A senior colleague asked me for thoughts on this paper describing a single-preferred-branch flavor of quantum mechanics, and I thought I’d copy them here. Tl;dr: I did not find an important new idea in it, but this paper nicely illustrates the appeal of Finkelstein’s partial-trace decoherence and the ambiguity inherent in connecting a many-worlds wavefunction to our direct observations.
We propose a method for finding an initial state vector which by ordinary Hamiltonian time evolution follows a single branch of many-worlds quantum mechanics. The resulting deterministic system appears to exhibit random behavior as a result of the successive emergence over time of information present in the initial state but not previously observed.
We start by assuming that a precise wavefunction branch structure has been specified. The idea, basically, is to randomly draw a branch at late times according to the Born probability, then to evolve it backwards in time to the beginning of the universe and take that as your initial condition. The main motivating observation is that, if we assume that all branch splittings are defined by a projective decomposition of some subsystem (‘the system’) which is recorded faithfully elsewhere (‘the environment’), then the lone preferred branch — time-evolving by itself — is an eigenstate of each of the projectors defining the splits. In a sense, Weingarten lays claim to ordered consistency [arxiv:gr-qc/9607073] by assuming partial-trace decoherenceNote on terminology: What Finkelstein called “partial-trace decoherence” is really a specialized form of consistency (i.e., a mathematical criterion for sets of consistent histories) that captures some, but not all, of the properties of the physical and dynamical process of decoherence.… [continue reading]
In his new article in the NY Review of Books, the titan Steven Weinberg expresses more sympathy for the importance of the measurement problem in quantum mechanics. The article has nothing new for folks well-versed in quantum foundations, but Weinberg demonstrates a command of the existing arguments and considerations. The lengthy excerpts below characterize what I think are the most important aspects of his view.
Many physicists came to think that the reaction of Einstein and Feynman and others to the unfamiliar aspects of quantum mechanics had been overblown. This used to be my view. After all, Newton’s theories too had been unpalatable to many of his contemporaries…Evidently it is a mistake to demand too strictly that new physical theories should fit some preconceived philosophical standard.
In quantum mechanics the state of a system is not described by giving the position and velocity of every particle and the values and rates of change of various fields, as in classical physics. Instead, the state of any system at any moment is described by a wave function, essentially a list of numbers, one number for every possible configuration of the system….What is so terrible about that? Certainly, it was a tragic mistake for Einstein and Schrödinger to step away from using quantum mechanics, isolating themselves in their later lives from the exciting progress made by others. Even so, I’m not as sure as I once was about the future of quantum mechanics. It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means. The dispute arises chiefly regarding the nature of measurement in quantum mechanics…
The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities.
… [continue reading]
When talking to folks about the quantum measurement problem, and its potential partial resolution by solving the set selection problem, I’ve recently been deploying three nonstandard arguments. To a large extent, these are dialectic strategies rather than unique arguments per se. That is, they are notable for me mostly because they avoid getting bogged down in some common conceptual dispute, not necessarily because they demonstrate something that doesn’t formally follow from traditional arguments. At least two of these seem new to me, in the sense that I don’t remember anyone else using them, but I strongly suspect that I’ve just appropriated them from elsewhere and forgotten. Citations to prior art are highly appreciated.
Passive quantum mechanics
There are good reasons to believe that, at the most abstract level, the practice of science doesn’t require a notion of active experiment. Rather, a completely passive observer could still in principle derive all fundamental physical theories simply by sitting around and watching. Science, at this level, is about explaining as many observations as possible starting from as minimal assumptions as possible. Abstractly we frame science as a compression algorithm that tries to find the programs with the smallest Kolmogorov complexity that reproduces observed data.
