Quantum interpretations and Buddhism Part 6: Experiment part 2 Spin

 

Below is a selection of the important experiments which helped to form quantum mechanics. It's presented in table form.

Rough year	Name of the experiment	Name of relevant physicists and contribution	What's the deviation compared to classical	Impact
1900	Thermal radiation of different frequencies emitted by a body.	Max Planck, for putting the adhoc solution E=nhf.	Classical theories can account for ends of high frequency and low frequency using two equations, Max Planck's one equation combined them both.	Light seems to carry energy in quantised quantity, the origin of quantum, thought of as mathematical trick.
1905	Photo electric effect	Albert Einstien, for taking seriously the suggestion that light is quantized.	We expect that light can expel   electron at any frequency, but reality is, only light with high enough frequency can expel electrons.	The beginning of taking the maths of quantum physics seriously as stories, that light is a particle called photon.
1913	Hydrogen Atomic spectra	Niels Bohr, for explaining the spectra lines with Bohr atomic model.	Updated the Rutherford model of the atom (just 2 years old then) to become Bohr model. Rutherford model has one positive nucleus at the centre and electrons just scattered around it, Bohr had the electron orbits around the nucleus, like a mini solar system, which is still our popular conception of the atom, even when it has been outdated.	Serves as a clue in the development of quantum mechanics. It predicts angular momentum is quantised, which leads to the Stern-Gerlach experiment.
1922	Stern–Gerlach experiment	Otto Stern and Walter Gerlach, for discovering that spatial orientation of angular momentum is quantised.	If atoms were classically spinning objects, their angular momentum is expected to be random and continuously distributed, the results should be some density distribution, but what is observed is a discrete separation due to quantised angular momentum.	1. Measurement changes the system being measured in quantum mechanics. Only the spin of an object in one direction can be known, and observing the spin in another direction destroys the original information about the spin. 2. The results of the measurement is probabilistic: any individual atom sent into the apparatus have equal chance of going up or down. Unless we already know from previous measurement its spin in the same direction.
1961	Young's double-slit experiment with electrons	Thomas Young did it with light   first in 1801, then Davisson and Germer in 1927 used electrons with crystals, finally Clauss Jönsson made the thought experiment a reality. In 1974, Pier Giorgio Merli did it with single electrons.	If electrons does not have wavelike properties like a classical ball, it would never have shown interference patterns. The double-slit experiment is now also capable of being done with single particles, interference still occurs. Classical expectation would not have allowed single particle to interfere with itself.	The double-slit experiment is still widely used as the introduction to quantum weirdness, likely popularised by Richard Feymann's claim that all the mysteries of the quantum is in this experiment. Since then, it's possible to explain single particles quantum behaviour without the mysteries. https://doi.org/10.1103/PhysRevA.98.012118
1982	Bell's Inequality Violation	Einstein, Podolsky, Rosen, for bringing up the EPR paradox, John Bell for formulating the paradox into a Bell inequality, Alain Aspect for testing CHSH, a version of Bell's inequality, B. Hensen et. al. did a loop hole free version in 2015.	If the world behaves classically, that is it has locality (only nearby things affect each other at most at the speed of light), counterfactual definiteness (properties of objects exist before we measure them), and freedom (physical possibility of determining settings on measurement devices independently of the internal state of the physical system being measured), then Bell's inequality cannot be violated. Quantum entangled systems can violate Bell's inequality. Showing that one of the three assumptions of the classical world has to be discarded.	The world accepts the existence1999 of quantum entanglement, this also leads to more research into fundamental quantum questions as EPR was for a long time considered unbeneficial fundamental question. However, on closer inspection as in with Bell's inequality, it revealed new stuffs to us, and helped usher in the age of quantum information technology.
1999	Delayed-choice quantum eraser	Yoon-Ho Kim et. al. for doing the experiment,  John Archibald   Wheeler thought of the original thought experiment of delayed choice.	Quantum eraser is that one can erase the which-way information after measuring it, thus determining the results of interference or no interference pattern on the double slit. The delayed choice means one can determine to erase or not after the measurement was done. So how we describe the past depends on what happens in the future, contrary to our intuition that the past is fully described by events happening in the past. Note what happens is the same, just that new information can be gained based on decisions in the future.	This is one of the popular counter-intuitive experiments commonly used to evaluate and test out our intuition about quantum mechanics and its interpretations. It's frequently used in many popular accounts of quantum physics.

We will only be looking at the last four experiments in detail.

 

Stern–Gerlach experiment

 

The set up is to shoot silver atoms to an unequal distribution (inhomogeneous) of magnetic field. As suggested by Bohr, angular momentum is quantised. You can think of spin as a form of angular momentum. For those who forgot what angular momentum is, it is mass times velocity times radius of rotation for a massive body rotating around an axis. It can be generalised to everything that rotates has angular momentum. All particles possess this spin property, we call it intrinsic angular momentum. That's not to say that it physically spin. Why?

 

Let’s assume that the electron is a small ball, of the radius 10^-19 m, corresponding to the smallest distance probed by Large Hadron Collider. In the standard model, the electron is basically zero size, a zero-dimensional point particle, but for the sake of imagining it spinning around, we give it size for now. The electron has an intrinsic angular momentum of 1/2 of reduced Planck’s constant. Numerically that’s 5.27 x 10^-35 kg m² s^-1. Moment of inertia of a solid sphere is 0.4 MR², for electron, that’s 3.6 x 10^-69 kgm². So calculating the angular velocity of the electron, we divide the angular momentum by the moment of inertia, we get 1.4 x 10³¹s^-1. That is the electron spins that many times per second, putting in radius of electron to calculate the velocity at the surface of the electron as sphere, we get 1.4 x 10¹² ms^-1. That’s much faster than light which is in the order of 10⁸ ms^-1. The smaller radius we give the electron, the higher the velocity we get. So we cannot interpret spin as the subatomic particles physically spinning.

