SomethingDeeplyHidden

• Great! Pushed me over the edge on many worlds, now firm believer! Sean Carroll one of my favorite authors!
• High-level statement of why QM is different:
  • The QM world (unlike classical mechanics) is not perfectly transparent. What we see when we look at the world is fundamentally different from what actually is.
  • Gives probabilities, not certainties. Bells theorem implies these are not the probabilities we are familiar with (lack of full knowledge of system: eg in stat mech)

Quantum Mechanics

• Physicists haven't been honest with themselves about what QM says. We use QM, but honest physicists admit that we dont truly understand QM.
• When we teach QM to students they are taught a list of rules. Many of the familiar type (eg: how the system evolves smoothly in time). But then there are a bunch of extra rules that have no analogue in any other theory of physics. These extra rules tell us what happens when we observe the system; and the behavior is completely different from how the system behaves when we are not observing it. What in the world is going on here?
• Two options: One is that the story we've been telling our students is woefully incomplete and for QM to qualify as a sensible theory we need to define (and understand) what a "measurement" of "observation" is and why it seems so different from what the system does otherwise. The other option is that QM represents a violent break from the way we have always thought about physics before, where the world does not exist independently of how we perceive it. Either way this should be discussed in the QM textbooks; its not!
• QM is unique among physical theories in drawing an apparent distinction between what we see and what really is.
• The quest to make sense of QM is not considered high-status specialty within modern physics.
• This book has three main messages:
  1. QM should be understandable and achieving this understanding should be a high-priority goal of modern science.
  2. We have made real progress toward this understanding.
  3. All this matters.
• Many worlds is the purest way of making sense of QM - its where we end up if we just follow the path of least resistance in taking QM seriously. Multiple worlds are predictions of the formalism that is already in place, not something added in by hand.

Many Worlds

• One of the themes of this book is that QM doesn't deserve the connotation of spookiness. But if there is something difficult or puzzling about a theory, the scientific response should be to solve the puzzle, not pretend it isn't there. There is every reason to think we can do that for QM just like all the other theories.
• Measurement problem: What exactly a measurement is, happens when we measure something, and what it tells us about the system being measured. There is no consensus within physics or philosophy about how to solve this problem.

Things where experts disagree

• Classical mechanics is perfectly transparent; no need to talk about "interpretations of CM". We can precisely measure everything there is to know about a classical system without altering it in any way. Clear connection between what we see and what the theory describes.
• QM is not perfectly transparent. What we see when we look at the world is fundamentally different from what actually is.

PhilosophyOfPhysics

• In contrast to classical physics, the rules of textbook QM come in two parts: 1st part exactly parallels that we are used to in classical physics. "Diff-eq of rate of change of state." 2nd part is describes what happens when we make a measurement.
• QM provides us probabilities rather than certainties. This may be annoying, but we can live with it. What should bug us is our lack of understanding of what is actually happening.
• QM in the form in which it is currently presented in physics textbooks, represents an oracle, not a true understanding.
• Originally thought the probabilities in QM were like those in statistically physics, representing our lack of knowledge of the true system. Bells theorem implies that this cannot be without non-local variables.

• Minimalist approach to QM:

  • Take the wave function seriously as a direct representation of reality. (Notes: - Anything else would posit additional structure over and above the wave function.
    • This is a dramatic step! Wave-functions are not what we observe when we look at the world! We see measurement outcomes not wave functions.)
  • Assume that the wave function always evolves smoothly according to the Schrodinger eq.

  Summary: There is a wave function and it always evolves according to a deterministic rule. That is all there is to say!