Active experiments are of course useful for at least two important reasons: (1) They gather strong evidence for causality by feeding a source of randomness into a system to test a causal model, and (2) they produce sources of data that are directly correlated with systems of interest rather than relying on highly indirect (and perhaps computationally intractable) correlations. But ultimately these are practical considerations, and an inert but extraordinarily intelligent observer could in principle derive general relativity, quantum mechanics, and field theoryOf course, there may be RG-reasons to think that scales decouple, and that to a good approximation the large-scale dynamics are compatible with lots of possible small-scale dynamics.… [continue reading]
[PSA: Happy 4th of July. Juno arrives at Jupiter tonight!]
This is short and worth reading:
The sharp distinction between Initial Conditions and Laws of Nature was initiated by Isaac Newton and I consider this to be one of his most important, if not the most important, accomplishment. Before Newton there was no sharp separation between the two concepts. Kepler, to whom we owe the three precise laws of planetary motion, tried to explain also the size of the planetary orbits, and their periods. After Newton's time the sharp separation of initial conditions and laws of nature was taken for granted and rarely even mentioned. Of course, the first ones are quite arbitrary and their properties are hardly parts of physics while the recognition of the latter ones are the prime purpose of our science. Whether the sharp separation of the two will stay with us permanently is, of course, as uncertain as is all future development but this question will be further discussed later. Perhaps it should be mentioned here that the permanency of the validity of our deterministic laws of nature became questionable as a result of the realization, due initially to D. Zeh, that the states of macroscopic bodies are always under the influence of their environment; in our world they can not be kept separated from it.
This essay has no formal abstract; the above is the second paragraph, which I find to be profound. Here is the PDF. The essay shares the same name and much of the material with Wigner’s 1963 Nobel lecture [PDF].The Nobel lecture has a nice bit contrasting invariance principles with covariance principles, and dynamical invariance principles with geometrical invariance principles.… [continue reading]
In a previous post of abstracts, I mentioned philosopher Josh Rosaler’s attempt to clarify the distinction between empirical and formal notions of “theoretical reduction”. Reduction is just the idea that one theory reduces to another in some limit, like Galilean kinematics reduces to special relativity in the limit of small velocities.Confusingly, philosophers use a reversed convention; they say that Galilean mechanics reduces to special relativity.a Formal reduction is when this takes the form of some mathematical limiting procedure (e.g., ), whereas empirical reduction is an explanatory statement about observations (e.g., “special relativity can explains the empirical usefulness of Galilean kinematics”).
Rosaler’s criticism, which I mostly agree with, is that folks often conflate these two. Usually this isn’t a serious problem since the holes can be patched up on the fly by a competent physicist, but sometimes it leads to serious trouble. The most egregious case, and the one that got me interested in all this, is the quantum-classical transition, and in particular the serious insufficiency of existing limits to explain the appearance of macroscopic classicality. In particular, even though this limiting procedure recovers the classical equations of motion, it fails spectacularly to recover the state space.There are multiple quantum states that have the same classical analog as , and there are quantum states that have no classical analog as .b
In this post I’m going to comment Rosaler’s recent elaboration on this ideaI thank him for discussion this topic and, full disclosure, we’re drafting a paper about set selection together.c :
Reduction between theories in physics is often approached as an a priori relation in the sense that reduction is often taken to depend only on a comparison of the mathematical structures of two theories.
… [continue reading]
Last week I saw an excellent talk by philosopher Wayne Myrvold.
The Reeh-Schlieder theorem says, roughly, that, in any reasonable quantum field theory, for any bounded region of spacetime R, any state can be approximated arbitrarily closely by operating on the vacuum state (or any state of bounded energy) with operators formed by smearing polynomials in the field operators with functions having support in R. This strikes many as counterintuitive, and Reinhard Werner has glossed the theorem as saying that “By acting on the vacuum with suitable operations in a terrestrial laboratory, an experimenter can create the Taj Mahal on (or even behind) the Moon!” This talk has two parts. First, I hope to convince listeners that the theorem is not counterintuitive, and that it follows immediately from facts that are already familiar fare to anyone who has digested the opening chapters of any standard introductory textbook of QFT. In the second, I will discuss what we can learn from the theorem about how relativistic causality is implemented in quantum field theories.
