## 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!

# Meet the Parents of Quantum Gravity: Quantum Field Theory and General Relativity

Quantum Field Theory (QFT) and General Relativity (GR) form the theoretical and mathematical foundations for modern physics and cosmology.  QFT is an extension of Quantum Mechanics (QM), accounting for creation and annihilation of particles.  The primary entities in QFT are fields rather than particles, and it can be expressed in a Lorentz-invariant form, consistent with Einstein’s Special Theory of Relativity.  GR is, of course, Einstein’s brain child that explains gravity as the curvature of space and time, induced by matter and energy.  GR enabled Einstein to correctly calculate the magnitude of the precession of Mercury’s perihelion and the deflection of light by the Sun, and almost enabled him to predict the expansion of the cosmos.

These two paradigms, QFT and GR, have enjoyed unprecedented success in their range of validity, precision of experimental verification, and the amazing technologies that they have made possible.  However, many questions remain unanswered.  Puzzles include: what was the physics of the early universe and the pre-universe, what is dark matter, what is dark energy, what is the origin and nature of spacetime, what goes on at the horizon of a black hole and at a black hole singularity, how can gravity be united with the other three forces in a unified theory, what is the role of gravity in quantum decoherence?  Answering these questions may require finding a more general theory that merges QFT and GR into a unified framework encompassing both paradigms, a theory known as Quantum Gravity (QG).

QFT is essentially the theory of the very small, where quantum effects dominate and gravity can be ignored because it is so weak. GR is essentially the theory of the very large or heavy, where gravity dominates and quantum effects disappear.  A theory of QG must be able to predict and explain situations where both quantum effects and strong-field gravity are important.  Quantum Gravity in under five minutes:

# The Apparently Incompatible Natures of Quantum Gravity’s Parents

QFT and GR are founded on seemingly different premises for how the universe works.  For example, in QFT, particle fields are embedded in the flat (Minkowski) spacetime of Special Relativity.  In GR, time flows at different rates depending on the spacetime geometry.  And gravity is due to the curvature of spacetime, which changes as gravitational masses move.  The most straight-forward ways of combining the two theories by quantizing gravity are non-renormalizable.  This means that calculations run away to infinity and cannot be tamed through a redefinition of certain parameters, as is done in QFT.

This problem is related to the fact that all particles attract each other gravitationally, and energy as well as mass create spacetime curvature.  When quantizing gravity, there are infinitely many independent parameters needed to define the theory.  At low energies, this form of quantum gravity reduces to the usual GR.  But, at high energies (small distance scales), all of the infinitely many unknown parameters are important and predictions become impossible.

A workable theory of quantum gravity must make use of some deep principle that reduces the infinitely many unknown parameters to a finite and measureable number.  Attempts at a workable theory of quantum gravity include string theory, loop quantum gravity, non-commutative geometry, causal dynamical triangulation, and a holographic universe.  Of course, which hypothesis you prefer is not a decision to be taken lightly:

The challenge of uniting QFT and GR is further compounded by the lack of experimental results that could point to a breakdown of either QFT or GR; or results from experiments that are sensitive to both theories.   Scientists are turning to a variety of astrophysical as well as table top experiments to address this issue.

# Searching for Common Ground Between Quantum Field Theory and General Relativity

Testing the predictions of quantum theory on macroscopic scales is one of the outstanding challenges for modern physics.  Some experiments are not tests of a specific theory of quantum gravity, per se.  Rather, they look for a deviation from some fundamental tenet of either QFT or GR, with the hope that this will guide theorists in how to supplant either QFT or GR.  Other experiments attempt to create or observe conditions that are sensitive to both theories, to see how they play together.

Common to many philosophical or phenomenological approaches to QG is the possibility that fundamental symmetries, essential in our current understanding of the universe, may not hold at extremely small distance scales or high energy scales, due to a discrete structure of spacetime. Or, perhaps these symmetries do not hold in a highly curved spacetime with boundaries, such as in the vicinity of a microscopic black hole or the cosmological horizon of an inflationary universe.

These symmetries include Lorentz Invariance (LI) and CPT symmetry (charge conjugation – parity transformation – time reversal).  Lorentz invariance means that a property or process remains invariant under a Lorentz transformation. That is to say, it is independent of the coordinate system and independent of the location or motion of the observer, and the location or motion of the system.  CPT symmetry requires that all physical phenomenon are invariant under the combined operations of charge conjugation (swapping matter and antimatter), parity transformation (reflection in a mirror), and time reversal (viewing the process in reverse).

The IceCube South Pole Neutrino Observatory has weighed in on this issue, setting extremely tight limits on a possible violation of Lorentz Invariance.  Neutrinos, lacking strong or electromagnetic interactions and moving at essentially the speed of light (due to their teeny, tiny, and as-yet un-measureable, mass), are sensitive probes of these effects.  IceCube uses data from interactions of high energy atmospheric and astrophysical neutrinos in the South Pole ice.  See Search for a Lorentz-violating sidereal signal with atmospheric neutrinos in IceCube”, Stringent constraint on neutrino Lorentz-invariance violation from the two IceCube PeV neutrinos, and Probing Planck scale physics with IceCube.

