Quantum collapse

Quantum collapse is hypothesised in some interpretations of quantum mechanics and refers to the transition of a quantum system from a superposition of states to a component state. The process is also known as collapse of the wave function or collapse of quantum states.

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There have been several different proposed interpretations of what brings about the collapse and what it actually represents. Some of the more questionable interpretations of quantum mechanics are used by believers of pseudoscience in an attempt to give support to their perspectives.

What is a collapse?

A quantum mechanical system can be treated as a vector (or "state") within a state space. Given a property of that system, there will be vectors within the state space that are distinguished by the property in question having definite values. For example, a quantum particle in a box only has access to very specific energy levels (as opposed to a classical particle, which can have any positive value for its energy), and associated with each of those energy levels is a different state. Similarly, an electron in a hydrogen atom has access to specific discrete energy levels. Associated with each state is a wave function. From the wave function, one can determine the probability that a measurement performed on the system will yield a particular result. For instance, if we know the wave function of an electron in a hydrogen atom, we can find the probability that a measurement of the electron's position will find it at 1 angstrom (10^-10 meters) away from the nucleus. We can also find the probability that the electron will be found 1 meter away from the nucleus (it's very low), or half an angstrom away from the nucleus (probably higher).

A counter-intuitive property of quantum systems is that each state can be expressed as a linear combination of other states (this is known as a "superposition" of the other states). Given a sufficiently large number of states, every other state can be expressed as a superposition of the original states. A well-known illustration of superposition is Schrödinger's cat.

When a measurement of a property is carried out, the system "collapses" to one of the state with a defined value for that property, and the measurement corresponding to that particular state is observed. A system in a superposition of states 1, 3, 5, and 6 might collapse to state 3. The probability of collapsing to a given state is determined by the wave function of the system before the collapse.

Note that a superposition of states is never actually observed, since the system collapses to a single state at the instant that a measurement takes place. The superposition can be interpreted as the description of potential measurement outcomes, while the state of the system after the collapse takes place is the actual realized outcome. The collapse can thus be defined as the transition between the potential and the actual. However, the situation is a bit more complicated than that, since whether something is a "superposition" of states, or a "pure" state, depends on the property being measured. A state with a well-defined position will be a superposition of states with well-defined momentum, and a state with well-defined momentum will be a superposition of states with well-defined position (the fact that no state has both well-defined is related to the Heisenberg uncertainty principle).

Example

For illustrative purposes, suppose that we have a hypothetical quantum system with several states with well-defined momentum. Those states can be represented by (1), (2), (3), (4), etc. Now suppose that the system is in a superposition of states (1), (5), and (6). Now, say that we want to measure its momentum. The instant we make the measurement, the system collapses to one of the basis states. If it collapses to (1), we measure the value for momentum that is associated with the state (1). If it collapses to (5) instead, we measure a value for momentum that is associated with the state (5). The same is true if the system collapses to state (6).

Interpretations of the collapse

The nature of the process of collapse invokes some interesting questions:

1. What brings the collapse about?
2. When does the collapse occur?

There have been several proposed answers to these questions, each bringing a different interpretation of the process. Some of the higher-profile interpretations are:

• The Mainstream Interpretation, the most popular interpretation among scientists
• The Many-Worlds Interpretation, in which all possible outcomes occur across several "splits" of the Universe
• The Consciousness Interpretation, in which collapse occurs when a consciousness becomes aware of it

Mainstream interpretation

The interpretation accepted by most physicists is called the Copenhagen interpretation.

Many-worlds interpretation

The many-world interpretation tries to evade the concept of a collapse. Instead, it states that rather than a strict "collapsing" of the wave function into a single state, all possible outcomes occur when a measurement is made. It's just that the universe "splits" for each possible outcome, and each unique outcome is assigned to a different universe. If there are two possible outcomes for a measurement (call them A and B), then the universe splits in two — one universe in which outcome A occurs, and another in which outcome B occurs. Carrying this idea into the macroscopic realm, you could say that there's a universe in which Hitler wins, or Hannah Montana becomes a successful pop sensation. We're just lucky that we live in a universe in which Hitler lost and Miley Cyrus isn't popular. Of course, that's assuming that such timelines actually exist within the set of possible collapse sequences. Additionally, the number of universes with a trait such as "Nazi victory" would itself be near-infinite; if you're wondering "what would have happened" 'if a different side had won a particular war, the many-worlds model couldn't give you a more concise answer than "everything that possibly could have, quantum states permitting".

