It remains embarrassing that physicists haven’t settled on the best way of formulating quantum mechanics (or some improved successor to it). I’m partial to Many-Worlds, but there are other smart people out there who go in for alternative formulations: hidden variables, dynamical collapse, epistemic interpretations, or something else. And let no one say that I won’t let alternative voices be heard! (Unless you want to talk about propellantless space drives, which are just crap.)
So let me point you to this guest post by Anton Garrett that Peter Coles just posted at his blog:
It’s quite a nice explanation of how the state of play looks to someone who is sympathetic to a hidden-variables view. (Fans of Bell’s Theorem should remember that what Bell did was to show that such variables must be nonlocal, not that they are totally ruled out.)
As a dialogue, it shares a feature that has been common to that format since the days of Plato: there are two characters, and the character that sympathizes with the author is the one who gets all the good lines. In this case the interlocutors are a modern physicist Neo, and a smart recently-resurrected nineteenth-century physicist Nino. Trained in the miraculous successes of the Newtonian paradigm, Nino is very disappointed that physicists of the present era are so willing to simply accept a theory that can’t do better than predicting probabilistic outcomes for experiments. More in sorrow than in anger, he urges us to do better!
My own takeaway from this is that it’s not a good idea to take advice from nineteenth-century physicists. Of course we should try to do better, since we should alway try that. But we should also feel free to abandon features of our best previous theories when new data and ideas come along.
A nice feature of the dialogue between Nino and Neo is the way in which it illuminates the fact that much of one’s attitude toward formulations of quantum mechanics is driven by which basic assumptions about the world we are most happy to abandon, and which we prefer to cling to at any cost. That’s true for any of us — such is the case when there is legitimate ambiguity about the best way to move forward in science. It’s a feature, not a bug. The hope is that eventually we will be driven, by better data and theories, toward a common conclusion.
What I like about Many-Worlds is that it is perfectly realistic, deterministic, and ontologically minimal, and of course it fits the data perfectly. Equally importantly, it is a robust and flexible framework: you give me your favorite Hamiltonian, and we instantly know what the many-worlds formulation of the theory looks like. You don’t have to think anew and invent new variables for each physical situation, whether it’s a harmonic oscillator or quantum gravity.
Of course, one gives something up: in Many-Worlds, while the underlying theory is deterministic, the experiences of individual observers are not predictable. (In that sense, I would say, it’s a nice compromise between our preferences and our experience.) It’s neither manifestly local nor Lorentz-invariant; those properties should emerge in appropriate situations, as often happens in physics. Of course there are all those worlds, but that doesn’t bother me in the slightest. For Many-Worlds, it’s the technical problems that bother me, not the philosophical ones — deriving classicality, recovering the Born Rule, and so on. One tends to think that technical problems can be solved by hard work, while metaphysical ones might prove intractable, which is why I come down the way I do on this particular question.
But the hidden-variables possibility is still definitely alive and well. And the general program of “trying to invent a better theory than quantum mechanics which would make all these distasteful philosophical implications go away” is certainly a worthwhile one. If anyone wants to suggest their favorite defenses of epistemic or dynamical-collapse approaches, feel free to leave them in comments.
Last week I had the pleasure of giving a seminar to the philosophy department at the University of North Carolina. Ordinarily I would have talked about the only really philosophical work I’ve done recently (or arguably ever), deriving the Born Rule in the Everett approach to quantum mechanics. But in this case I had just talked about that stuff the day before, at a gathering of local philosophers of science.
So instead I decided to use the opportunity to get some feedback on another idea I had been thinking about — our old friend, the claim that The Laws of Physics Underlying Everyday Life Are Completely Understood (also here, here). In particular, given that I was looking for feedback from a group of people that had expertise in philosophical matters, I homed in on the idea that quantum field theory has a unique property among physical theories: any successful QFT tells us very specifically what its domain of applicability is, allowing us to distinguish the regime where it should be accurate from the regime where we can’t make predictions.