The Fermi Gamma-ray Space Telescope is also a member of this club, using photons rather than neutrinos: Constraints on Lorentz Invariance Violation with Fermi-LAT Observations of Gamma-Ray Bursts and Constraints on Lorentz Invariance Violation from Fermi -Large Area Telescope Observations of Gamma-Ray Bursts.

Another sweet spot is the equivalence principle (EP), which provides the foundational basis for GR. The EP is the idea that the effects of acceleration are indistinguishable from the effects of a uniform gravitational field. The EP requires that gravitational and inertial mass are equivalent; that a particle’s coupling to a gravitational field is equal to its inertial mass.  See, for example, Expanded solar-system limits on violations of the equivalence principleor A millisecond pulsar in a stellar triple system.

# Foundational Principles of Quantum Mechanics and the Cosmic Microwave Background

I have previously discussed the resurgence of de Broglie-Bohm mechanics, despite its historical neglect, in Hydrodynamic Quantum Analogs”.

In Beyond the Quantum, Antony Valentini follows the logical consequences of Louis de Broglie’s pilot wave theory to predict evidence of quantum non-equilibrium in the Cosmic Microwave Background (CMB).   Pilot-wave theory makes use of hidden variables.  The canonical interpretation of quantum mechanics says that there are no well-defined trajectories.  But in pilot-wave theory, these hidden variables describe the trajectories for whatever particles or fields a system may contain.  They can also explain the apparently random outcomes of quantum measurements.

Pilot-wave theory gives the same observable results as conventional quantum theory if the hidden variables have a particular distribution, a quantum equilibrium distribution, analogous to an ensemble of particles being in a thermal equilibrium.  But, as Valentini points out, there is nothing in de Broglie’s dynamics that requires this assumption to be made.  When the hidden variables have an equilibrium distribution, superluminal signaling is not possible; any attempted non-local signals would average out to zero.  However, if the hidden variables are not in an equilibrium distribution, superluminal signals may become controllable and observable! Relativity theory would be violated; time would be absolute rather than relative to each observer!

To help understand this, Valentini provides an analogy with classical physics:

“…For a box of gas, there is no reason to think that the molecules must be distributed uniformly within the box with a thermal spread in their speeds. That would amount to restricting classical physics to thermal equilibrium, when in fact classical physics is a much wider theory. Similarly, in pilot-wave theory, the `quantum equilibrium’ distribution – with particle positions distributed according to the Born rule – is only a special case. In principle, the theory allows other `quantum non-equilibrium’ distributions, for which the statistical predictions of quantum theory are violated – just as, for a classical box of gas out of thermal equilibrium, predictions for pressure fluctuations will differ from the thermal case. Quantum equilibrium has the same status in pilot-wave dynamics as thermal equilibrium has in classical dynamics. Equilibrium is a mere contingency, not a law.

…It seems natural to assume that the universe began in a non-equilibrium state, with relaxation to quantum equilibrium taking place during the violence of the Big Bang.

…The crucial question is whether the early non-equilibrium state could have left traces or remnants that are observable today.”

Quantum non-equilibrium at the onset of inflation would modify the spectrum of anisotropies (differences from place-to-place) in the CMB sky.  Hence, measurements of the CMB can test for the presence of quantum non-equilibrium during the inflationary phase.

See also: Samuel Colin and Antony Valentini, Mechanism for the suppression of quantum noise at large scales on expanding space, where the authors present numerical simulations showing how the expansion of space can slow down the relaxation to quantum equilibrium in the super-Hubble regime:

“Given these results it is natural to expect a suppression of quantum noise at super-Hubble wavelengths. Such suppression could have taken place in a pre-inflationary era, resulting in a large-scale power deficit in the cosmic microwave background”.

A variety of tests of fundamental physics, conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, are discussed in David Rideout, et al., Fundamental quantum optics experiments conceivable with satellites — reaching relativistic distances and velocities:

“We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. …the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity.”

# Table-Top Tests of Quantum Mechanics and General Relativity

The question of simultaneously observing the effects of quantum physics and GR in a table-top experiment can be framed as simply as this: The idea that particles can be in superpositions of multiple states (states with different trajectories, different spins, different energies, etc.) is an essential feature of quantum mechanics.  If a particle is in a superposition of states with different paths through a gravitational field, for example, the different superpositions should be effected differently by the different trajectories through spacetime.  If a particle is in a superposition of different energy states, these different superpositions should create different gravitational fields.  If a macroscopic object could be placed in a superposition of oscillating and non-oscillating, for example, its gravitational field should also split into a superposition.  What does a superposition of gravitational fields look like and how does it behave?

Unfortunately, quantum superpositions are very delicate. As soon as a particle in a superposition interacts with the environment, it appears to collapse into a definite state (see Decoherence and the Quantum to Classical Transition; or Why We Don’t See Cats that are Both Dead and Alive).  Only tiny particle-sized entities can be maintained in quantum superpositions for any significant period of time.  However, only macroscopic objects have detectable gravitational fields.  So this presents immense technical challenges for experimentalists.  People are working very hard to improve upon these limitations.  See, for example, Brian Pepper, et al, Optomechanical superpositions via nested interferometry and Macroscopic superpositions via nested interferometry: finite temperature and decoherence considerations.

