Book · General · Language · Media

Quantum reality, quantum worlds – new book explores quantum foundations

[“Quantum foundations” series] [Updated December 2019]

Introduction to this topic

If Murray Gell-Mann was right that Niels Bohr brainwashed a generation of physicists to accept the Copenhagen Interpretation, either his influence has waned or he didn’t do a very good job in the first place.

For in an informal poll conducted at an international meeting in 2011 on ‘quantum physics and the nature of reality’, fewer than half of the attendees professed an allegiance to Bohr’s position. True, his was still the most popular interpretation by a considerable margin. But it can hardly claim to represent a consensus.

Sixteen years previously, another show of hands had been taken by the MIT physicist Max Tegmark at a similar meeting in Maryland. The Copenhagen Interpretation triumphed on that occasion too, albeit also without a majority. But Tegmark was delighted to note that in second place was his own favoured view of quantum mechanics: the Many Worlds Interpretation (MWI).*1 – Ball, Philip. Beyond Weird (p. 288). University of Chicago Press. Kindle Edition. [*1 It’s been suggested, however, that what these polls really tell you is who organized the meeting. – Ibid (p. 360)]


Theoretical physicist Sean Carroll recently published a new book. I’ve read some of his books. His blog, podcast. Articles. He has a robust online media presence. And is skilled at promoting his new book (or has a skilled publicist). So, I’ve read several articles on different sites about his new book, as well as downloaded a Kindle sample of the book.

Here’re a few examples of articles promoting the new book, Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime.

• PBS NewsHour: YouTube video “Sean Carroll: Universe a ‘tiny sliver’ of all there is” (published on Sep 15, 2019)

The “many worlds” theory in quantum mechanics suggests that with every decision you make, a new universe springs into existence containing what amounts to a new version of you. Bestselling author and theoretical physicist Sean Carroll discusses the concept and his new book, “Something Deeply Hidden,” with NewsHour Weekend’s Tom Casciato.

• NPR: In ‘Something Deeply Hidden,’ Sean Carroll Argues There Are Infinite Copies of You (September 13, 2019) by Adam Frank, astrophysics professor at the University of Rochester

• Whatever: The Big Idea: Sean Carroll (September 12, 2019) by John Scalzi, author of the “Old Man’s War” series of novels

• Wired: Sean Carroll Thinks We All Exist on Multiple Worlds (September 10, 2019) by Sophia Chen

• New York Times: Even Physicists Don’t Understand Quantum Mechanics
Worse, they don’t seem to want to understand it
(September 7, 2019) by Sean Carroll, theoretical physicist at the California Institute of Technology

After almost a century of pretending that understanding quantum mechanics isn’t a crucial task for physicists, we need to take this challenge seriously.

I found NPR’s book review particularly interesting. That article recaps around a 100 year old debate about quantum mechanics and realism, a debate harkening back to its original seminal figures and regaining new life in the last few years after decades of what has been characterized as “shut up and calculate” successes.

There are a variety of reasons that this debate about quantum foundations – foundational questions related to quantum mechanics (QM) and quantum theory – has renewed vigor. Often cited are the rarified mathematics of current theories (particularly those pushing beyond the Standard Model), questions about the future of particle physics (viability of further discoveries by the LHC and investment in even greater colliders), and new perspectives by some modern well-known physicists.

The NPR review notes that no matter what your QM interpretation or perspective is (or take on the many popular tropes about what QM says), Carroll’s emphasis is that foundational questions be returned from the backwaters of legitimate research – whether you agree with his advocacy of the Everettian many-worlds interpretation of QM.

Carroll’s Everettian many-worlds perspective is included in his July 10, 2018, podcast “Episode 2: Carlo Rovelli on Quantum Mechanics, Spacetime, and Reality” – an interview with Carlo Rovelli. [1] Here’s an excerpt.

Carroll: But it’s not so far from mine in that part in the sense that I am an Everettian, a believer in the many worlds interpretation, at least I think that’s my favorite. I’m happy to change my mind some day down the road, but Everett himself, when he invented it in the 1950s, when he published his paper, he called it the relative state interpretation. And the point that he was trying to emphasize was that what you see is only relative to the thing seeing it. This interaction creates an impression of the measurement outcome, that is intrinsically part of the relationship between the thing that is doing the measuring and the thing that is being observed. So I think that there’s some similarity of words there.

Rovelli: Some similarities. I shouldn’t talk for you, but let me try it for one second. I think what you would add to what I say, is that you want to take a realist position where beyond that there is nevertheless a deterministic non-relational overall quantum state of the system, that we may take as the proper description of reality.

Carroll: I would like to say that, yeah …

Rovelli: Would that be so?

Carroll: Yeah, I would. I’m a realist. I can’t even imagine what it would be like to be a scientist and not be a realist about reality. [laughter] And yet I know …

Rovelli: Right, so I would like to be a realist, but less radically so. …

And so I find that if we want to be a realist about the wave function, we have … Actually, let me step back for a moment. I think, given the strangeness of quantum mechanics, any way we think it is, comes with a price. So we have options. We have a number of options, and we have been talking about two options, okay, the sort of many world interpretation, in which you have this wave function of everything, which come with a price, or the sort of strictly relational view which I described, which also come with a price. And there are others and they have their own price.

Carroll: Right, that’s right.

Rovelli: And many discussions about quantum mechanics are, “Well, which price are we ready to pay?” And the price of the relational interpretation I described is this weakening of realism. So to say, what the state of the system … Well, I don’t know, it doesn’t matter, it doesn’t have a state, it only has a state with respect to A, and it is the same with respect B, and it is the same with respect to C, and there is no solid objective, overall picture. The price of the many world interpretation, is that I have to accept …

Carroll: Many worlds.

Rovelli: In some sense all these many worlds.

Carroll: Yes, absolutely, it’s a big price, it’s a big price.

Rovelli: So it comes with an enormous ontology, a very heavy ontology, and which price do we wanna pay. In one way or the other, it contradicts our previous way of thinking of reality.

Carroll: Absolutely, and I … So I couldn’t agree more about the idea that there is a price to be paid. I could disagree a little bit about the heaviness of the ontology that is associated with many worlds, but I think that this is a good lesson, because all we need for today’s conversation is the clear fact that we have at the same time, a way to do quantum mechanics, we use quantum mechanics as physicists every day, it’s been spectacularly verified experimentally. We know how to use it, we have a recipe, we have a black box.

Rovelli: Yeah, and it works, it works fantastically well.

Carroll: And we don’t have anything close to an agreement on what it is, what the fundamentals of it really say. So that will be a wonderful thing to figure out once and for all, but maybe we don’t need to do that for the question of quantizing gravity. So just to put the puzzle, the task, in perspective, since we grew up, we human beings, as classical people, classical mechanics was invented first. It is very intuitive to us, even if pendulums and inclined planes tortured us as undergraduates, we kind of get it in a fundamental, visceral way. So we always start by thinking about systems from this classical point of view and then we quantize them, we elevate the classical description to some quantum mechanical theory. Now, presumably nature or God doesn’t work that way.

Okay, what’s my personal take on this topic? Well, I agree that quantum foundations is important. Studying philosophy (including philosophy of science) has shaped my perspective. Generally, I side more with Rovelli than Carroll on realism and QM.

Carroll is well grounded in the mathematical framework of QM, and my grasp of that is all too limited. I sometimes think that his conviction (no matter how provisional) is based on mathematics for which any explanation to “mere mortals” is problematical; so, metaphorical language misses the core of the argument.

[Carroll] And we look at and say yes, I see the worlds, there they are. I see them in my math. I don’t see them in my telescopes or microscopes.

