# The Theory of Relativity (Interdisciplinary Extreme Mode)

@compositehiggs#17785

That's a pretty interesting proposition for how to think about randomness in games. I hope you don't mind if I use it as a jumping-off point to talk a bit about quantum mechanics and classical statistical mechanics. As you mentioned the former, it inspired me to write about a topic of research that is closely related to what I work on and since I already wrote it, it would be a waste not to post it.

To everyone in the thread: I tried to write for a mix of a general audience and people with at least some technical knowledge of quantum mechanics, but it may be really bad for both audiences for that very reason. But hopefully someone will find it comprehensible and interesting.

One of the more interesting research directions in recent years in my (somewhat biased) opinion is the relation between classical statistical physics/thermodynamics and quantum mechanics. In quantum mechanics, the time-evolution of the quantum state is unitary and entirely deterministic determined by a linear equation (the Schrödinger equation) which means that a priori even pseudo-randomness associated with chaos is not possible (this requires nonlinear equations). The “randomness” of quantum mechanics is related to measurement outcomes for which probabilities can be assigned based on the quantum state. A measurement is therefore a dynamical process which is seemingly very different from the one described by the linear Schrödinger equation. This is a somewhat hairy issue and not what I want to talk about.

Instead, I'd just like to point out that the unitary quantum dynamics of pure quantum states can lead to dynamical behavior of observables that is seemingly chaotic and more importantly equilibrium expectation values described by a classical thermodynamic probabilistic ensemble. The ontology of the quantum state (wavefunction) is still a topic which is up for debate and in some sense the real objects of interest are physical observables. Nonetheless, we generally describe a quantum system by its quantum state and derive values of observables from this quantum state. What we can measure are the observables, however, and these can behave in ways that are not obvious by simply considering the quantum state (for example they can be chaotic). In quantum mechanics, an observable can be assigned an expectation value which is essentially the average of that observable with respect to the quantum state. This is generally different from a classical ensemble and arises due to the superposition of quantum states, not lack of knowledge about the state. In fact, it is possible to include the latter within the quantum formalism and simply combine classical statistical physics with quantum theory, but we are concerned with a so-called pure quantum-state (isolated and undergoing unitary evolution) and whether classical equilibrium statistical mechanics can emerge from the quantum “probabilities”.

In general most physical systems consists of many interacting particles. However, many quantities of interest are few-body observables. This includes quantities such as particle momentum, position and energy. This means their expectation values can be determined by “averaging out” the effect of the large system on the few-body observable (tracing out the rest of the system) and can be effectively described with respect to a reduced few-body quantum state. In such a process information about the full system is thrown away, but the full system still has an effect on the reduced few-body system, with correlations in the many-body system giving rise to so-called mixed reduced states (states that are described by classical probabilities in addition to the quantum “probabilities”). Note that the full system is pure, the introduction of statistical probabilities is due to information loss when averaging over the rest of the many-body system. So already we see that it is possible to obtain classical probabilities from a pure quantum state if we are only looking at a subsystem. This might seem obvious, if we don't have the full knowledge of the system we describe it probabilistically. The reason this is actually interesting is that we very rarely have access to the full state, most of the processes we are interested in concern observables of reduced subsystems. Classical probabilities are therefore related to correlations with an environment. In fact, some people think that environment-induced decoherence in which the system end up being described by purely classical probabilities solves the measurement problem, but I am not currently convinced. It does, however at least show how interference associated with quantum superposition can be destroyed by environmental interactions and that quantum systems can look classical when larger numbers of particles are considered.