Magdalena Zych and his colleagues are searching for evidence of gravitationally-induced time dilation and its effects on the phase of a quantum state: Quantum interferometric visibility as a witness of general relativistic proper time, (also available here).  They propose using a Mach-Zehnder interferometer (MZI) in a gravitational field.  According to GR, proper time flows at different rates in different regions of spacetime.  Their proposed experiment requires a particle with evolving internal degrees of freedom, such as spin or internal vibrations, that can act as a clock.  And the two different legs of the MZI are at different gravitational potentials.

Difference between probabilities to find the particle in different outputs of the Mach–Zehnder interferometer as a function of the time ΔT for which the particle travels in a superposition of two trajectories (corresponds to changing the length of the interferometric arms). Without the ‘clock’ degrees of freedom, the dashed, black line would be the result. With the ‘clock’ and the predictions of GR, the predicted result is the blue line. From “Quantum interferometric visibility as a witness of general relativistic proper time”.

If there is a difference in proper time elapsed along the two legs of the interferometer, the particle’s internal clock will evolve into two different quantum states.  This is a consequence of the prediction that the clock ticks at different rates when placed in different gravitational potentials.  As a result of the quantum complementarity between interference and which-path information (in the form of the different internal clock values), the general relativistic time dilation will cause a decrease in the interferometric visibility (see the adjacent figure).

“Such a reduction in the visibility is a direct consequence of the general relativistic time dilation, which follows from the Einstein equivalence principle. Seeing the Einstein equivalence principle as a corner stone of general relativity, observation of the predicted loss of the interference contrast would be the first confirmation of a genuine general relativistic effect in quantum mechanics.”

# Conclusion

This has been just a sampling of the work underway to pry nature’s secrets from her grasp.  For theorists and experimentalists, working on the interplay between QFT and GR with the ultimate goal of creating a theory of QG, is one of the most challenging and stimulating areas of research in fundamental physics.  If this brief discussion has piqued your interest, let me know.  I can point you towards more resources concerning the theoretical and experimental work taking place on the road to quantum gravity.

# 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.

# Additional information:

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:

# Re-evaluating Your Quantum Upbringing

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.

# Skepticism, Critical Thinking, and Quantum Physics

I have decided to expand this website a little and address quantum woo and quantum mysticism more directly.  Quantum woo is the justification of irrational beliefs using confused, vague, and ambiguous references to quantum physics.  Many people do not understand quantum physics.  But, they know that it predicts and explains some weird things.  So, con-artists dupe their audiences by stringing together a series of terms and phrases from quantum physics and asserting that it explains whatever it is they are pushing.  Ignorant and credulous consumers are eager to buy their quantum healing, or quantum self-help programs, or their “proof” of an afterlife.  It’s much easier to simply believe them than to try to comprehend the mathematical and experimental constraints that science requires you to understand.

Examples of quantum woo include quantum healing, quantum touch, healing through “frequencies” or “energies”, claims of a “one-ness” with the universe or a consciousness that pervades the universe, or the ability to shape one’s destiny with your mind (specifically, they mean directly influencing and manipulating your world with your thoughts, not by your thoughts motivating your actions which then influence your surroundings).  Products such as The Secret or What the Bleep Do We Know!? are excellent examples of this.  Also, just about anything written or said by Deepak Chopra.  Any claims that quantum physics proves the existence of an afterlife or a universal consciousness also fall into this category.

# The Challenge of Being Skeptical About Quantum Woo

Over the years, many authors have written books that claim evidence for some deep role of consciousness in guiding the universe, or a connection between quantum physics and Eastern Mysticism, for example.  Some of these authors have even been credentialed scientists.  That, along with the vague interpretation and description of quantum mechanics adopted by its creators in the first half of the twentieth century (i.e. the Copenhagen Interpretation), makes it difficult to convince the casual reader that this quantum nonsense should be dismissed out of hand.  However, these individuals were mistaken; their claims or conjectures were wrong.  Using them to justify continued support for nonsense that has since been theoretically and experimentally de-bunked makes no more sense than using the fact that Isaac Newton studied alchemy to justify someone’s claim that he or she can transmute anything into gold just by touching it.

So why worry about the perpetuation of quantum woo?  The potential harm includes:

• Financial exploitation of gullible audiences.
• Health risks for those that decide to rely on “quantum healing” or similar nonsense in place of proven treatments.
• Encouraging people to avoid dealing with the real sources behind their problems.
• Encouraging political or educational complacency (why work hard to solve “real” problems; why work hard to learn “real” science).
• Misdirection of research funds, resources, and priorities, towards dead-end claims.
• Wasted careers for those that pursue “research” in these areas; making no contribution to furthering our understanding of the universe; no contribution to improving the quality of life for mankind.
• Misleading of the public about the nature and limits of science.
• Erosion of public confidence in the scientific process and legitimate scientific results.
• A waste of time and a distraction for those who want to learn real science, but who may not yet be able to distinguish the difference between science and pseudoscience.

First and foremost, the best defense against quantum woo and the charlatans that promote it, is knowledge and a proper conceptual understanding of quantum mechanics.  So, I will continue to write about quantum physics theory and experiments; providing background knowledge as well as separating myth, misconception, and fact.  I will also expound on the history of quantum physics and it’s portrayal in the classroom and in the media.  Additionally, I will be adding some additional pages to this website, pages with information and resources for skepticism and critical thinking.

