Why Quantum Mechanics is Currently Wrong and How to Fix It.

It is now almost a century since "quantum mechanics" became established as the dominant paradigm for thinking about the structure and motion of matter on the nanoscale. And yet the one thing quantum mechanics cannot do is explain what it purports to describe. Sure, quantum mechanics can predict the probability of measurements. However, no one knows how it does this. 

Presently, no one understands the foundations of quantum mechanics. 

Feynman's quote to this effect is still accurate. It has recently been restated by David Deutsch, for example:

"So, I think that quantum theory is definitely false. I think that general relativity is definitely false." (t = 1:16:13)

"Certainly, both relativity and quantum theory are extremely good approximations in the situations where we want to apply them... So, yes, certainly, good approximations for practical purposes, but so is Newton's theory. That's also false." (t = 1:28:35)

—David Deutsch on Sean Carroll's podcast.

I listened to these striking comments again recently. This time around, I realised that my conception of quantum field theory (QFT) was entirely wrong. I have a realistic picture in my head, i.e. when I talk about "waves", something is waving. This is not what GFT says at all. The "fields" in question are entirely abstract. What is waving in quantum mechanics is the notion of the probability of a particle appearing at a certain location within the atom. Below I will show that this thinking is incoherent. 

There have been numerous attempts to reify the quantum wavefunction. And they all lead to ridiculous metaphysics. Some of the most hilarious metaphysics that quantum mechanics has produced are:

1. The universe behaves one way when we look at it, and a completely different way when we don't.
   
2. The entire universe is constantly, and instantaneously, splitting into multiple copies of itself, each located in exactly the same physical space, but with no connections between the copies.
   
3. Electrons are made of waves of probability that randomly collapse to make electrons into real particles for a moment.

None of these ideas is remotely compatible with any of the others. And far from there being a consensus, the gaps between "interpretations" are still widening. Anyone familiar with my work on the Heart Sutra will recognise this statement. It's exactly what I said about interpretations of the Heart Sutra.

Physics has lost its grip on reality. It has a schizoid ("splitting") disorder. I believe I know why.

What Went Wrong?

The standard quantum model embraces wave-particle duality as a fundamental postulate. In the 1920s, experiments seemed to confirm this. This is where the problems start.

Schiff's (1968) graduate-level textbook, Quantum Mechanics, discusses the idea that particles might be considered "wave packets":

The relation (1.2) between momentum and wavelength, which is known experimentally to be valid for both photons and particles, suggests that it might be possible to use concentrated bunches of waves to describe localized particles of matter and quanta of radiation. To fix our ideas, we shall consider a wave amplitude or wave function that depends on the space coordinates x, y, z and the time t. This quantity is assumed to have three basic properties. First, it can interfere with itself, so that it can account for the results of diffraction experiments. Second, it is large in magnitude where the particle or photon is likely to be and small elsewhere. And third, will be regarded as describing the behavior of a single particle or photon, not the statistical distribution of a number of such quanta. (Schiff 1968: 14-15. Emphasis added)

I think this statement exemplifies the schizoid nature of quantum mechanics. The Schrödinger model begins with a particle, described as a "wave packet", using the mathematics of waves. The problem is that physicists still want to use the wave equation to recover the "position" or "momentum" of the electron in the atom, as though it is a particle. I have seen people dispute that this was Schrödinger's intention, but it's certainly how Schiff saw it, and his text was widely respected in its day.

The obvious problem is that, having modelled the electron as a wave, how do we then extract from it information about particles, such as position and momentum? Mathematically, the two ideas are not compatible. Wave-talk and particle-talk cannot really co-exist. 

In fact, Schrödinger was at a loss to explain this. It was Max Born who pointed out that if you take the modulus squared value of the wave function (which outputs complex-numbered vectors), you get a probability distribution that allows you to predict measurements. As I understand it, Schrödinger did not like this at all. In an attempt to discredit this approach, he formulated his classic thought experiment of the cat in the box. A polemic that failed so badly, that the Copenhagen crowd adopted Schrödinger's cat as their mascot. I'll come back to this.

However, there is a caveat here. No one has ever measured the position of an electron in an atom, and no one ever will. It's not possible. We have probes that can map out forces around atoms, but we don't have a probe that we, say, can stick into an atom and wait for the electron to run into it. This is not how things work on this scale.

Can We Do Better? (Yes We Can!)

Electric charge is thought to be a fundamental property of matter. We visualise the electric charge of a proton as a field of electric potentials with a value at every point in space, whose amplitude drops off as the square of the distance. The electric field around a proton is observed to be symmetrical in three dimensions. In two dimensions, a proton looks something like this with radiating, evenly spaced field lines:

An electron looks the same, but the arrows point inwards (the directionality of charge is purely conventional). So if the electron were a point charge, an atom would be an electric dipole, like this:

This diagram shows that if the electron were a point mass/charge, the hydrogen atom would be subject to unbalanced forces. Such an atom would be unstable. Moreover, a moving electric dipole causes fluctuations in the magnetic field that would rapidly bleed energy away from the atom, so if it didn't collapse instantaneously, it would collapse rapidly. 

Observation shows atoms to be quite stable. So, at least in an atom, an electron cannot be a point mass/charge. And therefore, in an atom, an electron is not a point mass/charge.

Observation also shows that hydrogen atoms are electrically neutral. Given that the electric field of the proton is symmetrical in three dimensions, there is only one shape the electron could be and balance the electric charge. A sphere with the charge distributed evenly over it.

The average radius of the sphere would be the estimated value of the atomic radius. Around 53 picometers (0.053 nanometers) for hydrogen. The radius of a proton is estimated to be on the order of 1 femtometer.

Niels Bohr had a similar idea. He proposed that the electron formed a "cloud" around the nucleus. And this cloud was later identified as "a cloud of probability". Which is completely meaningless. The emperor is not wearing any clothes. As David Albert says on Sean Carroll's podcast:

“… there was just this long string of brilliant people who would spend an hour with Bohr, their entire lives would be changed. And one of the ways in which their lives were changed is that they were spouting gibberish that was completely beneath them about the foundations of quantum mechanics for the rest of their lives…” (emphasis added)

We can do better, with some simple logic. We begin by postulating, along with GFT, that the electron is some kind of wave. 

If the electron is a wave, AND the electron is a sphere, AND the atom is stable, AND the atom is electrically neutral, then the electron can only be a spherical standing wave.

Now, some people may say, "But this is exactly what Schrödinger said". Almost. There is a crucial difference. In this model, the spherical standing wave is the electron. Or, looked at from the other direction, an electron (in a hydrogen atom) is a physical sphere with an average radius of ~53 pm. There is no particle, we've logically ruled out particles.

What does observation tell us about the shape of atoms? We have some quite recent data on this. For example, as reported by Lisa Grossman (2013) for New Scientist, here are some pictures of a hydrogen atom recently created by experimenters.

The original paper was in Physical Review.

Sadly, the commentary provided by Grossman is the usual nonsense. But just look at these pictures. The atom is clearly a sphere in reality, just as I predicted using simple logic. Many crafty experiments, have reported the same result. It's not just that the probability function is spherical. Atoms are spheres. Not solid spheres, by any means, but spheres nonetheless.

We begin to part ways with the old boys. And we are instantly in almost virgin territory. To the best of my knowledge, no one has ever considered this scenario before (I've been searching the literature).

The standard line is that the last input classical physics had was Rutherford's planetary model proposed in 1911, after he successfully identified that atoms have a nucleus, which contains most of the mass of the atom. This model was debunked by Bohr in 1913. And classical physics has nothing more to say. As far as any seems to know, "classical physics says the electron is a point mass". No one has ever modelled the electron in an atom as a real wave. At least no one I can find.

This means that there are no existing mathematical models I can adapt to my purpose. I have to start with the general wave equation and customise it to fit. Here is the generalised wave equation of a spherical standing wave:

Where r is the radius of the sphere, θ and φ are angles, and t = time. Notice that it is a second-order partial differential equation, and that the rates of change in each quantity are interdependent. It can be solved, but it is not easy.

The fact is that, while this approach is not identical to existing quantum formalism, it is isomorphic (i.e. has the same form). Once we clarify the concept and what we are trying to do with it, the existing formalism ought to be able to be adapted. So we don't have to abandon quantum mechanics, we just have to alter our starting assumptions and allow that to work through what we have to date. 

An important question arises: What about the whole idea of wave-particle duality?