The many-worlds interpretation focuses on the so-called measurement problem (wave function collapse), and there are many tropes which blend the terms measurement, observation, and even decision (by the PBS NewsHour) – as splitting other worlds. Carroll is careful in discussing this point, repeatedly stating that it’s an open question as to what “measurement” means (what counts as an “observation” or whether consciousness is required or not, for example). Yet, I thought that advances in understanding decoherence had diffused the problem. As Philip Ball said, “The universe is always looking.” [3]

And indeed the PBS NewsHours’ characterization that QM claims that “two objects can occupy the exact same space at the same time” is misleading. Their use of the words “object” and “exact” miss even a visualization of radio waves (EM photons) overlapping or interfering: positional and spatial concepts of waves – wavelength and superposition. Discussing wave functions is even more arcane.

[Carroll] But what is the wave function? Is it a complete and comprehensive representation of the world? Or do we need additional physical quantities to fully capture reality, as Albert Einstein and others suspected? Or does the wave function have no direct connection with reality at all, merely characterizing our personal ignorance about what we will eventually measure in our experiments?

So, Carroll talks about the measurment problem. And Rovelli’s Relational quantum mechanics replaces measurement with interaction as the way to remain a “realist about the wave function.” That is, a “property becomes concrete when two systems interact.”

You replace measurement with interaction. But to make the machine work, you have to assume that when two systems interact, the property of one system becomes actual, with respect to the other system, and not with respect to everything else. And that point is really shocking.

There are a lot of quantities in physics which are relational, we know that they are. The velocity of an object is not a property of the object. There’s no sense in which the velocity of an object is a property of the object … The velocity of an object is a property of an object with respect to another object.

So I can say that the Earth is set to velocity with respect to the Sun, but the Sun is not measuring, it’s not going out with meters and kilometers. So we use this language, measuring, and we interpret this language to say that some properties are relational. I want to be a realist about relational properties. And I want to think of reality in a realistic way … to our direct experience of reality [observables]. I see the photons coming in, I see the table being the table …

But in his book, Carroll defines his Courageous Formulation of an Austere Quantum Mechanics this way:

This minimalist approach has two aspects. First, we take the wave function seriously as a direct representation of reality, not just a bookkeeping device to help us organize our knowledge. We treat it as ontological, not epistemic. That’s the most austere strategy we can imagine adopting, since anything else would posit additional structure over and above the wave function.

Personally I am not sure about the reality of the wave function – as ontic vs. epistemic.

Wiki: “If the wave function is physically real, in some sense and to some extent, then the collapse of the wave function is also seen as a real process, to the same extent.”

Fermilab’s Don Lincoln takes on this topic in his November 18, 2019, YouTube video “What is quantum mechanics really all about?” (below). In particular, regarding the reality of the wave function and its so-called collapse.

Quantum mechanics is perhaps the most misunderstood of modern physics topics, with many counterintuitive concepts like cats being both alive and dead and with claims that something doesn’t exist until a human looks at it. In this video, Fermilab’s Dr. Don Lincoln boils quantum mechanics down to its essence and demystifies this mystifying theory.
Additional videos from Carroll’s book tour

• Chicago Humanities Festival > Sean Carroll: Many Worlds (published November 14, 2019 on YouTube)

Sean Carroll is a theoretical physicist, a professor at CalTech, and an acclaimed science writer. And there might be more than one of him. At least, that’s what his newest book Something Deeply Hidden posits. In this groundbreaking work, Carroll lays out the Many Worlds Theory, which argues that the world is constantly generating new versions of itself, each representing different outcomes of particular events. If this all sounds a bit more science fiction than science, fear not: Carroll is known for his lucid and accessible thinking, which he’ll bring to CHF as he invites us to explore the awesome and enormous possibilities contained in our universe(s). This program is presented in partnership with the Illinois Science Council. This program was recorded on November 2, 2019.
Additional critiques of Carroll’s book

• Forbes > “Many Worlds, But Too Much Metaphor” by Chad Orzel, Contributor (Sep 17, 2019)

Orzel discusses the notion of a wavefunction of the universe (“in an indescribably complex superposition”), localized superposition, probability, measurement, and decoherence.

That process of interaction with the changing state of an unknown environment gets the name “decoherence,” and it’s what enables the bookkeeping trick that lets us split off pieces of the wavefunction and consider them in isolation. If the piece you’re interested in is big enough and interacts with the environment strongly enough, there’s no hope of doing the interference measurement that would show it’s in a superposition state. If you can’t do a measurement that would show the existence of the other piece(s) of the superposition, you can safely treat it as being in a single definite state.

Orzel sees the math much as Carroll does. But he concludes that the typical language in which the Many-Worlds Interpretation (MWI) is cast takes us down a counterproductive rabbit hole (much like the “rubber sheet” analogy for spacetime curvature in General Relativity). As mere mortals, we tend to become enchanted with a vivid metaphor – too literally – because the mathematics is so impenetrable.

As Philip Ball says in his book: “The Many Worlds Interpretation denies language, but gets away with it because language has a notorious capacity to express things that appear to have meaning yet do not. – Ball, Philip. Beyond Weird (p. 360). University of Chicago Press. Kindle Edition.

Orzel suggests an alternative perspective on “an otherwise incomprehensibly vast wavefunction.”

I actually like the start of Carroll’s presentation quite a bit, where he casts MWI as “Austere Quantum Mechanics,” with the only postulates being that the universe is described by a wavefunction, and that the wavefunction evolves according to the Schrödinger equation.

The problem is that after that austere beginning, Carroll dives back into the somewhat baroque metaphor that’s grown up around the simple initial idea, talking at great length about branches of the wavefunction that contain copies of everything in the universe that differ only in the results of particular measurements. This language is really an additional interpretive superstructure on top of the actual austerity of MWI, an extended metaphor for the experience of observers within the theory. It’s also where everything goes wrong, from the standpoint of communication.

Talking about “parallel worlds” or even “branches of the wavefunction” as real separate things invites a whole bunch of questions that are really about the metaphor, not the theory, and thus ultimately unproductive.

Thinking about MWI in this way – as a bookkeeping trick to simplify an otherwise incomprehensibly vast wavefunction – clears up most of the typical objections that arise from taking the “separate worlds” metaphor too literally. There’s no “Occam’s Razor” problem because there’s only one wavefunction obeying one set of rules. There’s no issue with “creating copies” of everything, because there are no copies: there’s one universe, with one set of components described by one wavefunction. It’s not even a problem that the criteria for “splitting” are kind of nebulous, because it’s clear that it’s a fundamentally arbitrary process – the choice of which pieces to isolate and discuss is purely a matter of bookkeeping convention for the convenience of puny human physicists.

So, that’s my argument for why the way we talk about the Everettian interpretation of quantum mechanics sucks, and should be revisited. Please note that I’m not saying that Sean Carroll or any of the other super-smart people who spend time and energy thinking about and working with MWI are Doing It Wrong in terms of the physics – mathematically, thinking of the different pieces we can carve out of the giant wavefunction of the universe as separate branches works perfectly well. That’s how you keep the books. All I’m arguing is that, on a conceptual level and in terms of the language used to communicate to non-experts, we should do a better job of making clear that it is just bookkeeping.

Rather than “Many-Worlds Interpretation,” I’d go with “Metaphorical Worlds Interpretation,” to reflect the fact that all the different ways of cutting up the wavefunction into sub-parts are fundamentally a matter of convenience, a choice to talk about pieces of the wavefunction as if they were separate, because the whole is too vast to comprehend.

• Quanta Magazine > “Why the Many-Worlds Interpretation Has Many Problems” by Philip Ball (October 18, 2018) > The idea that the universe splits into multiple realities with every measurement has become an increasingly popular proposed solution to the mysteries of quantum mechanics. But this “many-worlds interpretation” is incoherent, Philip Ball argues in this adapted excerpt from his new book Beyond Weird.

Ball’s article recaps the history of the Many-Worlds Interpretation (vs. multiverse hypothesis), with references to Bohr, Everett, DeWitt, Deutsch, Greene, Vaidman, Wallace … And how to characterize the breakdown of superpositions – as separations, splits, parallels, alternative outcomes, bifurcations, copies, etc. And how the theory of decoherence “helped to revitalize the MWI by supplying a clear rationale for what previously seemed a rather vague contingency.”