Armed with this knowledge of what quantum physics is and is not, my hope is that people can use the tools of skepticism and critical thinking to help make the world safe for science and reason.  My goal is not to convert the likes of Deepak Chopra.  Rather, I want to give people the tools to recognize BS when they see or hear it, and to apply skepticism and critical thinking to myths, misconceptions, and deceptions involving quantum physics.

# The Prototypical Quantum Woo-Master

Deepak Chopra is the poster child for the quantum woo movement.  He has made millions of dollars from people too ignorant and too gullible to realize that his books and speeches are nonsense.  One example is the Nightline Face-off debate: Chopra and Houston versus Shermer and Harris, Does God Have a Future?   You can watch the entire debate at that link.

An example of the word salad that Chopra likes to mix together is this: “Today, science tells us that the essential nature of reality is non-local correlation. Everything is connected to everything else.  But there is hidden creativity. There are quantum leaps of creativity. There’s something called the observer effect where intention orchestrates space-time events.”

First of all, the so-called observer effect in quantum mechanics has nothing to do with intention orchestrating space-time events.  And non-local correlations are present only in very specific systems and circumstances.  Moreover, the intrinsic randomness in quantum mechanics precludes us from using non-local correlations in any sort of “intentional” way.  Before you start catapulting from non-local correlations to speculations about “hidden creativity” or what exactly it means to be “connected to everything else”, you need to understand what the words used by scientists actually mean.  Chopra’s assertions are completely baseless and unsupported.

During the question/answer session of that debate, Sara Mayhew (illustrator, writer, and skeptic) asked an insightful question. I encourage you to check out her webpage and blog.   Her question to Deepak Chopra was:

“Deepak mentioned that there are deeper ways of knowing, …based on intuition and the subjective.  …If we don’t use the objective scientific method, how do we distinguish what is true from what we simply want to be true?”

Chopra does not answer the question but makes it painfully obvious that he does not understand the vocabulary of science, much less the concepts of science.  His response includes “nature does not decide that this is the subject, that is the object…”  He doesn’t understand the meaning of subjective versus objective claims, hence he cannot possibly understand the scientific process nor why it succeeds where hope, faith, and feelings do not.

subjective: based on or influenced by personal feelings, tastes, or opinions; dependent on the mind or on an individual’s perception for its existence.

For example, if I believe that I am connected with the universe through a universal consciousness because it makes me feel good or because I fear the alternative, that does not make it true.  If I believe that all super models would love to date me if only they had a chance to meet me, the idea may make me feel good, but it is nonetheless delusional.

objective: not influenced by personal feelings or opinions in considering and representing facts; not dependent on the mind for existence; actual.

This includes repeatable and verifiable experimental evidence.  For example, we use the scientific method to figure out what medications or treatments actually work, based on data and not based on opinion, wishful thinking, or desire.  Some subjective claims can be made objective by quantifying them, or making testable predictions based on them (rendering them falsifiable).

Apparently, Chopra does understand the meaning of obfuscation, because he is so effective at it: to render unclear, or unintelligible; to hide the intended meaning, to make communication confusing, willfully ambiguous, and harder to interpret.  One thing is certain.  If a conscious universe wants to be taken seriously, he/she has to find a better spokesperson, someone who understands the scientific process and understands why it works so well (when used correctly).

# “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 spreading of misinformation and misconceptions about the quantum world can be lumped into two different categories.  The first category are people who mean well, who want to advance science and scientific understanding.  Maybe they write a book, give public lectures, or create news articles about recent events in quantum science, for examples.  However, they use misleading analogies, miss essential features, fail to properly address alternatives to a failing orthodoxy, or mischaracterize apparently paradoxical phenomenon.  As a result, they end up misleading or confusing the general public or their students.  Another failure mode within this category is the use of excessive hype.  Due to their own passions or the desire to spread the excitement of physics, they mislead about the implications of quantum physics in general.  They over-promise when describing the latest incremental step in theoretical or experimental physics; or they mislead about the nature of reality.

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.

# Hollywood and Black Hole Analogs

The Big Bang Theory’s end-of-season cliff-hanger referred to a similarity between the equations of hydrodynamics and the equations of black holes, and the usefulness of hydrodynamic simulations to understand black holes.  Leonard joined a team put together by Stephen Hawking to search for the equivalent of Unruh radiation in water (at sea).  Here he is telling Penny that he will be on an ocean research vessel for four months:

## Hawking and Unruh: Radiation from the Vacuum

One of Hawking’s many contributions to our understanding of black holes is his prediction of Hawking radiation.  By combining concepts and math from General Relativity and Quantum Mechanics, Hawking showed that black holes have a surface temperature and radiate particles.  The possibility of actually detecting the equivalent of Unruh radiation in the ocean may have been an exaggeration.  But, as is typical for The Big Bang series, the physics that appears is based on actual physics and is inspired by current events in science.  See, for example, Black Hole Analogue Discovered in South Atlantic Ocean”  and Coherent Lagrangian Vortices: Our Oceans Have Their Own Kind Of Black Holes.”