The talk wasn’t recorded, but here are the slides. I recycled a couple of ones from previous talks, but mostly these were constructed from scratch.
The punchline of the talk was summarized in this diagram, showing different regimes of phenomena and the arrows indicating what they depend on:
There are really two arguments going on here, indicated by the red arrows with crosses through them. These two arrows, I claim, don’t exist. The physics of everyday life is not affected by dark matter or any new particles or forces, and its only dependence on the deeper level of fundamental physics (whether it be string theory or whatever) is through the intermediary of what Frank Wilczek has dubbed “The Core Theory” — the Standard Model plus general relativity. The first argument (no new important particles or forces) relies on basic features of quantum field theory, like crossing symmetry and the small number of species that go into making up ordinary matter. The second argument is more subtle, relying on the idea of effective field theory.
So how did it go over? I think people were properly skeptical and challenging, but for the most part they got the point, and thought it was interesting. (Anyone who was in the audience is welcome to chime in and correct me if that’s a misimpression.) Mostly, since this was a talk to philosophers rather than physicists, I spent my time doing a pedagogical introduction to quantum field theory, rather than diving directly into any contentious claims about it — and learning something new is always a good thing.
The idea that time isn’t “real” is an ancient one — if we’re allowed to refer to things as “ancient” under the supposition that time isn’t real. You will recall the humorous debate we had at our Setting Time Aright conference a few years ago, in which Julian Barbour (the world’s most famous living exponent of the view that time isn’t real) and Tim Maudlin (who believes strongly that time is real, and central) were game enough to argue each other’s position, rather than their own. Confusingly, they were both quite convincing.
Personally I think that the whole issue is being framed in a slightly misleading way. (Indeed, this mistaken framing caused me to believe at first that Lee and I were in agreement, until his book actually came out.) The stance of Maudlin and Smolin and others isn’t merely that time is “real,” in the sense that it exists and plays a useful role in how we talk about the world. They want to say something more: that the passage of time is real. That is, that time is more than simply a label on different moments in the history of the universe, all of which are independently pretty much equal. They want to attribute “reality” to the idea of the universe coming into being, moment by moment.
Such a picture — corresponding roughly to the “possibilism” option in the picture above, although I won’t vouch that any of these people would describe their own views that way — is to be contrasted with the “eternalist” picture of the universe that has been growing in popularity ever since Laplace introduced his Demon. This is the view, in the eyes of many, that is straightforwardly suggested by our best understanding of the laws of physics, which don’t seem to play favorites among different moments of time.
According to eternalism, the apparent “flow” of time from past to future is indeed an illusion, even if the time coordinate in our equations is perfectly real. There is an apparent asymmetry between the past and future (many such asymmetries, really), but that can be traced to the simple fact that the entropy of the universe was very low near the Big Bang — the Past Hypothesis. That’s an empirical feature of the configuration of stuff in the universe, not a defining property of the nature of time itself.
Personally, I find the eternalist block-universe view to be perfectly acceptable, so I think that these folks are working hard to tackle a problem that has already been solved. There are more than enough problems that haven’t been solved to occupy my life for the rest of its natural span of time (as it were), so I’m going to concentrate on those. But who knows? If someone could follow this trail and be led to a truly revolutionary and successful picture of how the universe works, that would be pretty awesome.
Last October I was privileged to be awarded the Emperor Has No Clothes award from the Freedom From Religion Foundation. The physical trophy consists of the dashing statuette here on the right, presumably the titular Emperor. It’s made by the same company that makes the Academy Award trophies. (Whenever I run into Meryl Streep, she’s just won’t shut up about how her Oscars are produced by the same company that does the Emperor’s New Clothes award.)
Part of the award-winning is the presentation of a short speech, and I wasn’t sure what to talk about. There are only so many things I have to say, but it’s boring to talk about the same stuff over and over again. More importantly, I have no real interest in giving religion-bashing talks; I care a lot more about doing the hard and constructive work of exploring the consequences of naturalism.
