I finally got done with finals, and as a reward, I decided to see if I could find a Coursera course to play with. I had been looking to see if there was a quantum computing MOOC available (and there are many), but among the search results was
Alain Aspect's Quantum Optics course on Coursera. This is, he says, the first of two MOOCs based on his textbook (at right*). It's a short course (4 weeks, basically four lectures), and so, just right for me.
The subject is interesting (and very similar to a special topics course I took as an undergraduate called "The Quantum Mechanics of the Laser"  I wish I'd kept those notes when I moved), but the lectures are dense. They do go over a lot of the material in Sakurai's Modern Quantum Mechanics*, which I worked through two summers ago, but of course with a focus on the meaning in terms of quantum optics. Already, some things I haven't heard of before, some that relate to experimental design (quantization volume), some straightforward interpretations of mathematical expressions (the energy of a single photon). The understand in terms of experimental parameters is particularly helpful to me (since I understand things in terms of experiments, due to my training).
The course, however, is not for those who are afraid of mathematics. Aspect's discussion in mathematically dense. Really dense. My students think I use too much mathematics in university physics classes, but this is all math. And Aspect expects you to have seen it all before: many times he references your prior knowledge. He doesn't quite say that you're an uneducated ignoramus if you can't recall trivialities like the photon energy or the uncertainty relations (he calls them dispersion relations, an aspect of his philosophy  it's nice to hear an expert talk explain the mechanics of physics in a way that makes it clear he has opinions). And the homework is tough. Not as tough as it sounds when you read it, but pretty tough.[1] Even on the internet, you're expected to know your stuff.
I have found that I had to speed his lectures up. I don't know if it's him, if it's because he's European, or because Coursera makes everyone speak like someone shilling their latest book in a bad TED talk, but he talks slowly. Last summer, I took Werner Krauth's MOOC,[2] from the same school but a different country, and he spoke with the same cadence. I found I had to speed up the lecture to 1.5x so that they spoke at a normal speed.
This minor technical problem aside, I certainly am enjoying the break this provides before I start preparing for my summer courses (How did I let myself get roped into summer courses? At least they're online so I can get a lot of the work out early).
[1] I didn't pay the $49.99, or whatever, it costs in order to get it graded, but I did work it. And it reinforced the advice I give to my students: try the homework before class, then the class will be more useful to you.
[2] Which was serendipitous, since I'd begun setting up to work through the book it was based on, Statistical Mechanics: Algorithms and Computation,* when Coursera sent me an email about it. I get the feeling there's as much shilling on Coursera as there is at TED talks. But it couldn't be more: a TED talk is just an advertisement for a book. If you're lucky, there's more to the book than just the TED talk. Obviously, though, there's more to a physics textbook than eight hours of lecture. Hell, there's more to a physics textbook than the forty hours of lecture in a semester.
* Note: These links are to Amazon pages. Purchases on those pages from the links will give me a commission (at least for now  every time I've tried to use the Amazon Associates program they've kicked me off for not selling anything, but I do like having the links in the show notes so that you can pick up the books we might reference in a discussion).
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Saturday, September 1, 2018
Quantum Sense and Nonsense by Jean Bricmont
I don't really know why I picked up Quantum Sense and Nonsense or when. I'm pretty sure it was in the last year when I was looking for some popular books to read after I finished The Wave Function, and this one, written by Jean Bricmont and published by Springer, stood out. The cover, and likely the description, seems a little misleading since it seems to say that the book will focus on crazy and unfounded assertions of psychic and mystical properties attributed to quantum mechanics (and as Bricmont has published with Sokal, that's exactly what you'd think), but instead the book focuses on two experiments (double slit experiments and EPRtype experiments, both of which seem to be recurring themes on Physics Frontiers) and the interpretation of each. Bricmont follows Bell in asserting that EPRexperiments like the Aspect experiment show that there is some kind of nonlocality at play in quantum mechanics and that the best way to interpret the meaning of the wave function (that is, what the wave function, itself, is) is to look toward an interpretation like the de BroglieBohm vision of the wave function (see Bell's, Speakable and Unspeakable in Quantum Mechanics).
