Molecules

Quantum Interpretations

• Copenhagen Interpretation - The mathematics of quantum theory dictates that quantum system exists in superposition of states. It is proposed that a certain state reveals its identity only through the measurement. This kind of interpretation is something extraneous to the mathematical formulaion - something that tacks on to the theory. Such situation does not bother practical physicists, who just carry out routine calculations or experiments, as long as the rules of quantum theory yield consistent results, and it is kept in mind that mathematical models do not always make sense to our everyday experience. It is the pure theorists and philosophers, who are very un-comfortable with such arbitrary rule. Schrodinger himself was particularly distressed about two things -- the idea that a quantum system could be in a superposition of states, and the requirement of an intelligent observer to "collapse the wave function", i.e., to force a quantum system to take up an unique state. He used a "thought experiment" to demonstrate the absurdity of such an interpretation, which could result in a cat half alive and half dead. This is known as the "Schrodinger's cat paradox".
  
  According to the idea of superposition of states, a radioactive nucleus could be half decayed and half not decayed, unless its state is measured. Schrodinger pointed out that the radioactive substance could be sealed in a box with a detector to monitor it. The

  detector is wired up to release a cloud of poison gas if the radioactive material decays; while the famous cat is kept inside. If the box is sealed and nobody looks into it, then the radioactive nucleus is in a fifty-fifty superposition of states, so are the poison gas (has and has not been released) and the cat (has and has not been killed, see Figure 12-06a). Thus, everything remains in limbo until an intelligent observer looks into the box. At this point, the superposition collapses and the cat becomes either dead or alive. The paradox has been resolved in 1970 by realizing that entanglement with the environment would collapse the cat's superposition almost instantly - the cat could not be both alive and dead (See superposition in Figure 05c, Mathematical Schrodinger's Cat). The Copenhagen interpretation is still enshrined in most textbooks as the standard interpretation.

  Figure 12-06a Schrodinger's Cat

  
  
• Decoherence - It is suggested that coupling between a quantum system in superposition and the environment in which it is embedded leads the system to 'collapse' or decay over time into one state or another. This is because in a large collection of atoms it is impossible for the quantum waves (in the superposition) to overlap sufficiently to allow them to combine into a state known as "coherence" (See "Mathematical Schrodinger's Cat"), in other words, they don't interfer with each other any more. The rate of decoherence depends on the size of the quantum system. Physicists can now create and maintain quantum particles such as atoms or photons in superpositions for significant periods of time, if the coupling to the environment is weak. But for a system as big as a

  cat, comprised of billions upon billions of atoms, decoherence happens almost instantaneously, so that the cat can never be both alive and dead for any measurable instant. Figure 12-06b is a crude attempt to depict decoherence in layman's perception. The undulating ocean wave represents the coherent state in which every water droplets moves in unison; while the wave breaker in the right panel is the environment which breaks (de-coheres) the wave into its individual components.

  Figure 12-06b Decoherence

  N.B. Decoherence can be considered as transfer of entanglement to the environment.

  
  The thought experiment of the Schrodinger's cat can now be implemented in its miniaturized version with an atom moving left or right to represent the dead or alive of the cat (quantum cat or qcat) and the radioactive trigger becomes the distance of the electron (yellow circle in Figure 12-06c) to the nucleus (red circle): closer separation mimics the decayed state while that further away is

  the un-decayed state. By using lasers to manipulate the atom, the motion and separation can be coupled (entangled) as shown in Figure 12-06c. Thus, the qcat is both dead and alive until a measurement of the atomic state is performed. Other experiments scale up this basic idea, so that huge numbers of atoms become entangled and enter states that classical physics would deem impossible. A small leap of imagination extends the same to the very special kind of large, warm system - life. Preliminary investigation suggests that migratory bird's eye has a type of molecule in which two electrons form an entangled

  Figure 12-06c Quantum Cat [view large image]

  pair with zero total spin. It would responses to the inclination of the Earth's magnetic field to direct the path of migration (through a sequence of bio-chemical processes).

  Recently in 2004, half-a-dozen experiments have been designed to determine the boundary between the classical and quantum world. One experiment shown in Figure 12-06d fires C70 (70 carbon atoms in the soccerball-like crystal of about 1 nm across) fullerene balls at 190 m/sec toward two diffraction gratings. The first grating creates the matter wave from the fullerenes. The wave is then diffracted by the second grating and the interference pattern is formed on the detecting screen demonstrating the wave property of the fullerenes. However, the interference pattern fades away if the fullerenes are heated by a laser heater (to about 2700oC) or collide with gas (leaking into the vacuum chamber of the experiment). No one has a definitive answer for how the striking photons or molecules switch between quantum and classical behavior. One explanation is that the interaction causes an uncertainty in the position of the fullerenes, blurring the interference pattern. Another argument asserts that the disappearance of the quantum property is caused by entanglement between the photons/molecules, the fullerenes, and the rest of the world (the wall of the chamber).