• Immediate problem: It sure seems like the wave function collapses when we do a measurement. There is a good reason why the pioneers of QM invented the idea of wave function collapse: that's what they appear to do. Turn the question around: Rather than starting with what we see and trying to invent a theory to explain it, start with minimalist QM (wave functions evolving only smoothly) and ask what people in a world described by this theory would actually experience.
• "There is no such thing as the position of the electron" There is only the electrons wave function. This is QM implying a profound difference between what we can observe and what there really is. Our observations aren't revealing preexisting facts of which we were previously ignorant; at best, they reveal a tiny slice of a much bigger, fundamentally elusive reality.
• In minimalist QM there is nothing zipping around: there is only the quantum state. Atoms aren't mostly empty space; they are described by wave functions that stretch throughout then extent of the atom. Quantum reality is a wave function; classical positions and velocities are merely what we are able to observe when we probe that wave function.

PhilosophyOfPhysics

• The minimalist QM attitude is that we shouldn't treat the measurement process as anything mystical or even in need of its own set of rules; the detector and electron simply interact with each other according to the laws of physics.
• If that where the whole story minimalist QM would be an untenable mess. Electrons in super-positions, detectors in super-positions, nothing much resembling the robust approximately classical world of our experience. However the cloud of probability vanishes into nothingness for most possible combinations of electron location and detector image. Rather than the electron and detector doing their own thing, there is a connection between the systems. You never feel like you have evolved into a superposition of different possible measurement outcomes; you simply think you have seen some specific outcome, which can be predicted with a definite probability. (This is why all the extra measurement rules where added to textbook QM)
• Constructing a scientific theory is not simply a matter of writing down some equations, we also need to indicate how those equations map onto the world. The right way to describe things after the measurement is not as one person with multiple ideas about where the electron was seen, but as multiple worlds, each of which contains a single person with a very definite idea about where the electron was seen.
• The price we pay for the vastly increased elegance of theoretical formalism is that the theory describes many copies of what we think of as "the universe" each slightly different, but each truly real in some sense. Whether the benefit is worth the cost is an issue about which people disagree (Note: it is).

Things where experts disagree

• Note: In stumbling on the Many-worlds formalism, at no point did we take ordinary QM and tack on a bunch of worlds. All we did was point out that the potential of superstitions is naturally actualized in the course of ordinary quantum evolution. Once you admit that an electron can be in a superposition of different locations, it follows that a person can be in a superposition of having seen the electron in different locations, and indeed that reality as a whole can be in a superposition, it becomes natural to treat every term in that superposition as a separate "world". We didn't add anything to QM, we just faced up to the what was there all along.
• The minimalist approach is the "courageous" formulation of QM. It embodies the philosophy that we should take seriously the simplest version of underlying reality that accounts for what we see, even if that reality differs wildly from our everyday experience. Do we have the courage to accept it?

• Every version of QM features two things:

  1. a wave function
  2. the Schrodinger equation

  The entirety of the minimalist (Everett) formalism is the insistence that there is nothing else.

• WE dont choose QM we can only choose to face up to it.
• Planck said that light of a fixed frequency is emitted in certain amounts of energy, while Einstein says that because light literally is discrete particles. Its the difference between saying that a certain coffee machine makes exactly one cup of at a time, and saying that coffee only exists in the form of one cup-size amounts.
• Bohr was trying to account for the behavior of electrons in atoms, he posited an ad hoc rule which said they could only move in certain orbits. This rule needed a new constant and to fit the data that constant ended up having a value that was the same as the new constant that Planck was forced to introduce when he was trying to account for the behavior of photons. This is the kind of thing that makes you think you are on the right track.
• Rutherford and Bohr worried about how electrons emit radiation. When an electron in a high-energy orbit emitted light to jump down, it seemed to have a choice about exactly how far down to go, which lower orbit to end up in. What made that choice? It seems like you have to assume that the electrons knows beforehand where it is going to stop, because it has to choose the right frequency of light to emit. This business about electrons "deciding" where to go foreshadowed a much more drastic break with the paradigm of classical physics.
• QM does not describe a world that is fundamentally discrete and pixelated. Its actually the opposite; QM describes the world as a smooth wave function. But in the right circumstances where individual parts of the wave function are tied down in a certain way, the wave takes the form of a combination of distinct vibrational modes. The world is fundamentally wavy; its apparent discreteness comes from the particular way those wave are able to vibrate.