But he then notes that MWI’s theoretical austerity (“parsimony of assumptions”) does not banish conceptual and metaphysical problems.

My own view is that the problems with the MWI are overwhelming — not because they show it must be wrong, but because they render it incoherent. It simply cannot be articulated meaningfully.

As Carroll does in his book tour (as in the Chicago Humanities Festival video from November 2019), Ball distinguishes between weak objections to MWI and strong ones. The better objections include:

• The insouciance with which MWI is cast – the casual egalitarianism of each of an infinty of infinte atomic quantum “measurements” (and the weighting of all those countless “Butterfly effects” on everyday macro objects and creatures).

• The notion of self and doppelgänger tropes and consciousness: “the level of the discourse about our alleged replica selves is often shockingly shallow.”

• The interpretation of probabilities: “If all outcomes occur with 100-percent probability, where does that leave the probabilistic character of quantum mechanics?”

He concludes that: “We are not just suspended in language; we have denied language any agency. The MWI — if taken seriously — is unthinkable.”

But (as Carroll might agree), Ball notes that MWI “should be valued for forcing us to confront some tough philosophical questions.”

Additional note

The chapter “There is no other ‘quantum’ you” in Ball’s book examines the Many-Worlds Interpretation (MWI) and the Everettian vision of the entire universe as an immeasurable incomprehensible wavefunction.

As [the ‘universal wavefunction’] evolves, some of these superpositions break down, making certain realities distinct and isolated from one another. In this sense, … we should speak of the unravelling of two realities that were previously just possible futures of a single reality.

And he notes the foundational question regarding reality of mathematical constructs (akin to Plato’s theory of Forms):

• The reification of Hilbert space: “Hilbert space – the mathematical construct that contains all the possible solutions of the variables in the Schrödinger equation … is a construct – a piece of math, not a place.”

Elsewhere is his book, he writes: “… the notion of a universal wavefunction is popular with cosmologists, for the perfectly valid reason that in the earliest moments of the Big Bang the entire universe was smaller than an atom and surely needs to be considered, in that moment, a quantum-mechanical entity.”

Related posts

Quantum trajectory theory?
Feynman’s legacy – quantum originality
The future of (particle) physics?

Related pages

Online video: Perimeter Institute Lee Smolin Public Lecture “Einstein’s Unfinished Revolution” (published on Apr 18, 2019)


[1] Other podcasts by Sean Carroll:

  • Episode 63 Solo: Finding Gravity Within Quantum Mechanics, September 9, 2019
  • Episode 59 Adam Becker on the Curious History of Quantum Mechanics, August 12, 2019
  • Episode 55 A Conversation with Rob Reid on Quantum Mechanics and Many Worlds, July 15, 2019
  • Episode 36 David Albert on Quantum Measurement and the Problems with Many-Worlds, March 4, 2019
  • Episode 31 Brian Greene on the Multiverse, Inflation, and the String Theory Landscape, January 28, 2019

[2] From Carroll’s Research overview page:

These days my physics research is a bit different, focusing on two big themes. The first theme is the foundations of quantum mechanics, especially connections to cosmology and emergent spacetime. I’m a proponent of the Everett (“many-worlds”) approach to quantum mechanics. It’s a great theory, but raises a number of questions to which the answers are not yet clear, including the origin of probability and how the furniture of our semi-classical world (space, time, fields) emerges from an underlying wave function in Hilbert space. 

[3] Wiki: Quantum decoherence

However, decoherence by itself may not give a complete solution of the measurement problem, since all components of the wave function still exist in a global superposition, which is explicitly acknowledged in the many-worlds interpretation. All decoherence explains, in this view, is why these coherences are no longer available for inspection by local observers. To present a solution to the measurement problem in most interpretations of quantum mechanics, decoherence must be supplied with some nontrivial interpretational considerations (as for example Wojciech Zurek tends to do in his existential interpretation). However, according to Everett and DeWitt, the many-worlds interpretation can be derived from the formalism alone, in which case no extra interpretational layer is required.

[4] Wave-particle duality

Published Aug 20, 2012 for other animations and explanations about quantum physics
Realisation Data-Burger, scientific advisor: J. Bobroff, with the support of : Univ. Paris Sud, SFP, Triangle de la Physique, PALM, Sciences à l’Ecole, ICAM-I2CAM
Copyright Bobroff 2012

[5] Quantum superposition of states and decoherence

Published Jun 19, 2019
See other animations at
Animations produced by the research groupe with support of labex PALM.
Schrödinger's cat
Credit: CC0 Public Domain > “Deconstructing Schrödinger’s cat” by Springer (February 14, 2020)
The idea of linking quantum collapse to gravity has already been proposed by the great English physicist and philosopher Roger Penrose, but he never developed his ideas into a complete theory. Laloë proposes a model that goes in the same direction, agrees with physical observations and may one day prove testable experimentally.

16 thoughts on “Quantum reality, quantum worlds – new book explores quantum foundations

  1. Scientific American > Quantum Physics May Be Even Spookier Than You Think – A new experiment hints at surprising hidden mechanics of quantum superpositions by Philip Ball (May 21, 2018)

    It is the central question in quantum mechanics, and no one knows the answer: What really happens in a superposition – the peculiar circumstance in which particles seem to be in two or more places or states at once? Now, in a new paper a team of researchers in Israel and Japan has proposed an experiment [using photons] that could finally let us say something for sure about the nature of this puzzling phenomenon.

    For decades researchers have stalled at this apparent impasse. They cannot say exactly what a superposition is without looking at it; but if they try to look at it, it disappears. One potential solution – developed by Elitzur’s former mentor, Israeli physicist Yakir Aharonov, now at Chapman University, and his collaborators—suggests a way to deduce something about quantum particles before measuring them.

    Now Elitzur and Cohen have teamed up with Okamoto and Takeuchi to concoct an even more mind-boggling experiment. They believe it will enable researchers to say with certainty something about the location of a particle in a superposition at a series of different points in time – before any actual measurement has been made.

    So, that was in 2018. What happened?

  2. A spin in the mix of art and science …

    In the realm of fictional novels and literary worlds, this Open Culture article from 2014 discusses famous author Philip K. Dick‘s view of many worlds in his novels and personal experience: Philip K. Dick Theorizes The Matrix in 1977, Declares That We Live in “A Computer-Programmed Reality” (February 3rd, 2014). The article contains an edited video of a 1977 interview.

    The Man in the High Castle may be Dick’s most straightforwardly compelling illustration of the experience of alternate realties, but it is only one among very many. In an interview Dick gave while at the high profile Metz science fiction conference in France in 1977, he said that like David Hume’s description of the “intuitive type of person,” he lived “in terms of possibilities rather than in terms of actualities.”

    In the interview, Dick roams over so many of his personal theories about what these “unexpected things” signify that it’s difficult to keep track. However, at that same conference, he delivered a talk titled “If You Find This World Bad, You Should See Some of the Others” (in edited form [video] above), that settles on one particular theory – that the universe is a highly-advanced computer simulation. (The talk has circulated on the internet as “Did Philip K. Dick disclose the real Matrix in 1977?”).

    Dick goes on to describe the visionary, mystical experiences he had in 1974 after dental surgery, which he chronicled in his extensive journal entries (published in abridged form as The Exegesis of Philip K. Dick) and in works like VALIS and The Divine Invasion. As a result of his visions, Dick came to believe that “some of my fictional works were in a literal sense true,” citing in particular The Man in the High Castle and Flow My Tears, The Policeman Said, a 1974 novel about the U.S. as a police state – both novels written, he says, “based on fragmentary, residual memories of such a horrid slave state world.” He claims to remember not past lives but a “different, very different, present life.”

    YouTube video
    Title: Philip K Dick – SIMULATION THEORY
    Published on Jul 11, 2017
    Channel: Were We Lied To

    [Description] One of the oldest videos we have been able to find discussing the possibility that our reality is a simulated one. Fascinating video for sure.

