A Quantum Analogy with Dice, Fans, and Basketball
This is as much for my own edification as anything else, but I’m trying to get across my understanding of what is called the quantum wave function collapse. After that, it goes off into my usual attempt to say something absolutely particular about absolutely everything in general.
From what I have gathered the quantum wave function is a statistical mean which may or may not correspond to a physical phenomenon.
Now, in QM we try to predict the probability density for a particle’s position (or momentum, or energy, or whatever). We could try to do this by writing an equation for how p(x) changes over time, but it turns out that doesn’t give us enough information; there are situations where particles start with identical p(x) but do different things as time goes on.
It’s found that we do get enough information to make predictions if we write an equation for a complex-valued function ψ(x), and derive the probability density from it as p(x)=ψ∗(x)ψ(x) The way the complex phase of ψ(x) varies from point to point encodes additional information about the particle’s momentum, which is necessary to predict its future behavior. It has units of the square root of a probability density, which is a bit weird but perfectly mathematically acceptable. This is of course the wavefunction, and the equation that determines how it varies is the Schrödinger equation.-source
From another source:
An observable is “something we can observe”, and is it represented in quantum mechanics by an operator, that is, something that operates on a quantum state. A very simple example of an operator is the position operator. We usually write the position operator along the x axis as x^ (which is just x with a “hat” on top of it).
If the quantum state |Ψ⟩ represents a particle, that means that it contains all the information about that particle, including its position along the x axis. So we calculate the following:
Note that the state |Ψ⟩ appears as both a bra and a ket, and the operator x^ in “sandwiched” in the middle.
This is called an expectation value. When we calculate this expression, we will get the value for the position of the particle that one would “expect” to find, according to the laws of probability. To be more accurate, this is a weighted average of all possible positions; so a position that is more probable would contribute more to the expectation value.
However, in many cases the expectation value is not even a value that the observable can get. For example, if the particle can be at position x=+1 with probability ½ or at position x=−1 with probability ½, then the expectation value would be x=0, whereas the particle could never actually be in that position. – source
In the terms of the dice analogy, the table above shows a bell curve function of probability density for the observables of the dice. To make this a metaphor for quantum observations I think it would look more this way:
The difference is that we can’t observe the wave function, we can only think of the set of possible observables for a given system and give it a name. This is important because in my view, quantum theory actually oversteps its mandate as a rational solution to a set of physical problems to become a faith-based solution to a set of metaphysical/mathematical problems.
There can never be any observation of quantum, there can only be qualitative observations from which we can infer quantitative ideas of relation*.
*note that ‘relation’ is itself an aesthetic quality which is dependent upon a preferred sense of grouping. This preference, so far as we can ever know, only occurs within a sensed experience in which aesthetic phenomena are presented as sharing a common quality. Physics in and of itself can have no relations, as general relation qualities cannot be decomposed into fundamental physical forces. No physical mechanism can make quantitative ‘relations’ happen.
What the quotes above are trying to say, in my view, is that
the wave function itself is an imaginary square root of the inferred probability density of the mentally counted sets of actually observed phenomena.
We want to think that quantum particles are the observed dice rolls: a pair of upturned faces of cubes containing a finite number of dots or ‘pips’, and that the wave function is the set of numbers 1 to 6 corresponding to each possible set of dots, but in reality there may not be two dice at all. The observable reality is that when we look at one die, the other one disappears, and we can only see both dice if we don’t look at the dots.
Two more analogies illustrating the reducibility of quantum ‘particles’ to qualitative sense:
1. Looking at a ceiling fan in motion, we can either see a circular blur, or if we follow the blur with our eyes at the same frequency as the fan, we can see the fan blades (or a standing-wave of averaged images of fan blades) but not really the circular blur.
2. I’m in my house and hear noises coming from outside. One sounds like a loud motor, and one sounds like a frequent thumping. I know from experience that the neighbors do like to play basketball in their driveway when the weather is nice. I also know that the neighbors across the street are having their roof replaced which may or may not involve some kind of compressor noise. Finally, I know that Saturday morning is a time when there are a lot of neighbors mowing their lawn.
The point of this example is to illustrate the common/superficial understanding of the wavefunction collapse would be analogous to me going outside and looking around. By observing, I find out whether there are roofers running some kind of noisy machine and pounding on shingles, or whether there is one neighbor mowing their lawn and another pounding on their fence or something, or whether there’s some combination of things going on which may include a basketball game. By ‘finding out’ what’s going on, I am collapsing the wave function of possibilities because I now know what the noises I heard inside my house refer to outside.
This is not correct as an analogy though either. It cannot be applied to quantum observables. The delayed choice quantum eraser and other experiments show surreal phenomena such as entanglement, contextuality, and the mutual exclusivity of entanglement and contextuality. It would be like me like going outside and seeing that the hammering is definitely coming from the roofers across the street, but then going outside again later and seeing that the there is a dude playing basketball instead and there were never any roofers.
Entanglement/Contextuality would be like if I went out and played basketball with the neighbors then as long as I was playing, suddenly no neighbor could have their roof repaired. In terms of the fan, it would be like if I had two fans in two separate rooms controlled by the same light switch, putting my hand in the way of one fan not only stops the other, but you can tell by filling the rooms with feathers that stopping one fan makes it so no feathers had ever blown around in the other room.
