Quantum Mechanics, Consciousness, Reality and Computation – Part III

What is fundamental?
Mathematics as an exercise?
Nature’s existence?
What I mean is quite a subtle question…
Can you describe Physics as applied Mathematics?
I would say yes because we have Mathematics that can describe any geometry, any equation, any self-consistent ‘thing’. We can talk about the mathematics of a universe that differs from our own.
Physics describes the universe we live in – and sometimes a universe we don’t live in – but it only does so through mathematics.
However Physics describes fundamental things through this application of Mathematics that exist and are true (or indeed false or indeterminate) whether or NOT we are here describing it. The charge on an electron may not be an inviolate property, or the speed of light may change, yet they do so without requiring us or anyone else to be around to understand or even acknowledge it.
My point? I’ve recently described the sciences as a heirarchy. Physics is applied maths, chemistry is applied physics, biology is applied chemistry and so on and so on… Geology is applied Chemistry, Physiology is applied Biology, Engineering is applied Physics+Maths.
That is to say that the Universe exists as it is, as we understand it, as anyone understands it, and as anything will ever understand it, regardless of whether we do so correctly or not or indeed whether we or any other conscious being exists to be capable of understanding it.
So approaching this topic from this angle: The Universe does not require sentience/consciousness.
This may seem like a digression but I would like to discuss consciousness, self, id, ego, sentience… whatever you call it. This is entirely central to Quantume Physics.
In Young’s Double Slit experiement a beam of light is projected towards two slits in a partition. Due to the wave-like properties of Electromagnetic radiation the light passes through both slits and disperses there just as a water wave disperses after passing through a narrow gap. These dispersed waves interfere with each other –  the peaks and troughs in the wave form interfere with each other to form bright and dark bands on the screen behind the partition.
This only makes sense in the context of wave-like light. However we can also describe other properties of light as being particle-like. For example in the way that light is absorbed and re-emitted by electrons. In fact from a given light source we can determine how many particle-like photons are being produced every second. We can engineer a source for Young’s double slit experiment of such low intensity that we can say with absolute certainty that only one photon is passing between the source and the screen at any time. Logically you would think that in such a case the photon can only possibly go through one slot or the other. So there should be no interference pattern. But if we use photographic paper to record where the photons hit the screen we still get an interference pattern, built up one tiny dot at a time. So despite there being just one photon in the experiment at a time it still behaves like a wave. Incredibly if you still think of the photon as particle-like it has somehow interfered with itself. Yet since the interference pattern is built up from individual dots we can say that as far as the screen is concerned the light is particle like, not wave-like.
How are we to make sense of this? In Quantum Mechanics we express everything as a wave function that describes the probability of finding our subject (in this case a photon) over a region of space. In this way the wave-like nature of light represents the fact that we don’t really know where the photon is. Somehow the photon’s existence is smeared out such that it’s wave function passes through both slits. There is a probability that it goes through one slit and a probability that it goes through the other. As confusing as this is it allows the single photon to interfere with itself.
Moreover in Quantum Mechanics we talk about ‘collapsing the wavefunction’. This is what happens when we measure our subject. We force the photon to decide where it is (not in any conscious manner on the photon’s part of course!). Our screen forces the wave function to collapse since the photon must hit it somewhere. Actually there’s always a probability that the photon will simply pass on through the screen and remain just a smeared out probability continuing along it’s way, but the ones doing that aren’t relevant to our experiment nor do they break anything discussed here.
A momentary recap. If the photon, passing through one slit, would interfere with itself passing through the other slit, would mean that at a position X on the screen they would cancel out each other (dark area on the screen), then the probability of the photon moving in that direction is 0. If at position Y they would nearly cancel out (dim area) then the probability is low. If at position Z they would reinforce (bright band) then the probability is high. There are many explanations of how this all may or may not work. Many interpretations of Quantum Mechanics. Feel free to look them up. Here I would just like to explore one further consequence of this experiment that is the main source of these differing interpretations.
When we say a wave function has been collapsed we talk about observing or measuring the photon. The screen measures the photon.
If we place a photon detector in one of the slits in our partition we force the wave function to collapse at that point and the pattern on our screen changes. We now get just two bands of light. One each for the light streaming through each slit.
Such is the confusing
as I will go on to discuss later.
To take the same thing from another direction though, consider this.

First let me make it clear that the laws of Quantum Mechanics, as far as science has pushed to date, are agreed upon by those Academics working in the field. Of course papers are published all the time and experiments done to further refine the theories or fill in areas that are still unknown but there are no schisms in the field of QCD. However there are somewhat philosophical disagreements on how one can best interpret the results of experiment that I described in the previous post about the Young’s Double Slit experiment. There is no, known, way to test which of these interpretations is correct which is why they are no more than philosophical in nature and it’s really personal choice between them.

So, to return to Young’s Double Slit Experiment and my closing questions in Part II. What constitutes a sensor that collapses the wave function?

