## Is Quantum Mechanics Just a Special Case of Classical Mechanics?

The bouncing is antiphase in (a) and (c) and in-phase in (b) and (d). From “Why bouncing droplets are a pretty good model of quantum mechanics.”

If you enjoyed my post from about three months ago on Hydrodynamic Quantum Analogs, or perhaps even if you didn’t, you will likely enjoy this new paper by Robert Brady and Ross Anderson at the University of Cambridge: “Why bouncing droplets are a pretty good model of quantum mechanics“.

They discuss the recent experimental work with silicon oil droplets bouncing on vibrating trays and the behaviors exhibited by these systems; behaviors normally associated with quantum mechanical systems.  They quantify the effective forces between the droplets and their environment.  Then, they go on to show how the classical physical and mathematical description is equivalent to the Schrodinger equation, with the substitution of a surrogate parameter for Planck’s constant.  See “Droplets moving on a fluid surface: interference pattern from two slits” for a similar discussion.

## Quantum Mechanics and Spin Statistics

What is perhaps most intriguing about this new paper is the demonstration of how spin-half behavior can arise in these classical systems.  One of the central characteristics of quantum physics, and indeed an essential feature of our Universe, is the difference between fermions (particles with half-integral spin; electrons, neutrinos, protons, etc.) and bosons (particles with integer spin; photons, W and Z bosons, etc.).  This feature results in these two classes of particles having completely different statistical properties; Fermi-Dirac statistics for fermions, and Bose-Einstein statistics for bosons.  It is what leads to the Pauli exclusion principle and the stability of atoms.  The overall wavefunction for a boson is an even function and the overall wavefunction for a fermion is an odd function.

A peculiar feature of fermions that is reproduced in the hydrodynamic wave field is the fact that, if the direction of a fermion’s angular momentum is rotated through 360 degrees, its wavefunction changes sign.  This has typically been assumed to be an exclusive behavior of the quantum realm.  But here it is, in a table-top, classical experiment.

## Is Quantum Mechanics Just a Special Case of Classical Mechanics?

These experiments continue to provide tantalizing and provocative insights into the quantum world, challenging our notions and assumptions.  Some of the questions that come to mind as I ponder the implications for interpretations of quantum mechanics in general, and de Broglie-Bohm pilot wave theory in particular, include:

Is Quantum mechanics just a special case of classical mechanics?  Is quantum physics simply a subclass of events where we recognize certain behaviors over other noise and interference?

What are the quantum parallels for the effective external forces in these hydrodynamic quantum analogs, i.e. gravity and the vibrations of the table?  Not all particles carry electric charge, or weak or color charge.  But they are all effected by gravity.  Is their a connection here to gravity? Quantum gravity?

In addition to helping us understand quantum mechanics, can these or similar experiments help us understand general relativity as an effective force?

What are the technical challenges to doing these experiments in a microgravity environment, like the International Space Station?  What about somehow curving or warping the oil surface?

Why does the quantum world seem to have no energy (or frequency or wavelength) dependence for the limiting speed c (contrary to hydrodynamic quantum analogs)?

Until next time, have fun pondering!

# What Would Happen if a Quantum Cheshire Cat Were to Visit the Leisure Hive?

Happy Holidays, Everyone!  Today’s article, just in time for your New Year’s Eve party, is on something extremely cool.  It has to do with a paradox that is completely unintuitive and that is only revealed by weak measurements.  A particle and its properties can be in different locations!

In the classic Doctor Who episode Leisure Hive, a so-called “science of tachyonics” serves as the basis for entertaining guests at a resort.  A person enters a booth and their head and limbs are seemingly separated from their body, yet remain animated and are then harmlessly reattached.

That is, of course, full-fledged science fiction.  However, a quantum particle such as a photon, an electron, or an atom, apparently can have its properties located in a position separate from the particle itself.

Recent theoretical and experimental work has invigorated the search for “quantum Cheshire cats”.  Before I continue, however, I want to stress that the reference to cats is strictly metaphorical.  Just as with the case of Schrödinger’s cat (Decoherence and the Quantum to Classical Transition; or Why We Don’t See Cats that are Both Dead and Alive), decoherence prevents macroscopic objects from displaying these quantum mechanical properties.

# In Search of a Quantum Cheshire Cat

The authors of Quantum Cheshire Cats (also available here) define a “quantum Cheshire cat” as a photon that is in one location while its circular polarization is in another.  The metaphor comes from the Cheshire cat in the story of Alice in Wonderland, whose smile persists independent of the cat:

The “cat” is the photon and its “smile” is the photon’s circular polarization state.  The photon is in one of two possible locations, the left or right side of a modified Mach-Zehnder interferometer.  Using weak measurements, including cleverly chosen pre-selected and post-selected states, leads to a sample of events where the photon went through the left arm with certainty.  However, a polarization detector in the right arm can still see a signal!

“We seem to see what Alice saw—a grin without a cat! We know with certainty that the photon went through the left arm, yet we find angular momentum in the right arm.”

The paradox is removed if conventional, strong measurements of position and polarization are performed.  The inevitable and apparent wave function collapse occurs and the photon’s position and angular momentum are found to be co-located.  This is analogous to directly measuring which slit the particle goes through in a double slit experiment, which prevents an interference pattern from forming.  Strong measurements are analogous to turning the light on and letting the cockroaches quickly scurry into hiding.  Everything looks normal.  But, weak measurements are like peering at what is going on in the dark, without scaring the roaches away.

Using weak measurements (The Strength of Weak Measurements in Quantum Physics), the disturbance on the state of the system can be reduced by accepting less precision.  Then, the measurement is repeated many, many times to achieve the desired accuracy.  This reveals that the circular polarization was in fact in the right leg of the interferometer while the photon was in the left, for certain pre- and post-selected events.

# What Do We Do With a Quantum Cheshire Cat Once We Catch One?

Conventional wisdom is that when you look at, or measure, a quantum system, the wave function collapses into something that makes sense from a classical level.  That is to say, strange or apparently contradictory paradoxes disappear.  However, that assumes strong measurements.  Until weak measurements were explored theoretically and experimentally in recent years, the distinction between strong and weak measurements was not appreciated.

Contemplating the implications of quantum Cheshire cats opens up several mind-boggling possibilities and opportunities.  Separating physical properties, such as mass, energy, charge, magnetic moment, etc., from what we conventionally understand to be a particle could lead to new and more precise measurements, new technologies, new materials…  Additionally, it has profound implications for our conceptual understanding of quantum physics and what a quantum system is up to between measurements or between interactions.  Scientists will be exploring this amazing field for many years to come.

In Quantum Cheshire Cats, the authors discuss a couple modifications (beyond the reach of existing technology, but should be possible eventually), where the signature of a quantum Cheshire cat should be unambiguous; ensembles of electrons, for example.

Proposed modifications to the setup discussed above, i.e. using entangled pre- and post-selected states to allow the linear as well as the circular polarization states to be separated from the photon, are discussed in The Complete Quantum Cheshire Cat.

Possible hints of the metaphorical quantum Cheshire cat have been seen: Observation of a quantum Cheshire Cat in a matter wave interferometer experiment  “…using a neutron interferometer… The experimental results suggest that the system behaves as if the neutrons went through one beam path, while their spin travelled along the other.”