In my view, any particle-like behaviour is a consequence of experimental design. Sticking with electrons, we may say that every electron detector relies on atoms in the detector absorbing electrons. And there are no fractional electrons. Each electron is absorbed by one and only one atom. It is this phenomenon that causes the appearance of discrete "particle-like" behaviour. At the nano-scale, any scientific apparatus is inevitably an active part of the system.

The electron is a wave. It is not a particle. 

Given the wild success of quantum mechanics (electronics, lasers, and so on), why would anyone want to debunk it? For me, it is because it doesn't explain anything. I didn't get into science so I could predict measurements, by solving abstract maths problems. I got into it so I could understand the world. Inj physics maths is supposed to represent the world and to have a physical interpretation. I'm not ready to give up on that.

The Advantages of Modelling the Electron as a (Real) Wave.

While they are sometimes reported as special features of quantum systems, the fact is that all standing waves have some characteristic features.

In all standing waves, energy is quantised. This is because a standing wave only allows whole numbers of wavelengths. We may use the example of a guitar string that vibrates in one dimension*.

*Note that if you look at a real guitar string, you will see that it vibrates in two dimensions: perpendicular to the face of the guitar and parallel to it.

The ends of the string are anchored. So the amplitude of any wave is always zero at the ends; they cannot move at all. The lowest possible frequency is when the wavelength equals the string length.

The next lowest possible frequency is when the wavelength equals half the string length. And so on.

This generalises. All standing waves are quantised in this way. This is "the music of the spheres". 

Now, spherical standing waves, with a central attractive force exist and were described ca 1782 by Pierre-Simon Laplace. These entities are mathematically very much more complicated than a string vibrating in one dimension. Modelling this is a huge challenge. 

For the purposes of this essay, we can skip to the end and show you what the general case of harmonics of a spherical standing wave looks like when the equations are solved and plotted on a graph.

Anyone familiar with physical chemistry will find these generalised shapes familiar. These are the theoretical shapes of electron orbitals for hydrogen. And this is without any attempt to account for the particular situation of an electron in an atom (the coulomb potential, the electric field interfering with itself, etc).

So not only is the sphere representing the electron naturally quantised, but the harmonics give us electron "orbitals". And, if we drop the idea of the electron as a particle, this all comes from within a classical framework (though not Rutherford's classical framework). 

Why Does Attempting to Reify Probability Lead to Chaos?

As already noted, Schrödinger tried and failed to relate his equation back to reality. Max Born discovered that the modulus squared of the wavefunction vector at a given point could be interpreted as the probability of finding the "the electron" (qua particle) at that point. This accurately predicts the probable behaviour of an electron, though not its actual behaviour. But all this requires electrons to be both waves and point-mass particles. 

Since the real oscillations I'm describing are isomorphic with the notional oscillations predicted by Schrödinger, we can intuit that if we were to try to quantify the probability of the amplitude of the (real) spherical standing wave at a certain point around the sphere, then any probability distribution we created from this would also be isomorphic with application of the Born rule to Schrödinger's equation.

What I've just done, in case it wasn't obvious, is explain the fundamentals of quantum mechanics (in philosophical terms at least) in one sentence. The predicted probabilities take the form that they do because of a physical mechanism: a spherical standing wave. And I have not done any violence to the notion of "reality" in the process. To my knowledge, this has not been done before, although I'm certainly eager to learn if it has.

However, the isomorphism is only causal in one direction. You can never get from a probability distribution to a physical description. Let me explain why by using a simple analogy that can be generalised.

Let's take the very familiar and simple case of a system in which I toss a coin in the air and, when it lands, I note which face is up. The two possible outcomes are heads H and tails T. The probabilities are well-known:

P(H) = 0.5 and P(T) = 0.5.

And as always, the sum of the probabilities of all the outcomes is 1.0. So:

P(H) + P(T) = 1.0

No matter what values we assign to P(H) and P(T), they have to add up to 1.

In physical terms, this means that if we toss 100 coins, we expect to observe heads 50 times and tails 50 times. In practice, we will most likely not get exactly 50 of each because probabilities do not determine outcomes. Still, the more times we toss the coins, the closer our actual distribution will come to the expected value.

Now imagine that I have tossed a coin, it has landed, but I have not yet observed it (call this the one-dimensional Schrödinger's cat, if you like). The standard rhetoric is to say that the coin is in a superposition of two "states". One has to be very wary of the term "state" in this context. Quantum physicists do not use it in the normal way, and it can be very confusing. But I am going to use "state" in a completely naturalistic way. The "state" of the tossed coin refers to which face is up. And it has to be in one of two possible states: H or T.  

Now let's ask what I know and think about what I can know about the coin at this moment before I observe the state of the coin.

I know that the outcome must be H or T. And I know that the odds are 50:50 that it is either one. What else can I know? Nothing. Despite knowing to 100 decimal places what the probability is, I cannot use that information to know what state the coin is in before I observe it. If I start with probabilities, I can say nothing about the fact of the matter (using a phrase David Albert uses a lot). If I reify this concept, I might be tempted to say that there is no fact of the matter. 

Note also that it doesn't matter if P(H) and P(T) are changing. Let us say that the probabilities change over time and that the change can be precisely described by a function of the coin: Ψ(coin). Are we any better off? Clearly not.

This analogy generalises. No matter how complex my statistical model, no matter how accurately and precisely I know the probability distribution, I still cannot tell you which side up the coin is without looking. There is undoubtedly a physical fact of the matter, but as the old joke goes, you cannot get there from here.

There are an infinite number of reasons why a coin toss will have P(H) = P(T) = 0.5. We can speculate endlessly. This is why the "interpretations" of quantum mechanics are so wildly variable and the resulting metaphysics so counter-intuitive. Such speculations are not bound by the laws of nature. In fact, all such speculations propose radical new laws of nature, like splitting the entire universe in two every time a quantum event happens. 

So the whole project of trying to extract meaningful metaphysics from a probability distribution was wrong-headed from the start. It cannot work, and it does not work. A century of effort by very smart people has not produced any workable ideas. Or any consensus on how to find a workable idea. 

Superposition and the Measurement Problem

The infamous cat experiment, in all its varieties, involves a logical error. As much as Schrödinger resisted the idea, because of his assumption about wave-particle duality, his equation only tells us about the probabilities of states; it does not and cannot tell us which state happens to be the fact of the matter. The information we get from the current formalism is a probability distribution. So the superposition in question is only a superposition of probabilities; it's emphatically not a superposition of states (in my sense). A coin cannot ever be both H and T. That state is not a possible state. 

Is the superposition of probabilities in any way weird? Nope.

The fact that P(H) = 0.5 or P(H) = Ψ(coin) and that P(T) = 0.5 or P(T) = Ψ(coin) are not weird facts. Nor is the fact that P(H) + P(T) = 1. These are common or garden facts, with no mystical implications.

If we grant that the propositions P(H) = 0.5 and P(T) = 0.5 are logically true, then it must also be logically (and mathematically) true to say that P(H) + P(T) = 1. Prior to observations all probabilities coexist at the same time.

For all systems we might meet, all the probabilities for all the outcomes always coexist prior to observing the state of the system. And the probabilities for all but one outcome collapse to zero at the moment we observe the actual state. This is true for any system: coins, cats, electrons, and everything. 

Note also that this is not a collapse of anything physical. No attempt to reify this "collapse" should be made. Probability is an idea we can quantify, but it's not an entity. No existing thing collapses when we observe an event. 

Moreover, Buddhists and hippies take note, our observing an event cannot influence the outcome. Light from the event can only enter our eye after the event has occurred, i.e. only after the probabilities have collapsed. And it takes the brain an appreciable amount of time to register the incoming nerve signal, make sense of it, and present it to the first-person perspective. Observation is always retrospective. So no, observation cannot possibly play any role in determining outcomes. 

One has to remember that probability is abstract. It's an idea about how to quantify uncertainty. Probability is not inherent in nature; it comes from our side of the subject-object divide. Unlike, say, mass or charge, probability is not what a reductionist would call "fundamental". We discover probabilities through observation of long-term trends. At the risk of flogging a dead horse, you cannot start with an abstraction and extract from it a credible metaphysics. Not in the world that we live in. And after a century of trying, the best minds in physics have signally failed in this quixotic endeavour. There is not even a working theory of how to make metaphysics from probabilities. 

The superposition or collapse of probabilities is in no way weird. And this is the only superposition predicted by quantum mechanics. 

In my model, the electron is a wave, and the wave equation that describes it applies at all times. Before, during, and after observation. 

In my model, probabilities superpose when we don't know the facts of the matter, in a completely normal way. It's just that I admit the abstract nature of probability distributions. And I don't try to break reality so that I can reify an abstraction.