So I decided on a cheerful topic: Death and Physics. I talked about modern science gives us very good reasons to believe (not a proof, never a proof) that there is no such thing as an afterlife. Life is a process, not a substance, and it’s a process that begins, proceeds along for a while, and comes to an end. Certainly something I’ve said before, e.g. in my article on Physics and the Immortality of the Soul, and in the recent Afterlife Debate, but I added a bit more here about entropy, complexity, and what we mean by the word “life.”
If you’re in a reflective mood, here it is. I begin at around 3:50. One of the points I tried to make is that the finitude of life has its upside. Every moment is precious, and what we should value is what is around us right now — because that’s all there is. It’s a scary but exhilarating view of the world.
I got to know Charles “Chip” Sebens back in 2012, when he emailed to ask if he could spend the summer at Caltech. Chip is a graduate student in the philosophy department at the University of Michigan, and like many philosophers of physics, knows the technical background behind relativity and quantum mechanics very well. Chip had funding from NSF, and I like talking to philosophers, so I said why not?
We had an extremely productive summer, focusing on our different stances toward quantum mechanics. At the time I was a casual adherent of the Everett (many-worlds) formulation, but had never thought about it carefully. Chip was skeptical, in particular because he thought there were good reasons to believe that EQM should predict equal probabilities for being on any branch of the wave function, rather than the amplitude-squared probabilities of the real-world Born Rule. Fortunately, I won, although the reason I won was mostly because Chip figured out what was going on. We ended up writing a paper explaining why the Born Rule naturally emerges from EQM under some simple assumptions. Now I have graduated from being a casual adherent to a slightly more serious one.
But that doesn’t mean Everett is right, and it’s worth looking at other formulations. Chip was good enough to accept my request that he write a guest blog post about another approach that’s been in the news lately: a “Newtonian” or “Many-Interacting-Worlds” formulation of quantum mechanics, which he has helped to pioneer.
In Newtonian physics objects always have definite locations. They are never in two places at once. To determine how an object will move one simply needs to add up the various forces acting on it and from these calculate the object’s acceleration. This framework is generally taken to be inadequate for explaining the quantum behavior of subatomic particles like electrons and protons. We are told that quantum theory requires us to revise this classical picture of the world, but what picture of reality is supposed to take its place is unclear. There is littleconsensus on many foundational questions: Is quantum randomness fundamental or a result of our ignorance? Do electrons have well-defined properties before measurement? Is the Schrödinger equation always obeyed? Are there parallel universes?
Some of us feel that the theory is understood well enough to be getting on with. Even though we might not know what electrons are up to when no one is looking, we know how to apply the theory to make predictions for the results of experiments. Much progress has been made―observe the wonder of the standard model―without answering these foundational questions. Perhaps one day with insight gained from new physics we can return to these basic questions. I will call those with such a mindset the doers. Richard Feynman was a doer:
“It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, ‘But how can it be like that?’ which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. … I think I can safely say that nobody understands quantum mechanics. … Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”
In contrast to the doers, there are the dreamers. Dreamers, although they may often use the theory without worrying about its foundations, are unsatisfied with standard presentations of quantum mechanics. They want to know “how it can be like that” and have offered a variety of alternative ways of filling in the details. Doers denigrate the dreamers for being unproductive, getting lost “down the drain.” Dreamers criticize the doers for giving up on one of the central goals of physics, understanding nature, to focus exclusively on another, controlling it. But even by the lights of the doer’s primary mission―being able to make accurate predictions for a wide variety of experiments―there are reasons to dream:
“Suppose you have two theories, A and B, which look completely different psychologically, with different ideas in them and so on, but that all consequences that are computed from each are exactly the same, and both agree with experiment. … how are we going to decide which one is right? There is no way by science, because they both agree with experiment to the same extent. … However, for psychological reasons, in order to guess new theories, these two things may be very far from equivalent, because one gives a man different ideas from the other. By putting the theory in a certain kind of framework you get an idea of what to change. … Therefore psychologically we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics.”
