It might seem a little strange for a blog about prehistoric artforms and cultural realities to engage in a discussion about quantum mechanics, but as outlined in the Introduction, a sojourn around some relevant scientific theories will eventually - at length! - bring us to a radically new image of the visionary human being. This overview of quantum mechanics is the first step in this journey, which will take in pertinent aspects of human neurology, Darwinism, linguistics and signal theory, and while patience is required to move through each aspect, the destination will be - I hope! - one of profound quality and insight for the 21st century.
I should also remark that I don't consider quantum mechanics to be a difficult discipline as such - strange for sure and profoundly absurd from a human perspective, but not difficult - though I am aware that some will find it challenging or disconcerting to engage with. Another point to note is that those expecting to see a validation of 'quantum mysticism' ideas of 'universal consciousness' will be here sorely disappointed!
I should also remark that I don't consider quantum mechanics to be a difficult discipline as such - strange for sure and profoundly absurd from a human perspective, but not difficult - though I am aware that some will find it challenging or disconcerting to engage with. Another point to note is that those expecting to see a validation of 'quantum mysticism' ideas of 'universal consciousness' will be here sorely disappointed!
Most modern students of a scientific field will be familiar in some way with the quantum phenomenon of wave-particle duality in which elementary particles such as electrons and photons exhibit properties that are particle-like in some situations and wave-like in others, and this example of complementarity is a fundamental property of the universe. Let us look at this duality in some detail, and the manner of its discovery, so that we can understand its import.
Bruce Rimell, Quantum Observations, 2015
In the early nineteenth century, Thomas Young demonstrated that light propagated through space as waves using an early form of the double-slit experiment to create interference patterns of identical characteristics to those seen in waves on the surface of water. Two transparent apertures were opened in an otherwise dark-painted sheet of glass and a beam of coherent light (that is to say, of a single wavelength) was directed at the glass such that the light only shone through the apertures. On the wall behind the glass, the light patterns did not simply project the openings but the two light beams interfered with each other, scattering the beams and producing linear patterns of light, faded and dark regions in the same manner as any other medium with wave-like characteristics. Young concluded therefore that light too was a wave, and modified his experiment to such a degree that he was able to make reasonably accurate estimations of the actual wavelengths of the light waves within the beams.
However, by 1887, Heinrich Hertz performed the experiment which led to his formulation of the photoelectric effect, in which ultraviolet light beams shone onto a zinc plate spontaneously generated electric currents within the plate only above certain wavelengths, or energies, of the light. Einstein concluded that this showed light also consisted of streams of a type of particle termed the photon, since light that was purely a wave would be expected to cause electric currents in the zinc even at low energy illuminations with radio waves or infra-red.
The double-slit experiment was further modified with advances in technology to allow a single photon to pass through the apertures at a time. The expectation was that when the photon arrived at the slits, it would behave as a particle and pass through only one gap, but a faint interference pattern was seen building up with each successive photon. However when one of the apertures was closed, the photon faintly illuminated the gap upon the wall. The same results were seen when the experiment was performed with single electrons, a mass-bearing particle rather than a force-bearing one such as the photon, and at a rate of one per second, the same interference pattern slowly became visible as more electrons passed through the slits.
This experiment remains remarkable, opening up the strangeness of the quantum world to human perception for the first time: electrons and photons behave as waves in some contexts and particles in others, and even when the sample size is reduced to a single particle, the wave-like characteristics are still observed and the particles interfere with themselves to produce the scattering patterns. Feynman commented that this duality was:
“a phenomenon which is impossible... to explain in any Classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]...”