On the other hand, my approach is technically classical. A classical approach that ought to predict all the important observations of quantum mechanics, but which can also explain them in physical terms. As such, there is no separation between classical and quantum in my model. It's all classical. And I believe that the implications of this will turn out to be far-reaching and will allow many other inexplicable phenomena to be easily explained.

The so-called measurement problem can be seen as a product of misguided attempts to hypostatise and reify the quantum wavefunction, which only predicts probabilities. It was only ever a problem caused by a faulty conceptualisation of the problem in terms of wave-particle duality. If we drop this obviously false axiom, things will go a lot more smoothly (though the maths is still quite fiendish).

No one ever has or ever will observe a physical superposition. I'm saying that this is because no such thing exists or could exist. It's just nonsense, and we should be brave enough to stand up and say so.

There is no "measurement problem". There's measurement and there is ill-advised metaphysical speculation based on reified abstractions.

What about other quantum weirdness?

I want to keep this essay to a manageable length, so my answer to this question must wait. But I believe that Peter Jackson's (2013) free electron model as a vortex rotating on three axes is perfectly consistent with what I outlined here. And it explains spin very elegantly. If the electron is a sphere in an atom, why not allow it to always be a sphere?

Jackson also elegantly explains why the polarised filter set-up to test Bell's inequalities is not quantum weirdness, but a result of the photon interacting with, and thus being changed by, the filter. At the nano-scale and below, there are no neutral experimental apparatus.

What about interference and the double-slit experiment? Yep, I have some ideas on this as well.

Tunnelling? I confess that I have not tried to account for tunneling just yet. At face value, I think it is likely to turn out to be a case of absorption and re-emission (like Newton's cradle) rather than Star Trek-style teleporting. Again, there is no such thing as a neutral apparatus on the nano-scale or below. If your scientific apparatus is made of matter, it is an active participant in the experiment and at the nano-scale, it changes the outcomes. 

It's time to call bullshit on quantum mechanics and rescue physicists from themselves. After a century of bad metaphysics, let's put the phys back into physics!

~~Φ~~

P.S. My book on the Heart Sutra is coming along. I have a (non-committal) expression of interest from my publisher of choice. I hope to have news to share before the end of 2025.

PPS. I'd quite like to meet a maths genius with some time on their hands...

PPPS (16 Apr). I now have an answer to the question "What is waving?". An essay on this is in progress but may take a while. 

Bibliography

Grossman, Lisa. (2013). "Smile, hydrogen atom, you're on quantum camera." New Scientist. https://www.newscientist.com/article/mg21829194-900-smile-hydrogen-atom-youre-on-quantum-camera/

Jackson, Peter. (2009). "Ridiculous Simplicity". FQXi. What is Fundamental? https://forums.fqxi.org/d/495-perfect-symmetry-by-peter-a-jackson

Schiff, Leonard I. (1968). Quantum Mechanics. 3rd Ed. McGraw-Hill.

Quantum Bullshit

I was appalled recently to see that a senior professor of Buddhism Studies—whose work on Chinese Buddhist texts I much admire—had fallen into the trap of trying to compare some concept from Buddhist philosophy to what he calls "quantum mechanics". Unfortunately, as seems almost inevitable in these cases, the account the Professor gives of quantum mechanics is a hippy version of the Copenhagen interpretation proposed by Werner Heisenberg back in the 1920s. In a further irony, this same Professor has been a vocal critic of the secularisation and commercialisation of Buddhist mindfulness practices. The same problems that he identifies in that case would seem to apply to his own misappropriation of quantum mechanics.

As I've said many times, whenever someone connected with Buddhism uses the word "quantum" we can safely substitute the word "bullshit". My use of the term "bullshit" is technical and based on the work of Princeton philosopher Harry Frankfurt (image left). I use "bullshit" to refer to a particular rhetorical phenomenon. Here is the anonymous summary from Wikipedia, which I think sums up Frankfurt's arguments about bullshit precisely and concisely:

“Bullshit is rhetoric without regard for truth. The liar cares about the truth and attempts to hide it; the bullshitter doesn't care if what they say is true or false; only whether or not their listener is persuaded.”

What I am suggesting is that Buddhists who refer to quantum mechanics are not, in fact, concerned with truth, at all. A liar knows the truth and deliberately misleads. The bullshitter may or may not know or tell the truth, but they don't care either way. Their assertions about quantum mechanics may even be true, but this is incidental. The idea is to persuade you of a proposition which may take several forms but roughly speaking it amounts to:

If you sit still and withdraw attention from your sensorium, another more real world is revealed to you.

Certain Buddhists argue that a specific man sitting under a specific tree ca 450 BCE, while ignoring his sensorium, saw such a reality (Though he neglected to mention this). And then this thesis is extended with the proposition:

The reality that one "sees" when one's eyes are closed is very like the descriptions (though not the mathematics) of quantum mechanics.

I imagine that these statements strike most scientists as obviously false. The first hint we had of a quantum world was in 1905 when Einstein formalised the observation that energy associated with atoms comes in discrete packets, which he called "quanta" (from the Latin with the sense "a portion"; though, literally, "how much?"). Even this nanoscale world, which we struggle to imagine, is established by observation, not by non-observation. Equally, there is no sign in early Buddhist texts that the authors had any interest in reality, let alone ultimate reality. They didn't even have a word that corresponds to "reality". They did talk a lot about the psychology of perception and about the cessation of perception in meditation, within the context of a lot of Iron Age mythology. Given that there is no prima facie resemblance between science and Buddhism whatever, we might well ask why the subject keeps coming up.

I think this desire to positively compare Buddhism to quantum mechanics is a form of "virtue signalling". By attempting to align Buddhist with science, the highest form of knowledge in the modern world, we hope to take a ride on the coat-tails of scientists. This is still the Victorian project of presenting the religion of Buddhism as a "rational" alternative to Christianity. Generally speaking, Buddhists are as irrational as any other religieux, it's just that one of the irrational things Buddhists believe is that they are super-rational.

Had it merely been another misguided Buddhism Studies professor, I might have let it go with some pointed comments on social media. Around the same time, I happened to watch a 2016 lecture by Sean Carroll on YouTube called, Extracting the Universe from the Wave Function. Then I watched a more recent version of the same lecture from 2018 delivered at the Ehrenfest Colloquium. The emphasis is different in the two forums and I found that watching both was useful. Both lectures address the philosophy of quantum mechanics, but in a more rigorous way than is popular amongst Buddhists. Sean thinks the Copenhagen interpretation is "terrible" and he convinced me that he is right about this. The value of the lectures is that one can get the outlines of an alternative philosophy of quantum mechanics and with it some decisive critiques of the Copenhagen interpretation. Sean is one of the leading science communicators of our time and does a very good job of explaining this complex subject at the philosophical level.

What is Quantum Mechanics?

It is perhaps easiest to contrast quantum mechanics with classical mechanics. Classical mechanics involves a state in phase space (described by the position and momentum of all the elements) and then some equations of motion, such as Newton's laws, which describe how the system evolves over time (in which the concept of causation plays no part). Phase space has 6n dimensions, where n is the number of elements in the state. Laplace pointed out that given perfect knowledge of such a state at a given time, one could apply the equations of motion to know the state of the system at any time (past or future).

Quantum mechanics also minimally involves two things. A state is described by a Hilbert Space, the set of all possible quantum states, i.e., the set of all wave functions, Ψ(x). It is not yet agreed whether the Hilbert Space for our universe has an infinite or merely a very large number of dimensions.

For the STEM people, there's a useful brief summary of Hilbert spaces here. If you want an image of what a Hilbert Space is like, then it might be compared to the library in the short story The Library of Babel, by Jorge Luis Borges. (Hat-tip to my friend Amṛtasukha for this comparison).

Mathematically, a Hilbert Space is a generalisation of vector spaces which satisfy certain conditions, so that they can be used to describe a geometry (more on this later). One thing to watch out for is that mathematicians describe Hilbert Spaces (plural). Physicists only ever deal with the quantum Hilbert Space of all possible wavefunctions and have slipped into the habit talking about "Hilbert Space" in the singular. Sean Carroll frequently reifies "Hilbert Space" in this way. Once we agree that we are talking about the space defined by all possible wave functions, then it is a useful shorthand. We don't have to consider any other Hilbert Spaces.