The quantum Cheshire cat is an example of an interaction free measurement.  Another example is the Elitzur–Vaidman bomb tester, also known as a quantum mechanical bomb tester.  Also see Using quantum mechanics to detect bombs.

Masters student Catherine Holloway lectures on the science behind a quantum bomb detector at the Quantum Cryptography School for Young Students, held at the Institute for Quantum Computing, University of Waterloo:

## The Strength of Weak Measurements in Quantum Physics

1940 Charles Addams cartoon for the New Yorker.
Which way did the skier take around the tree?

You may recall being told by your parents, as you were growing up, outmoded ideas or outright misconceptions about quantum mechanics.  Examples may have included: the uncertainty principle is due to momentum imparted by photons as you measure a particle’s position; in any given experiment you can observe wave or particle properties but not both; the wave function is a mathematical tool and not part of objective reality; you cannot ask what a particle is doing between measurements; you cannot simultaneously determine position and momentum; the phase of a wave function is not observable; you cannot discuss reality separately from what you choose to measure; you cannot ask what is really there when no one is looking; “just shut up and calculate”.

Maybe it was while you were in college rather than while you were growing up.  And perhaps it was your quantum mechanics (QM) instructor rather than your parents.  Nonetheless, much of what has been written and taught about QM since its inception has misled students, teachers, researchers, and the general public about the implications it has for reality and observation.

The above notions, and many other bits of nonsensical interpretational issues are being clarified and sometimes overturned by talented theorists and experimentalists.  These explorers continue to peel back the curtains to see what is really going on behind the cloak of quantum weirdness.   The techniques of weak measurements have become vital tools in this quest.  The article I wrote a couple weeks ago, Discontinuous Trajectories in Quantum Mechanics, was an example of weak measurements.  Today, I discuss weak measurements used to reconstruct particle trajectories in a double-slit experiment.

# Imagining Weak Measurements

Weak measurements were initially proposed by Yakir Aharonov, David Albert, and Lev Vaidman about twenty five years ago.  The idea is basically this: you prepare particles in some particular initial state (pre-selection) and later detect some of them in a particular final state (post-selection).  It may be that only a small subset of your particles end up in the particular final state that you make the selection on, but that is ok, you are going to repeat the experiment many, many times.

You want to know what your particles are doing between these initial and final states; how they get from point A to point B, for example.  So you need to do some measurements.  However, that would lead to apparent collapse of the state vector into a particular eigenstate, essentially re-setting the experiment.  If you measure the particle’s position somewhere along its trajectory, the momentum becomes uncertain and uncorrelated with any initial momentum it may have had.

The key insight that these gentlemen had was to make the disturbance from this intermediate measurement as small as necessary, so as not to disturb the wavefunction too much.  When measuring the position of a particle in a weak measurement, the velocity does not become random.  However, the uncertainty in the position measurement is large.  So, the second trick is to average over a very large number of trials.  This leads to precise information about the wavefunction itself.

# Weak Measurements in Action

In a Physics World article, In Praise of Weakness, Aephraim Steinberg and his colleagues discussed their use of weak measurements to map particle trajectories in a double-slit experiment.  Their article is also available here.  The green 3D plot below shows where a quantum particle is most likely to be found as it passes through the double-slit apparatus while behaving as a wave. The black lines on top of the green 3D surface are the average paths that the particles take through the experiment, as reconstructed from weak measurements.

Obtained through weak measurements, this 3D plot shows where a quantum particle is most likely to be found as it passes through a Young’s double-slit apparatus and exhibits wave-like behaviour. The lines overlaid on top of the 3D surface are the experimentally reconstructed average paths that the particles take through the experiment. (Courtesy: Krister Shalm and Boris Braverman).
Figure and caption from “In Praise of Weakness”: http://physicsworld.com/cws/article/print/2013/mar/07/in-praise-of-weakness.

From Steinberg, et al:

“…it is striking that the average result of such a measurement will yield exactly what common sense would have suggested. What we are arguing – and this admittedly is a controversial point – is that weak measurements provide the clearest operational definition for quantities such as “the average velocity of the electrons that are going to arrive at x = 1”. It is very tempting to say that this value, this hypothetical measurement result, is describing something that’s “really out there”, whether or not a measurement is performed. We should stress: this is for now only a temptation, albeit a tantalizing one. The question of what the “reality” behind a quantum state is – if such a question is even fair game for physics – remains a huge open problem.”

Aephraim Steinberg spoke about quantum mechanics and weak measurements in the Perimeter Institute Public Lecture Series.  The video of his talk: In Praise of Weakness Public Lecture.

# Exploring Weak Measurements Further

Dressel, et al, provide a review of the mathematics and applications of weak measurements in their recent paper: Understanding Quantum Weak Values: Basics and ApplicationsThey discuss three different types of experimental applications that are revolutionizing our ability to study and manipulate quantum systems using weak measurements: (1) amplifying a signal, enabling the sensitive estimation of unknown evolution parameters, such as beam detection, phase shifts, frequency shifts, time shifts, temperature shifts, etc.; (2) measuring the real and imaginary parts of a complex-valued parameter, enabling new methods for reconstructing the quantum state, including relative phase of the complex value; (3) finding conditioned averages of generalized observable eigenvalues, providing a window into non-classical features of a quantum mechanical system.

For additional discussion of the theory and mathematical background for directly measuring the wavefunction of a quantum system, it is worthwhile to read Direct Measurement of the Quantum Wavefunction and Direct measurement of general quantum states using weak measurement.

So where will all this lead?  This is still, very much, an evolving field of study.  In an area as unintuitive as quantum physics, you cannot just take one or two experimental results and assume you understand what is going on.  Perhaps the wavefunction is not just a mathematical tool, but rather something that is real and can be directly measured.  Perhaps these experiments will clarify the relationship between quantum and classical behaviors.  Perhaps these experiments will help reduce the confusion and misunderstanding concerning the meaning of measurement and observation in quantum mechanics.  The insights gained from weak measurements will certainly lead to a deeper conceptual understanding of the quantum realm.

# “It’s 10:00 pm, do you know where your photons are?”

As parents, we try to know where our kids are at all times.  We teach them that, when they want to play outside or at a friend’s house, they need to let us know where they will be.  If we were to ever find out that they were not where we expected them to be, we would go ballistic!  Well, could you imagine being the parent of a photon?

A group of scientists at Tel-Aviv University performed an experiment that shows you may not get a sensible answer when you ask a photon where it has been.  Soon to appear in Physical Review Letters, Asking photons where they have been,” demonstrates that the past of a photon cannot be represented by a continuous trajectory, or even by the superposition of continuous trajectories.  To quote from their paper:

“The photons tell us that they have been in the parts of the interferometer through which they could not pass!”

# Interrogating Discontinuous Trajectories in Quantum Mechanics

I have previously mentioned two puzzling aspects of the quantum universe: non-locality and the intrinsic, probabilistic nature of outcomes.  I typically caveat these two properties with “apparent”, i.e. apparent non-locality and apparent probabilistic nature.  That is because it is still possible (although not certain) that there could be some underlying causal and realist explanation.  In fact, explanations may already be available, we just do not know how to validate them.