PhilosophyOfPhysics

• There are quantities that are not merely unknown but to not even exist, even though we can seemingly measure them.
• One way or the other, its indisputable that something went through both slits as the electron traveled to the screen. The double slit experiment makes it difficult to cling to the belief that the electron is just a single classical point, and the wave function simply represents our ignorance about where the point is. Ignorance doesn't cause interference patterns. There is something real about the wave function.
• The simple geometric fact underlying the Born rule. Amplitudes don't add up to one, but there squares do. That is exactly like an important feature of probability: the sum of probabilities for different outcomes add to one. The Born rule is essentially Pythagoras's theorem applied to the amplitudes of different branches.
• Entanglement arises because there is only one wave function for the entire universe, not separate wave functions for each piece of it.
• There are approximately 10⁸⁸ particles in the observable universe, mostly photons and neutrinos.
• The other potentially doubtable assumption in Bells theorem seems uncontroversial at first glance: that measurements have definite outcomes. Bells result does not imply that we have to include spooky action at a distance in minimalist QM as it does for the boring old single-world theories. The correlations dont come about because of any kind of influence being transmitted faster than light, but because of branching of the wave function into different worlds, in which correlated things happen. If you're happy with many-worlds and trying to puzzle out how to map the theory onto our observed experience, Bells result is an automatic consequence of the underlying equations, not an additional constraint you need to worry about moving forward.

PhilosophyOfPhysics

• Einsteins primary concerns about QM were not with randomness but with realism and locality.
• One of Wheeler's favorite principles "Radical conservatism"
• IF you know how the system evolves starting from two different states, the evolution of a superposition of both states will just be a superpositions of the two evolutions.
• The Schrodinger equation says that an accurate measuring apparatus will evolve into a macroscopic superposition which we will ultimately interpret as branching into separate worlds. We didn't put the worlds in; they were always there (as possible states in the Hilbert space), and the Sch eq inevitably brings them to life. The problem is that we never seen to come across superpositions involving big macroscopic objects in our experience of the world. The traditional remedy has been to monkey with the fundamental rules of QM in one way or another. Some say that the Sch eq inst always applicable, others add hidden variables.
• Everett didn't introduce anything new in QM; he removed some extraneous clunky pieces from the formalism. Every non-Everettian version of QM is a "disappearing worlds" theory. If you are bothered by multiple worlds, you have to fiddle with either the nature of quantum states or their ordinary evolution to get rid of them. (Is it worth it?)
• To the modern Everettian, decoherence is absolutely crucial to making sense of QM. It explains why wave functions seem to collapse when you measure the system and indeed what a "measurement" really is. The simple process of macroscopic objects becoming entangled with the environment, which we cannot keep track of – is decoherence; it comes with universe-altering consequences. Decoherence causes the wave function to split or branch into multiple worlds.
• Being decohered means that the two parts of the electrons wave function can no longer interfere with each other. It means they cant interact at all. So for all intents and purposes, they are part of separate worlds.
• The price we pay for such a powerful and simple unification of quantum dynamics is a large number of separate worlds.
• We should treat QM in its own right as a fundamental theory without any dependence on classical physics, if fact, we must derive classically physics from it.
• Bryce DeWitt wrote a letter to Everett complaining that the real world obviously didn't "branch", since we never experience such things. The reply: "Do you feel the motion of the earth?"
• What would it feel like if many worlds were true? eg: The Schrodinger eq is perfectly deterministic, Why do probabilities enter at all? And why do they obey the born rule?
• Probability in many-worlds is a statement about what we should BELIEVE and how we should ACT, not about how often things happen. "What we should believe" isn't something that really has a place in the postulates of a physics theory, it should be implied by them. There actually is neither any room for an extra postulate, nor any need for one. Given the basic structure of QM, the Born rule is natural and automatic. Since we see the Born rule in nature, this should give us confidence that we are on the right track. A framework in which an important result can be derived from more fundamental postulates should be preferred to one where it needs to be separately assumed. The many worlds predicts a world that closely is approximated by classical physics except for quantum measurements, during which the probability of obtaining any particular outcome is given by the Born rule.