(Download MP4 video here.)
The topic was well-defined, and of reasonable scope. The theorem is easily and commonly misunderstood. And Wayne’s talk served to dissolve the confusion around it, by unpacking the theorem into a handful of pieces so that you could quickly see where the rub was. I would that all philosophy of physics were so well done.
Here are the key points as I saw them:
The vacuum state in QFTs, even non-interacting ones, is entangled over arbitrary distances (albeit by exponentially small amounts). You can think of this as every two space-like separated regions of spacetime sharing extremely diluted Bell pairs.
… [continue reading]
[Other parts in this series: 1,2,3,4,5,6,7.]
In discussions of the many-worlds interpretation (MWI) and the process of wavefunction branching, folks sometimes ask whether the branching process conflicts with conservations laws like the conservation of energy.Here are some related questions from around the web, not addressing branching or MWI. None of them get answered particularly well.a There are actually two completely different objections that people sometimes make, which have to be addressed separately.
First possible objection: “If the universe splits into two branches, doesn’t the total amount of energy have to double?” This is the question Frank Wilczek appears to be addressing at the end of these notes.
I think this question can only be asked by someone who believes that many worlds is an interpretation that is just like Copenhagen (including, in particular, the idea that measurement events are different than normal unitary evolution) except that it simply declares that new worlds are created following measurements. But this is a misunderstanding of many worlds. MWI dispenses with collapse or any sort of departure from unitary evolution. The wavefunction just evolves along, maintaining its energy distributions, and energy doesn’t double when you mathematically identify a decomposition of the wavefunction into two orthogonal components.
Second possible objection: “If the universe starts out with some finite spread in energy, what happens if it then ‘branches’ into multiple worlds, some of which overlap with energy eigenstates outside that energy spread?” Or, another phrasing: “What happens if the basis in which the universe decoheres doesn’t commute with energy basis? Is it then possible to create energy, at least in some branches?” The answer is “no”, but it’s not obvious.… [continue reading]
[Other parts in this series: 1,2,3,4,5,6,7.]
I am firmly of the view…that all the sciences are compatible and that detailed links can be, and are being, forged between them. But of course the links are subtle… a mathematical aspect of theory reduction that I regard as central, but which cannot be captured by the purely verbal arguments commonly employed in philosophical discussions of reduction. My contention here will be that many difficulties associated with reduction arise because they involve singular limits….What nonclassical phenomena emerge as h → 0? This sounds like nonsense, and indeed if the limit were not singular the answer would be: no such phenomena.
— Michael Berry
One of the great crimes against humanity occurs each year in introductory quantum mechanics courses when students are introduced to an limit, sometimes decorated with words involving “the correspondence principle”. The problem isn’t with the content per se, but with the suggestion that this somehow gives a satisfying answer to why quantum mechanics looks like classical mechanics on large scales.
Sometimes this limit takes the form of a path integral, where the transition probability for a particle to move from position to in a time is
where is the integral over all paths from to , and is the action for that path ( being the Lagrangian corresponding to the Hamiltonian ). As , the exponent containing the action spins wildly and averages to zero for all paths not in the immediate vicinity of the classical path that make the action stationary.
Other times this takes the form of Ehrenfest’s theorem, which shows that the expectation values of functions of position and momentum follow the classical equations of motion.… [continue reading]
[This post was originally “Part 1” of my HTTAQM series. However, it’s old, haphazardly written, and not a good starting point. Therefore, I’ve removed it from that series, which now begins with “Measurements are about bases”. Other parts are here: 1,2,3,4,5,6,7. I hope to re-write this post in the future.]
It’s often remarked that the Aharonov–Bohm (AB) effect says something profound about the “reality” of potentials in quantum mechanics. In one version of the relevant experiment, charged particles are made to travel coherently along two alternate paths, such as in a Mach-Zehnder interferometer. At the experimenter’s discretion, an external electromagnetic potential (either vector or scalar) can be applied so that the two paths are at different potentials yet still experience zero magnetic and electric field. The paths are recombined, and the size of the potential difference determines the phase of the interference pattern. The effect is often interpreted as a demonstration that the electromagnetic potential is physically “real”, rather than just a useful mathematical concept.