 

Silver atoms also has spin. As silver atoms are made up of charged parts, and moving charges generates magnetic fields, all particles made out of charged parts or has charges behave like little magnets (magnetic dipole). And these little magnets should be deflected by the inhomogeneous magnetic field. We use silver atoms to have neutral electrical charge, so that we only see spin in the following experiment.

 

Say, if we imagine electrons, protons etc as physically spinning (which I warned is the wrong picture), we would expect that the magnet can point in any direction along the up-down axis. To make it more concrete, look at the picture and take the Cartesian coordinates z as the direction in which line 4 points at, the up or down along the screen. y-coordinate is the direction from the source of the Silver atoms, 1 to the screen. x-coordinate is left and right of the screen then. So the measurement of the spin is now orientated along the z-axis, the up-down axis. If the spin is fully pointing along up or down z direction, it will have maximum deflection as shown on 5. If the spin has y-components, so that it can have a distribution of values between the ups and downs of z-axis, then we would expect 4 to be the results of the experiment. This again is the classical picture of thinking of spin as physical rotation, so classical results are 4 on the screen.

 

Experimentally, the results are always 5. Never any values in between. This might look weird, and indeed is the start of many of the weird concepts we will explore below which is fundamental in the Copenhagen Introduction to quantum mechanics.

 

Some questions you might want to ask is, do the spins have ups and downs initially (stage one), but they are snap into up or down only via the measurement (stage two)? Or is it something else more tricky?

 

Stern–Gerlach experiment: Silver atoms travelling through an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic field, (4) classically expected result, (5) observed result

Photo by Tatoute - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=34095239

 

Further magical property is that if I remove the screen, put another inhomogeneous magnetic field pointed along the x-axis (henceforth called a measurement in x-axis) on the beam of atoms which has up z-spin. (The same results happens even if I choose the down z-spin.) Then what I have is two streams pointed left (x+) and right (x-). That's to be expected. If I bring apply again the z-axis measurement onto any of these left or right spins, the results split again into up and down z-axis.

 

If you think that this tells us that we cannot assume that the particle remembers its previous spin, then apply another z-axis measurement onto the up z-spin particles, they all go up as shown in the picture below. S-G stands for Stern-Gerlach apparatus, the measurement apparatus which is basically just the inhomogeneous magnetic field. One way to interpret this is that depending on how you measure, measurement changes what is measured.

 

Picture from Wikipedia

 

If you put another x-axis measurement as the third measurement on the middle part, one for each beam, the beam which has up x-axis (x+) will 100% go up again, and the one with down x-axis (x-) will go 100% go down again.

 

It seems that the rules are

 

a. Measurement changes the system being measured in quantum mechanics. Only the spin of an object in one direction can be known, and observing the spin in another direction destroys the original information about the spin.

 

b. The results of the measurement is probabilistic: any individual atom sent into the apparatus have an equal chance of going up or down. Unless we already know from previous measurement its spin in the same direction.

 

This does lead to two things which is troubling to classical thinking. Contextuality or the answer depends on the question. And inherent randomness. More on contextuality later, for now, we focus on randomness. Normal randomness we have in the classical world is due to insufficient information in the world. If we gather enough data, we can always predict the results of coin toss or dice roll. Yet, in the quantum systems, there seems to be no internal mechanism for them (or is there? Look out for hidden variables interpretation), we have the maximum information from its wavefunction (according to Copenhagen interpretation) and thus the randomness is inherent in nature.

 

Some people do not like inherent randomness, some do. Why? Classical physics is very much based on Newtonian clockwork view of the universe. With the laws of motion in place, we had discovered also how heat flows, how electromagnetism works, even all the way to how spacetime and mass-energy affect each other in general relativity. One thing is common to all of these. They are deterministic laws. That is if by some magic, we can get all the information in the world at one slice of time (for general relativity, it means one hypersurface), plug it into the classical equations, we can predict all of the past and future to any arbitrary accuracy, without anything left to chance, randomness. That's a worldview of the universe which is deterministic, clockwork, incompatible with anything which has intrinsic, inherent randomness.

 

So, some view that the main goal of interpretation is to get back into the deterministic way of the universe. Yet, others see this indeterminism as an advantage as it allows for free will. More on that later. For now, let us jump on board to try to save determinism.

 

If we do not like intrinsic randomness, if we insist that there is some classical way to reproduce this result, then one fun way to think about it is that each particle has its own internal if-then preparations. The particle instructions are: If I encounter the z measurement, I will go up, if x, then I will go left, if z after x, then I will go down, or else I will go up. And so on. We shall explore this in detail in the next section on playing a quantum game, to try to use classical strategies to simulate quantum results.

 

For Buddhists, here’s a motivation to follow the quantum game analysis (it gets heavy). We believe in cause and effect relationships. So intrinsic randomness seems to be at odds with causal relationships. Think about it. The same atoms of silver prepared the same way, say after it exited the z-axis, we only select the spin up z-axis silver atoms. When we put in another cause of putting a measurement of x-axis to it, it splits into up x and down x. Same atoms with the exact same wavefunctions, thus same causes, same conditions of putting measurement on x-axis, different results of up and down in x-axis. That intrinsic randomness according to some quantum interpretations has no hidden variables beneath it. So if we wish to recover predictability and get rid of intrinsic randomness, we better pay attention to try to simulate the quantum case using classical strategies to avoid intrinsic randomness.

Quantum interpretations and Buddhism Part 5: Mathematical Structure of Quantum Physics

 

Below are the postulates of quantum physics. Postulates are assumed to be true and doesn’t need proof. Usually in classical mechanics, the postulates are obvious, fits in our common sense and thus we accept them without question. In quantum physics, the postulates are mostly mathematical in nature, not intuitive and not easy to digest. Thus the suggestion that the postulates are not irreducible (not fundamental), and not really complete. When I saw this in my quantum mechanics classes in University, I indeed do not understand quantum mechanics at all. It’s just a system of rules to do calculations and then we somehow get the answers to explain or predict experimental results. So I will attempt to remove the mathematical side as much as possible and explain it with much comparison with the classical physics we are intuitively familiar with.