In the spirit of finding alternative versions of quantum mechanics―whether they agree exactly or only approximately on experimental consequences―let me describe an exciting new option which has recently been proposed by Hall, Deckert, and Wiseman (in Physical Review X) and myself (forthcoming in Philosophy of Science), receiving media attention in: Nature, New Scientist, Cosmos, Huffington Post, Huffington Post Blog, FQXi podcast… Somewhat similar ideas have been put forward by Böstrom, Schiff and Poirier, and Tipler. The new approach seeks to take seriously quantum theory’s hydrodynamic formulation which was developed by Erwin Madelung in the 1920s. Although the proposal is distinct from the many-worlds interpretation, it also involves the postulation of parallel universes. The proposed multiverse picture is not the quantum mechanics of college textbooks, but just because the theory looks so “completely different psychologically” it might aid the development of new physics or new calculational techniques (even if this radical picture of reality ultimately turns out to be incorrect).
Let’s begin with an entirely reasonable question a dreamer might ask about quantum mechanics.
“I understand water waves and sound waves. These waves are made of particles. A sound wave is a compression wave that results from particles of air bunching up in certain regions and vacating other. Waves play a central role in quantum mechanics. Is it possible to understand these waves as being made of some things?”
There are a variety of reasons to think the answer is no, but they can be overcome. In quantum mechanics, the state of a system is described by a wave function Ψ. Consider a single particle in the famous double-slit experiment. In this experiment the one particle initially passes through both slits (in its quantum way) and then at the end is observed hitting somewhere on a screen. The state of the particle is described by a wave function which assigns a complex number to each point in space at each time. The wave function is initially centered on the two slits. Then, as the particle approaches the detection screen, an interference pattern emerges; the particle behaves like a wave.
Figure 1: The evolution of Ψ with the amount of color proportional to the amplitude (a.k.a. magnitude) and the hue indicating the phase of Ψ.
There’s a problem with thinking of the wave as made of something: the wave function assigns strange complex numbers to points in space instead of familiar real numbers. This can be resolved by focusing on |Ψ|2, the squared amplitude of the wave function, which is always a positive real number.
Figure 2: The evolution of |Ψ|2.
We normally think of |Ψ|2 as giving the probability of finding the particle somewhere. But, to entertain the dreamer’s idea about quantum waves, let’s instead think of |Ψ|2 as giving a density of particles. Whereas figure 2 is normally interpreted as showing the evolution of the probability distribution for a single particle, instead understand it as showing the distribution of a large number of particles: initially bunched up at the two slits and later spread out in bands at the detector (figure 3). Although I won’t go into the details here, we can actually understand the way that wave changes in time as resulting from interactions between these particles, from the particles pushing each other around. The Schrödinger equation, which is normally used to describe the way the wave function changes, is then viewed as consequence of this interaction.
Figure 3: The evolution of particles with |Ψ|2 as the density. This animation is meant to help visualize the idea, but don’t take the precise motions of the particles too seriously. Although we know how the particles move en masse, we don’t know precisely how individual particles move.
In solving the problem about complex numbers, we’ve created two new problems: How can there really be a large number of particles if we only ever see one show up on the detector at the end? If |Ψ|2 is now telling us about densities and not probabilities, what does it have to do with probabilities?
Removing a simplification in the standard story will help. Instead of focusing on the wave function of a single particle, let’s consider all particles at once. To describe the state of a collection of particles it turns out we can’t just give each particle its own wave function. This would miss out on an important feature of quantum mechanics: entanglement. The state of one particle may be inextricably linked to the state of another. Instead of having a wave function for each particle, a single universal wave function describes the collection of particles.