PhilosophyOfPhysics

• Amplitudes squared naturally look like probabilities, they're positive and sum to one. The deeper issues is why there is anything unpredictable about Everettian QM at all, and if so, why there is any specific rule for attaching probabilities.
• If Everett is right there is 100% probability that each possibility is realized in some particular world (branch of the wave function). There really are such worlds. This is quite different from the frequentist paradigm for probabilities. Instead use the epistemic probability, having to do with what we know rather than some hypothetical infinite number of trials. But, in what sense is there anything we dont know about Everettian QM, its totally deterministic. One answer that is tempting but wrong: "which world we end up in". Wrong b/c it implicitly relies on a notion of personal identity that simply isn't applicable in a quantum universe (We end up in all the worlds)
• At any one moment we have no trouble identifying a specific person that is undeniably "myself". QM suggests that were going to have to modify this somewhat. In a classical universe what matters to personal identity is the pattern that we form, and the continuity of the pattern with time, especially the memories of the person under consideration. The idea of a unified you is useful not because all of these different collection of atoms at different moments of time are literally the same, but because they are related to one another in an obvious way. The new features in QM is the duplication of that pattern when the wave function branches. Everyone of the people in the different branches has a reasonable claim of being "you". None of them is wrong. Each of them is a separate person, all of whom trace their beginnings back to the same person.

• Instead of "which branch will I end up on", think about the moment immediately after decoherence (which is an extraordinarily fast process). The branching happens first and we know about it slightly later. There are now two copies of you that are identical, each lives on a distinct branch, but neither knows which one it is on. There is "self-locating uncertainty" you know everything there is to know about the universe except where you are within it. That ignorance is where the probabilities come in. They can assign credence to being on one branch or the other. What should the credence be? Two ways to go: -) Use the structure of QM to pick out a preferred set of credences that rational observers should assign (If you're willing to accept that, you'll end up assigning credences exactly according to the Born rule) -) Deny that it makes sense to assign any definite credences at all.

  Now, part of science is predicting what will be observed. IF there were an arbitrary collection of ways to assign credences, and each of them seemed just as reasonable as the other, we would be stuck. But of the structure of the theory points unmistakably to one particular was to assign such credences – and that way is in agreement with our experimental data – we should adopt it.

• If we didn't know about the Born rule, might think that the amplitudes are completely irrelevant to assigning probabilities. Might try simply counting branches, can easily show that this doesn't work. (inconsistencies arise with repeated measurements p144) More restrictive version that says we need to assign equal probabilities when the amplitudes are the same. It turns out that this (+ the requirement that repeated measurements do not lead to inconsistencies ) is all you need to shows that when the branches have different amplitudes we should use the born rule.

• The hard part isn't deriving the actual formula, its providing a solid grounding for what probability means in a deterministic theory. Here we have explored one possible answer (credences for being on different branches immediately after the wave function branches) All of your descendants will be in exactly the same epistemic position (assigning Born rule probabilities). So it makes sense that you adopt these probabilities now. We have been forced to shift the meaning of what probability is from a simple frequentist model to a more robust epistemic picture, but how we calculate things goes through exactly as before. That's why physicists have been able to do interesting work while avoiding these subtle questions all this time.

[BROKEN LINK: 9M0N1O2P-3Q4R-5S6T-7U8V-9W0X1Y2Z3A4B]

• Decision theory is another way (maybe more popular in the foundations of physics) to derive the Born theory A rational agent in an Everettian universe acts precisely as if they live in a non-deterministic universe where probabilities are given by the born rule. If we live in the world of textbook QM with wave function collapse, it would be rational to calculate our expected utility in a certain way. Deutsch and Wallace have shown that if we live in a deterministic Many-Worlds universe it is rational to calculate our expected utility in exactly the same way.