But instead of wondering when a collapse occurs, we have a clear statement when a split in the universe occurs.

Worlds irrevocably "split" at the sites of measurement-like interactions associated with thermodynamically irreversible processes. [1]

The many-worlds interpretation is nice fodder for science fiction stories, but there are some glaring issues with it. By replacing the concept of a collapse to a single state with a split in the universe, it only replaces one mystery with another. Furthermore, the idea would seem to require that there be no limit to the number of universes that can exist, which presents something of a difficulty. All other things being equal, theories that require infinities are not generally regarded as superior to those without them. Of course an infinitude of mutually incompatible superpositional states is also a problem for many people, some people intuitively prefer many universes, others prefer many superpositions.

Consciousness interpretation

The consciousness interpretation addresses the question of when the collapse occurs by stating that it happens when a consciousness (usually human, but sometimes otherwise) becomes aware of the result of a measurement, and not before.

Postulates that the observer obeys different physical laws than the non-observer, which is a return to vitalism.[2]

This interpretation is based on the idea that consciousness is a separate entity from the material world and the mathematical descriptions of it; after all, the mathematical formalism of quantum mechanics does not explicitly describe a collapse. The idea is that the intersection of consciousness and the physical world is what causes a collapse. This idea is logically consistent, and there are, and have been, a fair number of respected physicists that took a very long look at it. However, you can probably already see that there's a ton of room for pseudoscience to operate here, and it has.

An interesting argument against this interpretation has been put forward by Shimon Malin.[3] Malin's argument is presented below.

Suppose a measurement of an electron's spin component along some direction is being measured. The result can either be "up" or "down". The result of the measurement is automatically communicated to a printer that can either print "up" or "down". If human consciousness is what causes the collapse to the observed state, then the collapse would only occur when someone read the printout, and not before. Now suppose that the printer has just enough ink to print "up", and not enough ink to print "down". Furthermore, if the printer runs out of ink, a bell sounds in a secretary's office. If the secretary hears the bell, a collapse to "down" has clearly occurred before the bell sounded. If the secretary does not hear the bell, a collapse to "up" must have occurred--and no human interaction was necessary at all.

Some people have suggested that the consciousness involved in the collapse process is not a human consciousness, but God himself. That type of idea is not the kind of thing that science can address. However, it can be considered logically. One problem with it is that it would require that God be less than all-knowing, because otherwise he would always be observing all particles at all times – in which all particles would remain in a "collapsed" state, and collapse wouldn't even exist as a scientific idea.

Many New Agers believe this interpretation, and may not even be aware that it is not the mainstream scientific consensus. The idea that consciousness causes collapse is one basis for quantum woo and quantum healing, which may both be summarized as "the universe does that which conscious minds expect it to." Notice, however, that the original hypothesis merely posits that conscious observation is necessary for collapse – not conscious anticipation. There is no experimental evidence even remotely suggesting that collapse will occur in accordance with what the experimenter is thinking about. Hence, a more scientifically-consistent model of quantum healing might say that you are simultaneously sick and healthy until the practitioner examines you, at which point you "collapse" into one state or the other – but we have no means of influencing that state, even if we think very good thoughts.

About 6% of physicists appear to believe in that interpretation as well, among them some rather big names like Eugene Wigner, Roger Penrose, and John von Neumann.[4] This is quite a bit more than the number of climate scientists that disbelieve in human-caused global warming (about 3%) or biologists that disbelieve in evolution (perhaps 0.01%), but probably isn't enough to call it a "mainstream" minority view like Many Worlds Interpretation.[5]

See also

• Quantum woo
• Non-materialist neuroscience

References

1. http://kuoi.com/~kamikaze/doc/many-worlds-faq.html
2. http://kuoi.com/~kamikaze/doc/many-worlds-faq.html
3. Malin, Shimon. Nature Loves To Hide. New York: Oxford University Press, 2001.
4. M. Schlosshauer; J. Koer; A. Zeilinger (2013). "A Snapshot of Foundational Attitudes Toward Quantum Mechanics".
5. A cautionary note — even assuming the sample was representative of physicists at large, the low sample size of the survey gives a margin of error of no less than ±8% at minimum.