The universal wave function takes as input a position for each particle as well as the time. The position of a single particle is given by a point in familiar three dimensional space. The positions of all particles can be given by a single point in a very high dimensional space, configuration space: the first three dimensions of configuration space give the position of particle 1, the next three give the position of particle 2, etc. The universal wave function Ψ assigns a complex number to each point of configuration space at each time. |Ψ|2 then assigns a positive real number to each point of configuration space (at each time). Can we understand this as a density of some things?
A single point in configuration space specifies the locations of all particles, a way all things might be arranged, a way the world might be. If there is only one world, then only one point in configuration space is special: it accurately captures where all the particles are. If there are many worlds, then many points in configuration space are special: each accurately captures where the particles are in some world. We could describe how densely packed these special points are, which regions of configuration space contain many worlds and which regions contain few. We can understand |Ψ|2 as giving the density of worlds in configuration space. This might seem radical, but it is the natural extension of the answer to the dreamer’s question depicted in figure 3.
Now that we have moved to a theory with many worlds, the first problem above can be answered: The reason that we only see one particle hit the detector in the double-slit experiment is that only one of the particles in figure 3 is in our world. When the particles hit the detection screen at the end we only see our own. The rest of the particles, though not part of our world, do interact with ours. They are responsible for the swerves in our particle’s trajectory. (Because of this feature, Hall, Deckert, and Wiseman have coined the name “Many Interacting Worlds” for the approach.)
Figure 4: The evolution of particles in figure 3 with the particle that lives in our world highlighted.
No matter how knowledgeable and observant you are, you cannot know precisely where every single particle in the universe is located. Put another way, you don’t know where our world is located in configuration space. Since the regions of configuration space where |Ψ|2 is large have more worlds in them and more people like you wondering which world they’re in, you should expect to be in a region of configuration space where|Ψ|2 is large. (Aside: this strategy of counting each copy of oneself as equally likely is not so plausible in the old many-worlds interpretation.) Thus the connection between |Ψ|2 and probability is not a fundamental postulate of the theory, but a result of proper reasoning given this picture of reality.
There is of course much more to the story than what’s been said here. One particularly intriguing consequence of the new approach is that the three sentence characterization of Newtonian physics with which this post began is met. In that sense, this theory makes quantum mechanics look like classical physics. For this reason, in my paper I gave the theory the name “Newtonian Quantum Mechanics.”
There’s a claim out there — one that is about 95% true, as it turns out — that if you pick a Wikipedia article at random, then click on the first (non-trivial) link, and keep clicking on the first link of each subsequent article, you will end up at Philosophy. More specifically, you will end up at a loop that runs through Reality, Existence, Awareness, Consciousness, and Quality (philosophy), as well as Philosophy itself. It’s not hard to see why. These are the Big Issues, concerning the fundamental nature of the universe at a deep level. Almost any inquiry, when pressed to ever-greater levels of precision and abstraction, will get you there.
Take, for example, the straightforward-sounding question “Does Santa Exist?” You might be tempted to say “No” and move on. (Or you might be tempted to say “Yes” and move on, I don’t know — a wide spectrum of folks seem to frequent this blog.) But even to give such a common-sensical answer is to presume some kind of theory of existence (ontology), not to mention a theory of knowledge (epistemology). So we’re allowed to ask “How do you know?” and “What do you really mean by exist?”
These are the questions that underlie an entertaining and thought-provoking new book by Eric Kaplan, called Does Santa Exist?: A Philosophical Investigation. Eric has a resume to be proud of: he is a writer on The Big Bang Theory, and has previously written for Futurama and other shows, but he is also a philosopher, currently finishing his Ph.D. from Berkeley. In the new book, he uses the Santa question as a launching point for a rewarding tour through some knotty philosophical issues. He considers not only a traditional attack on the question, using Logic and the beloved principles of reason, but sideways approaches based on Mysticism as well. (“The Buddha ought to be able to answer our questions about the universe for like ten minutes, and then tell us how to be free of suffering.”) His favorite, though, is the approach based on Comedy, which is able to embrace contradiction in a way that other approaches can’t quite bring themselves to do.