Despite being much different than what I thought the book would be, this made the Quantum Sense and Nonsense an excellent read.
The double slit experiment as performed by Thomas Young in the first decade of the 19th century showed that coherent light from the sun interfered with itself, showing that light is, in fact, a wave  and brought about the belief in a mysterious Ether in which the light waves propagated. When Einstein showed the photoelectric effect requires quantization of light,* this made the interpretation more difficult. And de Broglie's prediction that electrons, really all material objects, have a wavelength and the subsequent discovery of electron diffraction, brought the same problem to all matter. And the interference is so strong that when a single photon or a single electron is sent through the slits, and the results of the experiments accumulated, the interference fringes are still seen. Material objects interfere with themselves.
A very strange property, and one that leads to many strange interpretations of quantum mechanics, is that if you set up a detector at one of the slits in the double slit experiment to see which slit the particle passes through, then the interference fringes will disappear. This leads to the idea that observation causes a change in the wave function, what is termed the wave function collapse. Many strange ideas come out of this, even from physicists (Bricmont's target). People use this idea to give consciousness a role in the measurement of quantum systems, Bricmont uses quotes from the following physicists to show the sloppy thinking on these points: d'Espagnat, Wheeler, and Mermin (to name only those I've heard of): they all give some role to the human mind in the collapse of the wave function. To be fair, understanding the collapse is impossible in the standard "Copenhagen" interpretation of quantum mechanics, which is what Schroedinger's cat was intended to show.
The EPR experiments, violations of Bell's theorem, are the second cause of sloppy thinking because they show one of two things: either (1) quantum mechanics is nonlocal or (2) quantum mechanics is noncausal. Those are the two assumptions that Bell uses to derive his inequalities beyond ordinary statistics and quantum theory. If you have to choose one of the two assumptions to invalidate, (1) is the more likely (although we recently published a podcast on retrocausality and Yakir Aharonov has a different version of a localitypreserving assumption, presented in his Quantum Paradoxes book as well as old papers). But once you remove locality from your assumptions about the world, people start babbling about telepathy and similar nonsense.
As befits someone of Bricmont's station, the descriptions of these experiments are exemplary, and Quantum Sense and Nonsense would be worth a read if only they were presented here. However, he does us another service by giving us a rich, logical and convincing description and defense of the de BroglieBohm pilot wave theory of quantum mechanics. In this theory, the wave and particle are broken up into two objects, an oscillation in space time that drives the motion of an otherwise deterministic particle. The randomness of quantum mechanics then ceases to be the mystical randomness associated with Bohr and Heisenberg and Copenhagen in general and becomes the deterministic randomness of statistical mechanics.** Bricmont goes so far to say that because of this and the fact that it can be mathematicised, de BroglieBohm is the only interpretation of quantum mechanics;*** the others (including statistical, Copenhagen, and manyworlds) don't meet that bar. Obviously, it doesn't mean that Bricmont is right, since he's delved into philosophy or worse in the comparison of interpretations by their linguistic characterizations, but it is a good way of thinking about the interpretations.
So I would recommend this book. I do think that it is a little too popular for most people that would read this, and he often refers to his own, more technical Making Sense of Quantum Mechanics quite a bit for more quantitative details. He also says that this is only "slightly" more rigorous and would probably point you to P. Holland's The Quantum Theory of Motion for a really rigorous treatment. I haven't read either of those two books, however, so I can't recommend them to you.

I wrote this review a little faster than I'd like because I'd just finished the book yesterday and Google sent me a "news story" on my phone today, which I read over my morning coffee. It was a rather infantile post by Luboš Motl, someone I've never heard of, who calls himself a "freelance string theorist" (but who has a reasonably impressive pedigree) reviewing books by science journalists. It makes me sad when a physicist does as bad a job of presenting science as a science journalist does.