According to the equivalence principle, physics in a uniform gravitational field should be the same as that in a uniformly accelerating reference frame.  So, a particle or object undergoing uniform acceleration should also emit (thermal) radiation, analogous to the surface of a black hole.  This is essentially what Unruh radiation is.  Unruh radiation has the same mathematical relationship as Hawking radiation, except it is proportional to the uniform acceleration rather than gravity.  To reach detectable levels, the acceleration needs to be pretty drastic.  Experimentalists hope to use intense lasers to accelerate electrons sufficiently to detect Unruh radiation.  Unruh radiation is different from the usual radiation emitted by accelerated charged particles.  It is independent of the particle’s mass and charge and also has a different frequency distribution and angular distribution, features that will be used to identify its presence.

# Hydrodynamic Quantum Analogs

Now, on to the subject of hydrodynamic quantum analogs.  In a previous post, I mentioned experiments with silicon droplets that were mimicking quantum physics:  The Folly of Physics: Interpretations of Quantum Physics, Part 1:  De Broglie-Bohm mechanics at work?”  If you missed it, take a look at this amazing clip from the Science Channel’s Through the Wormhole:

This Science Channel video shows how the results of the canonical double slit experiment can be reproduced by a silicon droplet (the “particle”) riding on an actual, physical wave (a “pilot-wave”, reminiscent of de Broglie-Bohm pilot-wave theory).  Physicists and mathematicians continue to explore this rich environment to further advance our understanding of nature.

## Getting into the Experimental Details of Hydrodynamic Quantum Analogs

You can take a look at the MIT web page of John Bush for highlights of some of his group’s work on hydrodynamic quantum analogs.   Their work is further discussed in “Wavelike statistics from pilot-wave dynamics in a circular corral”, which is also available here“Exotic states of bouncing and walking droplets” (also available at this location), explains the experimental setup in more detail and digs deeper into the theory and math.

A silicon-filled tray is placed on a vibrating table.  The depth and geometry of the tray are chosen to enable studying the desired behavior or phenomenon.  The intensity of the vibration is adjusted to just below the threshold at which waves would be generated on the surface of the fluid by the vibrations.  When a droplet of silicon is then placed on the surface of the vibrating fluid, a cushion of air between the drop and the fluid bath prevents the drop from coalescing. The droplet bounces and “walks” on the vibrating surface.  This bouncing causes a wave field to be generated on the surface of the bath, similar to skipping a rock on a pond.  The wave field becomes more and more complex as waves from subsequent bounces interfere with each other and reflect off of the boundaries of the surface (or off of other obstacles placed in the fluid bath).

The motion of the particle depends on its current location as well as its history, due to the complex wave field generated by previous bounces.  The motion also depends on the environment; the geometry and depth of the tray, depth changes, boundaries and obstacles, etc.  In addition to a vertical component, there is a horizontal component to the force on the droplet.  This is due to the droplet landing on a sloping part of a wave.  Under the right conditions, the droplet achieves resonance with its self-generated wave field and is propelled horizontally along the surface.  This two-dimensional motion displays properties of a microscopic quantum system.  The trajectories that are observed, and the probability distributions mapped out by the areas in which the droplet spends the majority of its time, are equivalent to the results of quantum physics experiments with microscopic particles.

## Visualizing Hydrodynamic Quantum Analogs

Take a look at this YouTube video, provided by MIT, to help visualize what is going on.  It is important to note that in the images where you see the droplet walking across the surface, the camera is being strobed in synch with the bouncing – so you just see the horizontal motion, not the vertical bouncing.

If the silicon bath is rotating, in addition to vibrating vertically, the droplet will lock into an orbit determined by the troughs of its self-generated wave pattern.  This is precisely a demonstration of “quantization” of the allowed orbitals for a subatomic particle confined in a potential.

Similar experiments have demonstrated other behaviors that are typically assumed to be exclusive to the quantum realm.  These phenomenon include diffraction, tunneling, quantized orbits, orbital level splitting, and more (see “Wavelike statistics from pilot-wave dynamics in a circular corral” and references therein).  To mimic tunneling, for example, a walking droplet approaching a barrier that it will on most occasions simply bounce off of, will once in a while receive enough energy from the wave enabling it to jump over the barrier.

## Interpreting Hydrodynamic Quantum Analogs

The authors of “Wavelike statistics from pilot-wave dynamics in a circular corral” state that:

“Our study indicates that this hydrodynamic system is closely related to the physical picture of quantum dynamics envisaged by de Broglie, in which rapid oscillations originating in the particle give rise to a guiding wave field.”

Louis de Broglie is perhaps best recognized for postulating in his PhD thesis that all matter (not just photons) has wave properties.  He received the Nobel Prize in Physics in 1929, “for his discovery of the wave nature of electrons”.  Clinton Davisson and George Paget were jointly awarded the Nobel Prize in Physics in 1937, “for their experimental discovery of the diffraction of electrons by crystals”.

Louis de Broglie generalized Einstein’s theory of the photon to propose that all matter has wave-like behaviors. The story of his pilot-wave theory is one that is still being written. (image from Wikipedia)

de Broglie presented his theory of pilot waves at the famous Solvay conference in 1927.  However, his idea lost out to the personalities of Bohr, Heisenberg, and others, in favor of the Copenhagen Interpretation (CI) of Quantum Mechanics.  There is a substantial debate in the literature over whether the adoption of the CI was the result of personalities, politics, and personal ambitions, rather than a deliberative and unbiased review of the available alternatives.  See, for example, “Quantum Theory at the Crossroads.  My personal opinion is that the CI was adopted prematurely and went unquestioned by the bulk of the physics community for far too long. As a result, experimental and theoretical progress towards a fundamental conceptual understanding of the universe has been delayed.  I plan to address this issue in more detail, from a historical and current events perspective, eventually; either in this blog or in a book.  Nonetheless, it is intriguing to consider what conclusions would have come out of the Solvay Conference if de Broglie could have shown the above video.