Most people tend to have a pre-existing take on the Santa question. Hence, the book trailer for Does Santa Exist? employs a uniquely appropriate method: Choose-Your-Own-Adventure. Watch and interact, and you will find the answers you seek.
Stephen Hawking did not actually attend our meeting — he was at the hotel for a different event. But he stopped by for an informal session on the arrow of time. Photo by Vishnya Maudlin.
It was a thought-provoking meeting, but one of my thoughts was: “We don’t really have a well-defined field called Philosophy of Cosmology.” At least, not yet. Talks were given by philosophers and by cosmologists; the philosophers generally gave good talks on the philosophy of physics, while some of the cosmologists gave solid-but-standard talks on cosmology. Some of the other cosmologists tried their hand at philosophy, and I thought those were generally less successful. Which is to be expected — it’s a sign that we need to do more work to set the foundations for this new subdiscipline.
A big part of defining an area of study is deciding on a set of questions that we all agree are worth thinking about. As a tiny step in that direction, here is my attempt to highlight ten questions — and various sub-questions — that naturally fall under the rubric of Philosophy of Cosmology. They fall under other rubrics as well, of course, as well as featuring significant overlap with each other. So there’s a certain amount of arbitrariness here — suggestions for improvements are welcome.
Here we go:
In what sense, if any, is the universe fine-tuned? When can we say that physical parameters (cosmological constant, scale of electroweak symmetry breaking) or initial conditions are “unnatural”? What sets the appropriate measure with respect to which we judge naturalness of physical and cosmological parameters? Is there an explanation for cosmological coincidences such as the approximate equality between the density of matter and vacuum energy? Does inflation solve these problems, or exacerbate them? What conclusions should we draw from the existence of fine-tuning?
How is the arrow of time related to the special state of the early universe? What is the best way to formulate the past hypothesis (the early universe was in a low entropy state) and the statistical postulate (uniform distribution within macrostates)? Can the early state be explained as a generic feature of dynamical processes, or is it associated with a specific quantum state of the universe, or should it be understood as a separate law of nature? In what way, if any, does the special early state help explain the temporal asymmetries of memory, causality, and quantum measurement?
What is the proper role of the anthropic principle? Can anthropic reasoning be used to make reliable predictions? How do we define the appropriate reference class of observers? Given such a class, is there any reason to think of ourselves as “typical” within it? Does the prediction of freak observers (Boltzmann Brains) count as evidence against a cosmological scenario?
What part should unobservable realms play in cosmological models? Does cosmic evolution naturally generate pocket universes, baby universes, or many branches of the wave function? Are other “universes” part of science if they can never be observed? How do we evaluate such models, and does the traditional process of scientific theory choice need to be adapted to account for non-falsifiable predictions? How confident can we ever be in early-universe scenarios such as inflation?
What is the quantum state of the universe, and how does it evolve? Is there a unique prescription for calculating the wave function of the universe? Under what conditions are different parts of the quantum state “real,” in the sense that observers within them should be counted? What aspects of cosmology depend on competing formulations of quantum mechanics (Everett, dynamical collapse, hidden variables, etc.)? Do quantum fluctuations happen in equilibrium? What role does decoherence play in cosmic evolution? How does do quantum and classical probabilities arise in cosmological predictions? What defines classical histories within the quantum state?
Are space and time emergent or fundamental? Is quantum gravity a theory of quantized spacetime, or is spacetime only an approximation valid in a certain regime? What are the fundamental degrees of freedom? Is there a well-defined Hilbert space for the universe, and what is its dimensionality? Is time evolution fundamental, or does time emerge from correlations within a static state?
What is the role of infinity in cosmology? Can the universe be infinitely big? Are the fundamental laws ultimate discrete? Can there be an essential difference between “infinite” and “really big”? Can the arrow of time be explained if the universe has an infinite amount of room in which to evolve? Are there preferred ways to compare infinitely big subsets of an infinite space of states?