The blog does a good job of showing two very bad ways to think about the interpretations of quantum mechanics. The first is from the book he reviews (or really, the blog post that he reviews of the book that it reviews). In that case, the science journalist author, whose name is of no importance, suggests that all interpretations are valid. This seems quite odd to me, especially when most of them are logically contradictory: if you believe in a wave function collapse, then you can't coherently believe in the universal wave function of Everett. You can make up a pretty complex and silly rationale if you want to, but it will always end up being incoherent somewhere (and I'm not going to read it to find out where). The reason you would want to hold multiple conceptions in your head is to find out places where they disagree  and then to find an experiment that distinguishes them.
Motl himself presents to us the second version, which is to deny all interpretations. But that is clearly unsatisfactory. Although it is called the Copenhagen interpretation (by some, what is meant by that changes from philosopher to philosopher, physicist to physicist), you still have to have some interpretation. You have to have some ontological vision of the wave function to assert that information cannot travel faster than light during its collapse, for example, or to state that it would be impossible to ever use it for long distance communication. That you refuse to examine your beliefs doesn't mean that they're not there.
Bricmont does a good job of showing how to deal with interpretations without getting so dogmatic that his assertions become meaningless, just the opposite of Motl

* Planck's experiments don't show this. Since the quantized electromagnetic waves are coming out of an enclosed chamber, black body radiation could be interpreted as having something to do with standing waves in the oven.
** Interestingly, though, the roles of randomness are reversed. In statistical mechanics we measure macroscopic parameters associated with microstates. In quantum mechanics, and especially in the de BroglieBohm interpretation, the wave function is the microstate and the measurement is of the particle, or the microstate.
*** I should mention that de BroglieBohm is not excessively popular among physicists. Reading The Wave Function, however, I came out of it thinking it was extremely popular among professional philosophers of science.
Despite being much different than what I thought the book would be, this made the Quantum Sense and Nonsense an excellent read.
The double slit experiment as performed by Thomas Young in the first decade of the 19th century showed that coherent light from the sun interfered with itself, showing that light is, in fact, a wave  and brought about the belief in a mysterious Ether in which the light waves propagated. When Einstein showed the photoelectric effect requires quantization of light,* this made the interpretation more difficult. And de Broglie's prediction that electrons, really all material objects, have a wavelength and the subsequent discovery of electron diffraction, brought the same problem to all matter. And the interference is so strong that when a single photon or a single electron is sent through the slits, and the results of the experiments accumulated, the interference fringes are still seen. Material objects interfere with themselves.
A very strange property, and one that leads to many strange interpretations of quantum mechanics, is that if you set up a detector at one of the slits in the double slit experiment to see which slit the particle passes through, then the interference fringes will disappear. This leads to the idea that observation causes a change in the wave function, what is termed the wave function collapse. Many strange ideas come out of this, even from physicists (Bricmont's target). People use this idea to give consciousness a role in the measurement of quantum systems, Bricmont uses quotes from the following physicists to show the sloppy thinking on these points: d'Espagnat, Wheeler, and Mermin (to name only those I've heard of): they all give some role to the human mind in the collapse of the wave function. To be fair, understanding the collapse is impossible in the standard "Copenhagen" interpretation of quantum mechanics, which is what Schroedinger's cat was intended to show.
The EPR experiments, violations of Bell's theorem, are the second cause of sloppy thinking because they show one of two things: either (1) quantum mechanics is nonlocal or (2) quantum mechanics is noncausal. Those are the two assumptions that Bell uses to derive his inequalities beyond ordinary statistics and quantum theory. If you have to choose one of the two assumptions to invalidate, (1) is the more likely (although we recently published a podcast on retrocausality and Yakir Aharonov has a different version of a localitypreserving assumption, presented in his Quantum Paradoxes book as well as old papers). But once you remove locality from your assumptions about the world, people start babbling about telepathy and similar nonsense.
As befits someone of Bricmont's station, the descriptions of these experiments are exemplary, and Quantum Sense and Nonsense would be worth a read if only they were presented here. However, he does us another service by giving us a rich, logical and convincing description and defense of the de BroglieBohm pilot wave theory of quantum mechanics. In this theory, the wave and particle are broken up into two objects, an oscillation in space time that drives the motion of an otherwise deterministic particle. The randomness of quantum mechanics then ceases to be the mystical randomness associated with Bohr and Heisenberg and Copenhagen in general and becomes the deterministic randomness of statistical mechanics.** Bricmont goes so far to say that because of this and the fact that it can be mathematicised, de BroglieBohm is the only interpretation of quantum mechanics;*** the others (including statistical, Copenhagen, and manyworlds) don't meet that bar. Obviously, it doesn't mean that Bricmont is right, since he's delved into philosophy or worse in the comparison of interpretations by their linguistic characterizations, but it is a good way of thinking about the interpretations.