On first encountering this fascinating paradox, one's instinctive responses are twofold: that these elementary particles must on some deeper level be one or the other, either a wave or a particle 'in reality', or perhaps deeper still there exists a hidden reality in which wave and particle are unified by some as yet unconceived truth. Underneath it all, we feel they must be secretly something else, or hiding their ultimate properties, but the startling conclusion according to the Copenhagen Interpretation of quantum mechanics is that the electron and photon here exhibit no underlying nature: they are waves in some contexts, primarily in those relating to propagation through space, and as particles in others, such as those in which measurements and observations occur. The emergence of string theory does nothing to resolve this issue to the satisfaction of a Classical mind, since string-like characteristics are simply manifest properties of mathematical models in the same way that wave-like and particle-like ones are.
There are those who question how the electron can 'know' that it finds itself in a given context so as to express the 'correct' property, and pseudo-scientifically formulate ideas of universal quantum consciousness, but this alleged 'knowledge' and 'consciousness' represent precisely the kind of hidden underlying nature of elementary particles that the mathematics and experimental observation of quantum mechanics precludes. Pilot wave and hidden variable theses of the double-slit experiment also occasionally appear, but these do not satisfy Bell's Theorem, of which more later.
Wave-particle duality is an aspect of complementarity, a fundamental principle in quantum mechanics in which the various properties of elementary particles cannot be measured accurately or observed at the same time. This is expressed most prominently in Heisenberg's Uncertainty Principle which states that the more accurately one measures the position of a given particle, the less accurately one can know about its momentum and vice versa. This is not due to a shortfall in human observational processes but a fundamental limit inherent in all quantum systems and, by extension, the datum universe, and again we find that in the quantum realm, basic notions of the nature of the elementary particle are either closed to us on account of their non-existence or irrelevance, a profoundly counter-intuitive situation.
A perceptive reader at this point might raise the question that if an elementary particle is wave-like, then what are the waves made of or what medium are they moving through? While the Classical mind might immediately think of some kind of hidden aether-like substance immanently present, initially physicists like Schrödinger postulated that electrons were somehow 'smeared out' across space yet simultaneously elementary and indivisible, and it was this smearing that allowed the waves to self-propagate without the need for a medium. Max Born, Niels Bohr and their colleagues refined this suggestion into a mathematical principle that has become the foundational principle of the Copenhagen Interpretation, the majority view of quantum mechanics today. Greene narrates:
“Born's suggestion is one of the strangest features of quantum theory, but it is supported nonetheless by an enormous amount of experimental data. He asserted that an electron wave must be interpreted from the standpoint of probability. Places where the magnitude... of the wave is large are places where the electron [as a particle] is more likely to be found: places where the magnitude is small are places where the electron is less likely to be found.”
Probability is generally associated with statistical formulations where one's knowledge is incomplete, but here again we find this peculiar situation is fundamental to the quantum situation. The universe is not deterministic, but dependent on mathematical probabilities – wave functions – that indicate the likelihood rather than the actuality of finding an elementary particle in a given place. Should an accurate measurement of position occur at any point (and by implication, following Heisenberg, we become wholly ignorant of its momentum) the wave function collapses into the point location where the particle is observed, and it is as if the particle’s motion has entirely ceased during the period of observation. Similar wave functions exist for other properties exhibiting complementarity, such as spin and quantum field values.
This is unsettling: even Einstein attempted to refute this probabilistic view of reality, becoming famous for his adage that “God does not play dice with the Universe”.
Feynman formulated a slightly different interpretation of the double-slit experiment, which nonetheless agrees perfectly with observed experimental results, in which each electron, or photon, actually passes through both slits and many other paths but what is observed in the interference pattern constitutes the mathematical average of all these accumulated paths:
“...in travelling from the [light or electron] source to a given point on the... screen each individual electron actually traverses every possible trajectory simultaneously... It goes in a nice orderly way through the left slit. It simultaneously also goes in a nice orderly way through the right slit. It heads towards the left slit, but suddenly changes course and heads through the right. It meanders back and forth, finally passing through the left slit. It goes on a long journey to the Andromeda galaxy before turning back and passing through the left slit... And so on it goes... the electron simultaneously 'sniffs out' every possible path connecting its starting location with its final destination.”