The second requirement is an equation that tells us how the wave functions in Hilbert Space evolve over time. And this is Schrödinger's wave equation. There are different ways of writing this equation. Here is one of the common ways:

The equation is a distillation of some much more complex formulas and concepts that take a few years of study to understand. Here, i is the imaginary unit (defined as i² = -1), ħ is the reduced Planck constant (h/2π). The expression δ/δt represents change over time. Ψ represents the state of the system as a vector in Hilbert Space -- specifying a vector in a space with infinite dimensions presents some interesting problems. Ĥ is the all important Hamiltonian operator which represents the total energy of the system. And note that this is a non-relativistic formulation.

We owe this formalisation of quantum theory to the fact that John von Neumann studied mathematics with David Hilbert in the early 20th Century. Hilbert was, at the time, trying to provide physics with a more rigorous approach to mathematics. In 1915, he invited Einstein to lecture on Relativity at Göttingen University and the two of them, in parallel, recast gravity in terms of field equations (Hilbert credited Einstein so no dispute arose between them). In 1926, Von Neumann showed that the two most promising approaches to quantum mechanics—Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation—could be better understood in relation to a Hilbert Space.

[I'm not sure, but this may the first time a Buddhist has ever given even an overview of the maths in an essay about Buddhism and quantum mechanics.]

By applying the Born Rule (i.e., finding the square of the Wave Function) we can find the probability that any given particle will be found in some location at any given time. A common solution to the wave equation is a map of probabilities. For example, the probability plot for an electron in a resting state hydrogen atom looks like this (where shading represents the range probability and the black in the middle is the nucleus). And btw this is a 2D representation of what in 3D is a hollow sphere.

If we give the electron more energy, the probably map changes in predictable ways. An electron bound to an atom behaves a bit like a harmonic oscillator. A good example of a harmonic oscillator is a guitar string. If you pluck a guitar string you get a complex waveform made from the fundamental mode plus harmonics. The fundamental mode gives a note its perceived pitch, while the particular mixture of harmonics is experienced as the timbre of the note. The fundamental mode has two fixed points at the ends where there is zero vibration, and a maximum in the centre. The next mode, the 2nd harmonic takes more energy to produce and the string vibrates with three minima and two maxima - the pitch is an octave above the fundamental.

Using the fleshy parts of the fingers placed at minima points, it is possible to dampen extraneous vibrations on a guitar string and pick out the harmonics. Such notes have a very different timbre to regular notes. An electron bound to an atom also has "harmonics", though the vibrational modes are three dimensional. One of the striking experimental confirmations of this comes if we split sunlight up into a rainbow, we observe dark patches corresponding to electrons absorbing photons of a precise energy and becoming "excited". One of the first confirmations of quantum mechanics was that Schrödinger was able to accurately predict the absorption lines for a hydrogen atom using it.

And on the other hand, after we excite electrons in, say, a sodium atom, they return to their resting state by emitting photons of a precise frequency (in the yellow part of the visible spectrum) giving sodium lamps their characteristic monochromatic quality. The colour of light absorbed or emitted by atoms allows us to use light to detect them in spectral analysis or spectroscopy. For example, infrared light is good for highlighting molecular bonds; while green-blue visible and ultraviolet light are good for identifying individual elements (and note there are more dark patches towards the blue end of the spectrum).

The wave function applied to the electron in an atom gives us a map of probabilities for finding the electron at some point. We don't know where the electron is at any time unless it undergoes some kind of physical interaction that conveys location information (some interactions won't convey any location information). This is one way of defining the so-called the Measurement Problem.

rugby ball

I have a new analogy for this. Imagine a black rugby ball on a black field, in the dark. You are walking around on the field, and you know where you are from a GPS app on your phone, but you cannot see anything. The only way to find the ball is to run around blindly until you kick it. At the moment you kick the ball the GPS app tells you precisely where the ball was at that moment. But kicking the ball also sends it careering off and you don't know where it ends up.

Now, Buddhists get hung up on the idea that somehow the observer has to be conscious, that somehow consciousness (whatever that word means!) is involved in determining how the world evolves in some real sense. As Sean Carroll, says in his recent book The Big Picture:

“...almost no modern physicists think that 'consciousness' has anything whatsoever to do with quantum mechanics. There are an iconoclastic few who do, but it's a tiny minority, unrepresentative of the mainstream” (p.166).

The likes of Fritjof Capra have misled some into thinking that the very vague notion of consciousness plays a role in the measurement problem. As far as the mainstream of quantum mechanics is concerned, consciousness plays no part whatsoever in quantum mechanics. And even those who think it does have provided no formalism for this. There is no mathematical expression for "consciousness", "observer", or "observation". All of these concepts are completely nebulous and out of place around the wave equation, which predicts the behaviour of electrons at a level of accuracy that exceeds the accuracy of our measurements. In practice, our experiments produce data that matches prediction to 10 decimal places or more. Quantum mechanics is the most accurate and precise theory ever produced. "Consciousness" is the least well-defined concept in the history of concepts. "Observation" is not even defined.

In the image of the black rugby ball on a black field in the dark, we don't know where the ball is until we kick it. However, a ball and a field are classical. In the maths of quantum mechanics, we have no information about the location of the ball until we physically interact with it. Indeed, it appears from the maths that it's not physically in one place until information about location is extracted from the system through a physical interaction. And by this we mean, not a conscious observer, but something like bouncing some radiation off the electron. It's as though every time you take a step there is a possibility of the ball being there and you kicking it, and at some point, it is there and you kick it. But until that moment, the ball is (somehow) smeared across the whole field all at once.

Put another way, every time we take a step there is some probability that the ball is there and we kick it, and there is some probability that the ball is not there and we do not kick it. But as we step around, we don't experience a probability, and we never experience a ball spread out over all locations. Whenever we interact with the system we experience the ball as being at our location or at some specific other location. Accounting for this is at the heart of different interpretations of quantum mechanics.

Copenhagen

What every undergraduate physics student learns is the Copenhagen Interpretation of the measurement problem. In this view, the ball is literally (i.e., in reality) everywhere at once and only adopts a location at the time of "measurement" (although measurement is never defined). This is called superposition - literally "one thing on top of another". Superposition is a natural outcome of the Wave Equation; there are huge problems with the Copenhagen interpretation of how mathematical superposition relates to reality.

Firstly, as Schrödinger pointed out with his famous gedanken (thought) experiment involving a cat, this leads to some very counterintuitive conclusions. In my analogy, just before we take a step, the rugby ball is both present and absent. In this view, somehow by stepping into the space, we make the ball "choose" to be present or absent.

Worse, the Copenhagen Interpretation assumes that the observer is somehow outside the system, then interacts with it, extracting information, and then at the end is once again separate from the system. In other words, the observer behaves like a classic object while the system being observed is quantum, then classical, then quantum. Hugh Everett pointed out that this assumption of Copenhagen is simply false.

In fact, when we pick up the cat to put it in the box, we cannot avoid becoming entangled with it. What does this mean? Using the ball analogy if we kick the ball and know its location at one point in time then we become linked to the ball, even though in my analogy we don't know where it is now. If someone else now kicks it, then we instantaneously know where the ball was when it was kicked a second time, wherever we happen to be on the field. It's as though we get a GPS reading from the other person sent directly to our phone. If there are two entangled electrons on either side of the universe and we measure one of them and find that it has spin "up", then we also know with 100% certainty that at that same moment in time, the other electron has spin "down". This effect has been experimentally demonstrated so we are forced to accept it until a better explanation comes along. Thus, in Schrödinger's gedanken experiment, we always know from instant to instant what state the cat is in (this is also counter-intuitive, but strictly in keeping with the metaphor as Schrödinger outlined it).

As you move about the world during your day, you become quantum entangled with every object you physically interact with. Or electrons in atoms that make up your body become entangled with electrons in the objects you see, taste, touch, etc. Although Copenhagen assumes a cut off (sometimes called Heisenberg's cut) between the quantum world and the classical world, Hugh Everett pointed out that this assumption is nonsense. There may well be a scale on which classical descriptions are more efficient ways of describing the world, but if one atom is quantum, and two atoms are, and three, then there is, in fact, no number of atoms that are not quantum, even if their bulk behaviour is different than their individual behaviour. In other words, the emergent behaviour of macro objects notwithstanding, all the individual atoms in our bodies are obeying quantum mechanics at all times. There is no, and can be no, ontological cut off between quantum and classical, even if there is an epistemological cutoff.

In terms of Copenhagen, the argument is that wave function describes a probability of the ball being somewhere on the field and that before it is kicked it is literally everywhere at once. At the time of kicking the ball (i.e., measurement) the wave function "collapses" and the ball manifests at a single definite location and you kick it. But the collapse of the wave function is a mathematical fudge. In fact, it says that before you look at an electron it is quantum, but when you look at it, it becomes classical. Then when you stop looking it becomes quantum again. This is nonsense.

