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.