Another mystery that our classical brains struggle with is the apparent discontinuous nature of the trajectories of quantum particles.  What I love about this new result from the Tel-Aviv group (Danan, Farfurnik, Bar-Ad, and Vaidman) is that, not only does it demonstrate a unique and important property of quantum physics, it does so with a straight-forward and conceptually easy to understand experiment.

The scientists used a nested Mach-Zehnder interferometer (MZI).  You may recall that I discussed a MZI in “The Transactional Interpretation of Quantum Mechanics.”  However, in this case, they nested two MZI together – one leg of a MZI includes another MZI nested within one of it’s legs (see the figure below).

Schematic of the nested Mach-Zehnder interferometer used to interrogate photons as to their whereabouts. From “Asking photons where they have been,” http://arxiv.org/pdf/1304.7469.pdf.

Photons enter the apparatus from the source in the upper left corner of the figure.  The unlabeled squares represent beam splitters.  After passing through either the lower leg or the nested interferometer in the upper leg, photons are detected by a quad-cell photo-detector (D).  The unique and essential feature of this experiment is that the mirrors (A, B, C, E, and F) vibrate around their horizontal axes at different frequencies fA, fB, fC, fE, and fF, with very small amplitudes.  This induces oscillations of the vertical positions of photons after they encounter each particular mirror along their path.  Hence, each photon carries a record that describes which mirrors they encountered, and thus which path they took through the apparatus.

Each photon’s signature is extracted by measuring (at D) its position coming out of the interferometer. This data is then Fourier-analyzed to produce a power spectrum of the different frequencies present in the output signal.  When the vibration frequency of a certain mirror appears in the power spectrum, the scientists logically conclude that at least some of the photons have been near that particular mirror.

# Trajectories That Appear to be Continuous

The first run of the experiment that we will consider is the one depicted above.  One third of the beam power was sent into the lower arm and two thirds of the beam power was sent to the nested MZI in the upper arm (the beam splitter used to split the two legs of the outer interferometer was specifically designed for this one-third, two-thirds spilt; other beam splitters produced a 1:1 split).

The interferometers were aligned to ensure that all the photons ended up at the detector. The power spectrum showed peaks at all frequencies, as intuitively expected.  The peaks at fE and fF were higher due to the larger fraction of photons in contact with them.  The power spectrum at the output of the experiment shows, unsurprisingly, frequencies from all five mirrors.

# So Much for Common Sense: Discontinuous Trajectories in Quantum Mechanics

The surprising result was obtained when the interferometer was modified to be a “which-way” experiment.  By slightly shifting mirror B, the nested MZI was aligned so that there would be complete destructive interference between the light reaching mirror F from A and the light reaching mirror F from B (see the figure below but ignore the red and green lines for now).

So, in effect, there were no photons at F.  Hence, there were no photons that could possibly reach the detector D from the upper leg, right?  By that reasonable bit of logic, any photons detected at D should have come from the lower arm of the interferometer.  We would therefore expect that any photons reaching the detector would have interacted only with mirror C.  The punch-line is that the scientists observed three peaks in the power spectrum: the expected one at frequency fC, and two more peaks at frequencies fA and fB.

Nested Mach-Zender interferometer, tuned so that photons arriving at mirror F interfere destructively. Red and green (dashed) lines are explained in the text. From “Asking photons where they have been,” http://arxiv.org/pdf/1304.7469.pdf.

Common sense tells us that any photons passing through the inner interferometer (so that they could encounter mirror A or B and pickup oscillations at frequency fA and fB) must by necessity have also encountered mirrors E and F.  However, frequencies fE, and fF were not seen in the output power spectrum.  How did photons pick up oscillations at frequencies fA or fB, associated with mirrors A or B, and make it to the detector without also encountering mirror E or F?

# Interpreting Discontinuous Trajectories in Quantum Mechanics

Although the conventional interpretation of quantum mechanics can predict the correct outcome for this experiment, it offers little insight into what is going on.  The authors offer an alternative that provides an improved conceptual understanding.  The interpretation they prefer is the two-state vector formalism.  This is a time-symmetric interpretation of quantum mechanics; both forwards and backwards evolving quantum states are required to describe a quantum system. This includes a state vector that evolves from the initial conditions towards the future, and a second state vector that evolves backwards in time from the final conditions of the experiment.  That is to say, the state vector describing the pre-selected state as well as the state vector for the post-selected state are both required to fully describe the system.  This highlights another intrinsic aspect of QM that makes it distinct from classical physics: the past of a quantum particle does not uniquely determine its future.  Past and future measurements, taken together, provide complete information about the system.

In the present experiment (see the above figure), a standard forward evolving quantum state is depicted by the red line and a backward evolving quantum state is depicted by the green dashed line. There is no continuous path for the forward evolving state to proceed through the inner MZI and reach the detector.  However, there is a non-zero probability for the photon to have existed anywhere that both forward and backward quantum wave functions are present.  Hence, this includes the nested MZI in the upper leg, inside mirrors E and F, but in the region of mirrors A and B.

The transactional interpretation (TI) also provides a conceptual explanation of this experiment.  Additionally, at least in my opinion, the TI provides a more straight-forward way of calculating the probability for the photon to be in the inner interferometer, and hence simplifies the prediction of the power spectrum at the output.

# Will We Ever Understand Particle Trajectories, Much Less Quantum Physics?

Making progress towards the goal of fully understanding what nature is up to in the quantum world requires that you have a full grasp of the variety of experimental evidence and theoretical results.  If you have been reading my posts up to now, hopefully I have been filling in some gaps.  Don’t get too comfortable, yet.  There is a lot more to the story about trajectories, a story that is being told through “weak measurements”.

Considerations of pre- and post-selected systems lead to the theory and practice of weak measurements.  In an upcoming article, I plan to discuss what I mean by weak measurements, and how they are being used to survey and reconstruct the properties of quantum particles between pre-selection and post-selection measurements.  The results of these measurements are amazing just due to the fact that they are possible, as well as due to the enlightening results that they provide.  These experiments give me confidence that, as a result of the amazing work of skilled quantum physicists, we are making steady progress along the road to a proper conceptual understanding of our quantum universe.

# Conflating Science with Pseudoscience

The second category is just plain fraudulent; people who deliberately make things up to deceive others for profit.  Prominent examples of this include books and talks like the ones by Deepak Chopra, and movies like What the Bleep Do We Know!?  Rest assured, there is no such thing as quantum healing.  You cannot change your quantum state through your thoughts.  Real harm is done by these quacks when, for example, someone forgoes proven medical treatments for pseudoscience.

My contention is that because we do not do enough to mitigate the negative impact of the first category, the fraudulent category is able to spread easily and quickly amidst fertile grounds.  The public is susceptible to charlatans peddling pseudoscience and quackery by throwing in sciency sounding phrases, and references to quantum physics that no one (including themselves) understands.  Moreover, their claims have no relationship to reality.

There will always be a certain number of people eager to believe whatever pseudoscience or pseudo-religion these hucksters want to sell.  But, if we want to influence the fraction of the public that is interested in separating fact from fantasy, we need to be clearer and more precise in our own presentations of physics.  Moreover, if we want to retain our credibility with the general public as we seek to dispel the drivel these hucksters distribute, we need to make sure we are precise about what QM is and what it is not, what we understand about it and what we do not.