Can the universe have a beginning, or can it be eternal? Does a universe with a first moment require a cause or deeper explanation? Are there reasons why there is something rather than nothing? Can the universe be cyclic, with a consistent arrow of time? Could it be eternal and statistically symmetric around some moment of lowest entropy?
How do physical laws and causality apply to the universe as a whole? Can laws be said to change or evolve? Does the universe as a whole maximize some interesting quantity such as simplicity, goodness, interestingness, or fecundity? Should laws be understood as governing/generative entities, or are they just a convenient way to compactly represent a large number of facts? Is the universe complete in itself, or does it require external factors to sustain it? Do the laws of physics require ultimate explanations, or can they simply be?
How do complex structures and order come into existence and evolve? Is complexity a transient phenomenon that depends on entropy generation? Are there general principles governing physical, biological, and psychological complexity? Is the appearance of life likely or inevitable? Does consciousness play a central role in accounting for the universe?
Chances are very small that anyone else interested in the field, forced at gunpoint to pick the ten biggest questions, would choose exactly these ten. Such are the wild and wooly early days of any field, when the frontier is unexplored and the conventional wisdom has yet to be settled. Feel free to make suggestions.
Sure it should. Here’s a new video from Closer to Truth, in which I’m chatting briefly with Robert Lawrence Kuhn about the question. “New” in the sense that it was just put on YouTube, although we taped it back in 2011. (Now my formulations would be considerably more sophisticated, given the wisdom that comes with age).
Sean Carroll - Is the Universe Religiously Ambiguous?
It’s interesting that the “religious beliefs are completely independent of evidence and empirical investigation” meme has enjoyed such success in certain quarters that people express surprise to learn of the existence of theologians and believers who still think we can find evidence for the existence of God in our experience of the world. In reality, there are committed believers (“sophisticated” and otherwise) who feel strongly that we have evidence for God in the same sense that we have evidence for gluons or dark matter — because it’s the best way to make sense of the data — just as there are others who think that our knowledge of God is of a completely different kind, and therefore escapes scientific critique. It’s part of the problem that theism is not well defined.
One can go further than I did in the brief clip above, to argue that any notion of God that can’t be judged on the basis of empirical evidence isn’t much of a notion at all. If God exists but has no effect on the world whatsoever — the actual world we experience could be precisely the same even without God — then there is no reason to believe in it, and indeed one can draw no conclusions whatsoever (about right and wrong, the meaning of life, etc.) from positing it. Many people recognize this, and fall back on the idea that God is in some sense necessary; there is no possible world in which he doesn’t exist. To which the answer is: “No he’s not.” Defenses of God’s status as necessary ultimately come down to some other assertion of a purportedly-inviolable metaphysical principle, which can always simply be denied. (The theist could win such an argument by demonstrating that the naturalist’s beliefs are incoherent in the absence of such principles, but that never actually happens.)
I have more sympathy for theists who do try to ground their belief in evidence, rather than those who insist that evidence is irrelevant. At least they are playing the game in the right way, even if I disagree with their conclusions. Despite what Robert suggests in the clip above, the existence of disagreement among smart people does not imply that there is not a uniquely right answer!
The setup for the traditional (non-quantum) problem is the following. Some experimental philosophers enlist the help of a subject, Sleeping Beauty. She will be put to sleep, and a coin is flipped. If it comes up heads, Beauty will be awoken on Monday and interviewed; then she will (voluntarily) have all her memories of being awakened wiped out, and be put to sleep again. Then she will be awakened again on Tuesday, and interviewed once again. If the coin came up tails, on the other hand, Beauty will only be awakened on Monday. Beauty herself is fully aware ahead of time of what the experimental protocol will be.
So in one possible world (heads) Beauty is awakened twice, in identical circumstances; in the other possible world (tails) she is only awakened once. Each time she is asked a question: “What is the probability you would assign that the coin came up tails?”
Modified from a figure by Stuart Armstrong.