The state of a quantized system: The state of a quantum mechanical system is completely defined by its wavefunction. There is this mathematical thing we call the wavefunction, which exist in a mathematical space called complex Hilbert space which can represent all states of a system. If you know the states or wavefunction of the system, you can answer any questions asked about the system. Where is the electron, how fast is it moving, etc, all these information are contained in its wavefunction. Those who do not believe that wavefunction completely captures the information of the state considers that quantum physics is incomplete. In classical physics, we can just directly observe the position, momentum of the object in question, but in quantum physics, they are encoded in the wavefunction. The following postulates explains how to read those values from the wavefunction. 

Physical Observables: Observables are represented in quantum theory by a specific class of mathematical operators. Following Jim Baggott’s introduction in his book, quantum reality, this is like having the right sets of keys. Apply the right key to the wavefunction, we get to read the value of the properties we want to measure. For example, if we want to know the position of an electron, we apply the position operator onto the electron wavefunction and outcomes the expectation values of where we might find the electrons. This is a bit going ahead for it’s in postulate no. 3. In classical physics, we don’t need to have such troublesome mechanism, we can directly see the things we want to observe in the equations of motions of a classical ball. The quantum difference is also that different sets of quantum operators can be non-commutable. This means that the order of measuring one thing or another for non-commutable things matter. Example of some non-commutable operators are: position-momentum, energy-time, spin in x-axis vs spin in y-axis vs spin in z-axis. So in classical physics, everything is commutable, the order of which we measure this or that first doesn’t matter, but in quantum, if we measure first one thing or another, we don’t get the same results if we switch the order. The act of measuring itself seems to change the wavefunction to give different answers to the second part which is not commutable. 

Expectation values:  The average value of an observable is given by the expectation value of its corresponding operator. This is open the box. With the key above, we can get the average value of the things we want to measure. A key difference with classical physics is that classical physics directly gives us the value exactly, or to as much precision as we want. In quantum, the individual results of each time we see where an electron is, we cannot predict the exact position for each time we see the electron. If we measure identically prepared electrons (same wavefunction) in the same way on their position (position operator), we can get an average value for their position, which is capable of been calculated via this math procedure. 

Born’s Rule: The probability that a measurement will yield a particular outcome is derived from the square of the corresponding wavefunction. As hinted above, the individual measurement outcomes are probabilistic in nature, Born’s rule allows us to calculate the exact probabilities for each possible results. That’s the best we can do for quantum. In classical, any probabilities is due to ignorance, and if we gathered enough data, we can predict anything to exact values. This seems not to be so in quantum, depending on the interpretation. The Born’s rule is also regarded as unsatisfactory as it’s added in to bridge the quantum calculation to what we directly observe in experiments. So wavefunction collapses to the results we get, but before measurement, we don’t know which results we will get. Jim Baggott calls it: what we get. 

Evolution of wavefunction: In a closed system with no external influences, the wavefunction evolves in time according to the time-dependent Schrödinger equation. How we get from here to there. Without measurement, the wavefunction evolves deterministically based on their past in accordance to the time-dependent Schrödinger equation. This smooth evolution of wavefunction when meeting measurement, abruptly changes the wavefunction to correspond to the results we get, we call this collapse of wavefunction. Some people don’t like this collapse and thus came out with the quantum many-worlds interpretation. In classical physics, we have a similar evolution of the states of classical objects being deterministic, but we lack the sudden collapse and probabilistic results from Born’s rule. 

Let’s use a simple test case to just illustrate how quantum works. Say using the double-slit experiment for electrons.

We have an electron gun, shooting electrons at the same velocity, thus the same momentum, and thus same wavelength to the double-slit on the order of the wavelength of the electron. Behind the slit, we place phosphor screen which emits lights when electrons hit them. So we can directly see the results of the electrons passing through the slit. 

First, the wavefunction of the electron identically prepared by the electron gun behaves like a wave from the gun all the way to the screen, interfere with itself, producing interference patterns, we see many lines on the screen, not just two lines from the slit. The physical observable measured here is position of electron as they hit the screen. The screen acts as the measuring device. The expectation values depend on the wavefunction, and we do see interference pattern because we didn’t try to see which holes do the electrons go through to make it exhibit particle behaviour. Born’s rule comes in when we reduce the intensity of the electron beam to only one electron coming out at a time. So for each electron, the exact location where it hits the screen is unknown, but we can calculate the probability of it hitting the screen. 

For the evolution of the wavefunction, just picture a wave from the gun, through the double-slit, interfere with itself, and hits the screen. The amplitudes of the wave when squared shows the probability of individual electrons hitting the screen and leave it long enough, we get the interference pattern nicely imprinted upon the screen. Nothing too complicated right? 

When you try to look at which slit did an individual electron goes through, you’re introducing measurement at the slits area. So due to the measurement, we should apply collapse of wavefunction of the electron just after the slits. Either the electron goes through the left or the right slit. For those which are blocked by the plate which contains the double-slit, we can just ignore those electrons as not within the area of interest. So when you try to ask the electron to reveal their position way before they hit the screen, the picture on the screen changes into just two lines, corresponding to the two slits. The interference effect due to the wave property is gone. The act of measurement changes the nature of the electron from wave to particle. 

Wait, I am sorry, this is not an unbiased view of what happened. What I had just described was in accordance with the Copenhagen interpretation. It’s basically very bare-bones, what’s in the mathematical structure is all that is to quantum. We have collapse of wavefunction, the wave and particle nature of the electrons are complimentary, etc. It’s the first interpretation which got popular and because the religion of quantum, of nothing interesting beneath the maths, so just shut up and calculate. For back in 1920-30s quantum is still yet to be applied to the nuclear, atomic, subatomic physics, particle physics, molecular bondings in chemistry and so on. A lot of work of calculations was to be done by the physicists of that time instead of worrying about the philosophical implications of quantum theory. What it means, is there a reality beneath? Why is nature so weird and not classical? Which classical assumptions must we abandon?   