    As noted in Wiki:

    Dick’s stories typically focus on the fragile nature of what is real and the construction of personal identity. … [As noted by Charles Platt,] “A protagonist may find himself living out another person’s dream, or he may enter a drug-induced state that actually makes better sense than the real world, or he may cross into a different universe completely.”

    Carroll mentioned that personal identity is an issue with the many-worlds interpretation.

  3. On September 21, 2019, Sean Carroll added a post to his blog: “The Notorious Delayed-Choice Quantum Eraser.” The post is sort of an appendix to his new book. He discusses an alternative double-slit experiment (the experiment which Feynman characterized as the “heart of quantum mechanics”).

    As Wiki notes, the delayed-choice quantum eraser experiment, first performed in 1999, investigates a paradox.

    The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

    In the basic double-slit experiment, … The emergence of an interference pattern suggests that each particle passing through the slits interferes with itself, and that therefore in some sense the particles are going through both slits at once. This is an idea that contradicts our everyday experience of discrete objects.

    Detecting through which slit a photon goes – the which-way experiment – results in no interference pattern. “This which-way experiment illustrates the complementarity principle that photons can behave as either particles or waves, but not both at the same time.”

    However, in 1982, Scully and Drühl … proposed a “quantum eraser” to obtain which-path information without scattering the particles or otherwise introducing uncontrolled phase factors to them. Rather than attempting to observe which photon was entering each slit (thus disturbing them), they proposed to “mark” them with information that, in principle at least, would allow the photons to be distinguished after passing through the slits. Lest there be any misunderstanding, the interference pattern does disappear when the photons are so marked. However, the interference pattern reappears if the which-path information is further manipulated after the marked photons have passed through the double slits to obscure the which-path markings.

    Wiki also notes the recent use of entangled photons: “in order to avoid any possible ambiguity concerning the quantum versus classical interpretation, most experimenters have opted to use nonclassical entangled-photon light sources to demonstrate quantum erasers with no classical analog.”

    Furthermore, use of entangled photons enables the design and implementation of versions of the quantum eraser that are impossible to achieve with single-photon interference, such as the delayed-choice quantum eraser, …

    While the result of the delayed-choice quantum eraser is similar to that of the basic double-slit experiment, the significance is harder to understand. There’s more logic involved in decoding the data. The experiment uses entangled “signal” and “idler” photons. More photon paths – more beam splitters and detectors. And a coincidence counter which helps filter – “pull out” (recover) the interference (pattern) from – the photon mixture.

    … what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler [photon] was not made until 8 ns after the position of the signal photon had already been measured by [detector] D0. … interference at D0 is determined by whether a signal photon’s entangled idler photon is detected at a detector that preserves its which-path information (D3 or D4), or at a detector that erases its which-path information (D1 or D2). … an interference pattern may only be pulled out for observation after the idlers have been detected (i.e., at D1 or D2).

    I liked Carroll’s blog post. His short story of the (thought) experiment is crisper than Wiki’s discussion (above). He uses entangled “traveling” and “recorder” photons. And quantum state Ψ notation.

    The post helped me understand his many-worlds stance better. Connecting interference, bookended entanglement, and decoherence. (He says, “Entanglement of any sort kills interference.”)

    There was secretly interference hidden in what initially looked like a featureless smudge.

    There’s a temptation, reinforced by the Copenhagen interpretation, to think of an electron as something “with both wave-like and particle-like properties.” If we give into that temptation, it’s a short journey to thinking that the electron must behave in either a wave-like way or a particle-like way when it passes through the slits, and in any given experiment it will be one or the other.

    All of these temptations should be resisted. The electron is simply part of the wave function of the universe. It doesn’t make choices about whether to be wave-like or particle-like.

    There’s no need to invoke retrocausality to explain the delayed-choice experiment. To an Everettian, the result makes perfect sense without anything traveling backwards in time. The trickiness relies on the fact that by becoming entangled with a single recording spin rather than with the environment and its zillions of particles, the traveling electrons only became kind-of decohered.

    It’s refreshing to see Carroll use some visuals (tables and diagrams) in chapter one of his book to characterize the differences between classical and quantum physics. Maybe a visualization of an identical simple system for each set of rules? – using modern measuring apparatuses in each case.

    Certainly the so-called measurement problem is important. Even more interesting for me is the evolution of physics from (1) a mechanics of the time evolution of positions & velocities of macroscopic objects responding to “forces” to (2) that of positions & momentum of objects responding to energy dynamics to (3) that of energy wave functions which yield probabilistic measurements.


    Wiki > Delayed-choice quantum eraser

    Wiki > Complementarity (physics)

    Wiki > Laplace’s demon

    Wiki > Wave function collapse

  4. And speaking of the double-slit experiment as witness to the “heart of quantum mechanics” (Feynman), here’s another article by Paul Sutter: “Is It a Wave or a Particle? It’s Both, Sort Of” (September 30, 2019). The article has some useful visualizations.

    Image: Light behaves as both particles and waves at the same time, and scientists have been able to observe this duality in action using an ultrafast electron microscope. The wave nature is demonstrated in the wavy upper portion, while the particle behavior is revealed below, in the outlines showing energy quantization. (Image: © Fabrizio Carbone/EPFL)

    Video: Is light a wave or a particle?

    Video: The Mysterious quantum nature of light survives space trips [delayed-choice experiment in space]

    Video: Is matter a wave or a particle?

    Sutter recaps the essential notions of a particle and a wave. A particle is a localized object which can “bounce” off other objects. A wave is not localized – it’s spread out. Waves wiggle and interfere with each other rather than bounce off each other. “Both waves and particles are described by very, very different sets of mathematical equations.”

    So, different kinds of physics experiments were revealing different kinds of properties of light. Sometimes, light acted like a wave, and sometimes, light acted like a particle. Which was it? The answer is that it’s both.

    Then Louis de Broglie proposed that matter particles have a wavelength. And later the double-slit experiment with an electron beam exhibited interference. [1]

    In the deep mathematics of quantum mechanics, an electron (an electron’s wave function) is “a [delocalized] wave of probability representing all the possible places where a particle might be the next time we go looking for it” or “a cloud of where it might be” – something which can interfere with itself (as in the double-slit experiment).

    Sutter jokes about being careful not to throw ourselves through narrow slits. But he doesn’t discuss the experiments which research how far we can go with the size of particles in double-slit experiments, as noted in my comment about 2000-atom molecules. That limit is being explored.

    Why can’t we beam golf balls, baseballs, tennis balls, etc., and demonstrate interference?

    The Wired article hints at the difficulty of maintaining the molecules in a coherent state. Tricky.

    “It’s surprising that this works in the first place,” says Timothy Kovachy of Northwestern University, who was not involved in the experiment. It’s an extremely difficult experiment to pull off, he says, because quantum objects are delicate, transitioning suddenly from their wavelike state to their particle-like one via interactions with their environment. The larger the object, the more likely it is to knock into something, heat up, or even break apart, which triggers these transitions. To maintain the molecules in a wave-like state, the team clears a narrow path for them through the tube, like police cordoning off a parade route. They keep the tube in a vacuum and prevent the entire instrument from wobbling even the slightest bit using a system of springs and brakes. The physicists then had to carefully control the molecules’ speed, so they don’t heat up too much. “It’s really impressive,” says Kovachy.

    And if the wavelength is too small to measure:

    Related post > Eigen what?

    [3] At the macroscopic level, every object (rather than a dynamic system of objects) may be viewed as in its own “eigenstate.” A baseball, for example, is in a state of composite quantum decoherence. All its (emergent) properties appear definite. No quantum behavior is observable — there are no coherent aggregates (as in lasers and superconductors). And the de Broglie wavelength of a baseball is too small to ever measure (~10^–34 m).


    [1] And the whole basis of modern transmission electron microscopes in fact depends on the waviness of electrons (so-called point particles) – that the wavelength of electrons is smaller than light.

    Wiki >

    Transmission electron microscopes are capable of imaging at a significantly higher resolution than light microscopes, owing to the smaller de Broglie wavelength of electrons. This enables the instrument to capture fine detail—even as small as a single column of atoms, which is thousands of times smaller than a resolvable object seen in a light microscope.