The magnetic Aharanov-Bohm effect. The wavepacket of an electron approaches from the left and is split coherently over two paths, L and R. The red solenoid in between contains magnetic flux
. The region outside the solenoid has zero field, but there is a non-zero curl to the vector potential as measured along the two paths. The relative phase between the L and R wavepackets is given by
However, Vaidman recently pointed out that this is a mistaken interpretation which is an artifact of the semi-classical approximation used to describe the AB effect. Although it is true that the superposed test charges experience zero field, it turns out that the source charges creating that macroscopic potential do experience a non-zero field, and that the strength of this field is dependent on which path is taken by the test charges.… [continue reading]
[Edit: Scott Aaronson has posted on his blog with extensive criticism of Integrated Information Theory, which motivated Tegmark’s paper.]
Max Tegmark’s recent paper entitled “Consciousness as a State of Matter” has been making the rounds. See especially Sabine Hossenfelder’s critique on her blog that agrees in several places with what I say below.
Tegmark’s paper didn’t convince me that there’s anything new here with regards to the big questions of consciousness. (In fairness, I haven’t read the work of neuroscientist Giulio Tononi that motivated Tegmark’s claims). However, I was interested in what he has to say about the proper way to define subsystems in a quantum universe (i.e. to “carve reality at its joints”) and how this relates to the quantum-classical transition. There is a sense in which the modern understanding of decoherence simplifies the vague questions “How does (the appearance of) a classical world emerge in a quantum universe? ” to the slightly-less-vague question “what are the preferred subsystems of the universe, and how do they change with time?”. Tegmark describes essentially this as the “quantum factorization problem” on page 3. (My preferred formulation is as the “set-selection problem” by Dowker and Kent. Note that this is a separate problem from the origin of probability in quantum mechanicsThe problem of probability as described by Weinberg: “The difficulty is not that quantum mechanics is probabilistic—that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.” HT Steve Hsu.a .)
Therefore, my comments are going to focus on the “object-level” calculations of the paper, and I won’t have much to say about the implications for consciousness except at the very end.… [continue reading]
When I’m trying to persuade someone that people ought to concentrate on effectiveness when choosing which charities to fund, I sometime hear the worry that this sort of emphasis on cold calculation risks destroying the crucial human warmth and emotion that should surround charitable giving. It’s tempting to dismiss this sort of worry out of hand, but it’s much more constructive to address it head on.I also think it gestures at a real aspect of “EA cultural”, although the direction of causality is unclear. It could just be that EA ideas are particularly attractive to us cold unfeeling robots.a This situations happened to me today, and I struggled for a short and accessible response. I came up with the following argument later, so I’m posting it here.
It’s often noticed that many of the best surgeons treat their patients like a broken machine to be fixed, and lack any sort of bedside manner. Surgeons are also well known for their gallows humor, which has been thought to be a coping mechanism to deal with death and with the unnatural act of cutting open a living human body. Should we be worried that surgery dehumanizes the surgeon? Well, yes, this is a somewhat valid concern, which is even being addressed (with mixed results).
But in context this is only a very mild concern. The overwhelmingly most important thing is that the surgery is actually performed, and that it is done well. If someone said “I don’t think we should have doctors perform surgery because of the potential for it to take the human warmth out of medicine”, you’d rightly call them crazy! No one wants to die from a treatable appendicitis, no matter how comforting the warm and heartfelt doctors are.… [continue reading]
This is a follow up on my earlier post on contextuality and non-locality. As far as I can tell, Spekken’s paper is the gold standard for how to think about contextuality in the messy real world. In particular, since the idea of “equivalent” measurements is key, we might never be able to establish that we are making “the same” measurement from one experiment to the next; there could always be small microscopic differences for which we are unable to account. However, Spekken’s idea of forming equivalence classes from measurement protocols that always produce the same results is very natural. It isolates, as much as possible, the inherent ugliness of a contextual model that gives different ontological descriptions for measurements that somehow always seem to give identical results.