  Figure 12-06d Matter-Wave Experiment and quantum-classical boundary

  Report in 2007 indicates that quantum effects have been detected in objects as large as buckyballs, but not viruses. The boundary seems to be located at about 10 nm (see Figure 12-06d). It is found that beside decoherence, the coarseness of detecting instruments also plays a role to induce transition from quantum to classical reality. Nevertheless, there are many more attempts to apply quantum theory to macroscopic world such the "Many World Interpretation" and the "Quantum Universe" with dubious validity.
  
  

  Hidden Variables - This interpretation is based on the assumption that all the usual versions of quantum mechanics are incomplete, and that there is an underlying layer of reality which contains additional information about the world. This additional information is in the form of the hidden variables. If physicists knew the values of these hidden variables, the arguments goes, they could predict the precise outcomes of particular measurements, not just the probabilities of getting particular results. A helpful analogy can be made with a deck of playing cards prepared by a cheating card dealer (Figure 12-06e). He knows precisely the sequence in the deck; only the ignorant gamblers insist that the chance of picking a particular card is 1 in 52. The idea on hidden variables can be traced back to the 1920s and 1930s in the form of EPR (Einstein-Podolsky-Rosen) paradox. These scientists had a lot of problems with quantum mechanics in general and entanglement in particular.

  Figure 12-06e Hidden Variables [view large image]

  
  Entanglement occurs for example, in the decay of the pi meson into an electron-positron pair (Figure 12-06f). Since the spin for the pi meson is 0, the spin for the electron-positron pair must be opposite according to the conservation of angular momentum. Therefore, no matter how far apart are the members of this pair, if the spin is flipped for one of the member, the spin for the other member will also be flipped to the opposite at precisely the same moment. This non-local influence (objects can influence each other only locally according to classical physics) occur instantaneously, as if some form of communication, which Einstein called a

  "spooky action at a distance", operates not just faster than the speed of light, but infinitely fast. According to EPR (Einstein-Podolsky-Rosen), all the weird aspects come about due to our lack of the complete understanding of the subatomic world. No faster-than-light signaling between the entangled pair need be invoked if their properties had been set from the start. These well-defined properties, which quantum mechanics does not describe, are known as "hidden variables". On the other hand, quantum enthusiasts would argue that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

  Figure 12-06f Entanglement [view large image]

  The paradox is a thought experiment in which the particles can have both their position and momentum accurately measured in violation of the uncertainty principle; unless measuring one particle instantaneously affects the other (entanglement) in violation of special relativity.

  
  Then a seminal paper by John Bell in 1964 shows that if EPR were correct, the results found by two widely separated detectors measuring certain properties of the two entangled particles (such as the spin orientations about various randomly chosen detecting axes) would have to agree (match) more than 50% of the time - this is known as the Bell's theorem, or Bell's inequality. Starting

  	in early 1970s, technology has improved significantly to enable the required experiments for resolving the paradox. It culminated in the early 1980s, when the Aspect experiment firmly established that measurements from the two detectors do not agree more than 50% of the time. Quantum mechanics survived the test and entanglement will stay with us into the
  Figure 12-06g Bell's Theorem for Dummies [view large image]	quantum computing age. Figure 12-06g provides a very specific example to illustrate how underlying pre-arrangement (the hidden variables) can bump up the chance of ramdon match.

  A theory published in Nature Physics 2012 asserted that the wave function cannot be interpreted as the result of missing information. Similar to the Bell's theorem, it shows that theories that treat the wave function in terms of lack of knowledge of a system's physical state will also fail to reproduce the predictions of quantum mechanics. Experimental checking of this new theorem is being arranged.
  
  The tests on the Bell's theorem have at least two loopholes until 2015 when new technology allows experiment to skirt such problems. One problem is known as the "detection loophole" with the lost up to 80% of the entangled qbits (in the forms of photons) and it is not sure that the remaining 20% is the true representative. The use of closely spacing atoms may retain more qbits for the measurements, but it could be masked by under speed of light communication, and it thus earns the name as

  "communication loophole". The 2015 experiment at Delft University solves both problems as shown in Figure 12-06h. It produces entanglement of two electrons inside two diamonds respectively (separated by 1.3 km - enough to close the communication loophole and with no lost of entangled qbits) via the entanglement of the photons emitted by each. The occurrence is not very often - just a few per hour. Eventually, 245 measurements were taken to show that the standard quantum view is valid. Difficulty of the experiment produced a p-value of only 4% - a statistical significance just passes the usual 5% and is much shorter than the 1/106 standard for experiment in physics. Anyway, this experiment also guarantees the security in "quantum cryptography", which may be hacked through the loopholes.

  Figure 12-06h Bell Test, 2015

  See more detail in "Quantum 'spookiness' passes toughest test yet".