    Wiki > Matter wave

    Schrödinger’s quantum mechanical waves are conceptually different from ordinary physical waves such as water or sound. Ordinary physical waves are characterized by undulating real-number ‘displacements’ of dimensioned physical variables at each point of ordinary physical space at each instant of time. Schrödinger’s “waves” are characterized by the undulating value of a dimensionless complex number at each point of an abstract multi-dimensional space, for example of configuration space.

    Wiki > Quantum coherence

    In quantum mechanics, all objects have wave-like properties (see de Broglie waves). For instance, in Young’s double-slit experiment electrons can be used in the place of light waves. Each electron’s wave-function goes through both slits, and hence has two separate split-beams that contribute to the intensity pattern on a screen. … This ability to interfere and diffract is related to coherence (classical or quantum) of the waves produced at both slits.

  5. And here’s perhaps the source of the image at the top of Sutter’s article (noted in my previous comment): LiveScience > “Image Captures Light’s Spooky Dual Nature for 1st Time” by Tia Ghose (March 3, 2015).

    Image caption: A clever technique and an ultrafast electron microscope have caught an image of light behaving as both particle and wave at the same time. Here, the wave nature is demonstrated in the wavy upper portion, while the particle behavior is revealed below, in the outlines showing energy quantization.(Image: © Fabrizio Carbone/EPFL)

    It’s a fascinating image indeed. I’d need to read commentary on the original journal article to understand LiveScience’s description of the experiment (below).

    “This experiment demonstrates that, for the first time ever, we can film quantum mechanics — and its paradoxical nature — directly,” study co-author Fabrizio Carbone, a researcher at the École Polytechnique Fédérale de Lausanne in Switzerland, said in a statement.

    To catch this particle-wave duality in real time, Carbone and his colleagues shot a beam of laser light at charged electrons inside a nanoscale wire, giving the charged particles a boost in energy. This energy bump caused the particles to vibrate, which, in turn, created an electromagnetic field that forced the light to go back and forth along the wire.

    When the two waves traveling in opposite directions collided, they formed a stationary wave.

    From there, the research team fired electrons at the wire. As the electrons approached the wire, the electrons bumped into the light particles, or photons, in the standing wave, which then changed the speed of the electrons. But the photons changed speed (sped up or slowed down) in finite amounts called quanta or “packets” of energy, according to the statement. These packets of energy show that the light was acting as a particle.

    Because the whole interaction was caught in images by an ultrafast electron microscope, the lightning-quick changes in electron speed were captured in real time.

    The findings were published yesterday (March 2, 2015) in the journal Nature Communications.

    [Question: The photons changed speed?]


    Wiki > Wave–particle duality

    In fact, the modern explanation of the uncertainty principle … depends even more centrally on the wave nature of a particle. Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a “pulse” wave traveling down a string, particles do not have perfectly precise momenta that corresponds to the inverse of wavelength. Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength, and thus momentum. And conversely, when momentum, and thus wavelength, is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.

  6. Last month, in another article promoting his new book, Sean Carroll discussed probability and how that concept is used in quantum mechanics.

    Quanta Magazine > “Where Quantum Probability Comes From” by Sean Carroll, Contributing Columnist (September 9, 2019) > There are many different ways to think about probability. Quantum mechanics embodies them all.

    Laplace’s demon [as portrayed in A Philosophical Essay on Probabilities (1814) by Pierre-Simon Laplace] was never supposed to be a practical thought experiment; the imagined intelligence would have to be essentially as vast as the universe itself. And in practice, chaotic dynamics can amplify tiny imperfections in the initial knowledge of the system into complete uncertainty later on. But in principle, Newtonian mechanics is deterministic.

    Researchers continue to argue over the best way to think about quantum mechanics. There are competing schools of thought, which are sometimes referred to as “interpretations” of quantum theory but are better thought of as distinct physical theories that give the same predictions in the regimes we have tested so far. All of them share the feature that they lean on the idea of probability in a fundamental way. Which raises the question: What is “probability,” really?

    Like many subtle concepts, probability starts out with a seemingly straightforward, commonsensical meaning, which becomes trickier the closer we look at it.

    The “objective” or “physical” view treats probability as a fundamental feature of a system, the best way we have to characterize physical behavior. An example of an objective approach to probability is frequentism, which defines probability as the frequency with which things happen over many trials, as in … coin-tossing …

    Alternatively, there are “subjective” or “evidential” views, which treat probability as personal, a reflection of an individual’s credence, or degree of belief, about what is true or what will happen. … Bayesians [as an example] imagine that rational creatures in states of incomplete information walk around with credences for every proposition … In contrast with frequentism, in Bayesianism it makes perfect sense to attach probabilities to one-shot events, …

    Quantum mechanics as it is currently understood doesn’t really help us choose between competing conceptions of probability, as every conception has a home in some quantum formulation or other.

    Each of these [conceptions of probability] represents a way of solving the measurement problem of quantum mechanics.

    Dynamical-collapse theories offer perhaps the most straightforward resolution to the measurement problem. They posit that there is a truly random component to quantum evolution, according to which every particle usually obeys the Schrödinger equation, but occasionally its wave function will spontaneously localize at some position in space. … All the particles in a large system will be entangled with each other, so that when just one of them localizes in space, the rest are brought along for the ride [so, no superpositioned Schrödinger’s cat].

    Dynamical-collapse theories fit perfectly into an old-fashioned frequentist view of probability. What happens next is unknowable, and all we can say is what the long-term frequency of different outcomes will be. Laplace’s demon wouldn’t be able to exactly predict the future, even if it knew the present state of the universe exactly.

    pilot-wave theories bring us back to the clockwork universe of classical mechanics, but with an important twist … It characterizes our knowledge, …

    many-worlds … is my personal favorite approach to quantum mechanics [Carroll: the simplest formulation of all the alternatives.], but it’s also the one for which it is most challenging to pinpoint how and why probability enters the game.

    In many-worlds, we can know the wave function exactly, and it evolves deterministically. There is nothing unknown or unpredictable. Laplace’s demon could predict the entire future of the universe with perfect confidence.

    An answer [as to how probability is involved in this view] is provided by the idea of “self-locating,” or “indexical,” uncertainty. [Carroll: Self-locating uncertainty is a different kind of epistemic uncertainty from that featured in pilot-wave models. … it requires a bit of work to convince yourself that there’s a reasonable way to assign numbers to your belief.]

    … the wave function branches incredibly fast, on timescales of 10−21 seconds or less. That’s far quicker than a signal can even reach your brain. [In the many-worlds view] there will always be some period of time when you’re on a certain branch of the wave function, but you don’t know which one.

    Can we resolve this uncertainty in a sensible way? Yes, we can, as Charles Sebens and I have argued, … Sebens and I needed to make a new assumption, which we called the “epistemic separability principle”: Whatever predictions you make for experimental outcomes, they should be unaltered if we only change the wave function for completely separate parts of the system.


    Born rule

    The Born rule is one of the key principles of quantum mechanics.


    Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

    The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses. That is to say, propositions whose truth or falsity is uncertain. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability.

  7. And following up Carroll’s article on quantum mechanics and probability is this article on probability for mere mortals.

    Towards Data Science > “Probability Theory 101 for Dummies like Me” by Sangeet Moy Das (Oct 13, 2019)

    In the Classical interpretation Probability is the measure of the likelihood that an event will occur in a Random Experiment; In other words, the frequency of the event occurring.

    Probability is often associated with at least one event. This event can be anything. Toy examples of events include rolling a die or pulling a colored ball out of a bag. In these examples the outcome of the event is random (you can’t be sure of the value that the die will show when you roll it), so the variable that represents the outcome of these events is called a random variable …

    The article discusses these concepts:

    Probability (as likelihood in tossing a coin, expressed as percents or fractions).

    Probability (frequentist) – frequencies of outcomes in large samples or repeated trials over time.