I also learned an extremely important thing in my background reading. Apparently John Bell discovered contextuality a few years before Kochen and Specker (KS).This is according to Mermin’s RMP on contextuality and locality. I haven’t gone back and read Bell’s papers to make sure he really did describe something equivalent to the KS theorem.a More importantly, Bell’s theorem on locality grew out of this discovery; the theorem is just a special case of contextuality where “the context” is a space-like separated measurement.
So now I think I can get behind Spekken’s idea that contextuality is more important than non-locality, especially non-locality per se. It seems very plausible to me that the general idea of contextuality is driving at the key thing that’s weird about quantum mechanics (QM) and that — if QM is one day more clearly explained by a successor theory — we will find that the non-local special case of contextuality isn’t particularly different from local versions.… [continue reading]
I wanted to understand Rob Spekkens’ self-described lonely view that the contextual aspect of quantum mechanics is more important than the non-local aspect. Although I like to think I know a thing or two about the foundations of quantum mechanics, I’m embarrassingly unfamiliar with the discussion surrounding contextuality. 90% of my understanding is comes from this famous explanation by David Bacon at his old blog. (Non-experts should definitely take the time to read that nice little post.) What follows are my thoughts before diving into the literature.
I find the map-territory distinction very important for thinking about this. Bell’s theorem isn’t a theorem about quantum mechanics (QM) per se, it’s a theorem about locally realistic theories. It says if the universe satisfies certain very reasonable assumption, then it will behave in a certain manner. We observe that it doesn’t behave in this manner, therefore the universe doesn’t satisfy those assumption. The only reason that QM come into it is that QM correctly predicts the misbehavior, whereas classical mechanics does not (since classical mechanics satisfies the assumptions).
Now, if you’re comfortable writing down a unitarily evolving density matrix of macroscopic systems, then the mechanism by which QM is able to misbehave is actually fairly transparent. Write down an initial state, evolve it, and behold: the wavefunction is a sum of branches of macroscopically distinct outcomes with the appropriate statistics (assuming the Born rule). The importance of Bell’s Theorem is not that it shows that QM is weird, it’s that it shows that the universe is weird. After all, we knew that the QM formalism violated all sorts of our intuitions: entanglement, Heisenberg uncertainty, wave-particle duality, etc.; we didn’t need Bell’s theorem to tell us QM was strange.… [continue reading]
andrelaszlo on HackerNews asked how someone could draw a reasonable distinction between “direct” and “indirect” measurements in science. Below is how I answered. This is old hat to many folks and, needless to say, none of this is original to me.
There’s a good philosophy of science argument to be made that there’s no precise and discrete distinction between direct and indirect measurement. In our model of the universe, there are always multiple physical steps that link the phenomena under investigation to our conscious perception. Therefore, any conclusions we draw from a perception are conditional on our confidence in the entire causal chain performing reliably (e.g. a gravitational wave induces a B-mode in the CMB, which propagates as a photon to our detectors, which heats up a transition-edge sensor, which increases the resistivity of the circuit, which flips a bit in the flash memory, which is read out to a monitor, which emits photons to our eye, which change the nerves firing in our brain). “Direct” measurements, then, are just ones that rely on a small number of reliable inferences, while “indirect” measurements rely on a large number of less reliable inferences.
Nonetheless, in practice there is a rather clear distinction which declares “direct” measurements to be those that take place locally (in space) using well-characterized equipment that we can (importantly) manipulate, and which is conditional only on physical laws which are very strongly established. All other measurements are called “indirect”, generally because they are observational (i.e. no manipulation of the experimental parameters), are conditional on tenuous ideas (i.e. naturalness arguments as indirect evidence for supersymmetry), and/or involve intermediary systems that are not well understood (e.g.
… [continue reading]