PVV Reviews

Where I read and discuss whatever I'm feelin'

recent posts

about

  • Bell’s Theorem

    I hesitate to tell people that I’m interested in quantum mechanics, which stems in part from the fact that it sounds pretentious and in part from the fact that even after a respectable amount of time and brain power devoted to the topic, my actual grasp of the subject (and ability to articulate the underlying concepts) is embarrassingly thin and/or in many cases, incorrect. I think there are two main factors to blame here: first, we view our world through the lens of classical (Newtonian) mechanics, where everything is deterministic and causes precede effects in an orderly way. Never in my day-to-day have I really encountered entanglement or wave-particle duality in an obvious way, which makes those topics difficult to conceptualize. Second, and maybe more importantly, I simply cannot do the math that underlies quantum mechanics. A mathematical formalism underlies QM and its various concepts, and I’m of the belief that at a certain point, unless you can engage with QM via its equations, you’ve gone as far as you can go.

    Fortunately, I do not think I’ve yet reached that point, and despite my pessimism and misgivings about my autodidactic foray into QM, I think I’ve gained a lot of valuable insights and can go deeper into the topic still.

    This lengthy prelude is all to say that the purpose of this blog post, which will explore the work done on the foundations of QM by Scottish physicist John Bell, is really to force myself to organize my own thoughts about QM in a coherent way and prove that I have come away with some understanding of the theory (and maybe in the process provide a somewhat useful, if extremely surface level, discussion of an important development in QM). I chose Bell’s Theorem because I was reading about it recently and I really try not to think too deeply about what I’m going to write about here.

    By the time John Bell started thinking deeply about QM in the mid 20th century, QM had firmly been established as our most accurate description of the physical world. However, questions remained around whether we should take QM seriously as a description of the world, and if so, what is QM actually saying about reality. The dominant camp answered the first question in the negative, and insisted that QM is just a tool that allows us to make and test predictions, which is the entire function of science, and we shouldn’t try to extrapolate metaphysical claims about the world based from the mathematical formalism of QM.

    Others, including Albert Einstein, disagreed, and believed that our scientific theories should be telling us about reality, and we need to spend time and energy thinking about how QM maps onto our world. This approach, while noble, unfortunately forces one to confront a whole host of issues. For example, QM’s equations seem to tell us that, say, an electron exists as a wavelike state whose location (and other properties) can only be described as a set of probabilities, until the electron is measured or observed, at which point it exists in its better known particle-like state at a specific point in space. QM therefore introduces that idea that an observer actually has a bearing on the outcome of measurements of systems. Contrast this with classical mechanics, where we could have equations describing a ball rolling down a hill and be perfectly capable of describing the ball’s position with precision at any given point in time, regardless of whether there is an observation or measurement made on the ball. QM turns this nice and familiar notion on its head, purportedly saying that not only can be we not say for certain where a particle is located until we observe/measure it, but makes the further claim that the particle is not in any one place at all, instead existing as a superposition of different possibilities. Many questions naturally follow, including: what is an “observer”? Does it need to be human? Does it need to be conscious? Does the particle even exist until we observe it? Is it really a wave in one moment and then a particle in the next? Does that vocabulary even make sense?

    Some people took the apparent absurdities of QM to mean that the theory must be incomplete, and developed their own variations. One such person was David Bohm, who created what is called a “hidden variables theory” of QM, which propose that the concepts of superpositions and probabilities are a result of our incomplete knowledge of the quantum state. Specifically, there are hidden variables within a quantum state which, if known to us, would give us the information needed to do away with superpositions and observer-dependent measurement outcomes. Bohm’s own “Pilot Wave Theory” posited that particles exist in definite positions at all times and are guided by a “pilot wave”.

    The scientific community did not take Bohm’s Pilot Wave Theory seriously, in large part because of a supposed proof by John Von Nuemann showing that all hidden variable theories (not just Bohm’s Pilot Wave Theory) are not viable.

    This, at long last, takes us to John Bell, who read Bohm’s Pilot Wave Theory and could find no inconsistencies in it, despite Von Nuemann’s proof (which Bell was aware of). So he looked for flaws in Von Nuemann’s proof, and found one key error – Von Nuemann had failed to appreciate contextuality as a key feature of the quantum world, and therefore of hidden variable theories. “Contextuality” just means (and I’m stealing very hard from Adam Becker’s wonderful book “What Is Real” for this explanation) that the outcome of a measurement performed on a quantum system will depend on what else was measured. For example, if you measure both the spin and momentum of a particle, the value you get for the spin will be different than if you measured both the spin and the momentum of the particle. This all stems from the idea that in QM, you can’t really separate what’s being measured from the measuring device – by observing or measuring a system you necessarily alter the outcome of the measurement, therefor the “context” of the measurement (i.e., what features of the system you are measuring) will determine the values.

    Having established that hidden variable theories are possible, Bell remained troubled by the fact that they were inherently non-local. “Locality” is the idea that objects can only be effected by other objects in their immediate vicinity. In order for one object to assert an influence over another, that influence must travel between the space between the two objects. If they are next to each other, the cause/effect can be simultaneous (that’s locality). If they are far away, a simultaneous cause/effect means the influence is traveling faster than the speed of light, which is non-locality and is what people like Einstein feared QM implied, given the principle of quantum entanglement.