So far this is relatively old news in physics, what I think is really cool and more recent goes one step further and asks whether or not these classical probabilities can be related to those of statistical mechanics. In essence, it is concerned with the old question of how probabilistic laws emerge from seemingly deterministic microscopic processes. Complicated many-body quantum systems are often chaotic. As I mentioned initially, this statement makes no sense on the level of the quantum state, but looking at few-body observables, behavior commensurate with classical notions of chaos can be observed. It has been shown that for such systems and observables and an arbitrary initially pure quantum state the expectation values of these observables will in fact thermalize!
That is, despite the unitary and reversible nature of the time-evolution the system will equilibrate to an equilibrium value (seemingly an irreversible process) determined by a set of classical probabilities and this equilibrium value is equivalent to the classical microcanonical ensemble. Note that this ensemble value is obtained from the quantum coefficients and the emergent description in terms of classical probabilities is entirely due to unitary quantum evolution with the Schrödinger equation. A priori there is no reason to expect it to be equivalent to the microcanoncial ensemble, indeed for so-called integrable systems (which have many conserved quantities, in addition to the energy) it is not.

The point is that for few-body observables the many-body system behaves as its own environment and we observe equilibration with equilibrium expectation values that are entirely equivalent to those obtained by statistical equilibrium ensembles and the systems can therefore be described by the latter, despite the underlying description being quantum mechanical. This helps bridge the gap between quantum “probabilities” and classical probabilities and shows the emergence of statistical physics from unitary time-evolution.

To take it back to the initial point, I think that a statistical description of the universe is more fundamental than some make it out to be as it is a natural consequence of environmental correlations that cannot be taken fully into account in a description of a given system. Many processes are therefore effectively statistical as they concern few-body physical quantities in a many-body correlated world. This is a different notion than the pseudorandomness associated with classical chaos which is related to the fact that one can never measure initial conditions with 100% accuracy. Note that this is from a purely physical point of view about how processes work in the physical world, I don't think this brings anything particularly new to a more fundamental philosophical understanding of randomness.

To bring it back to the original topic, I agree that it might be interesting to think about implementing probabilities in games in terms of correlations and players not having access to the full system, but I’m not really sure what such a system would look like in practice and whether it would be meaningfully different. If it were, it would mean that the player has to somehow be able to gain access to more information about the full system and thereby figure out the deterministic full process or at least get a better approximation.

I understand

@SU2MM#18117 Are you a physicist too?

Whether the statistical description of the universe is more fundamental really depends on what you think about the wave function. If wave functions are the true underlying ontological object then the universe is really deterministic and the statistical view supervenes upon them. If not, then non-determinism of some kind is a real feature of the universe.

Have you read Quantum Computing Since Democritus (Aaronson)?

My midlife crisis took the form of revisiting some of this material since I skipped a lot of it in graduate school. After thinking really carefully about regular quantum mechanics (RIG Hugues's Structure and Interpretation of Quantum Mechanics is a great text for this) I decided the problem couldn't really be resolved studying non-reletavistic Quantum Mechanics (why should it surprise us at all if regular quantum mechanics is weird when combined with relativity - its manifestly frame dependent?) and so for the last few years I've been trying to pick up enough General Relativity and Quantum Field Theory to understand the philosophical debate.

As you might imagine, this is kind of hard. What I have sort of concluded from all this reading is that nobody really knows what is going on at the fundamental level in terms of ontology and that the question may itself be ill-posed somehow. I barely have time to do any deep thinking these days, unfortunately.

Listen chums, I’m a social scientist, and we use the term ontology in very different ways.

equally incomprehensible ways, turns out.

@compositehiggs#18153

Yes, I am. At a much earlier state though, I am just finishing my PhD and will start a postdoc in May. Ironically I'm not sure that this is particularly conducive to thinking deeply about these issues, at least for me, as I tend to focus on the day-to-day research questions, not so much fundamental questions. So more related to specific models and to a relatively restricted subset of physics. I work in the cold atom community which is a hodgepodge of people with backgrounds in nuclear physics, AMO (atomic molecular, optical) physics, quantum information, statistical physics and condensed matter. The main unifying theme is that utilizing cold atoms many interesting few- and many-body models can be engineered very cleanly in laboratories and interesting regimes can be explored. Particularly simulations of condensed matter systems, the few-to-many body crossover, quantum information and statistical physics of isolated quantum systems is of interest.

