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Quantum reality, quantum worlds – new book explores quantum foundations

[“Quantum foundations” series]

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 …

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.”

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)

Notes

[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
http://www.toutestquantique.fr 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 http://www.QuantumMadeSimple.com
Animations produced by the research groupe www.PhysicsReimagined.com with support of labex PALM.

7 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.

    References

    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 Space.com 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).

    Notes

    [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?]

    Reference

    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.

    References

    Born rule

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

    Bayesianism

    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.

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