Quantum and Buddhism Part 1: Introduction to Quantum

So finally, I am going to attempt the big work which is always popular amongst the people who compare science and Buddhism. Quantum.

Last time, I had said that there are too many interpretations of quantum and it's a lot of work to look at them one by one. So here is the effort to look at them one by one and compare them to Buddhism. So yes, this can fill a whole book and more, be prepared.

Most of the popular books you can find out there explaining quantum physics does it by using concepts already inherent in the Copenhagen interpretation. If we start there and then move onto other interpretations, it may cause bias onto you so that you prefer the original or first interpretation you learn, and you might not know which part exactly is common to all quantum and which part is specific to Copenhagen.

So here's the strategy. I'll highlight the experiments of the world which reveals quantum phenomenon. Here quantum phenomenon means cannot be explained by classical means in a straightforward way. Classical here means all of classical physics, including Newtonian and Einstein dynamics, kinematics, thermodynamics, electromagnetism etc.

So after getting the experiments, we go through the interpretations so that the story is created to explain the experiments one by one.

In Buddhism analogy, the experiments is the sense experience, what we directly perceive. The interpretation is the story which we create to explain the sense experience, including the notion of self, the world etc.

But first, even before we get into the nitty-gritty, advance practicing Buddhists can already disengage. What's important is not the story. The story is always delusion. What's important is to see things as they really are. So there is no need to go further. There might be no reward in playing with stories, only suffering. But to physicists, the story, the concept has so far helped in creating technologies for us. If there is an underlying story behind quantum, the one true interpretation of how the world really works, it can help give us more power to help reduce physical suffering, or just understand the world. So let's move in.

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 were 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.

First sign of quantum is when Max Planck used the Planck’s constant, h to fit in the data for the black body radiation. 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 carries a discrete amount of energy depending on its frequency. This also explains the photoelectric effect where light only kicks out electrons from a 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.

Next came Niels Bohr, who introduced the atomic model which explains how atoms can be stable and the emission lines of 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 changed particles, and the positive ones in the middle can exist at all.

Bohr suggest that electrons can only occupy some orbits, the ones which respects 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 is at the lowest orbit, it means that it cannot fall into a smaller orbit. It's angular momentum is at the lowest and cannot be reduced. There is 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.

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

Rough year	Name of 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 quantized 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 quantized, 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 quantized.	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 quantized 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 inteference patterns. The Double slit experiment is now also capable of being done with single particles, inteference 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 popularized 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 behave 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 existance 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.

Now, there are plenty more of these experiments, but to continue elaborating on the experiments might be too dry to you. It's better to have some concepts first to better understand the experiments. So the next big highlight should be on the theory side. Now we have to go a bit of mathematical structure of quantum physics.

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

Both concepts has 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 has a system of evolution which can tell how change happens. In Heisenberg picture, the state remains constant and it's the observable that changes in time; whereas the opposite happens in the Schrodinger 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 Schrodinger'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 Schrodinger picture, quantum systems has 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 practise, 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 Schrodinger'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 Schrodinger'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 Schrodinger'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 a 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, then we can predict how the ball will behave. That's because the classical laws directly paints an obvious story for us to see and once we internalize 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 theater performance as an analogy in his book: The Fabric of Reality. In the theater, 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 changes 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.

Before that, we need to know the front of the theater well first in Part 2: Experiments.