I often wonder, why don’t the atoms and molecules in the air the light passes through constitute a sensor? I think the answer is that atoms are actually so empty that only the tiniest fraction of photons would be absorbed and thereby ‘recorded’. Of this tiny portion only another tiny portion would be re-emitted in the right directions to travel through the two slits and so form a deterministic pattern on the screen, which would barely register compared to those photons that would pass through undetected to form the probabilistic interference pattern.

So what are these interpretations of Quantum Mechanics I have mentioned? From the very birth of Quantum Mechanics Physicists have developed different ways to understand the Wave Function and its Collapse. The disagreements don’t affect how the Physics work but they are most interesting.

One of the best known schools of thought is the Copenhagen Interpretation (CI). It maintains that the Wave Function is not real but is purely a tool for computation. In the Double Slit experiment this interpretation would say that light (indeed everything) is neither a particle or a wave but that any given experiment can show either wave-like or particle-like behaviour but never both. In terms of what constitutes an observer anything will do. The role of the observer is simply to register and turn the probabilistic nature of the unknown into certainties.

Among those who subscribe to this interpretation of QM there are plenty of subtle variations on the theme, as determined by the individual’s bent towards postivism or realism. If you haven’t guessed by now I’m the latter. There are some who one might call purists who would say that if something is not being observed then it does not exist. There are even some who claim that it takes a consciousness to collapse the Wave Function but I disregard this as nonsense… is the Moon not there if everyone looks away? And there are those who would say that although something might not be being observed we can still make informed guesses about them. But all of them would agree that the Wave Function is the complete description of a system and that it does collapse on observation.

I would agree with the latter stance but I have often thought that it should be very hard for something not to be observed. Everything has some kind of field – commonly gravitational and/or electromagnetic. It may be tiny but it has to be registered by everything else in the universe at all times! Of course a criticism of my own argument there is that the Double Slit experiment could not produce an interference pattern if everything was always being observed in some way through the interaction of the forces. Even photons are bent by gravity, but perhaps, just perhaps, if a photon is just following the curvature of space time and is not being absorbed by anything we can truly consider it ‘unobserved’ and it can pass through both slits as a wave? The truth must be subtle and I believe we are all far too limited in our ability to comprehend the Quantum world. Entities like the photon or electron are not particles and they are not waves. They behave in ways that resemble these familiar macroscopic  properties at different times but they aren’t either.

Famously Einstein criticised CI by saying “He [God] does not play dice”. He was very opposed to the idea that nature was described by probability and not by deterministic events. This remark is often latched onto by Theists who assume this meant Einstein was therefore a Theist himself but if you read his body of work you’ll find an Agnostic, possibly Atheist, with a way of writing that suggests a Pantheistic liberalism in interchanging the concept of ‘God’ with the concept of the ‘Universe’.

Einstein himself preferred the Ensemble or Statistical Interpretation of QM. Essentially it states that the Wave Function represents the probabilities of different outcomes in an ensemble of like systems and that a single system within that ensemble has only one state. Therefore the Wave Function in a single system never collapses and everything is Deterministic in a single system, regardless of whether it is known or not. So the Wave Function only means anything if we repeat an experiment many times. As far as I can determine though this interpretation is incapable of rationalising the Double Slit experiment with a single photon interfering with itself.

Flying in the face of CI are the Many Worlds models. The many variations on this theme all have one thing in common, which they share with the Ensemble model, that there is no Wave Function collapse. Instead they state that every possible outcome of every event exists in its own world or history. In popular literature these are often called Parallel Universes but one must remember that one has to exist for every possible quantum state of every possible quantum event since, and including the Big Bang. The number of such universes is uncountable, although not infinite.

There are many variations on this theory too but the important theme of them all is that we never collapse a Wave Function. On observation we merely discover which possible Universe we are in. Something called Quantum Decoherence. Most importantly this completely removes the need for an observer which causes so many paradoxes in CI. The classic example is Schroedinger’s Cat in which a cat in a box may be dead or may be alive based on an unknown radioactive event. In CI the cat is in some super-state of being both dead and alive until we observe and find out. In Many Worlds models the cat is definitely dead or alive, one Universe or History exists in which each is true. We may not know until we open the box which we are in but we are in one or the other.

Some of the variations on this theme attempt to explain the single-photon interference by stating that the many universes interfere with each other. Those that are closest in their overall quantum state interfere with each other more strongly than those which differ wildly. So the universe with the photon traveling through slot one interferes strongly with the one in which it travels through slot two but where everything else is identical, but interferes very weakly with a completely dissimilar universe.

This Wiki page has a good overview of the many other interpretations of QM, some of which are gaining traction in the Physics community.

A very good read for understanding what these different views are more deeply about is David Deutsch’s Fabric of Reality. He explains positivsm, realism and so on in great depth. I would highly recommend it but please bear in mind that whilst his arguments are compelling he is an ardent advocate of a Many World’s interpretation of QM and so his own personal bias comes to bear.

More soon!

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