So I would recommend this book. I do think that it is a little too popular for most people that would read this, and he often refers to his own, more technical Making Sense of Quantum Mechanics quite a bit for more quantitative details. He also says that this is only "slightly" more rigorous and would probably point you to P. Holland's The Quantum Theory of Motion for a really rigorous treatment. I haven't read either of those two books, however, so I can't recommend them to you.

I wrote this review a little faster than I'd like because I'd just finished the book yesterday and Google sent me a "news story" on my phone today, which I read over my morning coffee. It was a rather infantile post by Luboš Motl, someone I've never heard of, who calls himself a "freelance string theorist" (but who has a reasonably impressive pedigree) reviewing books by science journalists. It makes me sad when a physicist does as bad a job of presenting science as a science journalist does.
The blog does a good job of showing two very bad ways to think about the interpretations of quantum mechanics. The first is from the book he reviews (or really, the blog post that he reviews of the book that it reviews). In that case, the science journalist author, whose name is of no importance, suggests that all interpretations are valid. This seems quite odd to me, especially when most of them are logically contradictory: if you believe in a wave function collapse, then you can't coherently believe in the universal wave function of Everett. You can make up a pretty complex and silly rationale if you want to, but it will always end up being incoherent somewhere (and I'm not going to read it to find out where). The reason you would want to hold multiple conceptions in your head is to find out places where they disagree  and then to find an experiment that distinguishes them.
Motl himself presents to us the second version, which is to deny all interpretations. But that is clearly unsatisfactory. Although it is called the Copenhagen interpretation (by some, what is meant by that changes from philosopher to philosopher, physicist to physicist), you still have to have some interpretation. You have to have some ontological vision of the wave function to assert that information cannot travel faster than light during its collapse, for example, or to state that it would be impossible to ever use it for long distance communication. That you refuse to examine your beliefs doesn't mean that they're not there.
Bricmont does a good job of showing how to deal with interpretations without getting so dogmatic that his assertions become meaningless, just the opposite of Motl

* Planck's experiments don't show this. Since the quantized electromagnetic waves are coming out of an enclosed chamber, black body radiation could be interpreted as having something to do with standing waves in the oven.
** Interestingly, though, the roles of randomness are reversed. In statistical mechanics we measure macroscopic parameters associated with microstates. In quantum mechanics, and especially in the de BroglieBohm interpretation, the wave function is the microstate and the measurement is of the particle, or the microstate.
*** I should mention that de BroglieBohm is not excessively popular among physicists. Reading The Wave Function, however, I came out of it thinking it was extremely popular among professional philosophers of science.