In Schrödinger's cat-in-the-box analogy, as we put the cat in the box, we become entangled with the cat; the cat interacts with the box becoming entangled with it; and so on. How does an observer ever stand outside a system in ignorance and then interact with it to gain knowledge? The answer is that, where quantum mechanics applies, we cannot. The system is cat, box, and observer. There is no such thing as an observer outside the system. But it is even worse because we cannot stop at the observer. The observer interacts with their environment over a period of years before placing the cat in the box. And both cat and box have histories as well. So the system is the cat, the box, the observer, and the entire universe. And there is no way to get outside this system. It's not a matter of whether we (as macro objects) are quantum entangled, but to what degree we are quantum entangled.

This is a non-trivial objection because entanglement is ubiquitous. We can, in theory, speak of a single electron orbiting a single nucleus, but in reality all particles are interacting with all other particles. One can give a good approximation, and some interactions will be very weak and therefore can be neglected for most purposes but, in general, the parts of quantum systems are quantum entangled. Carroll argues that there are no such things as classical objects. There are scale thresholds above which classical descriptions start to be more efficient computationally than quantum descriptions, but the world itself is never classical; it is always quantum. There is no other option. We are made of atoms and atoms are not classical objects.

Carroll and his group have been working on trying to extract spacetime from the wave function. And this is based on an idea related to entanglement. Since 99.99% of spacetime is "empty" they ignore matter and energy for the moment. The apparently empty spacetime is, in fact, just the quantum fields in a resting state. There is never nothing. But let's call it empty spacetime. One can define a region of spacetime in terms of a subset of Hilbert Space. And if you take any region of empty spacetime, then it can be shown to experience some degree of entanglement with all the other regions nearby. In fact, the degree of entanglement is proportional to the distance. What Carroll has suggested is that we turn this on its head and define distance as a function of quantum entanglement between regions of spacetime. Spacetime would then be an emergent property of the wave function. They have not got a mathematical solution to the wave equation which achieves this, but it is an elegant philosophical overview and shows early promise. Indeed, in a much simplified theoretical universe (with its own specific Hilbert Space, but in which Schrödinger's wave equation applies), they managed to show that the degree of entanglement of a region of spacetime determined its geometry in a way that was consistent with general relativity. In other words, if the maths works out they have shown how to extract quantum gravity from just Hilbert Space and the wavefunction.

Other questions arise from this critique of Copenhagen. What is an "event"? What is an "observation"? The problem for Buddhists is that we assume that it has something to do with "consciousness" and that "consciousness" has something to do with Buddhism. The first is certainly not true, while the second is almost certainly not true depending on how we define consciousness. And defining consciousness is something that is even less consensual than interpreting the measurement problem. There are as many definitions as there are philosophers of mind. How can something so ill-defined be central to a science that is all about well-defined concepts?

More on Interpretations

In 2013, some researchers quizzed physicists at a conference about their preferred interpretation of the measurement problem. This gave rise to what Sean Carroll called The Most Embarrassing Graph in Modern Physics:

Sean Carroll comments:

 

I’ll go out on a limb to suggest that the results of this poll should be very embarrassing to physicists. Not, I hasten to add, because Copenhagen came in first, although that’s also a perspective I might want to defend (I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person). The embarrassing thing is that we don’t have agreement.

Just 42% of those surveyed preferred Copenhagen - the account of quantum mechanics they all learned as undergraduates. Mind you, Carroll's preferred interpretation, Everett, got even less at 18%. However, it may be more embarrassing than it looks, because there are multiple Everettian interpretations. And note that several existing interpretations had no supporters amongst those surveyed (the survey was not representative of the field).

In Carroll's account, Copenhagen has fatal flaws because it makes unsupportable assumptions. So what about the alternatives? I found Carroll's explanation of the Everett interpretation in this lecture quite interesting and compelling. It has the virtue of being parsimonious.

Just like other interpretations, Everett began with Hilbert Space and the Wave Equation. But he stopped there. There are no special rules for observers as classical objects because there are no classical objects (just classical descriptions). In this view, the rugby ball still both exists and does not exist, but instead of the wave function collapsing, the interaction between the ball, the field, the observer, and the world cause "decoherence". If there are two possible outcomes — ball present at this location, ball somewhere else — then both happen, but decoherence means that we only ever see one of them . The other possibility also occurs, but it is as though the world has branched into two worlds: one in which the ball is present and we kick it, and one in which it is somewhere else and we do not kick it. And it turns out that having split in this way there is no way for the two worlds to interact ever again. The two outcomes are orthogonal in Hilbert Space.

While this sounds counterintuitive, Carroll argues that the many worlds are already present in the Hilbert Space and all the other interpretations have to introduce extra rules to make those other worlds disappear. And in the case of Copenhagen, the extra rules are incoherent. Everett sounds plausible enough in itself, but given the number of particles in the universe and how many interactions there are over time, the number of worlds must be vast beyond imagining. And that is deeply counter-intuitive. However, being counter-intuitive is not an argument against a theory of quantum mechanics. Physics at this scale is always going to be counterintuitive because it's not like the world on the scale we can sense. And at this point, it will be useful to review some of the problems associated with differences in scale.

Scale (again)

I've written about scale before. It is such an important idea and so many of our misconceptions about the world at scales beyond those our senses register are because we cannot imagine very small or very large scales.

We understand our world as classical. That's what we evolved for. Modern humans have been around for roughly between 400,000 and 200,000 years. But we discovered that there are scales much smaller than we can experience with our senses only about 400 years ago with the development of the microscope. As our understanding progressed we began to see evidence of the world on smaller and smaller scales. Each time we had to adjust our notions of the universe. At the same time telescopes revealed a very much larger universe than we had ever imagined.

Quantum mechanics developed from Einstein's articles in 1905 and was formalised mathematically in the 1920s. It has never been intuitive and it is so very far from our experience that is unlikely ever to be intuitive.

Humans with good eyesight can see objects at around 0.1 mm or 100 µm. A human hair is about 20-200 µm. A small human cell like a sperm might be 10 µm, and not visible; while a large fat cell might be 100 µm and be visible (just). A water molecule is about 0.0003 µm or 0.3 nanometres (nm = 10^-9 m). But at this level, the physical dimensions of an object become problematic because the location in space is governed by quantum mechanics and is a probability. Indeed, the idea of the water molecule as an "object" is problematic. The classical description of the world breaks down at this scale. The average radius of a hydrogen atom at rest is calculated to be about 25 picometres or 25x10^-12 m, but we've already seen that the location of the electron circling the hydrogen nucleus is a probability distribution. We define the radius in terms of an arbitrary cut off in probability. The estimated radius of an electron is less than 10⁻¹⁸ m (though estimates vary wildly). And we have to specify a resting state atom, because in a state of excitation the electron probability map is a different shape. It hardly makes sense to think of the electron as having a fixed radius or even as being an object at all. An electron might best be thought of as a perturbation in the electromagnetic field.

The thing is that, as we scale down, we still think of things in terms of classical descriptions and we don't understand when classical stops applying. We cannot help but think in terms of objects, when, in fact, below the micron scale this gradually makes less and less sense. Given that everything we experience is on the macro scale, nothing beyond this scale will ever be intuitive.

As Sean Carroll says, the many worlds are inherent in Hilbert Space. Other theories have to work out how to eliminate all of the others in order to leave the one that we observe. Copenhagen argues for something called "collapse of the wave function". Why would a wave function collapse when you looked at it? Why would looking at something cause it to behave differently? What happened in the universe before there were observers? Everett argued that this is an artefact of thinking of the world in classical terms. He argued that, in effect, there is no classical world, there is only a quantum world. Subatomic particles are just manifestations of Hilbert Space and the Wave Equation. The world might appear to be classical on some scales, but this is just an appearance. The world is fundamentally quantum, all the time, and on all scales.

Thinking in these terms leads to new approaches to old problems. For example, most physicists are convinced that gravity must be quantised like other forces. Traditional approaches have followed the methods of Einstein. Einstein took the Newtonian formulation of physical laws and transformed them into relativity. Many physicists take a classical expression of gravity and attempt to reformulate it in quantum terms - leading to string theory and other problematic approaches. Carroll argues that this is unlikely to work because it is unlikely that nature begins with a classical world and then quantises it. Nature has to be quantum from the outset and thus Everett was on right track. And, if this is true, then the only approach that will succeed in describing quantum gravity will need to start with quantum theory and show how gravity emerges from it. As I say, Carroll and his team have an elegant philosophical framework for this and some promising preliminary results. The mathematics is still difficult, but they don't have the horrendous and possibly insurmountable problems of, say, string theory.