# Misconceptions about the Quantum to Classical Transition

Experimental setup for the Schrodinger’s cat thought experiment. Image from Wikipedia.

One example that contributes to the confusion is the parable of Schrödinger’s cat.  A cat, a flask of poison, and a radioactive source are placed in a sealed box (this is a hypothetical thought experiment, of course – no cats were harmed…).  If an internal monitor detects a single atom decaying, the flask is shattered, releasing the poison that kills the cat.  Naïve application of the Copenhagen interpretation of quantum mechanics leads to the conclusion that the cat is simultaneously dead and alive.  Up until it is measured by a conscious observer, the atom is in a superposition of having decayed and not decayed.  And this superposition allegedly extends to the radiation detector, the vial of poison, the hammer to break the vial, the cat, the box, and to you as you wait to open the box.

People trot out Schrödinger’s cat whenever they want to tout how strange QM is.  “See how weird and paradoxical QM is, how bizarre and unintuitive it’s predictions, how strange the universe is?  Anything is possible with quantum mechanics, even if you don’t understand it or I can’t explain it.”   No, quantum mechanics is not an “anything goes” theory.  A cat cannot be simultaneously dead and alive, regardless of whether or not we observe it.

References to the role of the observer or of consciousness in determining outcomes contributes to this mess.  Even in interpretations of QM that refer to a special role for an observer or a consciousness (interpretations that I believe miss the target of reality), the observer cannot control or manipulate outcomes by choice or thought.  He/she is merely triggering an outcome to become reality; the particular outcome that nature chooses is still random.  You cannot decide to pick out a different wave function for yourself.  Additionally, interpretations of QM that do not have any need for a special role for a conscious observer (and are thus, in my opinion, better approximations of reality) are readily available.  See, for example, the Transactional Interpretation.

# Isolating the Environment in Classical Physics

In “Decoherence, einselection, and the quantum origins of the classical, Wojciech Zurek had this to say:

“The idea that the “openness” of quantum systems might have anything to do with the transition from quantum to classical was ignored for a very long time, probably because in classical physics problems of fundamental importance were always settled in isolated systems.”

For centuries, progress in our understanding of how the world works has been made by isolating the system under study from its environment.  In many experiments, the environment is a disturbance that perturbs the system under investigation and contaminates the results of the experiment.  The environment can cause unwanted vibrations, friction, heating, cooling, electrical transients, false detections, etc.  An isolated system is an idealization where other sources of disturbance have been eliminated as much as possible in order to discover the true underlying nature of the system or physical properties under investigation.

Galileo Galilei is considered by many to be the founding father of the scientific method.  By isolating, reducing, or accounting for the secondary effects of the environment (in actual experiments and in thought experiments) he discovered several principles of motion and matter.  These principles, such as the fact that material objects fall at the same rate regardless of mass and what they are made of, had been missed or misunderstood by Galileo’s predecessors.  A famous example is the experiment where Galileo dropped two metal balls of different size, and hence different mass, from the top of a building (supposedly the leaning tower of Pisa). Luckily, the effects of air resistance were negligible for both balls, and they hit the ground at roughly the same time.  He would not have been able to do the experiment with a feather and a steel ball, for example, because air resistance has a much more dramatic effect on the light feather than on the steel ball.  Interesting bit of physics why that is the case, but I’ll avoid the temptation to take that detour for now.

During an Apollo 15 moon walk, Commander David Scott performed Galileo’s famous experiment in a live demonstration for the television cameras (see the embedded video below). He used a hammer (1.32 kg) and a feather (0.03 kg; appropriately an eagle feather).  He held both out in front of himself and dropped them at the same time.  Since there is no atmosphere on the moon (effectively, a vacuum) there was no air resistance and both objects fell at the same rate.  Both objects were observed to undergo the same acceleration and strike the lunar surface simultaneously.

# Superposition and Interference: the Nature of Quantum Physics

The situation is quite different in quantum mechanics.  First of all, the correlations between two systems can be of fundamental importance and can lead to properties and behaviors that are not present in classical systems.  The distinctly non-classical phenomena of superposition, interference, and quantum entanglement, are just such features.  Additionally, it is impossible to completely isolate a quantum system from its environment.

According to quantum mechanics, any linear combination of possible states also corresponds to a possible state.  This is known as the superposition principle.  Probability distributions are not the sum of the squares of wave function amplitudes.  Rather, they are the square of the sums of the wave function amplitudes.  What this means is that there is interference between possible outcomes.  There is a possibility for outcome A and B, in addition to A or B, even though our preconceived notions, based on our classical experiences of everyday life, tell us that A and B should be mutually exclusive outcomes.  Superposition and the interference between possible states leads to observable consequences, such as in the double-slit experiment, k-mesons, neutrino oscillations, quantum computers, and SQUIDS.

We do not see superpositions of macroscopic, everyday objects or events.  We do not see dead and alive cats.  Sometimes, our common sense intuitions can mislead us.  But this is not one of those times.  The quantum world is more fundamental than the classical world.  The classical world emerges from the quantum world.  So what happens that makes these quantum behaviors disappear?  Why does the world appear classical to us, in spite of its underlying quantum nature?

## Coherence, and Then Naturally, Decoherence

Two waves are said to be coherent if they have a constant relative phase.  This leads to a stable pattern of interference between the waves.  The interference can be constructive (the waves build upon each other producing a wave with a greater amplitude) or destructive (the waves subtract from each other producing a wave with a smaller amplitude, or even vanishing amplitude).  Whether the interference is constructive or destructive depends on the relative phase of the two waves.  One of the game-changing realizations during the early days of quantum mechanics is that a single particle can interfere with itself.  Interference with another particle leads to entanglement, and the fun and fascinating excitement of non-locality.

## Decoherence is the Key to the Classical World

The key to a quantum to classical transition is decoherence.  Maximillian Schlosshauer, in “Decoherence, the measurement problem, and the interpretations of quantum mechanics, states that

“Proponents of decoherence called it an “historical accident” that the implications for quantum mechanics and for the associated foundational problems were overlooked for so long.”

Decoherence provides a dynamical explanation for this transition without an ad hoc addition to the mathematics or processes of quantum mechanics.  It is an inevitable consequence of the immersion of a quantum system in its environment.  Coherence, or the ordering of the phase angles between particles or systems in a quantum superposition, is disrupted by the environment.  Different wave functions in the quantum superposition can no longer interfere with each other.  Superposition and entanglement do not disappear, however.  They essentially leak into the environment and become impossible to detect.

I typically love the many educational and entertaining short videos by Minute Physics. However, the video below about Schrödinger’s cat is misleading.  Well before the cat could enter into a superposition, coherence in the chain of the events leading up to his death (or not) has been lost to the environment.  The existence of a multiverse is not a logical consequence of the Schrödinger’s cat experiment.

Perhaps the muddled correspondence principle of the Copenhagen Interpretation could have been avoided, as well as myths and misconceptions about the role of consciousness and observers, if decoherence had been accounted for from the beginning.