Thursday, August 2, 2018
Physics Frontiers: Most Popular Episodes
All Time
1. Physics Frontiers 45: Loop Quantum Gravity
2. Physics Frontiers 46: Wigner's Friend
3. Physics Frontiers 44: Spooky Action at a Distance
4. Physics Frontiers 38: The Dimensionality of SpaceTime
5. Physics Frontiers 53: ElectromagnticGravitational Repulsion
2020
1. Physics Frontiers 53: ElectromagneticGravitational Repulsion
2. Physics Frontiers 55: Multiversality
3. Physics Frontiers 48: The Gerstenstein Effect
2019
1. Physics Frontiers 45: Loop Quantum Gravity
2. Physics Frontiers 46: Wigner's Friend
3. Physics Frontiers 44: Spooky Action at a Distance
2018
1. Physics Frontiers 38: The Dimensionality of SpaceTime
2. Physics Frontiers 33: The String Theory Landscape
3. Physics Frontiers 40: The Octonions
2017
1. Physics Frontiers 17: The Physics of Time Travel
2. Physics Frontiers 9: f(R) Theories of Gravity
3. Phyiscs Fronteirs 12: A Graviational Arrow of Time
Physics Frontiers Index
[Edited 12/8/2020]
1. Physics Frontiers 45: Loop Quantum Gravity
2. Physics Frontiers 46: Wigner's Friend
3. Physics Frontiers 44: Spooky Action at a Distance
4. Physics Frontiers 38: The Dimensionality of SpaceTime
5. Physics Frontiers 53: ElectromagnticGravitational Repulsion
2020
1. Physics Frontiers 53: ElectromagneticGravitational Repulsion
2. Physics Frontiers 55: Multiversality
3. Physics Frontiers 48: The Gerstenstein Effect
2019
1. Physics Frontiers 45: Loop Quantum Gravity
2. Physics Frontiers 46: Wigner's Friend
3. Physics Frontiers 44: Spooky Action at a Distance
2018
1. Physics Frontiers 38: The Dimensionality of SpaceTime
2. Physics Frontiers 33: The String Theory Landscape
3. Physics Frontiers 40: The Octonions
2017
1. Physics Frontiers 17: The Physics of Time Travel
2. Physics Frontiers 9: f(R) Theories of Gravity
3. Phyiscs Fronteirs 12: A Graviational Arrow of Time
Physics Frontiers Index
[Edited 12/8/2020]
Wednesday, July 25, 2018
Quantum Paradoxes by Aharonov and Rohrlich
You might think I like Quantum Paradoxes [Amazon] by Yakir Aharonov and Daniel Rohrlich. I mean, I started a podcast about it. I might even finish it someday.*
This book explores the meaning of quantum mechanics through paradoxical thought experiments. It uses a few standard ones, like Schrodinger's cat, and a lot of interesting variations of the double slit experiment and electron diffraction. The first eight chapters motivate mainly how quantum mechanics works using paradoxes. The last ten chapters motivate Aharonov and Rohrlich's interpretations.
I am very enamored of the format.
Each chapter follows a formula. After a short preamble, a paradox is presented in detail. The paradoxes are presented as thought experiments, first. This means that a detailed, if not physically possible, experiment is described, and then its physics discussed. The physics leads to two possible interpretations, such as: there is no physical difference in the dynamics of an electron on either side of a charged capacitor, but quantum mechanics predicts a phase shift in the wave function of the electron. How can that be?
Next, aspects of the physics are discussed in mathematical detail. In this case, what is the relationship between the gauge and the phase of the wave function. This leads to a choice, clarification, or reconciliation. The most interesting part of this for me has been the use of modular variables to clear up some points that have to do with the use of gauges, although the general setup of the interference experiments Aharonov and Rohrlich are discussing requires a bit of careful reading. Sometimes, a section or two follows with implications and real, physical experiments.
The second half of the book deals with the interpretation of quantum mechanics in the context of weak measurements. I really don't have a great idea about how to explain a weak measurement, but the two important facets are: (1) they allow you to measure the wave function without (completely) destroying it and (2) they are only approximations to the wave function. Aharonov and Rohrlich mainly deal with their own interpretation, and (a) the Copenhagen interpretation (a favorite among users of quantum mechanics) and (b) the manyworlds hypothesis (a favorite among string theorists). Mainly, I think, because these are their main competitors.
Their own interpretation has to do with temporal boundary conditions, which is very appealing to me because it's compatible with the block universe idea of relativity, at least conceptually. It's very important to remember that every fundamental physical theory must be compatible with every other fundamental physical theory  if two theories that should apply to a situation don't, you have a paradox. So, any interpretation of quantum mechanics must be compatible with relativity. This hasn't been a problem with the theory  quantum electrodynamics is exactly the integration of quantum mechanics and special relativity. It has been a major problem with interpretations, and the authors detail some of those problems in the book.
I don't want to go into more detail, but if you want to get more detail, then over the next thirtyfourodd weeks, I discuss each chapter with a friend of mine in a podcast. Contact me for the address if you're not already subscribed.