I must apologise again, for now, we shall turn to the front of the theatre, to see the experiments, to see what empirical reality tells us before we venture into the stories and metaphysics behind the interpretations. During this trip to the experiments, there will be detailed analysis for some of the experiments and what classical assumption might you need to throw out of the door when you are faced with the results of the experiments. Those analyses are essential to understand why certain classical intuition cannot be applied and quantum interpretations have the job of choosing which ones to retain and which ones to throw out. The results may be very surprising to you if you use classical expectations to anticipate the results. This is presented first in hopes of you not using your first interpretations to interpret the results and then be attached to the first one. Just see this as how nature works. We shall revisit these experiments in each of the interpretations later on to give the story of how this particular interpretation makes sense of the experiment. For now, enjoy the theatre show or if you like the magic show, not the backstage or how does the magician do it?

Quantum interpretations and Buddhism Part 4: Interlude: Experiment part 1 Double-slit

To better understand the maths, let’s get familiar with at least one experiment first to get a picture in the mind.

 

Young's double-slit experiment with electrons

 

The set up is just to put a traditional double slit in the path of an electron beam, shot out from an electron gun to see if there would be interference in the results or not.

Picture from Wikipedia

 

Historically, the issue of waves vs particle nature of things started all the way back to Newton. Newton thought that lights are particles, perhaps due to geometrical optics where you can trace the path of light through lenses by just drawing straight lines. There is also a common-sense answer (which ignores how small light's wavelengths are) that if light is a wave, how can our shadows be so sharp instead of blurry?

 

Thomas Young back in 1800s first did the double-slit experiment on light. It's basically the same set up as the picture above, just replace the electron gun with a light from a lamp, which is focused via a small hole. Laser hasn't been invented yet then. As light passes through the double slit, if it is made out of particles, we should only see two slits of light at the screen, yet we see an interference pattern!

 

Wait a minute you might say. You go get a torchlight, cut out two slits out of a cardboard and shine the torchlight through the slits, you see two slits of light shining through. Where is the interference pattern? The caveat for the double-slit is that the size of the slit and the distance between the slit should be roughly around the wavelength of whatever waves you wish to pass through it. And the wavelength of light is around 400 to 700 nanometres. For comparison, the size of a bacteria is about 1000 nanometres. The enlarged slits in the picture are merely for illustration purposes, it's not to scale.

 

What can produce an interference pattern? Waves. Observe the gif below. Waves can meet with each other and if they happen to be in phase at the position where they meet the screen, constructive interference happens, the amplitudes add up and you see light-gathering there. If they happen to have opposite amplitude at another position, destructive interference happens and you are left with a dark region. Destructive interference is also what happens when you use noise-cancelling headphones.

 

gif from wikipedia

 

So Thomas Young settled that lights are waves after all, with wavelengths being very small, thus our shadows seem sharp. Next up, Maxwell showed that light is electromagnetic waves with a calculable theoretical speed. Thus it was with great difficulty to accept again that light maybe particles in some other situations. That's why Planck didn't believe the mathematical trick he did had a physical significance. And Einstein was pretty much didn't get much support when he took the idea of photon (light as particles) seriously.

 

Louis de Broglie had some idea that if waves have particle-like properties, might not particles also behave like waves? It took a long time, but finally, the proper experiment was done using electron beams fired from electron guns towards the double slit only to find (to no one's surprise by then) that yes, electrons exhibit interference pattern too.

 

What's so hard for classical thinking and expectations to accept is that a thing is either a particle or a wave. How can it exhibit particle-like behaviour in some cases and wave behaviour in other cases just for the convenience of explaining what happens in certain cases? Quantum thinking would have to accept a certain relaxation of this criterion that a thing must be either a particle or a wave. So it could be that they have both properties which are real (as advocated by Bohm's interpretation), or that they behave like wave or particles depending on how we set up the experiment (Copenhagen interpretation). Or some other possibilities. It's a common practice to not be too concerned with our language to say it's a particle-wave. Usually, we just use the term particle and the wave properties are understood to be there when needed.

 

Let's take a breath here to reflect that you might not find the results so far as strange at all. I had to point out what kind of thinking (classical) would make these results weird. If you had at all heard that quantum physics upends a lot of classical notions, you would have already come in, prepared to have an open mind and not be attached to classical thinking. So you readily see nothing weird about quantum physics, just a different set of rules. You might be gradually be used to the quantum logic pathway to make sense of quantum, which are called the modal interpretations.

 

Continuing on the double-slit experiments, there are quite a few additions to the basic experiment to exhibit some other properties of quantum systems.

 

First, the experiment can be done with single particles. A single photon, or single electrons or other particles. Single as in the particles gets shoot through the slit one by one. If it passes the slit, we use a super-sensitive detector, capable of detecting one particle at a time and also recording the position of where is the particle detected. Over time, the interference pattern can be seen to be build up again. One by one, the particles somehow knows where to land in order to rebuild that interference pattern.

 

It gives a creepy feeling for people to think that somehow a single particle has to use its wave properties to feel both slits in order to land at the positions which is consistent with the interference pattern. So a particle can interfere with itself! Different interpretations will give different pictures of this phenomenon. So don't be attached to the first two sentences of this paragraph!

 

Second variation, we can try to observe which path did the particle took on its way to the screen. There are many subtle details and recent developments in this bit, elaborated more later on when we discuss wave-particle duality.

 

For now, the simplified version is if we put a measurement device to detect if the particles would go through one slit or another. As long as we can have the information of which path, left slit or right slit was taken by the individual particles as they pass, we see no interference pattern; the particles make a pattern of two slits on the detector.

 

For most Buddhists, this is likely not the first time you had heard of this double-slit experiment and you might be very eager to see the one thing you are interested from the popular telling of this experiment. The act of observing things (with or without consciousness involved is interpretation dependent) changes what happens to the thing you observe. Do take note that the observation need not necessarily involve consciousness and the most important thing is the measuring device is present. Also, we shall see this property that measurement changes quantum systems even in the Stern-Gerlach experiment later. The big technical name you can pin to this behaviour can be called contextuality. More technical treatment of contextuality follows later.