## The Measurement Problem

Decoherence occurs because the large number of particles in a macroscopic system are interacting with a large number of microscopic systems (collisions with air molecules, photons from the CMB, a light source, or thermal photons, etc.).  Even a small coupling to the environment is sufficient to cause extremely rapid decoherence.  Only quantum states that are robust in spite of decoherence have predictable consequences.  These are the classical outcomes.  The environment, in effect, measures the state of the object and destroys quantum coherence.

So does decoherence solve the measurement problem?  Not really, at least not completely. It can tell us why some things appear classical when observed.  But, it does not explain what exactly a measurement is and how quantum probabilities are chosen.  Decoherence by itself cannot be used to derive the Born rule.   Additionally, it does not explain the uniqueness of the result of a given measurement.  Decoherence never selects a unique outcome.

# The Universe and You

The International Space Station (ISS). Image from Wikipedia.

With care, mechanical, acoustic, and even electromagnetic isolation is possible.  But, isolating a system gravitationally, i.e. from gravitons, is another challenge.  In orbit around the Earth, like the space shuttle or the International Space Station, you are still in a gravitational field with a flux of gravitons that is not that much different than here on the surface of the Earth.  The apparent weightlessness is due to being in a continuous state of free fall (an example of microgravity).  Various theories have been developed that use the pervasiveness of gravitons to explain certain aspects of our quantum universe.

So, yes, the atoms and subatomic particles in your body are entangled with the universe.  That does not mean that you can do anything about it, or use it to your advantage in any way.  There is no superposition, no coherent relationship between you (1) as a millionaire dating a super model and (2) not a millionaire and not dating a super model.  Sorry about that.

# Violations of Bell’s Inequalities and Loopholes in Quantum Mechanics

Recall that, in 1935, Einstein, Podolsky, and Rosen wrote their famous paper that became known as the EPR paradox.  In it, they pointed out the bizarre consequences of the mathematics of quantum mechanics.  If two particles were in an entangled state, then measurement on one of the particles would immediately affect the results of a measurement on the other particle, even if the two particles were arbitrarily far apart at the time of the measurements.  This non-locality was later called “spooky action a distance” by Einstein.

In the 1960’s, John Bell came up with a set of equations, inequalities, that quantified the disagreement between the predictions of quantum mechanics and that of a purely local theory (i.e. one that assumed the distant measurement could not affect the local measurement).  Since then, violations of these inequalities have been experimentally verified on numerous occasions.  Thus, the inescapable conclusion is that nature does make use of non-locality, some how.  However, this conclusion is based on the assumption that nothing else unusual or unexpected is happening during the experiment.

## Scrutinizing Loopholes in Observed Violations of Bell’s Inequalities

Many different variations of the experiments have been done.  See, for example, my discussion at Quantum Weirdness: The unbridled ability of quantum physics to shock us.  Many more, different types of experiments have also been done.  In some of these experiments, the violation is more dramatic – not just a matter of the frequency of apparently correlated outcomes.  These experiments are go or no-go; they are designed to look for an event that would not happen under a purely local theory.  See Do We Really Understand Quantum Mechanics? or Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems for more in-depth discussions.

Given that the implication of these experiments is so profound, scientists have gone to great lengths to ensure that there is not some more benign, classical, local, or deterministic explanation that has been missed.  One possibility is that, since we do not detect every photon due to limitations in detector efficiency, we are detecting a special subset of events.  Another possibility is that the detector settings are not actually independent or random.  Typically, detector settings are chosen randomly; for example, by a quantum random number generator.  But if there were even some slight correlations between the choice of detector settings and some sort of local hidden variables in the system being tested, then the observed violations of Bell’s inequality could be explained without resorting to non-locality.

# Closing the Settings-Independence Loophole

Physicists at the Kavli Institute for Cosmological Physics in Chicago, and at MIT, have come up with a brilliant (and FUN) way to avoid the settings-independence loophole and also potentially further quantify non-locality.  See their paper  Testing Bell’s Inequality with Cosmic Photons: Closing the  Settings-Independence Loophole.

Fig. 1 from http://arxiv.org/abs/1310.3288; Schematic of the proposed “Cosmic Bell” experiment. Cosmic sources are used to determine detector settings in a Bell-type experiment.

Their idea is to use distant quasars or the Cosmic Microwave Background (CMB) to determine detector settings.  They would chose two distant quasars on opposite regions of the sky, or two separate patches of the CMB with sufficient angular separation.  Photons from these sources would be coming from events whose past light cones do not overlap.  These photons would then be used to determine the detector settings.

This experiment will close the settings-independence loophole (assuming the results remain consistent with QM and non-locality!).  If something unexpected is seen, it will enable mapping non-local correlations as a function of the overlap between light cones of the two independent photon sources.

Of course, the experiment will not be without some challenges.  The authors refer to a potential “noise loophole”.  They have to ensure that the cosmic photon detectors are not triggered by more local sources of photons, such as light pollution, scattered star light, zodiacal light, etc.  They also need to account for the impact of the intergalactic medium and Earth’s atmosphere on the cosmic photons.  It will be interesting to see where this leads in the coming years!

# Alternative Paths to an Interpretation of Quantum Mechanics

This is the real reason why we have not been able to discover a theory more fundamental than quantum mechanics. We no longer wear three piece suits to physics conferences.

If you have read my earlier posts, you have likely concluded that I am a realist with respect to the foundations of quantum mechanics (QM).  I believe there is some deeper reality behind the equations of QM.  This deeper reality, or more fundamental theory, will account for the apparent nonlocality that we see in quantum events.  It will also explain the intrinsic randomness in quantum theory, and how nature decides which option to choose.  In my opinion, the wave function (or state vector) represents more than just our knowledge of a system.  However, it may be just an approximation for the correct representation or description of reality.  I also believe that our preconceived notions of reality will need to be altered, just as they were when Einstein developed the Special (SR) and General (GR) Theories of Relativity.

My views contrast with those who believe that QM is the ultimate mathematical formulation.  Among those that believe QM is complete, there are two classes – those that believe it is not even appropriate to ask “why”, “how”, or “what”; and those that seek a set of principles that lead directly to QM.  Members of the first group hold that there is no such thing as objective reality.  Their position is that QM merely encodes what we know (or can not know) about the quantum world.  All we can talk about are the results of measurements that we make.  They argue that it is not even appropriate to ask nature to reveal a deeper understanding, because there is not one.  The second group looks for a deeper understanding, but they look for this conceptual or philosophical foundation within the framework of the current quantum theory.  I think both of these approaches are flawed.  In my opinion, the first approach amounts to forfeiture and the second is a dead end.  To move beyond QM and find a deeper conceptual understanding of the universe, we need to re-zero our preconceived notions and come at the problem from a new direction.

A search of the internet, or YouTube in particular, reveals multitudes of blogs and videos about QM.  There are many high quality documentaries and video clips, with excellent production qualities.  But, the vast majority parrot the ideas that “spooky action at a distance”, entanglement, wave function collapse, the mysterious role of an intelligent observer, etc., are intrinsic magical mysteries of the universe.  They give the impression that our knowledge of the quantum world is secure, and that we might as well accept this bizarre status quo.  Worse, I have seen expert speakers on these documentaries claim that it is not even correct to question these aspects of QM, these are not the “correct questions to ask”.  Metaphysical BS such as “each of us constructs our own version of reality” really gets me going.  No, we are not constructing alternate realities in our heads.  Each of us is constructing a different, flawed and approximated, representation or model of reality in our heads (some more flawed and approximated than others).  But this is not the same as creating a separate reality.  I believe there is some higher level theory, of which QM is an approximation, that will explain these issues.

