exists in well-defined (but time-dependent) states. Measurement is regarded as causing M and S to interact. After S interacts with M, it is no longer possible to describe either system by an independent state. According to Everett, the only meaningful descriptions of each system are relative states: for example the relative state of S given the state of M or the relative state of M given the state of S. In DeWitt’s formulation, the state of S after a sequence of measurements is given by a quantum superposition of states, each one corresponding to an alternative measurement history of S.

 

Schematic illustration of splitting as a result of a repeated measurement.

For example, consider the smallest possible truly quantum system S, as shown in the illustration. This describes for instance, the spin-state of an electron. Considering a specific axis (say the z-axis) the north pole represents spin “up” and the south pole, spin “down”. The superposition states of the system are described by (the surface of) a sphere called the Bloch sphere. To perform a measurement on S, it is made to interact with another similar system M. After the interaction, the combined system is described by a state that ranges over a six-dimensional space (the reason for the number six is explained in the article on the Bloch sphere). This six-dimensional object can also be regarded as a quantum superposition of two “alternative histories” of the original system S, one in which “up” was observed and the other in which “down” was observed. Each subsequent binary measurement (that is interaction with a system M) causes a similar split in the history tree. Thus after three measurements, the system can be regarded as a quantum superposition of 8= 2 × 2 × 2 copies of the original system S.

The accepted terminology is somewhat misleading because it is incorrect to regard the universe as splitting at certain times; at any given instant there is one state in one universe.

Relative state

The goal of the relative-state formalism, as originally proposed by Everett in his 1957 doctoral dissertation, was to interpret the effect of external observation entirely within the mathematical framework developed by Paul Dirac, von Neumann and others, discarding altogether the ad-hoc mechanism of wave function collapse. Since Everett’s original work, there have appeared a number of similar formalisms in the literature. One such idea is discussed in the next section.

The relative-state interpretation makes two assumptions. The first is that the wavefunction is not simply a description of the object’s state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations. The second is that observation or measurement has no special role, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation.

The many-worlds interpretation is DeWitt’s popularisation of Everett’s work, who had referred to the combined observer-object system as being split by an observation, each split corresponding to the different or multiple possible outcomes of an observation. These splits generate a possible tree as shown in the graphic below. Subsequently DeWitt introduced the term “world” to describe a complete measurement history of an observer, which corresponds roughly to a single branch of that tree. Note that “splitting” in this sense, is hardly new or even quantum mechanical. The idea of a space of complete alternative histories had already been used in the theory of probability since the mid 1930s for instance to model Brownian motion.

 

Partial trace as relative state. Light blue rectangle on upper left denotes system in pure state. Trellis shaded rectangle in upper right denotes a (possibly) mixed state. Mixed state from observation is partial trace of a linear superposition of states as shown in lower left-hand corner.

Under the many-worlds interpretation, the Schrödinger equation, or relativistic analog, holds all the time everywhere. An observation or measurement of an object by an observer is modeled by applying the wave equation to the entire system comprising the observer and the object. One consequence is that every observation can be thought of as causing the combined observer-object’s wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many “worlds”. Since many observation-like events have happened, and are constantly happening, there are an enormous and growing number of simultaneously existing states.

If a system is composed of two or more subsystems, the system’s state will be a superposition of products of the subsystems’ states. Once the subsystems interact, their states are no longer independent. Each product of subsystem states in the overall superposition evolves over time independently of other products. The subsystems states have become correlated or entangled and it is no longer possible to consider them independent of one another. In Everett’s terminology each subsystem state was now correlated with its relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.

 

Successive measurements with successive splittings

Comparative properties and experimental support

One of the salient properties of the many-worlds interpretation is that observation does not require an exceptional construct (such as wave function collapse) to explain it. Many physicists, however, dislike the implication that there are infinitely many non-observable alternate universes.

as of 2006, there are no practical experiments that distinguish between Many-Worlds and Copenhagen. There may be cosmological, observational evidence.

Copenhagen interpretation

In the Copenhagen interpretation, the mathematics of quantum mechanics allows one to predict probabilities for the occurrence of various events. In the many-worlds interpretation, all these events occur simultaneously. What meaning should be given to these probability calculations? And why do we observe, in our history, that the events with a higher computed probability seem to have occurred more often? One answer to these questions is to say that there is a probability measure on the space of all possible universes, where a possible universe is a complete path in the tree of branching universes. This is indeed what the calculations give. Then we should expect to find ourselves in a universe with a relatively high probability rather than a relatively low probability: even though all outcomes of an experiment occur, they do not occur in an equal way. As an interpretation which (like other interpretations) is consistent with the equations, it is hard to find testable predictions of MWI.