The combined average of all of this strangeness produced the same observed results as the Copenhagen Interpretation and thus Feynman showed that quantum mechanics doesn't necessarily require the odd-seeming probability waves, but in disposing of them, he postulated a situation even stranger still! As he once wrote:
“Quantum mechanics describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is – absurd.”
If it is not quite clear yet, our Classical Image of the World-Beyond-Worlds cannot withstand these revelations. There is neither a hidden reality of exemplary Forms which can inform the 'true nature' of elementary particles, nor do these particles partake of anything which resembles Aristotlean Essences. Wave-like and particle-like properties are exhibited, as are position and momentum, with no determinism or actuality independent of observation. All is probability, or averages of infinite trajectories, and those properties which can be observed are dependent on complementarities which reduce our capacity to know anything about the other properties: it is as if in measuring one characteristic, another vanishes.
There is nothing in any of this that can support, as the physics before the photoelectric effect once could, the literal interpretation of any kind of hidden reality or underlying truth. There is only observation and, perhaps, manifestation without any ‘essential’ foundation: quantum systems are indeterminate and any description of them, mathematical or otherwise, appears incomplete when viewed from a human ‘common sense’ perspective. This indeterminacy is startling indeed to the mythically-oriented human mind.
A theorem formulated in 1964 by the Irish theoretical physical John Bell, compounds this indeterminacy and apparent incompleteness by stating that no local system of hidden variables can reproduce all the predictions of quantum mechanics. This means that any mathematical explanation which posits that the properties of an elementary particle or quantum system have 'realism' or an a priori existence, that is to say have values or characteristics somehow independent of observation or of measurement methods, cannot accurately match the observed experimental data. Quantum systems have properties which are interdependent and contextual: they depend on which property is being observed and how that observation is being made as to whether they are seen, or indeed made manifest.
Bell’s Theorem wipes out all notions of this realism, and ‘objective’ reality independent of observation now becomes impossible. This is illustrated most aptly in the famous and near-mystical phenomenon of quantum entanglement, in which two particles become associated with each other by either forming part of the same quantum system, or through having been created together.
Let us imagine we have two electrons which have emerged from the same process and are thus forever associated – entangled in technical terminology – and we send them out across space such that they are a considerable distance from each other, but shielding them from observation, as it were placing each of the electrons in one of two secure boxes before their voyage into space. From other quantum theories not discussed here, we know that as a result of the process that created them, they will exhibit opposing spin, a quantum analogue of angular momentum, when they are observed, one with spin ‘up’ and one with spin ‘down’.
Once they are far away from each other, one of them is observed – a box is opened – and we find that this particular electron is seen to be spin ‘up’. Immediately then we know that the other electron, despite it being far away in another part of space, must be spin ‘down’. This thought experiment, which has since been performed in analogous sense with photons, was called the EPR Paradox after the three theorists, Albert Einstein, Boris Podolsky and Nathan Rosen who formulated it, and its implications for reality liberated one of the great controversies of quantum mechanics of the twentieth century.
Einstein held that the electrons’ spin values (‘up’ or ‘down’) were set at the moment of their creation, and thus had an a priori existence despite not being observed. As such, during our experiment, when the electrons were placed in their boxes and sent off into space, the spin values were already secretly there, enfolded into each electrons’ fundamental nature. This he called a statement of objective realism. However Bohr disagreed, holding that the spins were indeterminate – in other words, fundamentally non-existent – until the observation of one particle was made, at which point both particles’ spin were instantaneously called into existence and decided, a view which Einstein derided as “spooky action at a distance”.
What Bell conceived was a mathematical model which utilised probabilities to examine which interpretation was correct, along with an analogous experimental test, using photons and polarities rather than electrons and spin. Both his theorem and the experiment demonstrated that Bohr’s view (lacking realism, as did Feynman’s model) liberated the most accurate description of quantum mechanics, and thus that either some kind of instantaneous information transfer was passing between the entangled particles at the moment of observation – which contravened the relativistic view that nothing could travel faster than light, including information – or that quantum systems could be non-local, such that particles could continue to be associated with each other across vast distances of space and were subject to the same limitations on their properties such as spin as observed for particles within, for example, the same atom.