Pilot-wave mechanics was abandoned until David Bohm independently re-discovered something very similar to it in the 1950’s.  The theory has subsequently become known as Bohmian Mechanics, or de Broglie-Bohm Pilot-Wave Theory.  According to this model, particles are objective point-like objects with deterministic trajectories.  These trajectories are guided by pilot waves, which also objectively exist.  The pilot waves are described by the wave function.  Wave function collapse never happens (contrary to the assumption of the CI).  Hence, pilot-wave theory removes the measurement paradox.  It also provides a mechanism for explaining and visualizing wave-particle duality.  It is easy to see how the movement of a particle can appear to be determined by the interference of waves, because it is directly!

The mathematics used to describe damped harmonic oscillators and RLC circuits are equivalent.  Variables from one regime (such as displacement, mass, spring constant, and damping coefficient) can be mapped to the other regime (charge, inductance, capacitance, and resistance).  However, this does not mean that an RLC circuit is a mass on a spring oscillating in some viscous damping medium.  It just means that the two systems share similar dynamical properties.  It also means that you can use one system to study or visualize the other.  However, beyond the similarities, there remain significant differences between electromagnetism and classical mechanics.

# Implications of Hydrodynamic Quantum Analogs

Nonetheless, the equivalence between the motions mapped out by these classical droplet-wave systems and quantum mechanics is jaw-dropping.  And there is certainly a lot that we can learn from them.  These recent findings should help revive the question of whether there is a more fundamental dynamics in quantum physics.  Whether the correct conclusion is that the illusion of quantum mechanics is just that, and the quantum realm is nothing new (compared to classical systems) is yet to be seen.  There are certain phenomenon in quantum experiments, such as (apparently) discontinuous particle trajectories, for which the classical analog is not yet clear.  Additionally, in de Broglie-Bohm mechanics, there is no dynamic mechanism for the particle to influence the wave field as in the case of hydrodynamic quantum analogs.  But perhaps an extension of de Broglie-Bohm mechanics should account for this feedback?

Randomness is an intrinsic feature of the quantum world.  After reading these papers and watching the videos, it can be tempting to attribute this (apparent?) randomness to chaos theory.  Chaos theory applies to dynamical systems that are extremely sensitive to initial conditions.  Tiny differences in initial conditions lead to huge differences in future outcomes.  The idea to apply it to quantum theory would essentially involve assuming that there is some hidden information about a particle’s initial state that we cannot know well enough to enable a precise prediction for the future.  Hence, the best we can do is predict probabilities.  What bothers me about this idea, however, is that the intrinsic and unavoidable randomness in quantum mechanics is closely tied to non-locality.  Without the intrinsic and unavoidable randomness, problems with causality and relativity quickly show up. On the other hand, if it were true, that there is an underlying explanation for the intrinsic randomness in QM using chaos theory and hidden variables, the technological and conceptual breakthroughs would be astounding, I’m sure!

There are a lot of details that go into these experiments, including how the apparatus is set up and how it is filmed.  So they are definitely not a proof or refutation of any particular interpretation of QM at this point.  However, they are intriguing, and they offer an irresistible visualization that begs further investigation.  Quantum physics is typically presented as a mystical and bizarre subject, involving multiple universes, superimposed cats, and conscious minds deciding reality.  These experiments should push us to recognize that a belief in the mystical aspects of quantum mechanics is a choice and not a necessity.

# Encountering the Many Worlds Interpretation

Several years ago, I looked into the Ma­ny Worlds Interpretation (MWI) of quantum mechanics and concluded that it was not on the right track.  It seemed to be creating more conceptual and technical problems than it solved.  However, I frequently come across mention of it in the physics literature and in documentaries.  Several leading scientists refer to it as a ‘viable’ alternative to the canonical Copenhagen Interpretation (CI); some even calling it the ‘preferred’ interpretation.  So, I recently decided to take another look at the MWI.  Perhaps there was something I missed, or something important that I did not understand on the first go-around.

My initial instincts have been validated.  Reading about the MWI, including papers by its proponents as well as by its detractors, reminded me of the Hans Christian Andersen story called The Emperor’s New Clothes The Emperor and his ministers believe the hype about a fabric that is allegedly invisible to anyone who is unfit for their position.  They pretend that they can see the fabric so as not to feel left out.  While the Emperor is parading naked through the town, believing that he is wearing the best suit of clothes, a naïve young boy blurts out that the Emperor is naked!  Perhaps I can be that naïve young boy when it comes to untestable ideas like the MWI.  I may not be young, but bear with me.

## So what is the Many Worlds Interpretation?

As advertised, the main advantage of the MWI is that it solves the measurement problem. I discussed the measurement problem in two previous posts: Quantum Weirdness: The unbridled ability of quantum physics to shock us and Contrary to Popular Belief, Einstein Was Not Mistaken About Quantum Mechanics.  The measurement problem results from the apparent need for two distinct processes for the evolution of the state vector: (1) continuous and deterministic evolution according to the Schrödinger equation when no one is looking, followed by (2) spontaneous non-unitary evolution, or collapse, of the state vector upon measurement of an observable.  What constitutes a measurement and the dynamics of wave function collapse are not defined in the CI.  Additionally, special status is assigned to an intelligent observer who is treated as being outside the quantum system.