Quantum suicide

There is a rather more dramatic test than the one outlined above for people prepared to put their lives on the line: use a machine which kills them if a random quantum decay happens. If MWI is true, they will still be alive in the world where the decay didn’t happen and would feel no interruption in their stream of consciousness. By repeating this process a number of times, their continued consciousness would be arbitrarily unlikely unless MWI was true, when they would be alive in all the worlds where the random decay was on their side. From their viewpoint they would be immune to this death process. Clearly, if MWI does not hold, they would be dead in the one world. Other people would generally just see them die and would not be able to benefit from the result of this experiment. See Quantum suicide.

The universe decaying to a new vacuum state

Any event that changes the number of observers in the universe may have experimental consequences. Quantum tunnelling to new vacuum state would reduce the number of observers to zero (i.e. kill all life). Some Cosmologists argue that the universe is in a false vacuum state and that consequently the universe should have already experienced quantum tunnelling to a true vacuum state. This has not happened and is cited as evidence in favour of many-worlds.

Many-minds

The many-worlds interpretation should not be confused with the similar many-minds interpretation which defines the split on the level of the observers’ minds.

Reception

There is a wide range of claims that are considered “many-worlds” interpretations. It is often claimed by those who do not believe in MWI that Everett himself was not entirely clear as to what he believed; however MWI adherents (such as DeWitt, Tegmark, Deutsch and others) believe they fully understand Everett’s meaning as implying the literal existence of the other worlds. Additionally Everett’s reported belief in quantum immortality, requires belief in the reality of all the many-worlds represented by the components of the uncollapsed universal wavefunction.

“Many-worlds”-like interpretations are now considered fairly mainstream within the quantum physics community. For example, a poll of 72 leading physicists conducted by the American researcher David Raub in 1995 and published in the French periodical Sciences et Avenir in January 1998 recorded that nearly 60% thought many-worlds interpretation was “true”. Max Tegmark also reports the result of a poll taken at a 1997 quantum mechanics workshop. According to Tegmark, “The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations.” Other such polls have been taken at other conferences: see for instance Michael Nielsen‘s blog report on one such poll. Nielsen remarks that it appeared most of the conference attendees “thought the poll was a waste of time”. MWI sceptics (for instance Asher Peres) argue that polls regarding the acceptance of a particular interpretation within the scientific community, such as those mentioned above, cannot be used as evidence supporting a specific interpretation’s validity. However, others note that science is a group activity (for instance, peer review) and that polls are a systematic way of revealing the thinking of the scientific community.

A 2005 minor poll on the Interpretation of Quantum Mechanics workshop at the Institute for Quantum Computing University of Waterloo produced contrary results, with the MWI as the least favored.

One of MWI’s strongest advocates is David Deutsch. According to Deutsch, the single photon interference pattern observed in the double slit experiment can be explained by interference of photons in multiple universes. Viewed in this way, the single photon interference experiment is indistinguishable from the multiple photon interference experiment. In a more practical vein, in one of the earliest papers on quantum computing, he suggested that parallelism that results from the validity of MWI could lead to “a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it”. Deutsch has also proposed that when reversible computers become conscious that MWI will be testable (at least against “naive” Copenhagenism) via the reversible observation of spin.

Asher Peres was an outspoken critic of MWI, for example in a section in his 1993 textbook with the title Everett’s interpretation and other bizarre theories. In fact, Peres questioned whether MWI is really an “interpretation” or even if interpretations of quantum mechanics are needed at all. Indeed, the many-worlds interpretation can be regarded as a purely formal transformation, which adds nothing to the instrumentalist (i.e. statistical) rules of the quantum mechanics. Perhaps more significantly, Peres seems to suggest that positing the existence of an infinite number of non-communicating parallel universes is highly suspect as it violates those interpretations of Occam’s Razor that seek to minimize the number of hypothesized entities. Proponents of MWI argue precisely the opposite, by applying Occam’s Razor to the set of assumptions rather than multiplicity of universes. In Max Tegmark‘s formulation, the alternative to many-worlds is the undesirable “many words”, an allusion to the complexity of von Neumann’s collapse postulate.

MWI is considered by some to be unfalsifiable and hence unscientific because the multiple parallel universes are non-communicating, in the sense that no information can be passed between them. Others claim MWI is directly testable. Everett regarded MWI as falsifiable since any test that falsifies conventional quantum theory would also falsify MWI.

According to Martin Gardner MWI has two different interpretations: real or unreal, and claims that Stephen Hawking and Steve Weinberg favour the unreal interpretation. Gardner also claims that the interpretation favoured by the majority of physicists is that the other worlds are not real in the same way as our world is real, whereas the “realist” view is supported by MWI experts David Deutsch and Bryce DeWitt. However Stephen Hawking is on record as a saying that the “other worlds are as real as ours” and Tipler reports Hawking saying that MWI is “trivially true” (scientific jargon for “obviously true”) if quantum theory applies to all reality. Roger Penrose agrees with Hawking that QM applied to the universe implies MW, although he considers the current lack of a successful theory of quantum gravity negates the claimed universality of conventional QM.