So, I just love this book. It's a great way to not only explore quantum mechanics, but to explore what it means to be an interpretation of quantum mechanics in a rigorous and technical, but not exceedingly technical (to a physicist). If you have the mathematical background to play with differential equations, or even the intellectual fortitude to not be scared of them, I highly recommend this book. If you don't have that knowledge, then check out the podcast. It'll probably be more than enough for you.
* Update (5/24/2020): To be clear here: I've read through the book three times, once to get ideas for teaching well before I'd started any podcast, once when Randy agreed to do the Quantum Paradoxes podcast, and finally, once when we started the podcst over. I think we've given up hope on finishing the Quantum Paradoxes podcast.
This book explores the meaning of quantum mechanics through paradoxical thought experiments. It uses a few standard ones, like Schrodinger's cat, and a lot of interesting variations of the double slit experiment and electron diffraction. The first eight chapters motivate mainly how quantum mechanics works using paradoxes. The last ten chapters motivate Aharonov and Rohrlich's interpretations.
I am very enamored of the format.
Each chapter follows a formula. After a short preamble, a paradox is presented in detail. The paradoxes are presented as thought experiments, first. This means that a detailed, if not physically possible, experiment is described, and then its physics discussed. The physics leads to two possible interpretations, such as: there is no physical difference in the dynamics of an electron on either side of a charged capacitor, but quantum mechanics predicts a phase shift in the wave function of the electron. How can that be?
Next, aspects of the physics are discussed in mathematical detail. In this case, what is the relationship between the gauge and the phase of the wave function. This leads to a choice, clarification, or reconciliation. The most interesting part of this for me has been the use of modular variables to clear up some points that have to do with the use of gauges, although the general setup of the interference experiments Aharonov and Rohrlich are discussing requires a bit of careful reading. Sometimes, a section or two follows with implications and real, physical experiments.
The second half of the book deals with the interpretation of quantum mechanics in the context of weak measurements. I really don't have a great idea about how to explain a weak measurement, but the two important facets are: (1) they allow you to measure the wave function without (completely) destroying it and (2) they are only approximations to the wave function. Aharonov and Rohrlich mainly deal with their own interpretation, and (a) the Copenhagen interpretation (a favorite among users of quantum mechanics) and (b) the manyworlds hypothesis (a favorite among string theorists). Mainly, I think, because these are their main competitors.
Their own interpretation has to do with temporal boundary conditions, which is very appealing to me because it's compatible with the block universe idea of relativity, at least conceptually. It's very important to remember that every fundamental physical theory must be compatible with every other fundamental physical theory  if two theories that should apply to a situation don't, you have a paradox. So, any interpretation of quantum mechanics must be compatible with relativity. This hasn't been a problem with the theory  quantum electrodynamics is exactly the integration of quantum mechanics and special relativity. It has been a major problem with interpretations, and the authors detail some of those problems in the book.
I don't want to go into more detail, but if you want to get more detail, then over the next thirtyfourodd weeks, I discuss each chapter with a friend of mine in a podcast. Contact me for the address if you're not already subscribed.
So, I just love this book. It's a great way to not only explore quantum mechanics, but to explore what it means to be an interpretation of quantum mechanics in a rigorous and technical, but not exceedingly technical (to a physicist). If you have the mathematical background to play with differential equations, or even the intellectual fortitude to not be scared of them, I highly recommend this book. If you don't have that knowledge, then check out the podcast. It'll probably be more than enough for you.
* Update (5/24/2020): To be clear here: I've read through the book three times, once to get ideas for teaching well before I'd started any podcast, once when Randy agreed to do the Quantum Paradoxes podcast, and finally, once when we started the podcst over. I think we've given up hope on finishing the Quantum Paradoxes podcast.
Tuesday, May 22, 2018
The Wave Function: Essays on the Metaphysics of Quantum Mechanics
The Wave Function is a philosophy anthology about the wave function of
quantum mechanics. The wave function
specifies the state of the quantum mechanical system in a way similar to how
the ideal gas law specifies the state of a dilute gas. You can make more or less of that, if you
wish. But if you’re a philosopher, you’ll
make more.