 

Perhaps the most important take away is that do not place all your eggs onto one interpretation yet, just because of preconceived notion that it fits in with Buddhism (we shall see if it does and how it does). Have some patience and an open mind to keep on reading and participate in the analysis. As per the spirit of Kalama sutta, there are three main ways of deciding what to believe, revelation, reasoning and experience. The experience part is this section of experiment. The reasoning shall be done in the analysis, revelation is basically all the physics other people had discovered which you are soaking up now. As the experience part is most important in Buddhism, do place the same importance of it in physics. An interpretation of quantum mechanics means it currently has no way to experimentally distinguish itself from other interpretations, or the experiments done to do so had not been thought of yet, or it is not yet technically feasible, or it was done but not universally conclusive and persuasive yet. So no point to attach to one viewpoint (interpretation) based on the notion: it agrees with my view.

 

We shall move on to the mathematical structure of quantum and includes introducing the axiom of quantum as taught to physics undergraduates even now. Many of the terms are repeated there, so don’t worry. You’ll get a better picture of the maths there.

Quantum interpretations and Buddhism Part 3: History of the Development of Quantum Physics

 Let us start by appreciating the history first as this will be the basis of your mental picture of what quantum physics is before it gets very abstract in the mathematical structure.

Light in Newton’s days was considered to be particles, but Thomas Young with his famous double-slit experiment showed that light interferes with each other if the distance between the two slits is close to the light’s wavelength, thus light became a wave. This notion became solidified when Maxwell came out with the speed of light from the electromagnetic equations, showing that light is an electromagnetic wave, travelling at the speed of light. Thus we have the picture that electromagnetic waves unite all these radiations as one, just differing by their frequencies. From the shortest frequency to highest, we have radio waves, microwave, infrared, visible light from red to violet (following the rainbow colour arrangement), ultraviolet, X-rays and finally gamma rays. It is based on this wave theory of light which got us into the ultraviolet catastrophe. 

The first sign of quantum is when Max Planck used the Planck’s constant, h to fit in the data for the black body radiation in 1900. Basically, classical theories cannot explain how light interacts with matter, predicting that as light gets to a higher frequency, and lower wavelength, there will be more ways for energy to be emitted from the matter (like when the matter is heated up). When it goes further up the ultraviolet frequency, there should be even more amount of energy emitted. This is in contrast with the experimental fact where the most common frequency of a hot body peaks depending on its temperature. Thus you see fire changes colour from red to blue as it gets hotter, and not like spontaneously releasing unlimited gamma rays. Physicists called the failure of classical theories in this area as the ultraviolet catastrophe. The X-rays and Gamma rays haven’t been discovered and named yet, or else it would be called the gamma catastrophe, which would bring about the mental image of the Hulk in most people’s mind nowadays. Maybe it is fortunate naming because this has nothing to do with the Hulk.

Planck just helped to hack the system by fitting the data in by making sure energy exchanged between light and matter happens in the form of discrete amount of energy, proportional to its frequency, linked by Planck’s constant. This is instead of splitting the energy between modes of lights which increases with the square of frequency, and allowing continuous exchange of energy between matter and light as the classical theory assumed. Planck did felt that his fitting was a mathematical trick and do not believe what the equations told him about the nature of light. That it is quantised. Hence the word quantum in quantum physics came about. 

Albert Einstein then in 1905 provided the physical interpretation of this usual behaviour by suggesting that lights are particles. We call them photons. Photons as particles carry a discrete amount of energy depending on its frequency. This also explains the photoelectric effect where light only kicks out electrons from metal if its frequency goes high enough (hence enough energy per photon to kick out the electrons), regardless of its intensity (amount of photon). The electrons need a preset amount of energy to be kicked free from the metal, weak low-frequency photons can bump onto the metal all they want, but cannot combine their energy to kick out the electrons. Thus light is no longer considered as continuous wave containing continuous energy, but as photons, particles of light containing quantised energy. By the way, this is the reason Einstein got that Nobel Prize of his, not his general relativity.

This was the beginning of the crisis of interpretation. 

How can a particle explain the double-slit experiment? If we assume that many photons go through the slit then maybe the particles interfere with each other. However, experiments had gone to the point where we can send individual photons to the double-slit and still after collecting enough data, the interference pattern emerges! Did the particles somehow split into two and interferes with itself? Did it interacted with a split parallel universe version of itself and recombined to form the interference? Did the particle travel through time and go through both slits at once interfere with itself and came back to the present to land on the screen? Mental pictures of the quantum world are starting to break down as we insist on using classical concepts onto the quantum particle. Weirder still, try to find out which slits did the photon goes through, then once we know which slit and cannot erase the information, the interference is gone. We get two slits of light for light going through two slits. Light behaves like a particle when information about which slit it goes through is revealed and cannot be erased away without any copies of that information. So it seems that observation changes the outcome, something totally alien to the classical world of physics where it is assumed that the observer can observe and do not affect the observed system. You might have heard of this phenomenon is called wave-particle duality. Light behaves like a wave or particle depending on our decision to observe or not to observe which path it had taken.

It seems magical now, the nature or properties of light changes depending on what we do! Some take it as there is no underlying mechanics (reality/ nature) of quantum, some disagree, this becomes a matter of interpretation. Keep in mind that the experiments and ideas which physicists came out with helped them to develop the mathematical structure of quantum theory and step by step lead them away from having a classical mental picture of reality. However, those mathematics can be used to explain and predict experimental results, because it is developed mainly to fit in with experimental results.