Speculative implications

Speculative physics deals with questions also discussed in science fiction.

Quantum suicide thought experiment

It has been claimed that there is a thought experiment that would clearly differentiate between the many-worlds interpretation and other interpretations of quantum mechanics. It involves a quantum suicide machine and an experimenter willing to risk death. However, at best, this would only decide the issue for the experimenter; bystanders would learn nothing. The flip side of quantum suicide is quantum immortality.

Weak coupling

Another speculation is that the separate worlds remain weakly coupled (e.g. by gravity) permitting “communication between parallel universes”. This requires that gravity be a classical force and not quantized.

Similarity to Modal Realism

The many-worlds interpretation has some similarity to modal realism in philosophy, which is the view that the possible worlds used to interpret modal claims actually exist. Unlike philosophy, however, in quantum mechanics counterfactual alternatives can influence the results of experiments, as in the Elitzur-Vaidman bomb-testing problem or the Quantum Zeno effect.

Time travel

The many-worlds interpretation could be one possible way to resolve the paradoxes  that one would expect to arise if time travel turns out to be permitted by physics (permitting closed timelike curves and thus violating causality). Entering the past would itself be a quantum event causing branching, and therefore the timeline accessed by the time traveller simply would be another timeline of many. In that sense, it would make the Novikov self-consistency principle unnecessary.

Many-worlds in literature and science fiction

Main article: Parallel universe (fiction)

 

A map from Robert Sobel‘s novel For Want of a Nail, illustrates how small events – in this example the branching or point of divergence from our history is in October 1777 – can profoundly alter the course of history. According to the many-worlds interpretation every microscopic event is a branch point; all possible alternative histories actually exist.

The many-worlds interpretation (and the somewhat related concept of possible worlds) have been associated to numerous themes in literature, art and science fiction.

Some of these stories or films violate fundamental principles of causality and relativity, and are extremely misleading since the information-theoretic structure of the path space of multiple universes (that is information flow between different paths) is very likely extraordinarily complex. Also see Michael Clive Price’s FAQ referenced in the external links section below where these issues (and other similar ones) are dealt with more decisively.

Another kind of popular illustration of many-worlds splittings, which does not involve information flow between paths, or information flow backwards in time considers alternate outcomes of historical events. According to the many-worlds interpretation, all of the historical speculations entertained within the alternate history genre are realized in parallel universes.

Source: Wikipedia.com

Flash Forward: Schrödinger’s Cat

Schrödinger’s cat

Again, I will need some time to digest this episode six titled “Scary Monsters and Super Creeps.” Simon is no Charlie from LOST. Simon openly addresses the cause of the flashforward with a pretty lady he is seducing on a bullet train. He explains himself as a famous quantum physicist and that he knows what caused the flashforward. Simon puts it in terms of quantum physics and a kitten citing “quantum superpositions” and “Schrödinger’s cat.”

Until I can post my review over the next few days, I thought I would leave you with the thought experiment called Schrödinger’s cat.

Schrödinger’s cat

Schrödinger’s cat is a thought experiment, often described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung — literally, entanglement.

Origin and motivation

Schrödinger’s thought experiment was intended as a discussion of the EPR article, named after its authors — Einstein, Podolsky, and Rosen — in 1935. The EPR article had highlighted the strange nature of quantum superpositions. Broadly stated, a quantum superposition is the combination of all the possible states of a system (for example, the possible positions of a subatomic particle). The Copenhagen interpretation implies that the superposition undergoes collapse into a definite state only at the exact moment of quantum measurement.

Schrödinger and Einstein had exchanged letters about Einstein’s EPR article, in the course of which Einstein had pointed out that the quantum superposition of an unstable keg of gunpowder will, after a while, contain both exploded and unexploded components.

To further illustrate the putative incompleteness of quantum mechanics, Schrödinger applied quantum mechanics to a living entity that may or may not be conscious. In Schrödinger’s original thought experiment, he describes how one could, in principle, transform a superposition inside an atom to a large-scale superposition of a live and dead cat by coupling cat and atom with the help of a “diabolical mechanism”. He proposed a scenario with a cat in a sealed box, wherein the cat’s life or death was dependent on the state of a subatomic particle. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead (to the universe outside the box) until the box is opened.

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse. The thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger cat thought experiment remains a topical touchstone for all interpretations of quantum mechanics. How each interpretation deals with Schrödinger’s cat is often used as a way of illustrating and comparing each interpretation’s particular features, strengths, and weaknesses.

The thought experiment

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

The above text is a translation of two paragraphs from a much larger original article that appeared in the German magazine Naturwissenschaften (“Natural Sciences”) in 1935.