    Ok, so, Bell decided to test this by coming up with an inequality – a mathematical condition – that any local theory of nature has to satisfy. He then demonstrated that the predictions of QM violated that inequality, which left the physics world with two possibilities; either (1) the predictions of QM are wrong, and nature can be local, or (2) the predictions of QM are right, and nature is non-local. Eventually, people did experiments that showed that the predictions of QM are correct, and nature is non-local.

    That said, there are still interpretations of QM that save locality and can be consistent with Bell’s Theorem. Specifically, Hugh Everett’s Many Worlds Interpretation allows us to keep locality, since Bell’s Theorem assumed that there was really only one outcome for any given measurement, where as Many Worlds says that each measurement creates a “branch” – basically, another world – where the opposite outcome occurred.

    There’s a whole lot more to say on this, but this is all I’ve got in me. I’m sure I’ll be back to QM in a later post.

  • Weak Emergence (by Mark Bedau)

    My first exposure to the concept of emergence — the phenomenon of a given system containing features that cannot straightforwardly be attributed to its constituent parts — as an object of intellectual interest came in the form of Douglas Hofstadter’s classic Godel, Escher, Bach, which I read around seven years ago. Hofstadter’s book does not study the concept of emergence, but I think it’s ultimately about how intelligence and meaning emerge from seemingly unintelligent and meaningless lower-level processes. In subsequent years, I mainly came across the philosophical concept of emergence in the context of discussions on consciousness. Recently, however, I’ve come to understand it’s a broader concept that can stand alone as a subject of philosophical inquiry. There are a few places I could have started (for example, the Stanford Encyclopedia of Philosophy entry on emergence is written by Tim O’Connor), but Mark Bedau’s name came up a few different times as an influential philosopher in this area, so I decided to give his 1997 paper Weak Emergence a shot.

    A common example of emergence (given by both Bedau and O’Connor in his SEP article) is a tornado, which is obviously made up of numerous components (dust, debris, wind, or if you want to go smaller, molecules, atoms, etc.) but which as a macro state seems to be more than the sum of its parts and can act autonomously from them (to steal from O’Connor, consider the fact that you don’t need a degree in particle physics to understand how tornadoes work, even though particles ultimately comprise the tornado). Bedau’s paper is concerned with what he calls “weak emergence”, which occurs when the macro state of a given system that has a “micro-dynamic” governing how the system’s micro states evolve over time can be derived from the micro-dynamic and the external conditions of that system via simulation.

    This definition took me a few reads to get my arms around, but the idea is essentially that we can say a system (say, a tornado) is weakly emergent if and only if we can take (1) the physical laws governing the evolution of the system’s micro-states over time (so, the rules of particle physics or quantum mechanics or whatever that tell us exactly what the parts making up the tornado, such as the molecules and atoms and the like, will look like from one moment to the next), and (2) any conditions external to the system (so any outside influences that might interact with the system but aren’t themselves constitutive of the system), and input the information from (1) and (2) into something (say a computer) that can simulate what will happen over time given that specific input. Then, the results of that simulation give us the macro-state.

    That explanation was a bit wordy but I think makes it a bit clearer what Bedau wants to call “weak emergence.” It’s also important to distinguish this from “strong emergence”, which is just a system which cannot be reduced to just its micro-states. In other words, while there may be micro-states (e.g., particles and the like) that make up the system, the system has emergent qualities that cannot be explained purely by reference to how the micro-states evolve over time, making it truly more than the sum of its parts (and, on some accounts, involves “downward causation” on its lower-level, constitutive parts). Bedau, and many other philosophers and scientists, reject the entire notion of strong emergence, likening it to magic and criticizing it as unscientific.

    Bedau’s paper then goes through a few examples of weak emergence , such as Conway’s Game of Life, explains how his definition can map on to the study of complex systems, and argues that the concept of weak emergence is scientifically useful since it gives us a framework and vocabulary to study complex systems despite it ostensibly not being an especially interesting phenomenon (since it’s obvious to everyone that systems are just made up of constitutive parts).

    Weak Emergence was interesting and framed the issue well enough, but it was not immediately clear to me why it’s considered an important paper in the history of the philosophy of emergence. Some further reading on this topic, however, explained to me that Bedau’s real contribution here was the idea of simulation as a necessary condition to studying the weak emergence of a system (and importantly, the evolution of the micro-states need only be able to be simulated in principle to qualify — certain systems may be so complex that we lack the current computing technology to simulate their evolution, but we would still be able to call the system weakly emergent from its micro-states).