This book is not really about the wave function, what it
does, and how to care for it, it is a discussion of David Albert’s thesis
exposited in the 1996 paper, “Elementary Quantum Mechanics.” In this paper he looked the wave function as
a real thing, and said that if it is real, then the universe must exist in
3Ndimensions, where N is the number of particles in the universe. This is because the wave function a system of
particles is a collection of positions for those particles.
I’ll discuss each chapter in turn. You might think the description is a little short
for some of them, but the review has gotten pretty long.
1. David Albert, “Wave Function Realism”
In this essay, David Albert of the philosophy department of
Columbia University discusses his idea on how to view the wave function
realistically. Realist, in the
philosophical sense, of the wave function is a real thing, and so its nature
can be used to tell us something about the nature of the rest of the world.
Since this is the view that most of the remainder of the
essays discuss, and all address, it’s a good thing to go into detail about this
here. If the wave function is a real,
physical object, it is a kind of field.
In physics, the word field refers to an object that can be represented
as a function, which can be scalar, vector, or tensorvalued, that has
different values at different points in space.
The velocity field of a stream, for example, is a vector field that
tells you how fast and in what direction the water in that stream is moving at
that point. In a steady state, even
though the water is different at every instant, the current is the same at every
point. Its domain is the physical, three
dimensional space that composes the stream (technically, it could be all
space), and its range is the three dimensional velocity vectors that the water
can travel at (magnitudes and directions.
What Albert noticed is that the domain of the field is, in
all of physics, the 3D space that we live in or a subset of it. All of physics, that is, except in quantum
mechanics, where the domain of the wave function is the possible positions of
each of the particles that the wave function describes (is that true?*), and so
instead of being a 3dimensional space, it is a 3Ndimensional space with N
being the number of particles. Albert’s
leap was to say that since quantum mechanics is the foundational theory of the
world, this 3Ndimensional space is the REAL world whereas our usual
3dimensional space is an apparition based on the relationships between large
number of particles.
The reason why we don’t see the 3N world is basically a
braininavat type of problem.
2. Valia Allori, “Primitive Ontology and the Structure of
Physical Theories”
Valia Allori, a philosopher at Northern Illinois University,
tries to understand all this in a very philosophical way. She invents subcategories within categories
that you’d never heard of. In this case,
she starts talking about the “primitive ontology” of a theory. This is all, if I recall, along the same
program as Albert.
An ontology in the philosophy of science is the collection
of thing in the world on which the theory can function, whether they be atoms
or charges or point particles. A
primitive ontology is the minimum ontology for the theory to function. This varies from theory to theory, and it has
a set of “primitive variables” which create the minimum parameterization that
allows you to translate the objects of the primitive ontology into mathematics.
Allori analyzes three and a half theories with this system:
Bohmian mechanics, the GhirardiRiminiWeber (2x versions), and the manyworlds
interpretation. These three
interpretations keeps coming up, and not very many more, so I wonder if most of
the philosophy of quantum mechanics is a detailed response to John Bell,
especially the collection The Speakable and Unspeakable in Quantum Mechanics –
since those were, really the three that he detailed in that book.
3. Steven French , “Whither Wave Function Realism”
Steven French, a philosopher at the University of Leeds,
wonders whether the wave function is the right thing for the realist
philosopher of science to consider as part of the ontology of the theory. He feels that overestimating the importance
of the wave function in using quantum mechanics to tell us about the world
underdetermines the theory and leaves us with a rather vague idea about what
really exists.
4. Sheldon Goldstein and Nino Zanghi, “Reality and the Role
of the Wave Function in Quantum Theory”
Sheldon Goldstein, a mathematician at Rutgers, and Nino
Zanghi, a physicist at the University of Genoa,
wonder just what it is that a wave function can be, and there are
several things that look at. First of
all, there can be no such thing as the wave function in the world. It is just a computational tool. Next, it could be an epistemic representation
of our subjective knowledge of the system.
That is, it isn’t physical but it has something to do with the state of
something physical – basically, the state of our brains. Or it can be some fact or object in the world
– a thing in the world. That it, the
wave function could be nothing, it could be epistemic, or it could be real.