(Some other discussions switch the roles of heads and tails from my example.)
The Sleeping Beauty puzzle is still quite controversial. There are two answers one could imagine reasonably defending.
“Halfer” — Before going to sleep, Beauty would have said that the probability of the coin coming up heads or tails would be one-half each. Beauty learns nothing upon waking up. She should assign a probability one-half to it having been tails.
“Thirder” — If Beauty were told upon waking that the coin had come up heads, she would assign equal credence to it being Monday or Tuesday. But if she were told it was Monday, she would assign equal credence to the coin being heads or tails. The only consistent apportionment of credences is to assign 1/3 to each possibility, treating each possible waking-up event on an equal footing.
The Sleeping Beauty puzzle has generated considerable interest. It’s exactly the kind of wacky thought experiment that philosophers just eat up. But it has also attracted attention from cosmologists of late, because of the measure problem in cosmology. In a multiverse, there are many classical spacetimes (analogous to the coin toss) and many observers in each spacetime (analogous to being awakened on multiple occasions). Really the SB puzzle is a test-bed for cases of “mixed” uncertainties from different sources.
Chip and I argue that if we adopt Everettian quantum mechanics (EQM) and our Epistemic Separability Principle (ESP), everything becomes crystal clear. A rare case where the quantum-mechanical version of a problem is actually easier than the classical version. …
One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The Born Rule is then very simple: it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. (The wave function is just the set of all the amplitudes.)
Born Rule:
The Born Rule is certainly correct, as far as all of our experimental efforts have been able to discern. But why? Born himself kind of stumbled onto his Rule. Here is an excerpt from his 1926 paper:
That’s right. Born’s paper was rejected at first, and when it was later accepted by another journal, he didn’t even get the Born Rule right. At first he said the probability was equal to the amplitude, and only in an added footnote did he correct it to being the amplitude squared. And a good thing, too, since amplitudes can be negative or even imaginary!
The status of the Born Rule depends greatly on one’s preferred formulation of quantum mechanics. When we teach quantum mechanics to undergraduate physics majors, we generally give them a list of postulates that goes something like this:
Quantum states are represented by wave functions, which are vectors in a mathematical space called Hilbert space.
The act of measuring a quantum system returns a number, known as the eigenvalue of the quantity being measured.
The probability of getting any particular eigenvalue is equal to the square of the amplitude for that eigenvalue.
After the measurement is performed, the wave function “collapses” to a new state in which the wave function is localized precisely on the observed eigenvalue (as opposed to being in a superposition of many different possibilities).
It’s an ungainly mess, we all agree. You see that the Born Rule is simply postulated right there, as #4. Perhaps we can do better.
Of course we can do better, since “textbook quantum mechanics” is an embarrassment. There are other formulations, and you know that my own favorite is Everettian (“Many-Worlds”) quantum mechanics. (I’m sorry I was too busy to contribute to the active comment thread on that post. On the other hand, a vanishingly small percentage of the 200+ comments actually addressed the point of the article, which was that the potential for many worlds is automatically there in the wave function no matter what formulation you favor. Everett simply takes them seriously, while alternatives need to go to extra efforts to erase them. As Ted Bunn argues, Everett is just “quantum mechanics,” while collapse formulations should be called “disappearing-worlds interpretations.”)
Like the textbook formulation, Everettian quantum mechanics also comes with a list of postulates. Here it is:
Quantum states are represented by wave functions, which are vectors in a mathematical space called Hilbert space.
Wave functions evolve in time according to the Schrödinger equation.
That’s it! Quite a bit simpler — and the two postulates are exactly the same as the first two of the textbook approach. Everett, in other words, is claiming that all the weird stuff about “measurement” and “wave function collapse” in the conventional way of thinking about quantum mechanics isn’t something we need to add on; it comes out automatically from the formalism.
The trickiest thing to extract from the formalism is the Born Rule. That’s what Charles (“Chip”) Sebens and I tackled in our recent paper: …