  One argument for "hidden variables" suggests that the hidden links were established long time ago; it is there already before the measurement, free-will or random number generator in the measuring process notwithstanding. A 2017 experiment using star light (red, or blue) to trigger the measurement shows that quantum entanglement comes with the "action at a distance" property, i.e., no "hidden variables" to link the pair as far back as 600 years ago when the star light was emitted .
  
  See "Bell Test Experiments" over the years, and the 2020 update on the subject.
  
  

  Many Worlds - This interpretation states that whenever the world is faced with a choice at the quantum level, the universe divides into many, so that all possible options are followed, i.e., all the states are realized. Originally, it was suggested that we might think of the experiment with two slits in terms of two different realities, in one of which the electron goes thought slit 1 while in the other it goes through slit 2. Our world is a recombination of the two possibilities (the two worlds merge to become one again, see double slit pattern in Figure 12-06i), producing

  Figure 12-06i Double-Slit Experiment [view large image]

  interference between the two worlds. When we look to see which slit the electron goes through, we make one world real while the other disappears, so there is no interference (see single slit pattern in Figure 12-06i).

  The idea has been expanded further to include each possible outcome in the large-scale everyday world, and they all occur in different "parallel" universes. We only experience the copy for our own world. It has been shown that such interpretation leads to exactly the same predictions for the outcome of experiments as the other interpretations. The only problem is that there is no way to test, and it is difficult to imagine the mind-boggling idea of 10100 slightly imperfect copies of oneself all constantly splitting into further copies (see Figure 12-06j). However, some cosmologists find it useful to get around the puzzle, which is insurmountable in the Copenhagen interpretation (it requires an outside observer to work), of explaining what observation can collapse the wave function of the entire Universe and bring it into reality. Such interpretation has received a boost in 2007 from the research which links the branching structure of the multiverse to the probability interpretation of the wave function in

  Figure 12-06j Quantum Worlds [view large image]

  quantum mechanics, and thus provides an explanation for the origin of the empirical rule.

  
  

  Penrose Interpretation - Recently in 2005, Roger Penrose comes up with a new quantum interpretation. According to his theory each quantum event would create its own distortions in space-time, which requires energy to sustain. Since the stability of a system depends on the amount of energy involved (the lesser the easier to maintain), a macroscopic object tends to settle down in only one location (producing only one distorted space-time). According to his calculation, for microscopic objects such as electrons, atoms, and molecules the distortion is negligible; they can persist with the many quantum states (superposition) essentially forever as standard quantum theory predicts. Large objects, on the other hand, create such significant gravitational fields that the duplicate states vanish almost at once. For a dust speck, the process takes nearly a second - long enough that it might be possible to measure. Figure 12-06k shows a tabletop version of the more expensive and technically more difficult experiment for verifying the Penrose interpretation (in outer space). It directs a laser beam (separated by a beam splitter) toward a very tiny mirror to check if it can be in two states at the same time.

  Figure 12-06k Penrose Interpretation

  Until now, the experiment is running with a significantly smaller mirror than needed to test Penrose's theory. If the Penrose interpretation is correct, the two quantum states of the mirror (moved and unmoved) now consisting of a fullerene ball (a collection of seventy carbon atoms) will gradually change to just one state as the size of mirror increases to a dust speck. Figure 12-06l is a pictorial summary of the different kinds of interpretation.

  Figure 12-06l Interpretations

  This is Penrose's way of doing Quantum Gravity, that is, by introducing gravity into quantum theory instead of the usual way round (see earlier idea in "Models for Univetsal Reduction of Macroscopic Quantum Fluctuations", and "Gravitation and Quantum Mechanics of Macroscopic Objects").
  
  

  In an article commemorates the 50th anniversary of the "New Scientist" magazine, Roger Penrose suggests that there are three kinds of reality: the physical, the mental and the mathematical, with something (as yet unknown) profoundly mysterious in the relations between them. According to this view, the various "Quantum Interpretations" are attempts to link the mathematical reality to the physical or mental reality. Figure 12-06m shows the mathematical reality as the patterns of interference computed from a mathematical formula, while the physical reality is in the form of photographic plate with the darker strip corresponding to the higher value of the curve. The mental reality is the image of dark and white strips formed in the retina and perceived by our consciousness.

  Figure 12-06m Reality

  
  Another scheme is to consider the physical reality as primary, while the mental and mathematical realities as secondary. In this view, some processing steps are required to arrive at the secondary reality such as neuro-activity and computation. But the secondary reality does not always produce a corresponding primary reality. For examples, dreams and other altered mental states are not real; and mathematical formulas can generate result, which has no match in reality (unless the concept of multiverse is invoked).
  
  As Stephen Hawking points out in an article from "Extreme Physics" (published by Scientific American, 2013) each theory may have its own version of reality and none of them can be said to be more real than any other. It is similar to the concept of "Effective Theory", which employs different method to describe different system.

Table 12-01 Status of Various Quantum Interpretations

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