The main point of most of these papers is to analyze and
criticize Albert’s wave function realism, so it is the last that is
interesting. If the wave function is
real, there are two possibilities: it could be nomological or material, or at
least partially one or the other will a little subjectiveness or nothingness
thrown in. If it is nomological, it is
a fact about the world, like Gauss’ Law.
If it is material, it is a real thing, like a changed pith ball. But again, they give themselves a little
wiggle room by allowing the wave function to be either quasinomological or
quasimaterial. It might be factish or
thinglike.
Just like the Allori paper, Goldstein and Zanghi analyze a
group of different interpretations of quantum mechanics to determine what role
the wave function plays in each according to this categorization. If you’re interested enough in which is what
and what is which, you’re probably interested enough to read the book, so I’ll
save myself some time and not make out a table.
5. Peter Lewis, “Dimension and Illusion”
Peter Lewis, a Dartmouth philosopher that was at the
University of Miami when The Wave Function was published, gives a pragmatic
analysis of Albert’s thesis. And it’s no
surprise what a pragmatist will think about a 3Ndimensional world.
6. Tim Maudlin, “The Nature of the Quantum State”
Time Maudlin, New York University Philosopher, provides the
most direct assault on Albert in this book.
That is, he goes after the main method of analysis – producing an
ontology from the mathematics – in order to show that 3Ndimensional space isn’t
necessary. He does this both by careful
analysis of Alberts 1996 paper and with an analogy to Fourier’s Analytical
Theory of Heat, which provided a metaphysical cover for the caloric fluid model
of heat.
That particular induction was natural. The equations in the theory of heat flow are
the same as those as for current flow in liquids. So, if you don’t have any idea about
statistical mechanics, it’s the most natural thing in the world to see heat as a
current of some sort of fluid instead of just energy transfer.
And of course, that didn’t work.
Maudlin’s conclusion is justified: looking at the
mathematical form that a theory has to take does not require you to take
implications of the mathematics to be real – to be in the ontology of the
theory, as the philosophers put it. Not
only is not necessary, it’s not even a good reason.
7. Bradley Monton, “Against 3NDimensional Space”
Bradley Monton, who worked at the University of Colorado at
Boulder at the time but now philosophizes at Wuhan University, sets the tone
for this one with his first section “Quantum Mechanics is False.” Why does he say that? Because he feels that General
Relativity is the more fundamental theory of the two, mostly because quantum
mechanics synchronize their watches. This
may seem trivial, but it’s a major problem in using string theory to construct
a theory of gravity.
His main argument against the 3Ndimensional space and in
favor of 3dimensional space as being the fundamental dimensionality of the
world is that 3dimensional space more accurately reflects what physicists think
about the world and how they carry out experiments. And, Monton argues, unless 3Ndimensional
space can make itself useful, then there’s no good reason to take it as
fundamental.
8. Alyssa Ney, “Ontological Reduction and the Wave Function
Ontology”
Alyssa Ney, a philosopher at the University of California at
Davis, gives an account of “ontological reduction,” how one set of things can
be reduced to another set of things. In
this case, she gives an account of how our 3dimensional experience can reduce
to the 3Ndimensional space of the wave function. You can think of this in analogy to
scientific reductionism where biology can be reduced to chemistry, for example,
for a certain idea about what biology is.
Chemistry never gives you the full picture of biology, but we have faith
that between chemistry and physics, everything about living things can be
explained in some reasonable way – although not predicted.
9. Jill North, “Structure of the Quantum World”
Jill North, now of Rutgers, once of Cornell, discusses how
Albert’s program is supported by the dynamics of the world. If the wave function changes in
3Ndimensions, then a 3Nuniverse is the best explanation of it. I didn’t see it before, but I see it now:
North’s view of the wave function is of the universal variety, and the
universal wave function is the most physical assumption of the manyworld’s
hypothesis.
10. David Wallace, “A Prolegomenon to the Ontology of the
Everett Interpretation”
David Wallace moved from Oxford to the University of
Southern California to do his philosophizing.
Here, he talks a lot about the manyworlds interpretation.
* In the case of
identical particles, the wave function gives the probability amplitude of
finding *a* particle there. It doesn’t
tell you which one.
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