Next came Niels Bohr, who in 1913 introduced the atomic model which explains how atoms can be stable and the emission lines of the hydrogen atom. According to classical electromagnetic theory, if the atom is to behave like our solar system, with the nucleus of the atom in the middle like the sun and the electrons orbiting it like planets, then the electron is undergoing acceleration. Yet the electron is a charged particle, accelerating charged particle according to classical electromagnetic theory emits electromagnetic radiation. This is how radio and TV waves can be transmitted and received with the antenna. So if the electron is radiating electromagnetic waves, it must be losing energy and very soon sucked into the positively charged nucleus and the atom is destabilised. If the electrons do not move, then it will be attracted into the nucleus anyway. So it is an utter mystery how atoms which subparts of positive and negative charged particles, and the positive ones in the middle can exist at all. 

Bohr suggests that electrons can only occupy some orbits, the ones which respect discrete angular momentum. Angular momentum is like momentum, spinning objects tend to remain spinning without outside forces (or torque in this case). Thus if the electrons are at the lowest orbit, it means that it cannot fall into a smaller orbit. Its angular momentum is at the lowest and cannot be reduced. There are no in-between orbits between two lowest orbits, thus angular momentum is quantised, or discretised. This, by the way, is the origin of the concept: quantum jump. As electrons cannot be found in between orbits, but jump from one to another. This is in very much contrast with our usual notion of classical motion as there is no smallest unit of jump or movement unlike in quantum systems.

In 1924, Louis de Broglie proposed that since light can behave like particles, might not particles like electron can behave like waves? The de Broglie wavelength for particles is Planck's constant over the momentum of the particle. So for very massive objects, our wavelengths are far too small for quantum effects to manifest. However, for small objects, their momentum means that their wavelength can be calculated and we can put electrons to the double-slit experiment and see that it interferes as light does. Electrons do show wave properties! 

In 1925 and 1926, two different ways of getting the basic equations of quantum mechanics correct were discovered, first the matrix mechanics by Heisenberg, then the wave mechanics by Schrödinger. Both are shown to be equivalent to each other, that is different ways of expressing the same thing.

Both concepts have the concept of a state of the quantum system and an observable. The state of a quantum system is this abstract concept not directly accessible to us. What we see from experiments are the observables. Both have a system of evolution which can tell how change happens. In Heisenberg picture, the state remains constant and it is the observable that changes in time; whereas the opposite happens in the Schrödinger picture. We can call this the stage one of the quantum mechanics calculation: evolution equations. This is about the equivalent of any classical physics evolution in which time is part of the equation that tells how everything else in the equation changes or remain constant in time.

After seeing how the evolution happens, we want to know what we can observe. In classical physics, the things we can observe are obvious. Position, velocity, acceleration, force etc. Yet, state is not directly observable to us. So in quantum physics, we have to use Born's rule to translate the results of stage one of quantum mechanics to do stage two, the probabilistic part. Born's rule tells us that from the results of stage one, we can get the probability amplitude of the system. One for each possible results we can observe. Square the probability amplitude and we can get the probability density of finding each results of the experiments. And strange enough, that accurately describes all sorts of quantum experiments we care to do.

Now it is worth it to pause here and link this presentation to the usual ones you might have read in many popular physics books. If this is your first popular physics book, then just go along for the ride to recognise the terms on your second popular physics book which talks about the basic quantum theory.

Usually, the presentation uses only the Schrödinger’s picture. It's using an equation which is more familiar to physicists in the early 1900s. Wave equations. At that time, wave had united electromagnetism, optics, sound, linking to many dynamics and kinematics equations, have close relationship with the simple harmonic motion and so on. So physicists were very glad to see this familiar old friend in an unfamiliar new theory. At least for a while. 

In the Schrödinger picture, quantum systems have their own wavefunction, which is the state stated above. In the Copenhagen interpretation of quantum mechanics, the wavefunction contains all possible information for whatever questions or observable you wish to ask or measure on the system. In practice, we just write the wavefunction according to the relevant observable we are interested in. 

The observables can be position, momentum, energy and so on. It's the usual quantities classical physics can make sense of. So we can apply the wavefunction to the Schrödinger's equation, which roughly means how the total energy evolution of the system evolves for this particular state. The evolution here is deterministic, the same wavefunction going through the same Schrödinger's equation will yield the same resultant wavefunction to any time you care to set to. This is still stage one. 

In stage two we apply the observables unto the wavefunctions to get the respective probability amplitudes for each possible results of the observable. Eg. If I want to find the position of an electron in free motion, I apply no potential energy at the Schrödinger's equation, evolve its initial wavefunction to the one I want at a certain time. Stage one completed, stage two follows. Then measure the position at that time by applying the position observable unto the wavefunction, obtaining the probability density of the position of the electrons.

If you are not mathematically inclined or had never studied quantum physics with its maths before, the above might sound gibberish to you. And it sure is very much so to many physicists in a different way. To us, we can compare it to how do you find the position of a ball in free motion. Use Newton's first law. If the ball is at rest, there is no external force on it, it remains at rest. If it is in motion, without fiction, then it will continue to be in motion.

The difference is that the evolution equation operates at stage one in quantum, a stage which is mysterious, hidden from us and all we see is the probabilistic results of stage two. There is no stage one stage two in classical physics, the evolution is clear and visible to us.

And that folks, is quantum mechanics proper. Just the maths. The story of what it means is down to the interpretations. Here lies the mystery of the quantum. Why is there two stages in the calculation? What story, if any, can we give to why is stage two probabilistic, is nature inherently non-deterministic or is it some information is hidden in stage one which we cannot know even in principle?

When Richard Feynman said, "I can safely say nobody understands quantum mechanics", he was not referring to the maths side. He is referring to the story side. With the maths side, we have the knowledge and capability to calculate and predict the probability distributions of the experimental results and so far experiments had been on the side of quantum mechanics. The calculation of molecular bonds in theoretical chemistry rely on solving super complicated equations of quantum mechanics. We can do all of these if we understand how to use the maths, even if it is super complicated.

The surprising thing is, even without knowing the underlying story of the two stages of quantum calculations, the maths still works well, predictions can be made. Nature does not seem to care if humans demand for a story.