    Bedau’s paper is really focused on whether the concept of weak emergence is scientifically interesting/useful, but it’s helped spark my own interest in the topic of emergence more generally, since it seems to bear on a lot of interesting questions. For example, is phenomenal consciousness (i.e., subjective, experiential, qualitative feelings) weakly emergent such that it can be fully described by the neurochemistry of the brain? I’m also just intuitively skeptical of the claim that systems can ultimately be described in terms of the pieces that compose them + the laws of nature. Opponents of strong emergence agree that there are different levels of description that are more or less appropriate for a given system — for example, even if a tornado is just weakly emergent from its parts, it would not be particularly helpful if the weatherman tried to describe its flight path at the molecular level) — but I’m sympathetic to the idea that there are systems that cannot be described at all in terms of the micro-level interaction of their constituent parts. There’s also something appealing to me about the idea of systems exerting downward causation on their micro-states, as I don’t really see why we privilege the “bottom up” perspective of systems over the “top down”.

    Ultimately, I’m guessing I’ll be persuaded against strong emergence by arguments that it requires us to put credence in the existence of phenomena that are beyond our current best understanding of physical reality. But for now it’s fun to believe!

  • Why is There Something, Rather than Nothing? (Sean Carroll)

    Sean Carroll has been instrumental in sparking (and keeping aflame) my my interest in physics. He’s an accomplished academic, but he does a ton of writing and lecturing for the layman. He’s also one of the few serious scientists who takes philosophy seriously and considers the philosophical implications of his work. I was first introduced to that side of him in his writing on the foundations of quantum mechanics, but I’ve been thinking a lot about cosmology/the origin of the universe/the anthropic principle lately, so when I came across Why is There Something, Rather than Nothing?, I knew it was the perfect candidate for my next post.

    Carroll begins the article by making a key distinction between two different versions of what we may mean when we ask “Why is there something, rather than nothing?”. The first, “What mechanism brought the universe into existence?”, he characterizes as a question that could reasonably be the subject of scientific inquiry. The second, “What reason explains why anything exists at all?”, demands a little more thought, and an inquiry into how the modern scientists thinks about reasons at all.

    In essence, science does not think the language of “causes and effects” appropriately describes reality. Rather, reality is described by the laws of physics and the relations and patterns that emerge therefrom. Certain “why” questions (like why did the baseball break the glass window) can be described in terms of causes and effects, but when we’re looking at reality as a whole, it’s just not the right way to think about it. Still, there might be some underlying principle that explains why the universe has the laws of physics it has, etc., and in that sense of “why”, we can dig productively dig in. Even then, however, we could always ask a deeper “why” question into infinite regress. If we want to avoid infinite regress, we need to look for (i) an level of the explanatory regress that is necessarily true, (ii) a level of the explanatory regress that we accept as brute fact, or (iii) something in between that we take as a satisfactory explanation due to satisfying some criteria or another.

    This leaves us (so says Carroll) with five possible answers to why the universe exists: (i) it was created, (ii) it is one of many (infinite?) realities in a “metaverse”, (iii) its existence follows some underlying principle that necessitates its existence as opposed to other conceivable universes, (iv) its existence is necessary given the logical incoherence of “nothingness”, and (v) it just does (brute fact).

    Carroll returns to address each of these five possibilities at the end, using the sections between to arm the reader with the tools necessary to assess each possibility. The discussion gets a bit technical at times (at least for a poor liberal arts boy like myself), but a lot of it is spent on the question of whether (logically) the universe’s existence requires something external from itself to bring it into existence, or whether it can (as Carroll puts it) “simply be”. He first demonstrates that our current best scientific theories allow for both the possibility that the universe has always existed, and that it came into being, then arguing that if even there was a beginning to the universe, it can be completely described by laws of nature without the need to appeal to an external creator.

    I know I’m not doing justice to his arguments, so I’ll wrap up with a few other interesting observations:

    • Answering big philosophical questions with appeal to our most complicated, abstract scientific theories is a tricky business. A lot of Carroll’s arguments rely (in small or large part) on incomplete/unproven theories, such as quantum gravity. I don’t think this pokes a hole in any argument Carroll makes though. Just a thought.
    • Examining deeply the notion of cause and effect as applied to our reality is really powerful in dispelling theistic arguments about the existence of the universe. For example, enlightenment-era philosopher Gottfried Wilhelm Leibniz famously argued that everything, including the universe itself, must have an explanation, so ultimately, and in order to avoid infinite regress, we find our explanation in a necessary being (God) – this was his “Principle of Sufficient Reason”. As Carroll points out, “Once we think of the laws of nature as describing patterns rather than causal forces, and the notion of cause and effect as being appropriate to higher-level emergent descriptions of the world rather than the fundamental level, the [Principle of Sufficient Reason] loses its luster.”
    • Along those lines, even if the existence of a world hospitable to life presents a fine-tuning problem, it seems odd that a creator would put us in this tiny corner then bother to make an incomprehensibly vast amount of other stuff.

    Carroll ultimately concludes that if we want to approach questions about the universe from a scientific perspective, “why is there something rather than nothing” doesn’t seem like a productive question. I kind of agree.

  • Freedom and Resentment (P.F. Strawson)

    Subscribe to continue reading

    Subscribe to get access to the rest of this post and other subscriber-only content.

  • Hello World!

    Welcome to WordPress! This is your first post. Edit or delete it to take the first step in your blogging journey.