    Probability (subjective) – a measure of belief.

    Random variable – a variable whose value is determined by chance (typically within some range of values).

    Discrete random variable – a random varible whose values are specific and countable and not continuous, e.g., the outcome of a coin toss is either 0 (tails) or 1 (heads). Values are quantized.

    Continuous random variable – values can vary continuously, so that probabilities can be related to the area under the curve of a probability density function.

    Sample space – the collection of all possible outcomes.

    Complement – the probability of the complement of A includes the sum of all probabilities in the sample space that is not A.

    Mutually exclusive events (disjoint events).

    Independent events.

    Dependent events.

    And the rules or axioms of probabiity (sometimes using a deck of cards and lastly a game of Roulette):

    The range of probabilties and summation of those outcomes.

    Arithmetic on probabiities.

    The Law of Large Numbers.

    The types of probability: marginal, joint (cf. Venn Diagram), conditional.

    Bayes’ Theorem (for conditional probabilities).

    And the article closes with a discussion of the difference between probability and statistics.

    Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.

    Probability is primarily a theoretical branch of mathematics, which studies the consequences of mathematical definitions. Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world.

    This distinction will perhaps become clearer if we trace the thought process of a mathematician encountering his first craps game:

    If this mathematician were a probabilist, he would see the dice and think, “Six-sided dice? Presumably, each face of the dice is equally likely to land face up. Now assuming that each face comes up with probability 1/6, I can figure out what my chances of crapping out are.”

    If instead, a statistician wandered by, he would see the dice and think, “Those dice may look OK, but how do I know that they are not loaded? I’ll watch a while, and keep track of how often each number comes up. Then I can decide if my observations are consistent with the assumption of equal-probability faces. Once I’m confident enough that the dice are fair, I’ll call a probabilist to tell me how to play.’’

    In summary, probability theory enables us to find the consequences of a given ideal world, while statistical theory enables us to measure the extent to which our world is ideal.

    Frequentist vs. Bayesian View

    One thing that is worth mentioning is that in the introduction of this post I made a statement regarding the classic interpretation of probability. Specifically, this classic interpretation is referred to as the frequentist view of probability. In this view, probabilities are based purely on objective, random experiments with the assumption that given enough trials (long-run) the relative frequency of event x will equal to the true probability of x. Notice how all of the probabilities we reported in this post were based purely on the frequency.

    If you’ve done any statistics or analytics, you’ll likely have come across the term Bayesian statistics. In brief, Bayesian statistics differ from the frequentists view in that it incorporates subjective probability which is the degree of belief in an event. This degree of belief is called the prior probability distribution and is incorporated along with the data from random experiments when determining probabilities.

  8. Regarding Chad Orzel’s Forbes September 17, 2019, article noted above, here’s an excerpt from his earlier September 11, 2019, article:

    Forbes > “What I Was Wrong About In Physics” by Chad Orzel Contributor (Sep 11, 2019)

    Probably the most significant shift in my thinking about physics, specifically, is that these days I have a much more positive opinion of the Many-Worlds Interpretation of quantum physics. I don’t know that I would officially declare myself an Everettian – I’m still more of a “Shut Up and Calculate” guy by temperament – but I can see the appeal now in ways that I didn’t before.

    What changed my mind was writing a book on quantum physics, in which I necessarily had to talk about this question. In looking more closely at Many-Worlds, I saw that most of the problems I had with it were actually problems created by taking an analogy too literally. My view now is much more like that expressed by Sean Carroll in a talk at the March Meeting (and presumably in his new book, though I haven’t had a chance to read it yet): at bottom, Many-Worlds is just taking the Schrödinger equation seriously. The “parallel universe” language is just an analogy – there’s only one universe, with every particle existing in a complicated superposition of multiple states, entangled with all sorts of other particles in their own complicated superposition, but for bookkeeping purposes, we can treat some sub-parts of that universal wavefunction as separate universes. Almost every objection that people raise to Many-Worlds is rooted in the misconception that the separate universes are real, physical things, rather than a mathematical convenience.

    In a related development, I have become more convinced that research on the foundations of quantum physics is a worthwhile pursuit. Twenty-ish years ago, I would’ve called this a quaint sideline but not especially useful, but I’ve come around to the extent of writing a blog post defending the importance of quantum foundations research. I wouldn’t say that I’m confident this will lead directly to any breakthroughs regarding the fundamental issues, but working through the implications of a variety of interpretations may be a productive way to generate ideas about stuff that can be tested.

    But I’m not sure Carroll and Orzel are on the same page as to the reality of the wavefunction. Orzel’s statement:

    Almost every objection that people raise to Many-Worlds is rooted in the misconception that the separate universes are real, physical things, rather than a mathematical convenience.

    appears contrary to what Carroll writes in his book on the matter regarding his Courageous Formulation of an Austere Quantum Mechanics:

    This minimalist approach has two aspects. First, we take the wave function seriously as a direct representation of reality, not just a bookkeeping device to help us organize our knowledge. We treat it as ontological, not epistemic. That’s the most austere strategy we can imagine adopting, since anything else would posit additional structure over and above the wave function.

  9. SciTechDaily > “Pair of Civil Servants Rewrite Quantum Mechanics in Their Spare Time” by Aalto University (January 5, 2020). > Article | Open Access | Published: 27 December 2019 > “Quantum Mechanics can be understood through stochastic optimization on spacetimes” by Jussi Lindgren & Jukka Liukkonen in Scientific Reports volume 9, Article number: 19984 (2019).

    SciTechDaily presents the background for the research paper but the paper itself is available elsewhere (as noted above).

    Lindgren & Liukkonen’s research is connected to the exploration of quantum foundations (as in Sean Carroll’s latest book); and, in particular, the debate about the ontological status of the wave equation.

    SciTechDaily summarizes the story of Lindgren & Liukkonen’s dissatisfaction with certain postulates of quantum mechanics: “… you had to accept they were true without it being shown why.” And how they “devised a new method for expressing the laws of quantum mechanics using stochastic methods, a type of mathematics that deals with random chance and probability.”

    The paper, published December 27, 2019, in Scientific Reports explores how stochastic methods can be used to derive a variety of equations in quantum mechanics from first principles, as opposed to having to build from ad hoc prior postulates. “The method will be useful for teachers or learners because it gives a better understanding of the reason why something is correct,” said Jukka Liukkonen.

    The paper itself defines a fuller context for the research.

    Here’s their abstract:

    The main contribution of this paper is to explain where the imaginary structure comes from in quantum mechanics. It is shown how the demand of relativistic invariance is key and how the geometric structure of the spacetime together with the demand of linearity are fundamental in understanding the foundations of quantum mechanics. We derive the Stueckelberg covariant wave equation from first principles via a stochastic control scheme. From the Stueckelberg wave equation a Telegrapher’s equation is deduced, from which the classical relativistic and nonrelativistic equations of quantum mechanics can be derived in a straightforward manner. We therefore provide meaningful insight into quantum mechanics by deriving the concepts from a coordinate invariant stochastic optimization problem, instead of just stating postulates.

    The paper contains impenetrable mathematics beyond my ken, but the general framework is noteworthy.

    Since the inception of Quantum Mechanics (QM), there has been an on-going discussion on the ontology of the theory and its interpretations. In particular, there has been recently an intense debate on the validity of the so-called statistical interpretation of QM, see 1,2. The ontological problem of QM is manifested especially clearly in the measurement problem. Therefore, understanding the physical meaning of the wave function is paramount. To understand the wave function, one needs to understand the equations of quantum physics.

    Lindgren & Liukkonen grabbed my attention by noting the mathematical similarity of the Schrödinger equation to the ordinary diffusion equation, since I tend to explore quantum mechanics from a fluid dynamics perspective.

    And they discuss in particular how imaginary time (as in complex algebra) arises in the mathematics.


    This study shows that the imaginary nature of various variables in quantum mechanics is due to the structure of the Minkowski metric.

    In terms of future research, perhaps one should try to establish the wave equation in a general curved spacetime and thus generalise the metric into a more general form.