[BROKEN LINK: 9M0N1O2P-3Q4R-5S6T-7U8V-9W0X1Y2Z3A4B]

• Many-Worlds doesn't assume a large number of worlds. It assumes a wave function evolving according to the Schrodinger eq. The worlds are there automatically. Hilbert space is very big. Its not any bigger in many worlds than in other versions of QM; its exactly the same size, and that size is big enough to describe a large number of parallel realities. If your doing QM at all the potential for many worlds is there and ordinary Schrodinger eq evolution brings them about, like it or not. Other approaches just choose to somehow not make use of the full richness of Hilbert space.

PhilosophyOfPhysics

• Many worlds is pure minimalist QM, without any additional assumptions. If you want to introduce extra assumptions, do it, but then we can ask whether those new assumptions are testable.
• The other worlds could be detected in principle; Decoherence makes it fantastically unlikely for one world to interfere with another, but not metaphysically impossible.
• The number of branches of the wave function, like entropy only increases with time.
• Many worlds doesn't say "everything that's possible happens" it says "the wave function evolves according to the Schrodinger eq" Just because many things happen in minimalistic QM doesn't mean everything does.
• When one world divides in two, the energy in each world is basically the same as it previously was in the single world (as far as anyone living inside is concerned), but their contributions to the total energy of the wave function of the universe have divided in half, since the amplitudes have decreased. Each world got a bit "thinner" even thought the inhabitants cant tell.
• Despite the unrivaled empirical success of quantum theory, the very suggestion that it may be literally true as a description of nature is still greeted with cynicism, incomprehension, and even anger. Most people reject Everettian QM more out of a visceral sense of distaste than a principled set of worries. "I do not know how to refute an incredulous stare".
• The virtue of many-worlds is the simplicity of its basic formulation: the wave function + Schrodinger eq. All else is commentary. Some of that commentary (split into systems and environment, decoherence, and the branching of the wave function) is extremely useful and needed for making sense of our world.

PhilosophyOfPhysics

• If you are repulsed by all of the worlds out there, the task you face is to modify many-worlds in some way.
• GRW can be thought of as many-worlds plus a random process that cuts off new branches of the wave function as they appear. Its a great example to bring up to friends who complain that many-worlds or other approaches to QM aren't experimentally testable. You test theories in comparison with other theories, these two are manifestly different in their empirical predictions.

PhilosophyOfPhysics

• To each individual on some branch of the wave function, life goes on just as if they lived in a single world with truly stochastic quantum events.
• Any one individual can trace their lives backward to a unique person but going forward will branch into multiple people. There is not one future self that is picked out as "really you" and its just as true that there is no one person constituted by all of those future individuals. They are separate, much like identical twins are distinct people, despite descending from a single zygote.

[BROKEN LINK: Past-vs-Future]

• Physicists start by taking a classical theory and quantizing it, but of course that's not the way that nature works. Nature is quantum mechanical from the start. Many-worlds is uniquely suited to the task of throwing away all our classical intuition, being quantum from the start and determining how the approximately classical world that we see around us ultimately emerges from the wave function of the universe, spacetime and all.
• Space is so important because interactions are local.

PhilosophyOfPhysics

• Nothing forces us to think of the wave function as describing multiple worlds, even after decoherence has occurred. We could still talk of the entire wave function as a whole, its just really helpful to split it into worlds. But this is ultimately a convenience, not something the theory imposes on us. For a quantum version of Laplaces demon, with exact knowledge of the quantum state of the universe, there would never be any need to divide the wave function into a set of branches describing a collection of worlds. But it enormously convenient and helpful to do so, and we can exploit this convenience because the individual worlds dont interact with one another. Everettian worlds are real in the same way that tables and chairs are real.

PhilosophyOfPhysics

• Emergence is not a generic feature of physical systems. It happens when there's a special way of describing the system that involves much much less information than a complete description would, but nevertheless gives us a handle on whats going on. The generic situation in physics is that you need to keep track of all the parts to know what the system will do next. Loose just a little bit, and you know nothing. Emergence happens when the opposite is possible: we can throw always almost all the information, and still say quite a lot about what will happen.

