Quantum Mechanics by T L Hurst - Revised 25th November 2011X
This paper discusses aspects of Quantum Mechanics that are of interest to non-scientists, but seem to be widely misunderstood. The Uncertainty Principle, the Dual Slit experiment and the Observer Effect are briefly discussed, as are the standard and alternative interpretations of quantum mechanics. Two thought experiments are considered: Schrodinger's Cat, and the Light Switch.
In this paper we take a look at some aspects of Quantum Mechanics that are of interest to non-scientists, but seem to be widely misunderstood. These are the "observer effect", the two standard interpretations of QM, and an alternative interpretation. Two thought experiments are considered: Schrodinger's Cat, and the Light Switch.
But first, a brief introduction to some key concepts in quantum mechanics:
The Uncertainty Principle - If you measure one property of a sub-atomic particle, such as its position, other properties, such as its momentum, are uncertain. This is because quantum entities are fundamentally probabilistic rather than deterministic.
- Wave/Particle Duality - Light and sub-atomic particles can behave as waves or particles. See the dual slit experiment below...
The Dual Slit Experiment
The dual slit experiment illustrates the wave/particle duality of light:
A beam of coherent light shone on a barrier with one slit shows a single band of illumination when displayed on a screen. This behaviour is consistent with the light being made up of discrete particles.
A beam of coherent light shone on a barrier with two slits in it can show a regular interference pattern on the screen. That is because the light passing through the two slits alternately cancel and add depending on their phase amplitude when they meet on the screen. This behaviour is consistent with the light being made up of waves.
If the beam of light is reduced to a single photon at a time, an interference pattern slowly builds up on the screen, just as if there were multiple photons interfering. It is as if the photon is passing through BOTH slits, and interfering with itself.
- If a device is added to determine which slit the photon passes through, the interference pattern disappears, an is replaced by two overlapping bands of illumination. This is known as the "observer effect", and is discussed below...
The Observer Effect
The "observer effect" in quantum mechanics can, mistakenly, be interpreted as providing scientific evidence that supports the philosophic view that reality is mind-dependent.
The effect arises out of the idea that quantum entities are fundamentally probabilistic. I.e. Any property of a quantum entity, such as position, has a range of values with given probabilities. It is not meaningful to ask where the entity actually is. It is simultaneously in all the positions. This is known as "quantum superposition".
By contrast, macro entities exist in a single defined state at any one time. This gives rise to a quandary as macro entities are made up of quantum entities. Therefore, arguably, there is some point at which there is a transition from the quantum superposition of the quantum entities to the single state of the macro entity they form. This transition can be regarded as taking place when a quantum entity interact with its environment, such as by being observed. The interaction leads to an apparent collapse, or "decoherence", of the multiple states into a single defined state.
This gives rise to the impression that the mere act of observing the quantum entity can collapse the "quantum superposition" into single state. However, it is not necessarily the case that this collapse is a real event. Arguably, the quantum entity remains in its multiple states, whilst appearing to the outside world as if it were in one state.
Furthermore, there is no such thing as a "mere act of observing". To observe something on the quantum level, you need to use scientific instruments. The instrument records the events by interacting with the quantum entities. Therefore the act of observing physically affects what is observed.
Also, in this context, the term "observer" relates to any entity capable of recording the behavior of the quantum entity. So an instrument used to record quantum events is as much an "observer" as the human being who may be observing the output of the instrument.
So the "observer effect" is not a mysterious non-physical effect of a human observing a quantum event. It is, rather, an interpretation of what takes place when a quantum entity interacts with its environment, whether or not that involves a human observer.
The idea that the superposition of a quantum entity only appears to collapse into a single state is potentially confusing. So to help make this apparently contradictory situation more intuitively intelligible, two standard interpretations of QM have been proposed:
The Copenhagen Interpretation - This models a quantum entity as a wave function. Interaction of the wave with its environment supposedly "collapses" the quantum superposition of the entity into a single state.
- The Multiverse Interpretation - This suggests that the individual states that make up the superposition of a quantum entity exist in separate probable universes that make up a multiverse.
However, it can be argued that neither the Copenhagen nor the multiverse interpretations should be taken literally. They may be regarded as metaphors. In which case, it is not that either the Copenhagen or the multiverse interpretation is correct. They simply reflect different aspects of the quantum superposition, and its relationship to the macro universe. I.e. The Copenhagen interpretation treats the collapse of the wave function as an actual event. Whilst the multiverse interpretation reflects the fact that quantum decoherence is only apparent.
However, there is one feature of quantum decoherence that neither the Copenhagen nor the multiverse interpretation satisfactorily explains:
The Copenhagen interpretation explains how the wave function effectively collapses into a single state, but not which of the superposition of states it collapses to.