As you can guess from that all my work is related to non-relativistic quantum mechanics. I did also take courses on relativistic quantum field theories during my Master's, but it has been a long time since I've actively done anything related (although I've often used non-relativistic quantum field theory).

I do agree that one of the fundamental issues is the ontological character of the wavefunction or density matrix. I attended a pretty interesting talk by Prof. Berge Englert in which he argued that the “measurement problem” is only a problem insofar as we are ascribing a physical meaning to the wavefunction and if we simply consider it a mathematical object which describes our knowledge of a system, it is no surprise that we update our knowledge once new information is obtained. This is pretty close to Quantum Bayesianism as far as I can tell, although he was much less concerned with the specifically Bayesian approach to probability than some of the proponents of this are.

At the end of the day this seems to also walk squarely into the realism vs instrumentalism debate. What does it even mean for an object to exist? In my experience most physicists will start out professing some form of naive realism, but when pushed most seem to actually be instrumentalists. They think that a theory describing and being consistent with the largest amount of data is a sufficient criteria for it to be a good theory and that the question of whether it is the “true description” of the universe and whether the objects of the theory exist is fundamentally misguided. I am pretty sympathetic to this position, but then we do run into trouble with objects like the wavefunction, where this question is potentially important for how to think about it.

I will look into reading the books you mentioned when I have time. If you are interested in some of the topics I mentioned in my other post, this is a pretty nice review article https://arxiv.org/abs/1509.06411.

@CidNight#18158

Now I wonder, how do you use ontology? I'm guessing that it must somehow be related to the existence of something, being etc. as well or is it completely different?

Also, just out of curiosity, when you were talking about getting a job like yours, were you talking about research? Anyways, let me take it as an opportunity to rant a bit. While the situation is probably slightly different in the natural sciences versus the social sciences the fundamental problem is likely similar. In physics a lot of research is done by PhDs and postdocs who are, with a few exceptions depending on country, relatively low paid. Getting a permanent position is very difficult and it is not uncommon to do 2-4 postdocs (for a total of 4-10 years), moving every few years before you have a chance and even then nothing is guaranteed. I think the system is pretty terrible and essentially exploits our passion for science. As a single person the salary, at least in Japan, for a postdoc is fine (I will not get rich, but it's pretty close to the average Japanese salary) and I would like to stay here a few more years so I decided to go for one in Osaka.

In general it is not an optimal choice and makes it very difficult for people with a family to have a career in science, both due to the low salary in most places, but more importantly the constant moving which is often across national borders. I guess the one difference from what you described is that if you do succeed and become a professor in physics you will usually be paid relatively well. There are obviously many examples of much worse exploitation in our capitalist world, but this one sucks to. Partly it is because a lot of people have a passion for science and wants to do it, which means that universities and research institutions can get away with offering pretty bad conditions as there is always someone else willing to take the job if you don't (of course the quality of the candidates matter as well, but there are definitely more qualified candidates than positions). Unionizing across national boundaries is pretty difficult and I am not sure what the best way to improve the situation is right now without completely overhauling the scientific institutions/systems or simply increasing the number of positions, which unfortunately is probably not very realistic. Even with the amount of resources currently allocated, a better structure in which universities rely less on temporary scientific labor is possible, but there is no incentive to even attempt an implementation of such a structure currently.

alright you quantum smarties how many sides does a dithligonal heckahedron have

@SU2MM#18176

@SU2MM#18176

Responding separately to the more academic question on ontology. I‘m an archaeologist, and my phd is in anthropology, and while ontology is an important notion in all the social sciences, it has some particular heft in archaeology right now. So the dictionary definition of ontology is “the study of the nature of being” or the branch of metaphysics related to the nature of being. It’s really interesting to read your discussion about ontology as related to the nature of being of certain atomic elements (excuse my layman‘s terminology, I’m barely keeping up). Obviously on my end, we're generally interested in the somewhat philosophical contemplation on the nature of being of people, or groups of people.