  This is the case for Everettian worlds; we dont need to keep track of the entire wave function to make useful predictions, just what happens in an individual world. To a good approximation we can treat what happens in each world using classical mechanics, with just the occasional quantum intervention when we entangle with microscopic systems in superposition. Our individual branch of the wave function describes an emergent almost-classical world.

• Why do we end up seeing macroscopic objects with well-defined locations in space, rather than being in super positions of different locations ? "Why space"? (The answer is not b/c the objects are big, we have no problem describing big objects as in superpositions. The real answer is more interesting) Locality is what makes space special. Interactions occur between different objects that are close in space, not eg: close in momentum. (Not a requirement, but one that seems to hold quite well in our world) "Preferred-basis problem". Decoherence picks out a preferred basis based on interaction with the environment. Whether a particle in the environment interacts with the object or not depends on where the object is. The spatial basis of macroscopic objects are the ones we see because these objects interact consistently with their environments. "Pointer States" The pointer states or basis is where a well-behaved classical approximation makes sense, therefore its that basis that defines emergent worlds. Decoherence is the phenomenon that links the austere simplicity of minimalistic QM to the messy particularity of the world we see.
• In QFT every physically interesting state has an enormous amount o entanglement. The wave function in QFT is not a function of space, its a function of the set of all configurations of all the classical fields. All of this implicitly assuming the many worlds version of QM.
• The vacuum state in QFT can still have interesting structure if we ask about individual parts of the field.
• The Pointer states of the QFT look like collections of definite numbers of particles. These are the states that we see when we actually look at the world.
• Fields are more fundamental; its fields that provide the best picture we current have of what the universe is made of. Particles are simply what we see when we observe fields under the right circumstances.
• "Quantum fluctuations" or particles popping in and out of existence is more false than true. In empty space described by the QFT vacuum, nothing is fluctuating at all; the quantum state is absolutely stationary. The picture of particles popping in and out of existence is entirely different from the reality, in which the state is precisely the same from one moment to another. Why then are physicists constantly talking about quantum fluctuations? Its what we see, and we talk about what we see as being real, even thought QM keeps telling us to do better. Everettian QM is clear; empty space is described by a stationary, unchanging quantum state, where nothing is happening moment to moment. But if we measure the values of the quantum field in some small region, we would see what looked like a random mess. If we looked again a moment later we would see a different looking random mess. When we observe the quantum state we typically see something quite different from what the state was before we looked.

PhilosophyOfPhysics

• If you measure the total number of particles throughout all of space in the vacuum state of the QFT, with perfect confidence, detect no particles. But in the real world, we will be confined to do the experiment in some finite region of space, there will then always be a small probability of observing one or more particles. We shouldn't be asking how many particles are there really? We should be asking "What are the possible measurement outcomes when we observe the quantum state in this way? The number of particles we see isn't an absolute reality, it depends on how we look at the state.
• At the quantum level, the classical statement, "the fields tend to match at the boundary" turns into "The fields in the left and right regions tend to be highly entangled".
• the Reeh-Schlieder theorem implies that if we measure the quantum fields locally, there is some measurement outcome we could get that would be associated with a Taj-Mahal suddenly being on the moon.
• The entropy of a region of empty space is infinite. But if we impose a cutoff it is finite and it is proportional to the area of the regions boundary. Most of the entanglement is concentrated on nearby regions. The total entropy of a region of empty space depends on the amount of the entanglement across the boundary, which is proportional to how big that boundary is – its area.
• To be honest many physicists working on these problems dont think of themselves as using many-worlds though they are implicitly doing so. (they are certainty not using hidden variables, dynamical collapse, or an epistemic approach to QM)
• The behaviors of quantum fields can, under the right circumstances, be accurately modeled as the repeated interaction of many particles.