    … the results presented in this paper do not therefore support the interpretative thesis given by the PBR theorem, which claims to rule out the statistical interpretation of the quantum state. [1]

    … we advocate for a realistic interpretation of quantum mechanics. The model presented in this paper suggests that the test particle is moving under the influence of an external random spacetime force. This random movement of the particle induces the transition probability distribution.

    … one could make the conjecture that quantum mechanics or quantum field theory is only a phenomenological theory and the reason for the statistical nature lies within the stochastic nature of the spacetime itself.

    … this could mean in essence that the energy sources in the space-time have a random character ie. the stress-energy tensor has a random character, …

    According to the stochastic control paradigm presented in this paper, the Born rule for the test particle is related naturally to real part of the minimal expected action.

    The spacetime diffusion process takes the route which minimizes the expected action; this is the essence of how (transition) probability is tied to energy minimization. We firmly base our beliefs on the realistic philosophy of quantum mechanics, where reality exists independently of the observer. This inclination is put forward especially lucidly by Sir Karl Popper.


    [1] See also > quant-ph > arXiv:1811.01107 – “Does the PBR Theorem Rule Out a Statistical Understanding of Quantum Mechanics?” by Anthony Rizzi (Submitted on 2 Nov 2018).

    The PBR theorem gives insight into how quantum mechanics describes a physical system. This paper explores PBRs’ general result and shows that it does not disallow the ensemble interpretation of quantum mechanics and maintains, as it must, the fundamentally statistical character of quantum mechanics (QM). This is illustrated by drawing an analogy with an ideal gas. An ensemble interpretation of the Schrodinger cat experiment that does not violate the PBR conclusion is also given. The ramifications, limits, and weaknesses of the PBR assumptions, especially in light of lessons learned from Bell’s theorem, are elucidated. It is shown that, if valid, PBRs’ conclusion specifies what type of ensemble interpretations are possible. The PBR conclusion would require a more direct correspondence between the quantum state (e.g., |ψ>) and the reality it describes than might otherwise be expected. A simple terminology is introduced to clarify this greater correspondence.


    Action (physics)

    Markov chain

    Transition probability density

    Sum over all paths

    Relativistic invariance

    Minkowski spacetime, Minkowski metric

    Four-dimensional diffusion

    Metric tensor

    Planck scale

    Hamiltonian, Lagrangian

    Einstein summation

    Stueckelberg covariant wave equation

    Stochastic control scheme

    Dirac equation

    Telegrapher’s equation

    Born rule

  10. How big can an object be and still exhibit quantum behaviors? > “A New Experiment Hopes to Solve Quantum Mechanics’ Biggest Mystery” by Ramin Skibba – Physicists will try to observe quantum properties of superposition—existing in two states at once—on a larger object than ever before (February 5, 2020).

    The TEQ (Testing the large-scale limit of quantum mechanics) researchers are working to construct a device in the next year that would levitate a bit of silicon dioxide, or quartz, measuring nanometers in size—still microscopic, but much larger than the individual particles that scientists have used to demonstrate quantum mechanics previously. How big can an object be and still exhibit quantum behaviors?

    In GRW [Ghirardi–Rimini–Weber theory], microscopic particles exist in multiple states at once, known as superposition, but unlike in the Copenhagen interpretation, they can spontaneously collapse into a single quantum state. According to the theory, the larger an object, the less likely it is to exist in superposition, which is why matter on the human scale only exists in one state at any given time and can be described by classical physics.

    The scientists will … fire a laser at the quartz [suspended by an electric field and trapped in a cold, confined space, where its atomic vibrations will slow to near absolute zero] and see whether the scattering of the light shows signs of the object moving. The motion of the silicon dioxide could indicate a collapse, which would make the experiment a compelling confirmation of GRW predictions. (The theory predicts that objects of different masses have different amounts of motion related to a collapse.) If the scientists do not see the signals predicted from a collapse, the experiment would still provide valuable information about the quantum world of particles as it blurs with the classical world of everyday objects. Either way, the findings could be a quantum leap for quantum physics.


    The Ghirardi–Rimini–Weber theory (GRW; also known as spontaneous collapse theory) is a collapse theory in quantum mechanics. GRW differs from other collapse theories by proposing that wave function collapse happens spontaneously. GRW is an attempt to avoid the measurement problem in quantum mechanics. It was first reported in 1985, by Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber.

  11. Here’s a fascinating update on the double-slit experiment, noting its history and a recent innovative demonstration of interference for single atoms.

    Physics World > “Double slits with single atoms” by Andrew Murray, professor of atomic physics in the Photon Science Institute, Department of Physics and Astronomy, University of Manchester, UK (February 18, 2020) – Thomas Young’s double-slit experiment is famous for demonstrating the principle of interference. Andrew Murray explains why it’s now possible to carry out an equivalent experiment using lasers that have excited individual rubidium atoms.

    … Thomas Young performed his experiments in 1804 – long before we knew anything about electrons or the subatomic world.

    Young’s original double-slit experiments were in fact the first to demonstrate the phenomenon of interference. … These experiments, and their subsequent explanation, culminated in the classical laws of radiation enveloped by James Clerk Maxwell’s famous equations.

    Only in the 1960s did the link between Young’s double-slit experiment and wave–particle duality become clear when it was carried out for the first time with an electron beam.

    The link between Young’s experiments and wave–particle duality only became obvious last century once the basics of quantum mechanics had been firmly established …

    It was not until 2013 that the first experiments to convincingly demonstrate double-slit interference using single electrons were finally carried out …

    Our new version of Young’s double-slit experiment doesn’t involve firing particles through slits but uses lasers to excite rubidium atoms in different ways.

    If there was no interference between the two ionization pathways – as we’d expect from a classical interpretation of the ionization process – then both the interference term and the relative phase shift should be zero at all angles. But the values were not zero … This clearly demonstrated that the individual electrons emerging from each atom must therefore have a wave-like nature, until they are detected as real particles by the detector.

  12. YouTube > Sabine Hossenfelder > “The Trouble with Many Worlds” (Sep 26, 2019) – “In today’s video I want to tell you why I am not a fan of the many worlds interpretation of quantum mechanics. … It’s that I think you do not gain anything from this reinterpretation.

    (from transcript)

    We observe only one measurement outcome. The many worlds people explain this as follows. Of course you are not supposed to calculate the probability for each branch of the detector. Because when we say detector, we don’t mean all detector branches together. You should only evaluate the probability relative to the detector in one specific branch at a time.

    That sounds reasonable. Indeed, it is reasonable. It is just as reasonable as the measurement postulate. In fact, it is logically entirely equivalent to the measurement postulate.

    The measurement postulate says: Update probability at measurement to 100%. The detector definition in many worlds says: The “Detector” is by definition only the thing in one branch. Now evaluate probabilities relative to this, which gives you 100% in each branch. Same thing.

    And because it’s the same thing you already know that you cannot derive this detector definition from the Schrödinger equation. It’s not possible. What the many worlds people are now trying instead is to derive this postulate from rational choice theory.

    But of course that brings back in macroscopic terms, like actors who make decisions and so on. In other words, this reference to knowledge is equally in conflict with reductionism as is the Copenhagen interpretation. And that’s why the many worlds interpretation does not solve the measurement problem and therefore it is equally troubled as all other interpretations of quantum mechanics.

  13. Another take on the standing of key mathematical models in physics – whether representation is reality. With references to Eugene Wigner.

    When a mathematical model works so well (as an effective theory), does that mean it reflects reality?

    A model is by definition a simplification, eh? And works contextually. A practical (predictive) tool. What of bolder claims as to the nature of reality itself? So, Ptolemy-like craftsmanship or Plato-like revelation?

    • Scientific American > Math > Opinion > “Is the Schrödinger Equation True?” by John Horgan [1] (January 7, 2021)

    … how real are the equations with which we represent nature? As real as or even more real than nature itself, as Plato insisted? Were quantum mechanics and general relativity waiting for us to discover them in the same way that gold, gravity and galaxies were waiting?

