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around the nucleus, like a mini solar system, which is still our popular conception of the atom, even when it has been outdated.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.