Entanglement and contextuality are opposite orientations of the same thing. The entanglement view focuses on the synchronization of what has been connected experimentally while the contextuality view focuses on the strange contradiction to our expectations about causality extending from the past to the present.
Anyhow, this too is not correct in my view. What is being overlooked is that we are taking for granted that the quality of finality in our experience is identical to the property of factuality. We want to say that because we have actually seen the blades of the fan, they are the physical objects which exist and the circular blur is an optical illusion – true enough in the case of a fan. We want to say that seeing a roofer pounding nails into a shingle is evidence that roofing is what is actually going on and the idea that the sound we heard inside could have been a basketball bouncing was a misperception. This is not what physics is telling us, however. Instead, it is telling us, in my view, that there is no fan or basketball or roofer, nor is there any mistake of misperception, there are only sensory experiences, some of which acquire a higher aesthetic density of ‘realism’ than others. We say ‘seeing is believing’ because visual sense presents such an unambiguous seeming experience most of the time but we know from optical illusions and from comparing binocular differences that even seeing should not be believed.
What we are seeing when we look at something like the double slit experiment is a context in which perception itself is revealed to be
- more fundamental than the ‘object’ which is sensed and
- a revealing of (sense experience) itself as both a self-revealer and a self-concealer.
In the phenomenon of seeing visible light we have a metaphor about the relation between metaphor and non-metaphor which is expressed non-metaphorically. It is a context in which the contextualization of contextuality is presented as an uncontextualized/absolute text. (sense = the sole abtext?)
Philosophically, we should see that it is necessary to reverse the priority assigned by Galileo and Locke to tangible/physical qualities being primary and phenomenal qualities being secondary. Physics should be considered a set of phenomenal qualities which have been reduced by the subtraction of intangible modes of sensitivity. It is only in the intangible modes which nature can be fully appreciated as the self-revealing, self-concealing meta-phenomenon that it is.
Finally, here’s another serendipitous experiment with light. On a polished granite surface I see the reflection of a single overhead light as two separate reflections. With one eye open, I can see the image of the light is on the edge of the surface, while with the other eye open instead, the image of the light is in the center of the surface. Try it next time you see a floor or counter like this and can play with closing one eye or the other. Notice how you can choose between two separate but entangled images of the light which move as your head moves or, you can focus your sight so that there is only a single image of the light.
In the former case, the details of the surface are clear – you can see the patterns of granite and can tell exactly which colored spots seem to be illuminated by the overhead light. In the latter case, you have to look ‘through’ or passed the grain of the stone and focus your visual attention on the image which is reflected from the polished surface. To make the former view real is the materialist orientation. To make the latter view real is the information-theoretic orientation. Both orientations entail the disorientation/de-realization of the other. The materialist says the floor is the real thing being illuminated, while the computationalist says that the floor and light are only generic vehicles for the underlying reality of mathematical laws of relation.
What is left out of both of these views is the connection to the eye and the experience of seeing. The eye’s location is what is telling my experience of where the image of the light’s reflection appears to be. Indeed, that appearance *is* the actual location of the lights reflection as seen through one eye. When seen through the other eye, there is a different actual location. When seen through both eyes, there are either two semi-actual locations or there is one actual light reflection against a single blurred semi-actual location.
I cannot emphasize this enough: Quantum theory is about perceiving perception. It tells us not that the reality of nature is inconceivably weird and unfamiliar, but that nature is more than ‘reality’. The different concepts of wave function, probablility density, and observables map to quantum contextuality, quantum entanglement, and classical (collapsed) realism respectively. QM is about how appearances acquire density of realism by consensus of accumulated limits. For a quantum phenomenon (which is totally abstract) to begin to seem concretely ‘real’, the sense of contextuality or entanglement must in one frame of reference seem to be shared as an isomorphic sense in every other frame of reference, without contradiction. Thus there is no mysterious ‘classical limit’ at which quantum decoherence occurs, and no magical ‘emergent properties’ which appear out of nowhere to turn intangible figments of math into concrete objects – there is only a dynamic aesthetic phenomena (sense experiences or qualia) which merge and diffract as aesthetic meta-phenomena (veridical perceptions or ‘shared reality’). There is no ‘finding out’ what really happened, there is only an adding of dimensions of realism by sacrificing qualities that extend beyond realism.
This goes for our own consensus of sense modalities as well as a consensus among peer-reviewed scientific papers. The sense of realism arises from the multiplicity of limited perspectives, which then divides the total entropy of doubt/uncertainty. With only one slit or sense or scientific mind, any given phenomenon is presented as-is – an observed effect only. With multiple senses or slits or peers, we observe a different effect which enables a cross-reference that goes beyond the observation itself to an observation of the observation process. This opens the door not only to theories which connect the particular observations but which can apply to many other kinds of observations, as well as to theories of observation in general. In this way, the general/rational/contextual/illuminating and the particular/empirical/textual-entangled/illuminated can be reconciled as opposite ends of a single spectrum of sense/aesthetic/ab-textual/visibility.