    … the Schrödinger equation is far from all-powerful. Although it does a great job modeling a hydrogen atom, the Schrödinger equation can’t yield an exact description of a helium atom! Helium, which consists of a positively charged nucleus and two electrons, is an example of a three-body problem, which can be solved, if at all, only through extra mathematical sleights of hand.

    When I contemplate quantum mechanics, with all its hedges and qualifications, I keep thinking of poor old Ptolemy. We look back at his geocentric model of the solar system, with its baroque circles within circles within circles, as hopelessly kludgy and ad hoc. But Ptolemy’s geocentric model worked. It accurately predicted the motions of planets and solar and lunar eclipses.


    [1] (“About the author” blurb) John Horgan directs the Center for Science Writings at the Stevens Institute of Technology. His books include The End of Science, The End of War and Mind-Body Problems, available for free at For many years, he wrote the immensely popular blog Cross Check for Scientific American.

    Related posts

    Quantum mechanics math basics – tasting the notation

    Cosmological fact and fiction

    Eigen what?

  14. Here’s an article about preserving quantum state coherence in practical applications.

    • > “Researchers set record by preserving quantum states for more than 5 seconds” by Argonne National Laboratory (February 2, 2022)

    … researchers are still grappling with how to easily read the information held in these qubits and struggle with the short memory time, or coherence, of qubits, which is usually limited to microseconds or milliseconds.

    A team of researchers at the U.S. Department of Energy’s (DOE) Argonne National Laboratory and the University of Chicago has achieved two major breakthroughs to overcome these common challenges for quantum systems. They were able to read out their qubit on demand and then keep the quantum state intact for over five seconds – a new record for this class of devices. Additionally, the researchers’ qubits are made from an easy-to-use material called silicon carbide, which is widely found in lightbulbs, electric vehicles and high-voltage electronics.

  15. So, is representation the same as reality? Is quantum theory lost in math, as Sabine Hossenfelder says? Is there a place for a sort of nostalgic realism? A way out of the complexity and open-endedness of the Many Worlds interpretation and such?

    While Sean Carroll promotes an Austere Quantum Mechanics, this article (below) pitches a simpler foundational model – a plainer, more comprehensible connection to laws of motion for ordinary objects. But is it coherent?

    In prior posts and comments, I’ve discussed the debate over the physical interpretation of the wave function – “the central mathematical object used in quantum mechanics” [1]. The connection of the wave function with reality: whether part of an effective theory which mathematically models (approximates) the way the universe works; or as something which directly reflects those workings. The epistemic (“bookkeeping”) vs. ontic viewpoints.

    Are mathematical models free of any reduction in the nature of physical reality? Must the wave function be reified?

    This article even references Sean Carroll. And gets tangled up in entanglement.

    • Institute of Art and Ideas > “The quantum wave function isn’t real” by Eddy Keming Chen, Assistant Professor of Philosophy, University of California, San Diego, fellow of The John Bell Institute for the Foundations of Physics, recipient of the 2021 Karl Popper prize (April 29, 2022)

    The dominant interpretation of the quantum wave function sees it as real – as part of the physical furniture of the universe. Some even go as far as to argue that the entire universe is a quantum wave function.[2]

    Does quantum mechanics really reveal what exists at the fundamental level of the universe?

    What I suggest is that we stop thinking of the wave function as real, as part of physical reality, and instead interpret it as providing the basis for a simple law of nature [i.e., not a physical object, but a physical law].

    Here’re my bullets for how the article “reconsider[s] the realist interpretations of the wave function.”

    • “The space on which the wave function is defined” entails extremely high dimensions – about 10^80 (huh?).

    • As a real physical object, the wave function “leads to a surprising kind of holism” related to quantum entanglement – emergent group properties are disconnected from those of individual particles. That is, “most subsystems cannot be described by wave functions because of the phenomenon of quantum entanglement” (huh?).

    The whole is, as it were, more than its parts.

    • “Realist interpretations of the wave function seem to be in tension with Einstein’s relativity theory” via quantum entanglement’s ambiguous “way of slicing spacetime into space and time.”

    Chen then touches on information theory, the density matrix, emergent patterns, the proper conceptual “zoom” level for physical laws, and the arrow of time.

    According to the Past Hypothesis, “the universe started in a special state of very low entropy, at or near the Big Bang.” Which leads to “an attractive alternative to realist interpretations of the wave function.”

    Such a state can be characterized in relatively simple terms using macroscopic [classical] variables such as entropy, temperature, density, and volume. The Past Hypothesis, as it were, picks out the magnification level for the microscope. It strikes the perfect balance and selects just the right amount of information we need for specifying a simple and yet empirically adequate [good enough] law.

    Because of the simplicity of the Past Hypothesis, the coarse-grained pattern obtained from it can be described by a remarkably simple object. It carries much less information than a hypothetical wave function. It is sufficiently simple to be a candidate law of nature and sufficiently informative to determine the motion of ordinary objects. As a result, we do not need to reify the wave function as either a physical object or a physical law.

    Enter an idea pitched as the “Wentaculus,” which “reduces the types of randomness in the world.” And in which the wave function is one of “a collection of many different hypothetical wave functions.”

    Furthermore, the Wentaculus version of Everett’s many-worlds quantum mechanics is the first realistic and simple example of strong determinism [aha!], …

    While it includes homages to the historical debate, I find Chen’s article too abstract. As noted by a commenter, the “article is not written clearly enough to even form an opinion about it.”

    There’s a too casual use of the term particle (and no references to quantum field theory). Presentationally, key points feel blurred. There’re no visualizations of perspectives or of indicated puzzles.

    I do not see how this article advances discussion of the reality of the wave function.


    [1] See related posts and these comments, for example:

    • Quantum reality, quantum worlds – new book explores quantum foundations > December 9, 2019 and January 8, 2021.

    • Quantum mechanics math basics – tasting the notation > July 21, 2020

    [2] As mentioned above, Philip Ball notes in the chapter “There is no other ‘quantum’ you” of his book:

    “… the notion of a universal wavefunction is popular with cosmologists, for the perfectly valid reason that in the earliest moments of the Big Bang the entire universe was smaller than an atom and surely needs to be considered, in that moment, a quantum-mechanical entity.”

    Related posts

    Whence the arrow of time?

    Quantum mechanics math basics – tasting the notation

    Cosmological fact and fiction

    A universe without math?

    Effective theory

  16. This podcast with Sean Carroll re the quest for quantum gravity (cf. his latest book) includes his perspective on the wave function.

    • Quanta Magazine > “Where Do Space, Time and Gravity Come From?” by Steven Strogatz (May 4, 2022) – my note from podcast transcript.

    The wavefunction – “I think of the wavefunction as the fundamental thing … that’s what exists in reality.”

    [Getting back to the topic of emergence and connecting with quantum field theory (QFT) as a model] We just have an abstract quantum wavefunction [in an entangled canvas sans any such words like distance, or fields] and we’re asking, can we extract reality as we know it from the wavefunction? Space-time, quantum fields [including a field for gravity], all of those things, okay.

    … just our current best approximation … what seems to fit the data … because there still are fields even in empty space [abstract space, not spacetime?], you can say, is there entanglement between these two points of space? … And the answer is yes, it is always going to be entangled. … there is a relationship between the distance between two points and their amount of entanglement in the lowest-energy state of a conventional quantum field theory.

    Entanglement between different pieces of the wavefunction – a relational nodal network in Hilbert space

    … when the entanglement is strong, the distance is short. And I’m going to define something called the distance (in this big space in which the wavefunction lives). … do those nodes fit together to approximate a smooth manifold? And if you pick the right kind of laws of physics, they will.

    And then you can ask, if I perturb it a little bit, so I poke it, so it’s not in its lowest-energy state, it has a little bit of energy in it. Well, that’s going to be dynamical. That’s going to stretch space-time, that’s going to change the amount of entanglement. We can interpret that as a change in the geometry of space.

    Entangled verse

Comments are closed.