Anthropology is the study of humanity. I often argue to my students that makes it is just about the broadest study in the academy, jokingly comparing it to the work of physicists - saying that since there are no hard rules in human behavior, anthropology is actually much more complicated than physics. Like I said, this is said as a laugh-line, as I recognize that the well of weirdness in physics is deep and fascinating. But back to it. Anthropology is the study of humanity, and usually (although this is not a hard rule), the study of other people's cultures. Archaeology adds a layer of complexity even to that, because we usually study other people's cultures _from other times_. To quote David Lowenthal by way of L. P. Hartley, "the past is a foreign country, they do things differently there."

This makes ontology crucially important. How are we to determine the nature of human behavior (or for a more social term- human practice) in a foreign country _and_ a foreign time, if we do not understand the nature of the people themselves? Anthropologists have been frankly obsessed with isolating our own internalized biases since around the 1960s, with some hope that by understanding our own biases we can quantifiably subtract them from our interpretation of data. This has proven to be a fool's errand and in recent year a new theoretical paradigm has arisen to try and bypass modern bias and more directly assess human nature (that's a loaded term) in antiquity. That paradigm is called relational ontology.

Archaeologists didn't invent relational ontology, and we almost never do imagine our own theoretical positions. Instead we usually pilfer them from sociology and cultural anthropology. Quoth google: "Relational ontology is the philosophical position that what distinguishes subject from subject, subject from object, or object from object is mutual relation rather than substance." In archaeological settings, this mostly means we try to build an understanding of human practice in the past from the ground up by understanding the intersections of identity, history, belief, structure, etc that connect individuals. And not just people to people; more importantly it's about understanding the relationships between people and non-people. How do people relate to animals, to their cosmologies, to the earth, to their spirit? The thinking being that by coming to understand the complexities of these relationships, we can understand the way that people in the past navigated and negotiated their own worlds and their own cultural structures. Jury's still out on whether it works.

Take a poll: More or less confusing than the physicists?

LESS

@SU2MM#18176

It was my occasional habit in the pre-covid times to crash conferences on the interpretation of quantum mechanics. The field is relatively small and so the conferences are surprisingly welcoming, even if you are a bit of an outsider.

A few years ago I went to a conference in Long Island called "Quantum Mechanics: Paradigm or Ontology of Nature?" where I met one of Fuchs' grad students (whose name escapes me at the moment.)

I can try to express my problems with qbism in the following way. Consider that special relativity in particular is a relational turn in physics. Einstein's main idea was to recognize that certain apparent quantities were frame dependent and therefor ontologically suspect (presuming that one's frame of reference doesn't matter) while other quantities (perhaps not the obvious ones) were frame invariant. QBism tries to suggest that the outcome of certain experiments has the same character - certain sorts of quantum mechanical measurements give fundamentally frame dependent results which is why different observers can have different accounts of, for instance, when a wave function "collapses". They would argue that wave function collapse itself is an ill posed idea.

So far so good, I guess.

The issue is that special relativity identifies the true observables (things which transform appropriately under the Lorentz group) and then constructs genuinely new physics out of them. Physics which doesn't just explain why certain non-invariant quantities look the way they do in certain frames (boring) but also explains why gold is, for example, yellow. That is, identifying the true frame independent quantities leads to a new framework of physics which allows us to calculate new things.

Its this second part that qbism doesn't seem to offer anything towards. Yeah, its easy to say that measurement outcomes are in general not frame independent in quantum mechanics but that doesn't really lead us to any new physics (so far). Like I said, I'm pretty sure that Quantum Mechanics is not close enough to a real theory of the world to even be useful as a philosophical tool. I'm also pretty sure that QFT isn't well understood enough or well posed enough to constitute a genuine basis for philosophical discussion either.