# Quantum Theory as a Labor of Love (Vice Money)

There are several theoretical and experimental physicists doing work on interpretations of QM.  It is hard work.  Generations of physicists have gone before you and have not been able to understand quantum theory.  Additionally, you are working up hill against a field that is only slowly realizing the importance and applicability of your work.  Funding is hard to come by, as you compete with paradigms that have sapped man power and resources for decades.  Frustratingly, you are forced to compete in isolation with these fields despite their lack of actual physics results.  We need more people, and more funding, looking into the foundations and extensions of quantum mechanics.  Back in the 1980’s, many physicists believed that an end run had been found.  They believed that string theory was the theory of everything, from particle physics to cosmology, from the quantum world to black holes.  All the hype has not manifested itself in reality.  It is time to re-tool theoretical physics.  This may mean taking smaller steps, ensuring that we understand where our footing is at each hurdle.

The potential payoffs are huge.  This includes understanding and resolving open issues in Quantum Field Theory, which serves as the basis for the Standard Model of Particle Physics.  It may lead to a theory of quantum gravity, and explanations of dark matter and dark energy.  This would lead to a replacement for the Standard Model of Cosmology (the “Lamda Cold Dark Matter” model – beyond the scope of this post, perhaps more on that later).  These models that aspire to explain all of particle physics and all of cosmology have many free parameters.  The ability to tune these parameters to match the observations weakens our confidence in the uniqueness and correctness of these theories.  Hopefully, a new extension of QM will help fix some of these free parameters.

# Getting More Specific About What Lies Beyond Quantum Mechanics

I am not a fan of models that simply add additional mathematical structures to the Schrödinger equation in order to reproduce observed behavior.  Modified Schrodinger dynamics is one example of such attempts.  I am also not a fan of interpretations that ask us to accept too much without conceptual reimbursement, such as the Many Worlds Interpretation (MWI).  In the MWI, each quantum event creates a new universe.  With countless quantum events occurring throughout the universe every moment, the instantaneous proliferation of fully developed universes is staggering, to say the least.

Sean Carroll is a talented and prolific physicist and a wonderful writer. See, for example, his book From Eternity to Here: The Quest for the Ultimate Theory of Time, also linked from my Recommended Reading page.  Dr. Carroll recently gave an interview on interpretations of QM:

I agree with his assessment that the failure of physics to develop a conceptual understanding of quantum mechanics is an embarrassment.  However, I differ with him over his endorsement of the MWI.  There are other interpretations that can resolve the paradoxes of the canonical (Copenhagen) interpretation of QM without such wild assertions and assumptions.  Examples of these alternatives include de Broglie-Bohm mechanics, the Transactional Interpretation, or the Two-State Vector Formalism.  This does not mean that one of these other interpretations are necessarily correct.  It does mean that we should not be so eager and willing to swallow MWI.  The MWI will have to provide a better return on my investment before I start to take it seriously.

I have read several papers that attempt to derive quantum mechanics from invariance laws associated with information, probability, causality, contextuality, composability, etc., (name your principle).  While interesting, I just don’t have the sense that these approaches are on track to capture the essence of reality.  Perhaps the problem is that they are starting with the end in mind.  Although “begin with the end in mind” is one of Stephen Covey’s key tenets (The 7 Habits of Highly Effective People), in this case it may be a handicap.

Compare this situation with how Einstein discovered SR and GR.  Einstein was not trying to reproduce Newton’s absolute space and time or Newtonian gravitational theory.  He saw evidence in the world around him and in his thought experiments that led him to postulate a new invariance law.  For SR, it was the constancy of the speed of light.  For GR, it was the equivalence of gravitational and inertial mass.  He then followed these postulates to where ever they took him.  With his new theories, Einstein was able to explain experimental results that contradicted existing theories; the experiment by Michelson and Morley that failed to detect the ether and the anomalous precession of the orbit of Mercury, for examples.  More importantly, he was able to make additional testable predictions.

# Stating the Goal: Discovering the Path to What Lies Beyond Quantum Mechanics

So, another approach is to discover some fundamental physical principle(s) that leads to some new theory.  String theory is an example of this.  State a hypothesis: things are made up of strings rather than points.  Then, see where that leads.  However, you have to be willing and able to recognize when your hypothesis is not productive.  Hopefully, the new theory that explains QM will make some testable predictions that contradict other interpretations of conventional QM, so that we can tell which is right and which is wrong.  As if that would not be awesome enough, an even more amazing discovery would be a theory that reduces to QM in one limit, and GR in another.

I want to stress that I think this more fundamental theory will likely be founded on principles that seem, at first blush, to not have much to do with classical QM or GR.  And the math may look very different until approximations are made.  There may be additional hidden variables that are not accounted for in the current set of equations.  Something totally new.  Extra dimensions perhaps.  Not necessarily extra space or time dimensions.  But, some extra freedom for the “force carriers”, for entanglement, or for whatever advanced and retarded wave functions are representing.

Maybe some applicable insights can be found in the Aharanov-Bohm effect, Significance of Electromagnetic Potentials in the Quantum Theory.  Aharanov and Bohm showed that, contrary to classical mechanics and classical electromagnetism, the electromagnetic four-potential can have an observable effect on charged particles, even in regions where the electric and magnetic fields cancel (where there are no forces on the particle).

Fields such as a gravitational field, an electric field, or a magnetic field can be described in terms of a potential.  In the case of electromagnetism, you need a scalar and a vector potential.  Gravitational fields require a tensor potential.  The fields can be derived from the potentials.  However, the potentials can not be uniquely determined from the fields.  That is getting more in depth than we should for the present.  Suffice it to say, however, that prior to the prediction (and subsequent experimental verification) of the Aharanov-Bohm effect, physicists believed that all physically relevant dynamics could be expressed in terms of the fields.

In the Aharanov-Bohm effect, an electrically charged particle is affected by an electromagnetic field despite being confined to a region in which both the magnetic field and electric field are zero. This is an apparent nonlocality of the field interactions.  However, it can also be interpreted as the coupling of the electromagnetic four-potential with the phase of a charged particle’s wave function.  The effect is observed in interference experiments, where the phase difference of two interfering wave functions (state vectors) modifies the interference pattern.  The Aharonov–Bohm effect shows that the electric and magnetic fields do not contain full information about the physics.  The electromagnetic four-potential offers a more complete description of electromagnetism than the electric and magnetic fields alone can.

# Seeing Only the Shadows of the Quantum Universe

Like the prisoners in Plato’s Allegory of the Cave, what we see taking place at the quantum level may be just shadows of the true reality.

The title of this post, “Three Roads to What Lies Beyond Quantum Mechanics”, is a play on the title of Lee Smolin’s quantum gravity book: Three Roads To Quantum Gravity (Science Masters).