Quantum phenomena are thus non-local and objective realism must be rejected, and any thesis which includes either locality or realism in its formulation – that is, posits an a priori existence for properties of unobserved particles – does not accord with what is actually observed. The startling conclusion, then, is that things are only made real, or indeed made existent, through observation and interaction.
The majority view is that Bell's Theorem is supported by a vast body of experimental results like the one with photons mentioned above, and given that it rests implicitly in all aspects of modern quantum theory, it can perhaps be considered as one of the most rigorously tested theses in human history. There are thus no absolutes, no immutable truths. All is context, relativistic, indeterminate until observed, at which point it becomes partially real, partially manifest, informational rather than objective, and partaking of a fundamental incompleteness (from a human perspective of ‘common sense’, at least), which is backed by no hidden reality of any kind.
Our Classical Image of the World-Beyond-Worlds and all its associated aspects is wholly shattered.
However, by 1887, Heinrich Hertz performed the experiment which led to his formulation of the photoelectric effect, in which ultraviolet light beams shone onto a zinc plate spontaneously generated electric currents within the plate only above certain wavelengths, or energies, of the light. Einstein concluded that this showed light also consisted of streams of a type of particle termed the photon, since light that was purely a wave would be expected to cause electric currents in the zinc even at low energy illuminations with radio waves or infra-red.
The double-slit experiment was further modified with advances in technology to allow a single photon to pass through the apertures at a time. The expectation was that when the photon arrived at the slits, it would behave as a particle and pass through only one gap, but a faint interference pattern was seen building up with each successive photon. However when one of the apertures was closed, the photon faintly illuminated the gap upon the wall. The same results were seen when the experiment was performed with single electrons, a mass-bearing particle rather than a force-bearing one such as the photon, and at a rate of one per second, the same interference pattern slowly became visible as more electrons passed through the slits.
This experiment remains remarkable, opening up the strangeness of the quantum world to human perception for the first time: electrons and photons behave as waves in some contexts and particles in others, and even when the sample size is reduced to a single particle, the wave-like characteristics are still observed and the particles interfere with themselves to produce the scattering patterns. Feynman commented that this duality was:
“a phenomenon which is impossible... to explain in any Classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]...”
On first encountering this fascinating paradox, one's instinctive responses are twofold: that these elementary particles must on some deeper level be one or the other, either a wave or a particle 'in reality', or perhaps deeper still there exists a hidden reality in which wave and particle are unified by some as yet unconceived truth. Underneath it all, we feel they must be secretly something else, or hiding their ultimate properties, but the startling conclusion according to the Copenhagen Interpretation of quantum mechanics is that the electron and photon here exhibit no underlying nature: they are waves in some contexts, primarily in those relating to propagation through space, and as particles in others, such as those in which measurements and observations occur. The emergence of string theory does nothing to resolve this issue to the satisfaction of a Classical mind, since string-like characteristics are simply manifest properties of mathematical models in the same way that wave-like and particle-like ones are.
There are those who question how the electron can 'know' that it finds itself in a given context so as to express the 'correct' property, and pseudo-scientifically formulate ideas of universal quantum consciousness, but this alleged 'knowledge' and 'consciousness' represent precisely the kind of hidden underlying nature of elementary particles that the mathematics and experimental observation of quantum mechanics precludes. Pilot wave and hidden variable theses of the double-slit experiment also occasionally appear, but these do not satisfy Bell's Theorem, of which more later.