All this seems to be related to gravity, which has its own pile of philosophical problems. I have a totally intuitive hunch that this nut won't crack until we understand quantum gravity.

@espercontrol#18178 how many sides does the dithligonal heckahedron feel that it has?

@CidNight#18192

Physicists typically think of ontology as related to the question: What are the true, fundamental, degrees of freedom of the universe?

Per my previous post if we have a system of two particles special relativity tells us that the spatial distance between them _isn't_ such a fundamental degree of freedom because it depends on who measures it. (People moving in certain directions will measure a different distance than those stationary. In fact, what special relativity tells us is that there is no state of affairs whatsoever as to the question of what the distance between two objects is in space.) Instead, special relativity tells us that to find something that works somewhat like a distance but upon which everyone agrees we have to take into account not just the particle positions in space but their "position" in time and that only certain combinations of space and time indexes constitute things we can all agree upon.

@compositehiggs#18199

As an aside I sort of hate the way that special relativity is taught because a great deal of energy is spent on marveling at length contraction and time dilation when these things are, in fact, totally non-physical (at least at the level of special relativity). Length contraction and time dilation are totally illusory phenomena entirely a result of your frame of reference and cannot in any way effect the results of experiments.

I will say that at the level of standard quantum mechanics it is 100% clear (to me) that "wave function collapse" is not a physical event.

@compositehiggs#18199

That‘s fascinating and I think I see parallels to the way anthropologists use ontology to think about human relationships and identities. I would say that relational ontology is a relativist or non-essentialist body of theory. This means that it does not posit that humans have any sort of set identity or essential core of identity - and by extension, society does not have inherent, immutable structures. This means that it isn’t necessarily a given that a culture even has a religion, an economy, etc - much less that they have a specific type of these structures as it relates to anything else. This is in direct contrast to traditional anthropological theories of culture that were evolutionary in their approach. Meaning that as a culture becomes more ‘complex’ it must change along a set course. Hunter gatherers must be tribes, agriculturalists must be states. And by extension, individuals within an agricultural state must act a certain way, have a certain type of religion and so on. As with special relativity, anthropologists have become more aware of the great deal of flexibility, fluidity, and yes, subjectivity of the people we study. We have a subjective experience of them, they have a subjective experience of themselves, and none of it is unchanging.

@CidNight#18201

Of course, the "relativity" in the name "special relativity" is sort of historical accident. A name which points more directly at the surprising part of the theory rather than the fundamental elements of it. In the end, special relativity does posit that some quantities are universal and everyone agrees on them.

Even general relativity, which extends the set of quantities which are not frame independent, still identifies what appear to be (at least in the theory) the true, fundamental, degrees of freedom upon which all else supervenes.

I don't even know how to think about anthropology in these terms: its clear to me that even to be human is an approximate state of affairs (human is a cluster concept in Wittgensteinian terms). It doesn't seem particularly plausible that there could even be any true ontology of the human experience beyond the underlying ontology of the universe itself.

Can a mod split this stuff off into its own thread?

@yeso#18118 completely got it. no problems

@Syzygy#18205 Hmmm…

The theory of relativity: Explained! (in multiple disciplines, no less)

@compositehiggs#18202

Certainly anthropologists have thought a lot, at least since the emergence of post-modernism, about what you eloquently called “an approximate state of affairs” vis a vis human essentialism. Unlike philosophers though anthropologists tend to try not to get bogged down in questions like this. Ultimately if you want to study human culture, and human practice within that culture, it does not matter what the “true” nature of the human self is. It only matters how that particular culture, or better still individuals within that culture, perceive themselves to be.

looks like a couple of eggheads need to play pathologic 2

I feel partially responsible for the diversion into quantum mechanics. You are all welcome, mostly because it rules.