Note: for an interesting visualisation the range of scales, see The Scale of the Universe.


Conclusion

Quantum mechanics is a theory of how subatomic particles behave. It minimally involves a Hilbert Space of all possible wave functions and the Schrödinger wave equation describing how these evolve over time. Buddhism is a complex socio-religious phenomenon in which people behave in a wide variety of ways that have yet to be described with any accuracy. It's possible that there is a Hilbert Space of all possible social functions and an equation which describes how it evolves over time, but we don't have it yet!

Buddhists try to adopt quantum mechanics, or to talk about quantum mechanics, as a form of virtue signalling -- "we really are rational despite appearances", or legitimising. They either claim actual consistency between Buddhism and quantum mechanics; or they claim some kind of metaphorical similarity, usually based on the fallacy that the measurement problem requires a conscious observer. And this is patently false in both cases. It's not even that Buddhists have a superficial grasp of quantum mechanics, but that they have a wrong grasp of it or, in fact, that they have grasped something masquerading as quantum mechanics that is not quantum mechanics. None of the Buddhists I've seen talking or writing about quantum mechanics mention Hilbert Spaces, for example. I'm guessing that none of them could even begin to explain what a vector is let alone a Hilbert Space.

I've yet to see a Buddhist write about anything other than the Copenhagen interpretation. I presume because it is only the Copenhagen interpretation that is capable of being shoehorned into a narrative that suits our rhetorical purposes; I don't see any advantage to Buddhists in the Everett interpretation, for example. Buddhists read — in whacky books for whacky people — that the "observer" must be a conscious mind. Since this suits their rhetorical purposes they do not follow up and thus never discover that the idea is discredited. No one ever stops to wonder what the statement means, because if they did they'd see that it's meaningless.

Thus, Buddhists who use quantum mechanics to make Buddhism look more interesting are not concerned with the truth. They do not read widely on the subject, but simply adopt the minority view that chimes with their preconceptions and use this as a lever. For example, I cannot ever recall such rhetoric ever making clear that the cat-in-the-box thought experiment was proposed by Schrödinger to discredit the Copenhagen interpretation. It is presented as the opposite. Again, there is a lack of regard for the truth. Nor do Buddhists ever present criticisms of the Copenhagen interpretations such as those that emerge from Everett's interpretation. Other criticisms are available.

And this disregard for the truth combined with a concerted attempt to persuade an audience of some arbitrary argument is classic bullshit (as described by Harry Frankfurt). Buddhists who write about quantum mechanics are, on the whole, bullshitters. They are not concerned with the nature of reality, they are concerned with status, especially the kind of status derived from being a keeper of secret knowledge. It's past time to call out the bullshitters. They only hurt Buddhism by continuing to peddle bullshit. The irony is that the truth of Buddhism is far more interesting than the bullshit; it's just much harder to leverage for status or wealth.

~~oOo~~

Frankfurt, Harry G. On Bullshit. Princeton University Press.

For those concerned about the flood of bullshit there is an online University of Washington course Calling Bullshit.

If you have a urge to learn some real physics (as opposed to the bullshit Buddhist physics) then see Leonard Susskind's lecture series The Theoretical Minimum. This aims to teach you only what you need to know to understand and even do physics (no extraneous mathematics or concepts).

Experience and Reality

"Our relation to the world is not that of a thinker to an object of thought"

—Maurice Merleau Ponty. The Primacy of Perception and Its Philosophical Consequences.

Introduction

In this essay and some to follow, I want to look an an error that many philosophers and most meditators seem to make: the confusion of epistemology and ontology; i.e., the mixing up of experience and reality. This essay will outline and give examples of a specific version of this confusion in the form of the mind projection fallacy.

I agree with those intellectuals who think that we do not ever experience reality directly. This is where I part ways with John Searle who, for reasons I cannot fathom, advocates naïve realism, the view that reality is exactly as we experience it. On the other hand, I also disagree with Bryan Magee that reality is utterly different from what we experience and we can never get accurate and precise knowledge about it. He takes this view to be a consequence of transcendental idealism, but I think it's a form of naïve idealism.

The knowledge we get via inference is not complete, but we can, and do, infer accurate and precise information about objects. This makes a mind-independent reality seem entirely plausible and far more probable than any of the alternatives. So, we are in a situation somewhere between naïve realism and naïve idealism. 

This distinction between a mind-independent reality and the mind is not ontological, but epistemological. The set of reality includes all minds. However, the universe would exist, even if there were no beings to witness is. The universe is not dependent on having conscious observers. So by "reality" I just mean the universe generally; i.e., the universe made up from real matter-energy fields arranged into real structures that have emergent properties, one of which is conscious states. And by "mind" I specifically mean the series of conscious states that inform human beings about the universe. 

What I don't mean is reality in the abstract. I'm deeply suspicious of abstractions at present. For the same reason, I avoid talking about conscious states in the abstract as "consciousness". Things can be real without there necessarily being an abstract reality. Reality is the set of all those things to which the adjective "real" applies. Things are real if they exist and have causal potential. Members of this set may have no other attributes in common. Unfortunately, an abstract conception of reality encourages us to speculate about the "nature of reality", as though reality were something more than  a collection of real things, more than an abstraction. Being real is not magical or mystical.

I'm not making an ontological distinction between mental and physical phenomena. I think an epistemological distinction can be made because, clearly, our experience of our own minds has a different perspective to our experience of objects external to our body, but in the universe there are just phenomena. This is a distinct position from materialism, which privileges the material over the mental. What I'm saying is that what we perceive as "material" and "mental" are not different at the level of being.  

When we play the game of metaphysics and make statements about reality, they arise from inferences about experience. There are three main approaches to this process:

• we begin with givens and use deduction to infer valid conclusions.
• we begin with known examples and use induction to infer valid generalisations.
• we begin with observations and use abductions to infer valid explanations.

We can and do make valid inferences about the universe from experience. The problem has always been that we make many invalid inferences as well. And we cannot always reliably tell valid from invalid.

For example, we know that if you submerge a person in water they will drown. That tells us something about reality. However, for a quite a long time, Europeans believed that certain women were in league with the devil. They believed that witches could not be drowned. So they drowned a lot of women to prove they were not witches; and burned the ones who didn't drown. The central problem here being that witches, as understood by the witch-hunters, did not exist. The actions of some women were interpreted through an hysterical combination of fear of evil and fear of women, and from this witches were inferred to be real. It was a repulsive and horrifying period of our history in which reasoning went awry. But it was reasoning. And it was hardly an isolated incident. Reasoning very often goes wrong. Still. And that ought to make us very much more cautious about reasoning than most of us are.

One of the attractions of the European Enlightenment is that it promised that reason would free us from the oppression of superstition. This has happened to some extent, but superstition is still widespread. Confusions about how reason actually works are only now being unravelled. And this meant that the early claims of the Enlightenment were vastly overblown. If our views about the universe are formed by reasoning, then we have to assume that we're wrong most of the time, unless we have thoroughly reviewed both our view and our methods, and compared notes with others in an atmosphere of critical thinking, which combines competition and cooperation. The latter is science at its best, though admittedly scientists are not always at their best. 

Into this mix comes Buddhism with its largely medieval worldview, modified by strands of modernism. Buddhists often claim to understand the "true nature of reality"; aka The Absolute, The Transcendental, The Dhamma-niyāma, śūnyatā, tathatā,  pāramārthasatya, prajñāpāramitā, nirvāṇa, vimokṣa, and so on. Reality always seems to boil down to a one word answer. And this insight into "reality" is realised by sitting still with one's eyes closed and withdrawing attention from the sensorium in order to experience nothing. Or by imagining that one is a supernatural being in the form of an Indian princess, or a tame demon, or an idealised Buddhist monk, etc. Or any number of other approaches that have in common that seem to take the approach of trying to develop a kind of meta-awareness of our experience.To experience ourselves experiencing.

It's very common to interpret experience incorrectly. As we know the lists of identified cognitive biases and logical fallacies, which each have over one hundred items. From these many problems I want to highlight one. When we make inferences about reality we are biased towards seeing our conclusions, generalisations, and explanations as valid, and to believing that our interpretation is the only valid interpretation. This is the mind projection fallacy.