Without that story, for you, the general layperson to predict anything in quantum systems, you would have to learn the maths. Yet, there are a few general guidelines developed in the Copenhagen interpretation, not all of which is adopted by other interpretations. Some of it you might have heard of: wave-particle duality, complementarity, superposition of states, Heisenberg uncertainty principle, inherent randomness.

We will go through them later on so as not to overly bias you towards the Copenhagen interpretation.

Why is the story important? Notice that when I used the classical ball example, I can just quote one law (Newtonian mechanics), then we can predict how the ball will behave. That's because the classical laws directly paint an obvious story for us to see and once we internalise the story, we can use it to do predictions of what will happen. In other words, it gives us power. To understand how nature works. But haven't we already know how to do predictions with quantum mechanics? What's the difference? The difference is in the intuition. The world does not behave in a quantum behaviour in our everyday experience. So as we have the intuition of how classical physics works, we would like to see if there is any underlying mechanism behind the two stages.

Brian Greene uses a theatre performance as an analogy in his book: The Fabric of Reality. In the theatre, we see the front stage, that's the probability density calculated in stage two of the quantum calculation.

Yet there is also a backstage, the place where actors change clothes really fast, where the spotlights are directed, where special effects and props are prepared, hidden until it is used. That's the stage one of the quantum calculations, the state of the quantum systems, the wavefunction. Hidden from the audiences, we do not even know to consider them real quantities in the world, or just reflections of our understanding for us to do the maths. In classical physics, the backstage is clear to us, for example, general relativity we say mass-energy curves spacetime, spacetime tells mass-energy how to move.

To make such a simple statement (or more likely, paragraphs of statements) for quantum physics means selecting one of the interpretations.

Quantum interpretations and Buddhism Part 2: Understanding Quantum Physics

 

Quantum physics, popularly known as quantum mechanics is widely reputed to be not understood by anyone. For one thing, the term mechanics is a misnomer, which is why I am using the term quantum physics in this book. Mechanics, as in the classical sense implies that we know the underlying structure and how things link to cause from one thing to another in a very nice matter which we can explain, picture in our heads and use intuition to predict what happens next. Not so in quantum physics.

 

Before you get confused and think since no one understands quantum physics, “I will not even get the popular version of its explanation, so I also don’t understand quantum physics”, let me clarify by what physicist meant by “understanding”.

Understanding here I split into three levels.

 

I.   Ontology (Reality): The underlying reality of things, the mechanics of which you can form a mental picture and then use intuition and basic principles to predict what happens next. This part is the one which is referred to as no one understands quantum physics.

II. Epistemology (Knowledge): The mathematical structure of quantum physics which allows us to predict many experimental values, probabilities of results, and is the reason we have electronics, nuclear physics, particle physics and so forth. The bread and butter of physicists which can be worked with as long as they follow the rules of calculations and has no clear mapping onto the ontology. This part is understood by any good physicists worth their degree.

III.             Interpretation (Belief): This is the exciting field of interpreting what does the mathematics of quantum physics means. Some link it to the underlying structure, of which some commonly held assumption about the world has to be abandoned, some think the epistemology is the ontology, there is no deeper reality, some thinks a lot more weird stuff. Most of these differences either has no different prediction from the usual epistemology of quantum physics, or the prediction is still too hard to test. Which lead to some physicists to think that this is all philosophical, not worth pursuing. Yet, the mistake had been done before of not noticing non-locality sooner, thus the age of quantum entanglement came relatively late after the discovery of quantum physics more than half a century ago. So, most physicists nowadays have at least one favourite interpretation of quantum physics, which you can think of as their religion. This is because no one can prove that they have the right interpretation, at least not yet. So based on which interpretation you believe, you can say a myriad of things about quantum physics, including whether you have understood it fully or not.

 

So you can now confidently say physicists understand the knowledge of quantum physics but disagree on what is the reality of it, if any, based on their belief. Now, I shall attempt to make clear what is the epistemology of quantum physics or the mathematical structure of it without using equations. The following chapter follows up on the various interpretations which are out there in the market, oops, I mean the speculative field of cutting edge research realm of physics literature.

Quantum interpretations and Buddhism Part 1: Motivation

 This part deals with the ever-popular topic of quantum physics which the mystics like to use to justify, popularise, prove, or just market their product. Most of them unjustified if they had known the full picture of what is quantum physics and how little they have to do with so many things the mystics try to link them to. However, there is some link as we will explore. Thus we cannot blame the mystics fully for seeing by intuition perhaps how their field and quantum have some links. 

First, we will describe quantum physics as understood by the physics community (or roughly thereabouts) before going into the details.

1. Motivation.
2. Understanding quantum physics.
3. Historical development of quantum theory,
4. The mathematical axioms of quantum as taught to Physics majors in University to show why quantum is solid, but not satisfactory in the interpretations.
5. The various experiments which show quantum phenomenon.
6. Classical assumptions which seem to be in danger.
7. A brief overview of what each major interpretation of quantum says.
8. One by one, going through the experiments to see how each interpretation of quantum would say about it, that is how to interpret what really happened in the experiment, or how to think about the maths and experiments that we have. 
9. One by one, going through the major interpretations and what classical assumptions tradeoffs they make, as well as the philosophical implications of each interpretation for Buddhism. If you’re not a Buddhist, you can do your own thinking of it for your personal religion, having seen the example of what it means for Buddhism if this particular interpretation is true.

Motivation

As I write this chapter, analysing in detail on the interpretations of quantum and the mathematical structure, I realized that I am going a bit deep even without using equations. So it's not going to be easy for people who are not used to reading popular physics books about quantum to follow. So to motivate the Buddhists to follow, here are some questions you can keep at the back of your mind as you read the physics-heavy parts. 

 

You might have come across terms like quantum Buddhism, Buddhist emptiness and quantum agree on no reality, etc. A lot of these are very vague. What I would like to establish is to first look at what does emptiness say. 