As an added bonus, proponents of MWI claim that it enables independent derivation of quantum probability distributions without assuming the Born rule.  The Born rule for computing the probability of potential outcomes of a quantum event is an additional postulate of canonical quantum mechanics.  According to this rule (which has enjoyed phenomenal experimental verification time and time again throughout the past roughly ninety years), the probability for each potential outcome to become the realized outcome is given by the amplitude squared from the applicable terms in the state vector.

Hugh Everett developed the relative state formulation in his dissertation and his subsequent publication of  “Relative State” Formulation of Quantum Mechanics (also available at this link).  It was later given new life by Bryce DeWitt in 1970, with his work applying rational decision theory and game theory to quantum mechanics; see Quantum Mechanics and reality.  Since then, dozens of papers have been written attempting to patch holes in the theory, or to take it apart.

See the recent article by Sabine Hossenfelder, “The Multiverse is not a paradigm and it’s not shifting anything” for another perspective on multiverses in general.

The MWI hypothesis avoids the measurement problem by assuming that wave function collapse never happens.  A single result never emerges from an interaction or quantum measurement.  Instead, all possibilities are realized. Each possibility is manifested in a new branching universe.  With each observation, measurement, or interaction, the observer state branches into a number of different states, each on a separate branch of a multiverse.  All branches exist simultaneously and each branch is ‘equally real’.  All potential outcomes are realized, regardless of how small their probabilities.

# What is wrong with the Many Worlds Interpretation?

If you have read my earlier post Three Roads to What Lies Beyond Quantum Mechanics, you have already glimpsed my discontent with MWI.  You will find statements in the literature that claim MWI solves the paradoxes of the CI, and that it derives quantum probabilities without the use of an ad hoc assumption (as in the case of the Born rule in the CI).  Hugh Everett’s main goals when he gave birth to the ‘relative state formulation’, which subsequently became known as the MWI, were to get rid of non-unitary wave function collapse and to relegate the observer to just another part of the quantum system.  Unfortunately, MWI and its many variants does not live up to the product’s claims.

The MWI hypothesis requires an unimaginably large, perhaps infinite, number of universes, each spawned essentially instantaneously in a fully evolved state from it’s parent.  Your present universe is constantly branching, sprouting multiple universes at a fantastic rate.  Each new universe is identical to its parent IN EVERY WAY, except for the record of a single quantum event.  I don’t just mean in one you are the Queen or King of your senior prom, and in another you decide not to run for prom royalty.  Every quantum interaction, every quantum measurement, a countless infinity of which happen every day in what we conventionally call the universe, leads to multiple new universes.

According to Bryce DeWitt in Quantum Mechanics and reality,

“…every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself.”

Cloning and quantum teleportation Star Trek-style should be a breeze if quantum mechanics allows cloning the entire universe a countless number of times each second!  This may make for interesting and fun science fiction, but without testable predictions it is not physics.

This multiverse evolves in a continuous and deterministic way.  The apparent randomness that an observer in a particular universe (branch) perceives is in his/her mind; a consequence of the particular branch he/she finds him/herself in.  The emergence of macroscopic uniqueness, a consequence of state vector collapse in the CI, is just an illusion in the MWI.  That sounds like progress, right?  But wait.

## There’s More

The different branches are incoherent; they do not interfere with each other and observers in one branch cannot detect the existence of any of the other branches (this is the “no-communication” hypothesis).  The wave function collapse hypothesis has been replaced by the no-communication hypothesis.  Quantum decoherence has been used to justify and explain the no-communication hypothesis, with varying success.  But, it has also been used to justify and explain the wave function collapse hypothesis.  So there is nothing gained here by postulating a countless number of universes branching out from all of the interactions occurring throughout our universe.

As John Bell stated (while writing about the MWI, see p. 133 of Speakable and Unspeakable in Quantum Mechanics):

“Now it seems to me that this multiplication of universes is extravagant, and serves no real purpose in the theory, and can simply be dropped without repercussions.”

# Probabilities in the Many Worlds Interpretation

Everett sets out to show that the Born probability rule can be derived from within his model, as opposed to having to assume it.  He does this by assuming that the square of the amplitudes (from the state vector, same values that the Born rule uses) represent the ‘measure’ that should be assigned to each of the branches.  When an observer repeats the same experiment a large number of times, multiple branches appear corresponding to each of the possible outcomes for each performance of the experiment.  A particular observer will traverse a particular series of branches out of all the possible combinations of outcomes from all the trials.  By applying his weighting scheme, Everett shows that, in most cases, the observer is part of a branch where the relative frequency of the observed results agrees with the Born rule.

What exactly does it mean for different branches to have different weights, if each and every branch is ‘equally real’?  Are we to assume that the number of realizations of branches associated with a particular outcome of a particular measurement or interaction is proportional to the branch weight?  You may naively think that the probabilities of various outcomes should be related to the number of branches with that outcome (a simple counting measure).  What would then happen if the probability was an irrational number?  Combinatorial methods fail.  Even if you could use simple combinatorial methods, many observers would see outcome distributions that conflict with the Born rule.  The Born probability rule has been validated in countless experiments over the past 87 years.  Why have we never witnessed a deviation from it in any of the uncountable combinations of branches we have traversed to get where we are today?