Wave-particle duality is an aspect of complementarity, a fundamental principle in quantum mechanics in which the various properties of elementary particles cannot be measured accurately or observed at the same time. This is expressed most prominently in Heisenberg's Uncertainty Principle which states that the more accurately one measures the position of a given particle, the less accurately one can know about its momentum and vice versa. This is not due to a shortfall in human observational processes but a fundamental limit inherent in all quantum systems and, by extension, the datum universe, and again we find that in the quantum realm, basic notions of the nature of the elementary particle are either closed to us on account of their non-existence or irrelevance, a profoundly counter-intuitive situation.
A perceptive reader at this point might raise the question that if an elementary particle is wave-like, then what are the waves made of or what medium are they moving through? While the Classical mind might immediately think of some kind of hidden aether-like substance immanently present, initially physicists like Schrödinger postulated that electrons were somehow 'smeared out' across space yet simultaneously elementary and indivisible, and it was this smearing that allowed the waves to self-propagate without the need for a medium. Max Born, Niels Bohr and their colleagues refined this suggestion into a mathematical principle that has become the foundational principle of the Copenhagen Interpretation, the majority view of quantum mechanics today. Greene narrates:
“Born's suggestion is one of the strangest features of quantum theory, but it is supported nonetheless by an enormous amount of experimental data. He asserted that an electron wave must be interpreted from the standpoint of probability. Places where the magnitude... of the wave is large are places where the electron [as a particle] is more likely to be found: places where the magnitude is small are places where the electron is less likely to be found.”
Probability is generally associated with statistical formulations where one's knowledge is incomplete, but here again we find this peculiar situation is fundamental to the quantum situation. The universe is not deterministic, but dependent on mathematical probabilities – wave functions – that indicate the likelihood rather than the actuality of finding an elementary particle in a given place. Should an accurate measurement of position occur at any point (and by implication, following Heisenberg, we become wholly ignorant of its momentum) the wave function collapses into the point location where the particle is observed, and it is as if the particle’s motion has entirely ceased during the period of observation. Similar wave functions exist for other properties exhibiting complementarity, such as spin and quantum field values.
This is unsettling: even Einstein attempted to refute this probabilistic view of reality, becoming famous for his adage that “God does not play dice with the Universe”.
Feynman formulated a slightly different interpretation of the double-slit experiment, which nonetheless agrees perfectly with observed experimental results, in which each electron, or photon, actually passes through both slits and many other paths but what is observed in the interference pattern constitutes the mathematical average of all these accumulated paths:
“...in travelling from the [light or electron] source to a given point on the... screen each individual electron actually traverses every possible trajectory simultaneously... It goes in a nice orderly way through the left slit. It simultaneously also goes in a nice orderly way through the right slit. It heads towards the left slit, but suddenly changes course and heads through the right. It meanders back and forth, finally passing through the left slit. It goes on a long journey to the Andromeda galaxy before turning back and passing through the left slit... And so on it goes... the electron simultaneously 'sniffs out' every possible path connecting its starting location with its final destination.”
The combined average of all of this strangeness produced the same observed results as the Copenhagen Interpretation and thus Feynman showed that quantum mechanics doesn't necessarily require the odd-seeming probability waves, but in disposing of them, he postulated a situation even stranger still! As he once wrote:
“Quantum mechanics describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is – absurd.”
If it is not quite clear yet, our Classical Image of the World-Beyond-Worlds cannot withstand these revelations. There is neither a hidden reality of exemplary Forms which can inform the 'true nature' of elementary particles, nor do these particles partake of anything which resembles Aristotlean Essences. Wave-like and particle-like properties are exhibited, as are position and momentum, with no determinism or actuality independent of observation. All is probability, or averages of infinite trajectories, and those properties which can be observed are dependent on complementarities which reduce our capacity to know anything about the other properties: it is as if in measuring one characteristic, another vanishes.
There is nothing in any of this that can support, as the physics before the photoelectric effect once could, the literal interpretation of any kind of hidden reality or underlying truth. There is only observation and, perhaps, manifestation without any ‘essential’ foundation: quantum systems are indeterminate and any description of them, mathematical or otherwise, appears incomplete when viewed from a human ‘common sense’ perspective. This indeterminacy is startling indeed to the mythically-oriented human mind.