 

Let's use the term not-self. From Dhammapada verse 279: "All phenomena (dhammas) are without self." In Mahayana, the concept of emptiness is associated with not self. What it means is empty of independent existence. If there's anything anywhere which is independently existing, one may consider that as the essence and thus a self. The purpose of seeing emptiness is to abandon attachments. We tend to attach to things which are deemed as permanent to us because we want to seek reliability. A lot of physicists are attached to physics because some may consider the physical theories as eternally true, thus reliable. However, Buddha did tell us to let go even of the Dhamma (after crossing over samsara), what's more about things which are not Dhamma. 

 

What classical physics assume is that reality doesn't depend on us observers. If we have a universe without humans or any living beings in it, those matter, physics, star formation, planet formations would still be there without any minds to observe them. It's commonly thought of in quantum that this is not true. However, Jim Baggott in his book Quantum reality does nicely list out what do we mean when we say real. 

 

Realist Proposition #1: The Moon is still there when nobody looks at it (or thinks about it). There is such a thing as objective reality.

 

Realist Proposition #2: If you can spray them, then they are real. Invisible entities such as photons and electrons really do exist.

 

Realist Proposition #3: The base concepts appearing in scientific theories represent the real properties and behaviours of real physical things. In quantum mechanics, the ‘base concept’ is the wavefunction.

 

Realist Proposition #4: Scientific theories provide insight and understanding, enabling us to do some things that we might otherwise not have considered or thought possible. This is the ‘active’ proposition. When deciding whether a theory or interpretation is realist or anti-realist, we ask ourselves what it encourages us to do.

 

Many quantum interpretations reject Realist proposition no. 3, not so much no. 1 which a lot of people misunderstood. 

 

Let's look at what Buddhism might say towards these realist propositions. 

1. Perhaps the moon is there, but no one is there to observe it, so what's the point of positing it's there. We might also imagine a very far future where all beings in samsara are liberated and attained to the final death, the physical universe is empty of sentient beings. Does the physical universe still exist? Yes, it can. Emptiness in Buddhism doesn't mean that reality must depend upon observers or sentient beings. It's enough that there are equations describing the evolutions of the physical universe and these equations show that there's no independently existing entity. Equations itself denotes dependence. It's just important to note that objective reality of physical universe doesn't mean that they are reliable, as they too are impermanent. It's just that there might not need a link to the mind for physical universe to exist on its own. What Buddhism does say is that we as sentient beings, to us, we need to link things to the mind (the 6 senses linking to 6 sense consciounsess) to acknowledge them as existing, so we cannot escape this dependence on the mind to perceive and process the eternal and internal world. So the existence of a physical universe independent of mind is a metaphysics, one which cannot be verified by anyone. An assumption, which is also not required. 
2. There's no issue with Buddhism to accept that electrons and other subatomic particles are real too. They too are impermanent, empty of inherent existence.
3. Buddhists would also say that base concepts in classical theories just live in the heads of the physicists. Nature works as it is, the understanding of nature is also dependently arising, empty of inherent nature. This is how we can let go of even physics theories. 
4. This is the main interesting part to investigate the many interpretations of quantum and Buddhism. What does it mean for Buddhism if this or that interpretation is true? Can Buddhism accomdate this or that interpretation? Does Buddhism lend more support to certain interpretations or another? 

 

To properly follow in no. 4, we need to go in a lot of detailed analysis of quantum, the experiments and interpretations, physics-heavy. So if you're disinclined to follow, just know that Buddhism doesn't require insights into quantum physics for the emptiness, not self doctrine to be useful, appliable and true. Yet, if you wish to understand deeper and not depend upon the new age and many shallow comparisons of Buddhism and quantum out there, it's good to take the plunge. 

Another important reason to go through the physics is to avoid Quantum Flapdoodle. Quantum Mysticism is one of the infamous “interpretations” where a lot of new age, spiritual type people tries to use the weirdness in quantum physics to explain the weirdness of supernormal things in spiritual pursuits. Yes, I admit I might be trying to do a bit of that as well, but I would certainly not misuse the physics. Physicist Murray Gell-Mann coined the phrase "quantum flapdoodle" to refer to the misuse and misapplication of quantum physics to other topics.

The most important thing in order not to misuse and misapply the physics is to understand it. Thus, any Dhamma teacher who wishes to even comment on quantum and Buddhism would do well to read this whole chapter seriously and properly, as well as many other popular and if possible, technical quantum physics books before using it in any Dhamma talks. We certainly do not wish to be lumped together with the quantum quackeries of the New Age people. 

To add on, if ever you’re starting to wonder why physicists bother with quantum despite it being so complicated, obscure in giving no picture of reality and too many interpretations, just know that it is due to quantum that our modern electronics world exists. It is due to quantum that computers can fit into your pocket as your smartphones. It’s due to quantum that we build the Large Hadron Collider, predicted the Higgs Boson and discovered it. It’s due to quantum that we have the most accurate match between theory prediction and experimental discovery. It’s due to quantum that atoms are stable, that stars can undergo nuclear fusion to supply us with low entropic energy. 

In the 19th century, electricity changed the world, in the 20th century, quantum changed the world, in the 21st century, with the coming of quantum computers and quantum internet, it will change the world again. 

It is also about power. Nuclear bombs are possible only because we understand nuclear physics, and nuclear physics is very much in the quantum realm. Ever since the atomic bomb exploded, physics had gain the respect of being the science with the power to change the world. It’s funny that back then, more focus is given to the application of quantum rather than interpretations of quantum. And so, a theory which is close to a hundred years old now still have no clear picture of how to interpret it, nor is there a good popular book which covers the majority of the interpretation, only those few more popular ones gets quoted now and again. Only in 2020 did we get Quantum Reality by Jim Baggott. He covered ten quantum interpretations, but I will cover more and in a bit more detail in some aspects, less in other aspects. 

It’s good to examine your own motivation of why would you want to compare quantum to Buddhism, is it because of power too? To make use of the prestige of physics and quantum?