The Sunset Illusion

An excellent illustrative example of the mind projection fallacy is the sunset. If I stand on a hill and watch the sunset, it seems to me that the the hill and I are fixed in place and the sun is moving relative to me and the hill. Hence, we say "the sun is setting". In fact, we're known for centuries that the sun is not moving relative to the earth, but instead the hill and I are pivoting away on an axis that goes through the centre of the earth. So why do we persist in talking about sunsets?

The problem is that I have internal sensors that tell me when I'm experiencing acceleration: proprioception (sensing muscle/tendon tension) kinaesthesia (sensing joint motion and acceleration) and the inner-ear's vestibular system (orientation to gravity and acceleration). I can also use my visual sense to detect whether I am in motion relative to nearby objects. A secondary way of detecting acceleration is the sloshing around of our viscera creating pressure against the inside of our body.

My brain integrates all this information to give me accurate and precise knowledge about whether my body is in motion. And standing on a hill, watching a sunset, my body is informing me, quite unequivocally, that I am at rest.

I'm actually spinning around the earth's axis of rotation at ca. 1600 km/h or about 460 m/s. That's about Mach 1.5! And because velocity is a vector (it has both magnitude and direction) moving in a circle at a uniform speed is acceleration, because one is constantly changing direction. So why does it not register on our senses? After all, being on a roundabout rapidly makes me dizzy and ill; a high speed turn in a vehicle throws me against the door. It turns out that the acceleration due to going moderately fast in very large circle, is tiny. So small that it doesn't register on any of our onboard motion sensors. The spinning motion does register in the atmosphere and oceans where it creates the Coriolis effect.

Everyone watching a sunset experiences themselves at rest and the sun moving. It is true, but counterintuitive, to suggest that the sun is not moving. Let's call this the sunset illusion.

I'm not sure where it comes from, but in the Triratna Order we often cite four authorities for believing some testimony: it makes sense (reason), it feels right (emotion), it accords with experience (memory), and it accords with the testimony of the wise. Before about 1650, seeing ourselves as stationary and the sun and moving, made sense, it felt right, it accorded with experience, and it accorded with the testimony of the wise. The first hint that the sunset illusion is an illusion came when Galileo discovered the moons of Jupiter in January 1610.

Even knowing, as I do, that the sunset illusion is an illusion, doesn't change how it seems to me because my motion senses are unanimously telling me I'm at rest. This is important because it tells us that this is not a trivial or superficial mistake. It's not because I am too stupid to understand the situation. I know the truth and have known for decades. But I also trust my senses because I have no choice but to trust them.

The sunset illusion is sometimes presented as a 50:50 proposition, like one of those famous optical illusions where whether we see a rabbit or a duck depends on where we focus. The assertion is that we might just as easily see the sun as still and us moving. This is erroneous. Proprioception, kinesthesia, the vestibular organ, and sight make it a virtual certainty that we experience ourselves at rest and conclude that the sun moving. It takes a combination of careful observation of the visible planets and an excellent understanding of geometry to upset the earth-centric universe. If some ancient cultures got this right, it was a fluke.

The sunset illusion exposes an important truth about how all of us understand the world based on experience. Experience and reality can be at odds.

And note that we are not being irrational when we continue to refer to the sun "setting". Given our sensorium, it is rational to think of ourselves at rest and the sun moving. It's only in a much bigger, non-experiential framework that the concept becomes irrational. For most of us, the facts of cosmology are abstract; i.e., they exist as concepts divorced from experience. Evolution has predisposed us to trust experience above abstract facts.

Mind Projection Fallacy

The name of this fallacy was coined by physicist and philosopher E.T. Jaynes (1989). He defined it like this:

One asserts that the creations of [their] own imagination are real properties of Nature, and thus, in effect, projects [their] own thoughts out onto Nature. (1989: 2)

I think it's probably more accurately described as a cognitive bias, but "fallacy" is the standard term. Also, instead of imagination, I would argue that we should say "interpretation". The problem is not so much that we imagine things and pretend they are real, though this does happen, but that we have experiences and interpret them as relating directly to reality (naïve realism).

The sunset illusion tells us that reality is not always as we experience it. 

We all make mistakes, particularly these kinds of cognitive mistakes. We actually evolved in such a way as to make these kinds of mistakes inevitable. However, reading up on cognitive bias, I was struck by how some of the authors slanted their presentation of the material to belittle people. I don't think this is helpful. Our minds are honed by evolution for survival a particular kind of environment, but almost none of us live in that environment any more. So if we are error-prone, it is because our skill-set is not optimised for the lifestyles we've chosen to live. 

This fallacy can occur in a positive and a negative sense, so that it can be stated in two different ways:

1. My interpretation of experience → real property of nature
2. My own ignorance → nature is indeterminate

David Chapman has pointed out that there has been considerable criticism of Jaynes' approach in the article I'm citing and has summarised why. He suggests, ironically, that Jaynes suffered from the second kind of mind projection fallacy when it came to logic and probability. But the details of that argument about logic and probability are not relevant to the issue I'm addressing in this essay. It's the fallacy or bias that concerns us here. 

Interpreting Experience

A problem like the sunset illusion emerges when we make inferences about reality based on interpreting our experience. For example, when we make deductions from experience to reality, they invariably reflect the content of our presuppositions about reality. For example, a given for most of us is "I always know when I am moving". In the sunset illusion, I know I am at rest because motions sensors and vision confirm that it is so. The experience is conclusive: it must be the sun must be moving. My understanding of how the universe works and my understanding of my own situation as regards movement are givens in this case. We don't consciously reference them, but they predetermine the outcome of deductive reasoning. This means the deduction is of very limited use to the individual thinking about reality.

If I watch a dozen sunsets and they all have this same character, then I can generalise from this (inductive reasoning) that the sun regularly rises, travels in an (apparent) arc across the sky and sets. All the while, I am not moving relative to earth. What's more, I've experienced dozens of earthquakes in my lifetime, so I also know what it is like when the earth does move! From my experiential perspective, the earth does not move, but the sun does move. Given our experience of the situation, this is the most likely explanation (abductive reasoning).

So here we see that a perfectly logical set of conclusions, generalisations, and explanations follow from interpreting experience, which are, nonetheless, completely wrong. I am not at rest, but moving at Mach 1.5. The earth is not at rest. The sun is at the centre of our orbit around it, but it also is moving very rapidly around the centre of the galaxy. Our galaxy is accelerating away from all other galaxies. The error occurs because our senses evolved to help us navigate through woodlands, in and out of trees, and swimming in water. And we're pretty good at this. When it comes to inferring knowledge about the cosmos, human senses are the wrong tool to start with!

A common experience for Buddhists is to have a vision of a Buddha during meditation. And it is common enough for that vision to be taken as proof that Buddhas exist. But think about it. A person is sitting alone in a suburban room, their eyes are closed, their attention withdrawn from the world of the senses, they've attenuated their sense experience to focus on just one sensation and have focussed their attention on it. They undergo a self-imposed sensory deprivation. They've also spent a few years intensively reading books on Buddhism, looking at Buddhist art, thinking about Buddhas, and discussing Buddhas with other Buddhists. We know that sensory deprivation causes hallucinations. And someone saturated in the imagery of Buddha is more likely to hallucinate a Buddha. This is no surprise. But does it really tell us that Buddhas exist independently of our minds, or does it just tell us that in situations of sensory deprivation Buddhists hallucinate Buddhas? 

The Buddhist who has the hallucination feels that this is a sign; it feels important, meaningful, and perhaps even numinous (in the sense that they felt they were in the presence of some otherworldly puissance). They are immersed in Buddhist rhetoric and imagery, as are all of their friends. As I have observed before, hallucinations are stigmatised, whereas visions are valorised. So if you see something that no one else sees, then your social milieu and your social intelligence will dictate how you interpret and present the experience. If you mention to your comrades in religion that you saw a Buddha in your meditation, you are likely to get a pat on the back and congratulations. It will be judged an auspicious sign. And all those people who haven't had "visions" will be quietly envious. If you mention it to your physician, they may well become concerned that you have suffered a psychotic episode. On the other hand, in practice, psychotic episodes are rather terrifying and chaotic, and not all hallucinations are the result of psychosis. 

Not only do we have the problem of our own reasoning leading us to erroneous inferences, we have social mechanisms to reinforce particular interpretations of experience, especially in the case of our religiously inspired inferences. Our individual experience is geared towards a social reality. One of the faults of humans thinking about reality is to think that reality somehow reflects our social world. A common example is the nature of heaven. Many cultures see heaven as an idealised form of their own social customs, usually with the slant towards male experiences and narratives. Medieval Chinese intellectuals saw heaven as an idealised Confucian bureaucracy, for example. If we take Christian art as any indication, then Heaven is an all male club. The just-world fallacy probably comes about because we expect the world to conform to our social norms in which each member is responsive to the others in a hierarchy where normative behaviour is rewarded and transgressive behaviour is punished.

