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)?
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.
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).
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.
“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”.
“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?
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.”
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.
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 usandContrary 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.
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.
“…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.
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…).
Welcome to “The Fun Is Real“, a new blog that will explore wonders and mysteries of physics. In particular, I am interested in the questions that are not yet understood. These questions may be due to new experimental evidence that out-paces the theorists, like dark matter, dark energy, neutrino anomalies, etc. Or it may be areas where the theory works, but we don’t have a conceptual understanding of how/why the universe does what it does. One example of this is quantum physics and quantum non-locality.
The predictions of quantum mechanics have been confirmed, time and time again, by experimentalists, with greater precision than any other theory in the history of physics. In the history of science, for that matter! Additionally, the engineering breakthroughs that have created our information society, and the current trajectory of our technology, are dependent upon quantum mechanics. Yet, we do not understand how the universe pulls off some of the tricks inherent in quantum physics. We don’t understand why certain things are quantized. And entangled particles seem to be able to affect each other over arbitrary distances, without regard to time. I will expand more on these issues in future blogs. I also invite your inputs and ideas on the discussions.
In addition to quantum non-locality, examples of other areas that you will see discussed here in the coming months include: (1) Given that a charged particle undergoing acceleration gives off electromagnetic radiation (i.e. emits photons), and a gravitational field is equivalent to acceleration, then why don’t charged particles emit photons simply due to being in a gravitational field? Or do they? (2) Would time exist if there were no matter? (3) Why does the universe insist upon the use of “imaginary”, or complex, numbers to communicate it’s behavior? (4) Where does inertia come from and why does gravitational mass appear to be the same as inertial mass?
I don’t accept anthropomorphic explanations. That is, I don’t accept as adequate an argument that states “we would not be here if it were not so”. That does not contribute to our understanding of the how/why of the universe. I also don’t accept “the theory has to be that way to be consistent with the evidence”. I want to understand. I want to know why. I want to know how. I want to know how a particle can impact measurements done on it’s entangled partner, in apparent violation of locality and the speed of light; not just how to do the calculations.
This is a new website. I am trying to make it interesting and accessible. Let me know if you see problems or if you have ideas to make it better. Remember, the physics may be theoretical, but “The Fun Is Real“.