A theorem formulated in 1964 by the Irish theoretical physical John Bell, compounds this indeterminacy and apparent incompleteness by stating that no local system of hidden variables can reproduce all the predictions of quantum mechanics. This means that any mathematical explanation which posits that the properties of an elementary particle or quantum system have 'realism' or an a priori existence, that is to say have values or characteristics somehow independent of observation or of measurement methods, cannot accurately match the observed experimental data. Quantum systems have properties which are interdependent and contextual: they depend on which property is being observed and how that observation is being made as to whether they are seen, or indeed made manifest.
Bell’s Theorem wipes out all notions of this realism, and ‘objective’ reality independent of observation now becomes impossible. This is illustrated most aptly in the famous and near-mystical phenomenon of quantum entanglement, in which two particles become associated with each other by either forming part of the same quantum system, or through having been created together.
Let us imagine we have two electrons which have emerged from the same process and are thus forever associated – entangled in technical terminology – and we send them out across space such that they are a considerable distance from each other, but shielding them from observation, as it were placing each of the electrons in one of two secure boxes before their voyage into space. From other quantum theories not discussed here, we know that as a result of the process that created them, they will exhibit opposing spin, a quantum analogue of angular momentum, when they are observed, one with spin ‘up’ and one with spin ‘down’.
Once they are far away from each other, one of them is observed – a box is opened – and we find that this particular electron is seen to be spin ‘up’. Immediately then we know that the other electron, despite it being far away in another part of space, must be spin ‘down’. This thought experiment, which has since been performed in analogous sense with photons, was called the EPR Paradox after the three theorists, Albert Einstein, Boris Podolsky and Nathan Rosen who formulated it, and its implications for reality liberated one of the great controversies of quantum mechanics of the twentieth century.
Einstein held that the electrons’ spin values (‘up’ or ‘down’) were set at the moment of their creation, and thus had an a priori existence despite not being observed. As such, during our experiment, when the electrons were placed in their boxes and sent off into space, the spin values were already secretly there, enfolded into each electrons’ fundamental nature. This he called a statement of objective realism. However Bohr disagreed, holding that the spins were indeterminate – in other words, fundamentally non-existent – until the observation of one particle was made, at which point both particles’ spin were instantaneously called into existence and decided, a view which Einstein derided as “spooky action at a distance”.
What Bell conceived was a mathematical model which utilised probabilities to examine which interpretation was correct, along with an analogous experimental test, using photons and polarities rather than electrons and spin. Both his theorem and the experiment demonstrated that Bohr’s view (lacking realism, as did Feynman’s model) liberated the most accurate description of quantum mechanics, and thus that either some kind of instantaneous information transfer was passing between the entangled particles at the moment of observation – which contravened the relativistic view that nothing could travel faster than light, including information – or that quantum systems could be non-local, such that particles could continue to be associated with each other across vast distances of space and were subject to the same limitations on their properties such as spin as observed for particles within, for example, the same atom.
Quantum phenomena are thus non-local and objective realism must be rejected, and any thesis which includes either locality or realism in its formulation – that is, posits an a priori existence for properties of unobserved particles – does not accord with what is actually observed. The startling conclusion, then, is that things are only made real, or indeed made existent, through observation and interaction.
The majority view is that Bell's Theorem is supported by a vast body of experimental results like the one with photons mentioned above, and given that it rests implicitly in all aspects of modern quantum theory, it can perhaps be considered as one of the most rigorously tested theses in human history. There are thus no absolutes, no immutable truths. All is context, relativistic, indeterminate until observed, at which point it becomes partially real, partially manifest, informational rather than objective, and partaking of a fundamental incompleteness (from a human perspective of ‘common sense’, at least), which is backed by no hidden reality of any kind.
Our Classical Image of the World-Beyond-Worlds and all its associated aspects is wholly shattered.
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