# Double slit experiments and the root of quantum weirdness

You are probably familiar with the legendary double slit experiment.  It is a simple, straight-forward experiment that introduces the wave-particle duality and the weirdness that is at the foundation of quantum mechanics.  Many people read or hear about the generic double slit experiment and assume that it is the end of the story.  Worse, many intrinsically curious people erroneously assume that this phenomenon is understood.  Or, they believe that they have a benign explanation for a particular experimental result.  Hence, they don’t dig deeper into the challenge and excitement that can be found in the quantum world.  Digging through the layers of experimental results helps ensure we are questioning the implications of our hypothesis, and testing whether it remains consistent and valid.

In the typical double slit experiment, a beam of light is directed at a pair of slits in a wall.  The resultant interference pattern is then observed on a screen or some other sort of detector.  You can see a five-minute introduction to the double slit experiment by Dr. Quantum: “Double Slit Experiment”.  Photons are typically used, although according to de Broglie and confirmed by Davisson and Germer, electrons or any other particle will work.  Using photons greatly simplifies the technical difficulties and cost of the experiment.

The experimental apparatus consists of a coherent light source, a wall with two narrow slits (the width and separation of the slits are comparable to the wavelength of the light), and a detection screen behind the wall.  A narrow beam of light strikes the pair of slits.  The pattern on the detection screen is an interference pattern.  So what, light is a wave.  Or, at least it acts that way sometimes.  We can easily calculate the details of the interference pattern using the dimensions of the experimental setup and the frequency of the light.  The two different paths, (source – slit A – screen; or source – slit B – screen), have different path lengths.  Hence, the two interfering waves have different phases and can add constructively or destructively.

## Doubling the dosage of quantum weirdness

The rub comes in when you dial down the intensity of the beam of light so that only one photon at a time is passing through the slits.  One photon can’t pass through both slits, right?  It can’t interfere with itself, right?  Well, the interference pattern is still there.  Quantum mechanics tells us that the photon is in a superposition of states.  See Feynman’s QED: The Strange Theory of Light and Matter (Princeton Science Library) or Cox and Forshaw’s The Quantum Universe: (And Why Anything That Can Happen, Does)for excellent conceptual descriptions of how to visualize what the particle is up to.

I can contemplate how a single “particle” can act like a wave sometimes, a particle other times, or some combination thereof.  I can do that without feeling like I am losing my grip on reality.  But, here is where things start to get really weird.  If you modify the above experiment so that you can tell which slit the photon traveled through, the interference pattern goes away.  It is as if each photon realizes they are being watched and stops their shenanigans.  But how do they “know” they are being watched?  How do they know that it is time for wave function collapse”?  In wave function collapse, the photon discards the superposition of states and selects a specific value or path (a specific eigenstate).

## The quantum measurement problem

This is the crux of the quantum measurement problem:   Why are there two different processes describing the evolution of a particle’s wave function?  These two processes are (1) the continuous evolution described by Schrödinger’s equation, and (2) the spontaneous collapse into a specific eigenstate.  What triggers the collapse?  Why can’t we observe a superposition or the collapse process? How can a wave function that is spread out over arbitrary distances collapse seemingly instantaneously?  Some scientists have argued that wave function collapse is triggered by an interaction between the observer and the photon, or between the measurement apparatus and the photon.  For example, the momentum that is imparted to the photon by the act of measurement may break the superposition. The problem with this argument, however, is that clever experimentalists have already devised and carried out experiments using interaction-free measurements.

# Now for some truly bizarre quantum weirdness

If you have followed the discussion so far, it is still not safe to unfasten your seatbelt and start walking about the cabin.  This is the point where I start to feel my grip on reality slipping away.  Particles are doing something we completely do not understand, in apparent response to some trigger we completely do not understand.  Consider delayed choice experiments and quantum eraser experiments.  In delayed choice experiments, the decision to determine which path the photon used is made well after the photon has passed the slits*.  Yet, the results seem to indicate that the photon has retroactively collapsed its wave function and chosen a single path.  If you mark through which slit each photon went, the interference pattern is destroyed.  This happens even if you mark the path without disturbing the photons movement.  In quantum eraser experiments, photons are tagged based on which path they took. By itself, that tagging destroys the interference pattern.  However, when this path information is discarded (erased), the interference pattern is restored.

This begs the following questions: What happens to the discarded part of the wave function when wave function collapse occurs?  Some people argue that the wave function is not real, it just encodes our knowledge of the situation.  But when the tagging is erased, how does the quantum system “know” what superposition to re-enter?

Delayed choice quantum eraser” experiments combine all of the absurdities of the above experiments.  This experiment is arranged to identify which one of the paths the photon uses.  And, this information can be erased after the fact.  See the adjacent figure from Wikipedia.  Photons are emitted one at a time from the lower-left and then subjected to a 50% beam splitter.  After the beam splitter (green block), photons travel along two possible paths, the red or blue lines. Reminds me of a Tokyo subway map.  In the top diagram, the trajectory of each photon is known. If a photon emerges at the top of the apparatus, it appears to have come by the blue path.  If it emerges at the side of the apparatus, it appears to have come by the red path.  As shown in the bottom diagram, a second beam splitter is introduced at the top right.  This can direct either beam towards either path, erasing the which-path information.  So, the decision whether or not to remove the path information is made after-the-fact.  If you remove the path information, the interference pattern is restored.  The photon appears to recover its superposition properties.

Indeed, quantum physics is rich with paradoxes and non-intuitive behaviors.  While contemplating a certain experiment, it is important to ensure you have a complete picture of what the theorists and experimentalists are trying to tell us.  By merely considering one particular experiment, it is possible to convince yourself that you understand what is happening.  But, other experiments may contradict or invalidate your conceptual line of reasoning.  It seems to me that there is some deep, underlying concept or unifying principle that we are missing.  Some key piece of the puzzle that will show us that superposition and entanglement are fundamental, and apparently not constrained by space and time.  There must be some (comprehensible) reason for why matter behaves like this.