So, given the way our senses work, given the pitfalls of cognitive bias and logical fallacies, given the pressure to conform to social norms, the mind projection fallacy can operate freely. As we know, challenging the established order can be difficult to the point of being fatal. And understanding the power of something like the sunset illusion is important. Facts don't necessarily break the spell. Yes, we know the earth orbits the sun. But standing on a hill watching the sunset, that is just not how we experience it (our proprioception and vision tell us a different story that we find more intuitive and credible, even though it is wrong). And this applies to a very wide range of situations where we are reasoning from experience to reality.

If I Don't Understand It...

The second form of this fallacy was rampant in 19th century scholarship. In the first form, one erroneously concludes that one understands something and projects private experience as public reality. Mistaking the sunset as resulting from the movement of the sun, because our bodies tell us that we are at rest. This leads to false claims about reality.

In the second case there is also a false claim about reality, but in this case it emerges from a failure to understand and the assumption that this is because the experience or feature of reality cannot be understood. This is a problem which is particularly acute for intellectuals. Intellectuals are often over‑confident about their ability to understand everything. These days it is less plausible, but 150 years ago it was plausible for one intellectual to be well informed about more or less every field of human knowledge. So, if such an intellectual comes across something they don't understand, then they deduce that it cannot be understood by anyone. 

A common assertion, for example, is that we will never understand consciousness from a third person perspective (leaving aside the problematic abstraction for a moment). Very often such theories are rooted in an ontological mind/body dualism, which may or may not be acknowledged. Many Buddhists who are interested in the philosophy of mind, for example, cannot imagine that we will ever understand conscious states through scientific methods. They argue that no amount of research will ever help us understand. So they don't follow research into the mind and don't see any progress in this area. On the other hand, they hold that through mediation we do come to understand conscious states and the nature of them. Many go far beyond this and claim that we will gain knowledge of reality, in the sense of a transcendent ideal reality that underlies the apparent reality that our senses inform us about. In other words, meditation takes us beyond phenomena to noumena. 

Another common argument is that scientists don't understand 95% of the world because they don't understand dark matter and dark energy. People take this to mean that scientists don't understand 95% of what goes on here on earth. But this is simply not true. Scale is important, and being ignorant at one scale (the scale that effects galaxies and larger structures) does not mean that we don't understand plate tectonics, the water cycle, or cell metabolism, at least in principle. The popular view of science often seem to point towards a caricature that owes more to the 19th century than the 21st. Criticism of science often goes along with an anti-science orientation and very little education in the sciences. 

The basic confusion in both cases is mistaking what seem obvious to us, for what must be the case for everyone else, either positively or negatively. 

The Confusion

"It's not that one gains insight into reality, but that one stops mistaking one's experience for reality"

The basic problem here is a confusion between what we know about the world (epistemology) with what the world is (ontology). In short, we mistake experience for reality. And this problem is very widespread amongst intellectuals in many fields.

The problem can be very subtle. Another illuminating example is the idea that sugar is sweet. We might feel that a statement like "sugar is sweet" is straightforward. Usually, no one is going to argue with this, because the association between sugar and sweetness is so self-evident. But the statement it is false. Sugar is not sweet. Sugar is a stimulus for the receptors on our tongues that register as "sweet". We experience the sensation sweet whenever we encounter molecules that bind with these receptors. But sweet is an experience. It does not exist out in the world, but only in our own conscious states. Sugar is not sweet. Sugar is one of many substances that cause us to experience sweet when they come into contact with the appropriate receptors on our tongue. Equally, there is no abstract quality of sweet-ness, despite the effortless ease with which we can create abstract nouns in English. Sucrose, for example has nothing much in common with aspartame at a chemical level. And yet both stimulate the experience of sweet. Indeed, aspartame is experienced as approximately 200 times as sweet as sucrose, but this does not mean that it contains 200 times more sweetness. There is no sweet-ness. The experience of sweet evolved to alert us to the high calorific value of certain types of foods and the enjoyable qualities of sweet evolved to motivate us to seek out such foods. 

For Buddhists, the application of this fallacy comes from experiencing altered states of mind in and out of meditation. Meditators may experience altered states of mind that they judge to be more real than other kinds of states, causing them to divide phenomena into more real and less real. And they manage to convince people that this experience of theirs reflects a reality that ordinary mortals cannot see -- a transcendent reality that is obscured from ordinary people. 

The problem is that an experience is a mental state; and a mental state is just a mental state. No matter how vivid or transformative the experience was, we must be careful when reasoning from private experiences (epistemology) to public reality (ontology) because we usually get this wrong. I've covered this in many essays, including Origin of the Idea of the Soul (11 Nov 2011) and
 Why Are Karma and Rebirth (Still) Plausible (for Many People)? (15 Aug 2015), etc.

Most of us are really quite bad at reasoning on our own. This is because humans suffer from an inordinate number of cognitive biases and easily fall into logical fallacies. There are dozens of each and, without special training and a helpful context, we naturally and almost inevitably fall into irrational patterns of thought. The trouble is that we too often face situations where there is too much information and we cannot decide what is salient; or there is too little information and we want to fill the gaps. 

Our minds are optimised for survival in low-tech hunter-gatherer situations, not for sophisticated reasoning. The mind helps us make the right hunting and gathering decisions, but in most cases it's just not that good at abstract logic or reasoning. Of course, some individuals and groups are good at it. Those who are good at it have convinced us that it is the most important thing in the world. But, again, this is probably just a cognitive bias on their part. 

Conclusion

The whole concept of reason and the processes of reasoning are going through a reassessment right now. This is because it has become clear that very few people do well at abstract reasoning. Most of the time, we do not reason, but rely on shortcuts known as cognitive biases. A lot of the time our reasoning is flawed by logical fallacies. Additionally, we are discovering that most mammals and birds are capable of reasoning to some extent. 

In this essay, I have highlighted a particular problem in which one mistakes experience for reality. Using examples (sunset, visions, sweetness) I showed how such mistakes come about. Unlike others who highlight these errors, I have tried to avoid the implication that humans are thereby stupid. For example, I see the sunset illusion because my senses are telling me that I am definitely at rest, because they tune out sensations that are too small to affect my body. Social conditioning is a powerful shaping force in our lives, and visions are valuable social currency in a religious milieu.

In terms of our daily lives the sunset illusion or the sweetness illusion hardly matter. It's not like the mistakes cost us anything. Such problems don't figure in natural selection because our lives don't depend on them. We know what we need to know to survive. Although our senses and minds are tuned to survival in pre-civilisation environments, we are often able to co-opt abilities evolved for one purpose to another one. 

But truth does matter. For example, when one group claims authority and hegemony based on their interpretation of experience, then one way to undermine them is to point out falsehoods and mistakes. When the Roman Church in Europe was shown to be demonstrably wrong about the universe, the greater portion of their power seeped away into the hands of the Lords Temporal, and then into the hands of captains of industry. For ordinary people, this led to more autonomy and better standards of living (on average). Democracy is flawed, but it is better than feudalism backed by authoritarian religion.

But as Noam Chomsky has said:

“The system protects itself with indignation against a challenge to deceit in the service of power, and the very idea of subjecting the ideological system to rational inquiry elicits incomprehension or outrage, though it is often masked in other terms.”

In subjecting Buddhism to rational inquiry, I do often elicit incomprehension or outrage. And sometimes it's not masked at all. There are certainly Buddhists on the internet who see me as an enemy of the Dharma, as trying to do harm to Buddhism. As I understand my own motivations, my main concern is to recast buddhism for the future. I think the urge of the early British Buddhists to modernise Buddhism and, particularly, to bring it into line with rationality was a sensible one. However, as our understanding of rationality changes so Buddhism will have to adapt to continue being thought of as rational. But also we have to move beyond taking Buddhism on its own terms and to consider the wider world of knowledge. The laws of nature apply in all cases.

Whilst Buddhism is largely influenced by people who mistake experience for reality, Buddhism will be hindered in its spread and development. This particular error is one that we have to make conscious and question closely. Just because it makes sense, feels right, and accords with experience doesn't mean that it is true. The sunset illusion makes sense, but is wrong. It feels right to say that sugar is sweet, but it isn't. It accords with experience that meditative mental states are more real than normal waking states. But they are not. The testimony of the wise is demonstrably a product of culture, and varies across time and space.

~~oOo~~