- The multiverse interpretation explains that the individual positions in the quantum superposition continue to exist in separate probable universes, but does not explain which state becomes manifest in this universe.
The alternative interpretations of QM are a range of "hidden variable" theories. These are different from standard Quantum Mechanics in that they posit an unseen cause to seemingly random behavior. This "hidden variable" intervenes in the system to make one or the other eigenstate obtain. This is sometimes known as Bohmian mechanics, after David Bohm, who originated the Causal interpretation of QM.
Hidden variables interpretations suggest that QM is necessarily incomplete, i.e. QM describes only part of what is going on. On the other hand, standard interpretations of QM reject any hidden variable and say that QM is complete, and that the probabilities are in some fashion objective.
In our everyday experience, it is indeed reasonable to assume a cause for seemingly random behavior. But this is an induction. Nearly all physicists assert that QM is an exception. Furthermore, three deep problems arise in the case of QM with claiming determinism:
Why are the "hidden" variables so difficult to identify?
The best minds of the 20th century, with the best technology we've yet been able to develop have been applied to this problem. Thus far, all experiments, in 100% of cases, have had the result that there is no apparent difference between a physical system where x obtains and one where y obtains, prior to the actual measurement of x or y (where the superposition x|y was predicted by the Schrodinger equation prior to measurement).
This is not just a simple induction from one light switch (as in the Light Switch thought experiment below). In its total consistency, it has all the appearance of a law of nature.
Now, none of this necessitates that there is no cause. But should we continue to assume that a cause exists based on our metaphysical expectations, when a century of research seems to suggest the opposite?
Bohmian mechanics is incompatible with special relativity
If you accept special relativity, you are probably going to need to affirm that QM, and thus the physical world, is ultimately indeterministic regarding measurables. Conversely, if you accept Bohm's argument, you must reject special relativity. Bohmian mechanics, unlike standard QM, requires appeal to simultaneous events at various distances, which violates Lorentz invariance.
Bohmian mechanics allows that one could in principle send signals faster than light
This is something very strictly forbidden on the physical level by standard QM. (QM does allow effects to occur faster than light, but these effects cannot convey any actual information, unless supplemented by normal light-speed-bound communication.)
Bohm's model is completely deterministic and can reproduce all the same predictions as standard quantum mechanics. Aside from the fact that the mathematics are more elaborate, and must appeal to 'hidden variables' in the first place, the main reasons for rejecting it must then be either the wish to preserve special relativity, or the concern that Bohmian mechanics is positing that a bizarre string of events makes everything seem as though QM probabilities are real features of the universe, though they are not.
Shrodinger's Cat Experiment
Schrodinger's Cat is a thought experiment that was intended to show the illogicality of the Copenhagen interpretation of quantum mechanics. It was described by Shrodinger as:
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 entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
Thus he concludes that, according to the Copenhagen interpretation, the cat will be both dead and alive at the same time, until the human observer looks into the cage, thus collapsing the wave function. However it is apparent that the account of quantum superposition presented is inaccurate:
It assumes that the Copenhagen interpretation is to be taken literally.
- The Geiger counter is sufficient to act as an "observer", thus collapsing the wave function anyway.
So the fact that the human observer is unaware of whether an atom has decayed or not, does not mean that the cat is simultaneously both dead and alive until the person looks in the box. That view is anthropocentric. The cat would either die at some point in the hour (when an atom randomly decayed) or would not. Both situations would not occur in this universe.
The Light Switch Experiment
This thought experiment illustrates how a determinate system can appear indeterminate if key information is hidden...
I can see a light, and I want to know whether it is operated by a switch (A) that I can see but not touch. So I check the position of the switch from time to time, and note whether the light is on.
The results are:
This is the result we would expect from a purely random non-causal relationship. However, despite the obvious lack of any correlation, I suspect that the situation is actually determinate, i.e. that there is a hidden variable at work. I propose that there is a second switch that is presently hidden, and that when the settings of that switch is taken into account, the situation will be shown to be determinate. So I map the assumed settings of the second switch (B) as follows:
This also indicates a purely random non-causal relationship. However, when we combine the positions of both switches then, as suspected, we discover:
I.e. When the switches are in opposite positions, the light is always on, and when they are both in the same position, the light is always off. Assuming that the number of observations is statistically significant, we can deduce that there is a causal relationship between the switches and the light.
However, since the observation of either switch in isolation was indistinguishable from truly random behaviour, this illustrates the suggestion that random behaviour may be just a determinate causal relationship where one (or more) of the factors is hidden.