* Many experiments use alternative path-separation devices, such as mirrors or beam splitters.  Additionally, different techniques have been used to “tag” specific paths or to detect the photons.  The math and the concepts are the same in these various setups.  Different arrangements help to clarify the results and resolve concerns over subtle technical issues.

```"The supreme task of the physicist is to arrive at those universal
elementary laws from which the cosmos can be built up by pure
deduction. There is no logical path to these laws; only intuition,
resting on sympathetic understanding of experience, can reach
them."
- Albert Einstein```

# The issue

With this post, I begin to layout some concerns that I have with descriptions and interpretations of quantum physics.  We still do not have a conceptual understanding of what the heck is going on in quantum mechanical processes.  Albert Einstein took issue with several aspects of quantum theory: the inherent randomness, the nonlocality, and the lack of realism, for example.  We may need to accept these aspects of nature, but is it asking too much to be able to understand how/why/what the universe is doing in these situations?

## Quantum physics is a fickle mistress

Quantum Mechanics (QM) is perhaps one of the most successful hypotheses in the history of physics. That is, if you evaluate success based on agreement with experiment and ability to make predictions that are later confirmed by experiment.  And, quite frankly, that is (quite appropriately) how science judges hypotheses and theories.  Thousands of experiments have been performed, verifying the accuracy and relevance of QM.  These experiments include emission or absorption spectra predictions and measurements, magnetic moment predictions and measurements, and multiple variations of the double slit experiment, to name a few.  Physicists, chemists, and engineers have subjected matter to all kinds of bizarre tests that have validated the theory’s un-intuitive predictions.  Additionally, QM is not just a theoretical curiosity.  The range of technologies based on it is staggering.  Without QM, we would not have PCs, iPads, smart phones, laptops, modern TVs, modern medical imaging equipment, the microchips that control everything from our cars to our refrigerators, and so on.

Yet, after all this, we still do not understand HOW quantum physics works.  Even though the theory is a century old, we are far from a proper conceptual understanding of what it actually means and HOW the universe pulls off this behavior.  How does a particle manage to take every possible path?  How does a wave function seem to collapse, essentially instantaneously, across arbitrary distances?  How do entangled particles influence each other, seemingly without regard to time and space?  Why do certain quantities have to be quantized, rather than continuous?  These difficulties are related to the fact that a complex-valued state vector is used to describe a physical system.  So another way to ask these questions is, “why are complex quantities and a state vector required to quantitatively describe behavior at the quantum level?”

## Why is it so hard to visualize quantum physics?

We can visualize general relativity (GR).  It is understood as the interplay between matter and spacetime.  Apart from some warping and dilation, GR makes intuitive sense.  There is a speed limit and strict enforcement of locality.  With some mathematics, we can readily convince ourselves that causality is safe.  Electromagnetic and nuclear interactions are described mathematically and conceptually as due to the exchange of particles called bosons.  These particles (photons for electromagnetism, gluons for the strong nuclear force, W and Z bosons for the weak nuclear force) account for the transfer of momentum and energy between fermions (i.e. quarks, electrons, protons, etc.).  They also account for the transfer of conserved quantum numbers.  In none of these fundamental forces do we have “spooky action at a distance”, or nonlocality.  We do have virtual particles, which is another story and takes some time to get used to.  But at least, even then, we have a picture in our heads of what is going on.

In quantum physics, the state vector is not a physical description of the system.  And the evolution of the state vector seems to occur in two distinct phases.  First, a continuous evolution of the state vector occurs as the system evolves in time and space (described, for example, by the Schröedinger equation).  Then, there is an abrupt and discontinuous collapse of the state vector, into a particular eigenstate; the dynamics of which are not understood.  A common misconception is that this state vector collapse is caused by the interaction with the measurement device.  But clever, interaction-free measurement processes have been devised.  The collapse of the wave function has been verified in situations where interactions play no role in the measurement.  At least no known interactions.

# Why should we care about conceptualizing quantum physics?

Given that QM works so well, and (so far) no experiments have contradicted it, why should we care how it is interpreted?  QM does not provide a physical description of a process.  The old adage is to just “shut up and calculate” (David Mermin).  However, this lack of a conceptual understanding may be what is holding physicists back from uniting the two pillars of modern physics, QM and GR.  It may be the key to understanding many of the most fundamental and provocative questions physicists are struggling with:

• How do we unite the two theoretical paradigms of modern physics, QM and GR?
• What happened at (and before) the origin of the universe?
• What will be the ultimate fate of the universe?
• What is driving the apparent acceleration of the universe’s expansion (i.e. what is dark energy)?
• What happens inside a black hole?
• What is time?

It may also be necessary for the next great leap in technology, such as quantum computing.  Besides all that, I just want to know.  Is that asking too much?

## Competing interpretations of quantum physics

At least to some extent, I think QM has been a victim of its own success.  Since it has worked so well, there is little less motivation to fix it.  Additionally, it is very difficult to distinguish between the predictions of some of these different interpretations.  So it will be difficult to experimentally validate the correct interpretation, at least for some time.

Many different interpretations have been offered up over the years.  I will dig into some of these in later posts.  To name a few (Frank Laloë, “Do We Really Understand Quantum Mechanics?”):

• Statistical interpretation
• Relational interpretation
• Logical, or algebraic approach
• Veiled reality
• Modified Schröedinger dynamics
• Transactional interpretation
• History interpretation
• Everett interpretation
• Modal interpretation

One of my favorites is the de Broglie-Bohm pilot wave interpretation.  In this model, a particle’s motion is determined by a wave.  Hence, you can reproduce both particle and wave-like behaviors and the predictions of generic QM.  However, there are some issues with de Broglie-Bohm theory.  These include things like relativistic invariance and the dynamics for how the particle and wave influence each other.  “We’ll talk about that later”.

Unfortunately, alternative explanations have not been given full and proper consideration over the past 86 years (since the 1927 Solvay Conference and the birth of the Copenhagen interpretation).  Some alternatives have been appropriately disproven.  However, others have just been over-ridden or ignored.  A common theme is that someone publishes a paper “showing” that some interpretation is not workable.  Later, someone else shows how that paper was in error.  People remember the first paper and continue to assume that a certain idea is untenable.  Various interpretations are confused with each other, or assumptions are confused with conclusions.  Scientists are erroneously lead to believe that a particular approach is not valid.

These myths are perpetuated in text books and lectures.  One example is de Broglie’s hidden variables theory, which was relegated to the scrap heap after the 1927 Solvay Conference.  It was resurrected after David Bohm developed his theory in the 1950s, and the similarities between it and de Broglie’s earlier work were noticed.  Another example: experiments confirming the violation of Bell’s inequality and hence confirming the concerns of the famous EPR paper (Einstein, Podolsky, Rosen) are often cited as confirming hidden variables theories are unworkable.  They actually show that hidden variables theories cannot sidestep the apparent nonlocality, not that they are altogether un-viable.

## De Broglie-Bohm mechanics at work?

Take a look at this amazing video from the Science Channel’s Through the Wormhole, on Wave/Particle dynamics with silicon droplets.  It shows how the results of the double slit experiment can be reproduced by a silicon droplet (the “particle”) riding on an actual, physical “wave”.  There are a lot of details that go into this experiment, including how the apparatus works and how it is filmed.  So it is definitely not a proof of de Broglie-Bohm mechanics.  However, it is intriguing, and offers an irresistible visualization that begs further investigation.

I think a significant factor in our failure to develop a consistent and deep conceptual understanding of quantum physics is rooted in the dogmatic presentation of the prevailing interpretation.  For decades, up-and-coming physicists have been indoctrinated in the “Copenhagen interpretation”.  Presented with the implicit assumption that interpretation questions are settled, many students don’t dig deeper.   The development of a proper, conceptual understanding has been further hobbled by misconceptions that are perpetuated through textbooks and instructors.  Students either assume the issue is resolved and look elsewhere for research opportunities, or they are discouraged by their advisors and forced to conform to availability of funding and job opportunities.

I recall being confused and frustrated, as an undergrad physics student, when the explanations in the textbook or provided by the professor, just did not make sense and did not seem to be consistent with what the mathematics implied.  For example, the meaning and implication of the uncertainty principle are often explained as being due to the unavoidable transfer of momentum to the observed particle during a measurement.  However, experiments have been done that show this is not the case.  Moreover, it is an intrinsic property of the mathematics, in which momentum and position are Fourier transformations of each other, like time and frequency in everyday applications of Fourier theory to acoustic or electromagnetic signals.

# Conclusion

In the weeks and months ahead, I will expand on the specific points brought up in this article. It is entirely possible that Nature really is unknowable.  The Universe probably does not feel compelled to satisfy my desire for a visual, comprehensible model, unless it already intended to do that anyway.