Schrödinger’s famous thought experiment poses the question, when does a quantum system stop existing as a mixture of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The purpose of the thought experiment is to illustrate this apparent paradox. Our intuition says that no observer can be in a mixture of states; yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Albert Einstein, who was impressed by the ability of the thought experiment to highlight these issues. In a letter to Schrödinger dated 1950, he wrote:

You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gunpowder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.

Note that no charge of gunpowder is mentioned in Schrödinger’s setup, which uses a Geiger counter as an amplifier and hydrocyanic poison instead of gunpowder. The gunpowder had been mentioned in Einstein’s original suggestion to Schrödinger 15 years before, and apparently Einstein had carried it forward to the present discussion.

Copenhagen interpretation

In the Copenhagen interpretation of quantum mechanics, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement, or observation, is not well-defined in this interpretation. Some interpret the experiment to mean that while the box is closed, the system simultaneously exists in a superposition of the states “decayed nucleus/dead cat” and “undecayed nucleus/living cat”, and that only when the box is opened and an observation performed does the wave function collapse into one of the two states. More intuitively, some feel that the “observation” is taken when a particle from the nucleus hits the detector. This line of thinking can be developed into objective collapse theories. In contrast, the many worlds approach denies that collapse ever occurs.

Steven Weinberg said:

All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong; physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.

Everett’s many-worlds interpretation & consistent histories

In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist, but are decoherent from each other. In other words, when the box is opened, that part of the universe containing the observer and cat is split into two separate universes: one containing an observer looking at a box with a dead cat, and one containing an observer looking at a box with a live cat.

Since the dead and alive states are decoherent, there is no effective communication or interaction between them. When an observer opens the box, he becomes entangled with the cat, so “observer states” corresponding to the cat’s being alive and dead are formed, and each can have no interaction with the other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories. Only the “dead cat” or “alive cat” can be a part of a consistent history in this interpretation.

Roger Penrose criticises this:

“I wish to make it clear that, as it stands, this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat”,

although the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.

A variant of the Schrödinger’s Cat experiment, known as the quantum suicide machine, has been proposed by cosmologist Max Tegmark. It examines the Schrödinger’s Cat experiment from the point of view of the cat, and argues that by using this approach, one may be able to distinguish between the Copenhagen interpretation and many-worlds.

Ensemble interpretation

The ensemble interpretation states that superpositions are nothing but subensembles of a larger statistical ensemble. That being the case, the state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger’s Cat paradox a trivial nonissue.

This interpretation serves to discard the idea that a single physical system in quantum mechanics has a mathematical description that corresponds to it in any way; the problem should be renamed Schrödinger’s cats.

Objective collapse theories

According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility, etc.) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as “the cat observes itself”, or “the environment observes the cat”.

Objective collapse theories require a modification of standard quantum mechanics to allow superpositions to be destroyed by the process of time evolution.

Practical applications

The experiment is a purely theoretical one, and the machine proposed is not known to have been constructed. Analogous effects, however, have some practical use in quantum computing and quantum cryptography. It is possible to send light that is in a superposition of states down a fiber optic cable. Placing a wiretap in the middle of the cable that intercepts and retransmits the transmission will collapse the wave function (in the Copenhagen interpretation, “perform an observation”) and cause the light to fall into one state or another. By performing statistical tests on the light received at the other end of the cable, one can tell whether it remains in the superposition of states or has already been observed and retransmitted. In principle, this allows the development of communication systems that cannot be tapped without the tap being noticed at the other end. This experiment can be argued to illustrate that “observation” in the Copenhagen interpretation has nothing to do with consciousness (unless some version of panpsychism is true), in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different. Such a test would only work if the collapse occurs after (as opposed to before) observation; otherwise, it would appear collapsed whether it had been wiretapped or not.

In quantum computing, the phrase “cat state” often refers to the special entanglement of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1;

i.e., |00...0\rangle + |11...1\rangle.

Extensions

Although discussion of this thought experiment talks about two possible states (cat alive and cat dead), in reality, there would be a huge number of possible states, since the temperature and degree and state of decomposition of the cat would depend on exactly when and how (as well as if) the mechanism was triggered, as well as the state of the cat prior to death.

In another extension, prominent physicists have gone so far as to suggest that astronomers observing dark matter in the universe in 1998 may have “reduced its life expectancy” through a pseudo-Schrödinger’s Cat scenario, although this is a controversial viewpoint.

Another variant on the experiment is Wigner’s friend, in which there are two external observers, the first of whom opens and inspects the box and then communicates his observations to a second observer. The issue here is, does the wave function collapse when the first observer opens the box, or only when the second observer is informed of the first observer’s observations? Another extension is a scenario wherein the inside of the box is videotaped and played to an audience at a later time, or played back to the cat while in the box. If dead, there would be no observer to cause disentanglement; if alive, disentanglement would occur.

Source: Wikipedia