In Everett’s theorem, the observer is considered as a purely physical system.  This is a central part of his relative state formulation.  The observer is just one subsystem in the overall system under consideration.  Once one state is chosen for one part of the overall system, then the rest of the system is in a relative state; state X given that the one subsystem is in state Y.  This was, initially, an advantage of the MWI compared to the CI. However, attempts to patch some of the holes in the theory have relied heavily on rational decision theory and game theory, thrusting a conscious observer back into the spotlight.

## Throwing in Rational Decision Theory and Game Theory

Unfortunately, Everett’s approach to deriving the Born rule has been taken apart due to its use of circular reasoning.  David Deutsch used decision theory and game theory to derive the Born rule; see Quantum Theory of Probability and Decisions.  He demonstrated that if the amplitude squared measure is applied to each branch, then this value is also the probability measure for those branches.  He did this by arguing that it represents the preferences of a rational agent.  He considered the behavior of a rational decision maker who is making decisions about future quantum measurements.  By rational, he meant that the decision maker’s preferences must be transitive: if he/she prefers A to B, and B to C, then he/she must also prefer A to C.  (On a side note – many psychology studies have shown that personal preferences of so-called rational agents in the macro world are often not transitive).

According to Deutsch, if a rational decision maker believes all of quantum theory with the exception of assuming a probability postulate, he/she necessarily will make decisions (behave) as if the canonical probability rule is true.  I am not an expert on decision theory, but it seems to me that the strategy chosen by Deutsch’s rational observer is not unique; it just happens to be the one that correlates with the desired end point – the Born probability rule when the amplitude squared values are used as branch weights.  Additionally, if you accept Deutsch’s reasoning, methodology, and assumptions, I should think his results could equally well be used to demonstrate why the Born probability rule works in the CI, as well as in the MWI.

## Attempts to Make it Consistent

Many attempts to formulate a consistent and defensible version of Everett’s initial ideas have been discussed in the literature since Deutsch’s work.  Adrian Kent addresses many of them in One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation.  Kent points out some of the inconsistencies and contradictions that these attempts fall victim to, either when compared to each other or within themselves.  Given that every potential outcome is actually realized in a branch, regardless of likelihood, a rather tortured path has to be taken to explain the meaning of probability and uncertainty when applying decision theory.  Additionally, Kent is concerned by the lack of uniqueness in the assumptions and conclusions that can be made about the so-called rational decision-maker.  To apply decision theory or game theory reasoning to quantum mechanical events seems rather surreal to me.  But regardless of whether you take the approach seriously, there is little gained from it, unless you want to get extremely metaphysical about the role of consciousness. Which I do not.

# So Where Does This Leave Us With Respect to the Many Worlds Interpretation?

“…no matter how high you pile considerations upon nothing, and extend the boundaries of nothing, to nothing it must come at last”
Writings and speeches of Alvan Stewart, on slavery. Ed. by Luther Rawson Marsh. Stewart, Alvan, 1790-1849., Marsh, Luther Rawson, ed. 1813-1902.

The MWI does not deliver on its promises.  In particular, it does not solve the measurement problem unless you ignore the extra baggage that comes with the theory, such as the no communication hypothesis, the song and dance concerning rational decision theory, and the surreal role of the observer.  Nonetheless, the idea of countless multiple universes has mesmerized popular culture and theoretical physics.  The image of an infinite number of copies of ourselves, with slight variations in each universe, is quite tempting.  Some people claim that multiverses must be real because we are getting hints of one from multiple theories, including superstring theory, inflationary cosmology, and anthropic reasoning.  But each of these predictions are perched upon a mountain of assumptions.  And each posits a different cause for the multiverse.  It is not at all clear to me that satisfying the multiverse hypothesis of one model would necessarily satisfy that of the others.

The idea that the MWI is the only viable alternative to the CI is a myth.  Other viable alternatives already exist; and it is premature to assume no one will ever discover another.  These alternatives, such as de Broglie-Bohm mechanics and the Transactional Interpretation, need more work.  But at the very least, they serve as proof of concept that we should not be so eager to believe any wild idea offered to us, without evidence.  So, if you come across someone endorsing the Many Worlds Interpretation of quantum mechanics, remember the story of the Emperor’s New Clothes.  Let them know that you are aware the emperor is naked.  MWI does not provide a unique and independent derivation of probability, it does not remove the special treatment of the observer, and it replaces the collapse hypothesis with run-away multiverse branching and the no-communication hypothesis.

My upcoming posts will include:

• Discussion of hydrodynamic quantum analogues.  These experiments demonstrate how phenomenon and probability distributions normally associated only with the quantum world can be produced by macroscopic systems and classical dynamics.
• So-called weak measurements that are allowing physicists to directly measure the quantum wave function itself, and monitor its evolution.
• Introduction to de Broglie-Bohm mechanics.  Incidentally, wave function collapse does not occur in de Broglie-Bohm mechanics, and it does not require an infinite number of universes (just empty waves…).

# 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).