• Apustimelogist
    425
    1. The wave function describes a stochastic process.


    Some view the wave function as representing an actual physical state that exists at a given time and changes during the course of an experiment. Viewing it this way: when unobserved, individual particles do not have definite properties and can be seen as occupying multiple different states simultaneously in superposition. Particles take on definite properties only when we measure them; however, which particle state we eventually observe when measured occurs non-deterministically. We can only know the probability that a given state will occur, which can be derived directly from the wave function.

    The statistical interpretation removes the assumption that the wave function represents some unobserved physical state. Instead, it focuses on the fact that measurement outcomes for a given point in time during an experiment can be predicted using the probabilities derived directly from the wave function. Hypothetically, if we were to perform repeated experimental runs for that same particular experimental context, the long run relative frequencies of the outcomes would be what is described by these derived probabilities. By not representing a physical state per se, this makes the wave function solely a predictive model for possible measurement outcomes. Its evolution is not describing changes in some actual physical state but changes in the probabilities of finding a particle in various possible states as the experimental context changes with time. Specifically then, what the wavefunction is describing is the behavior of a stochastic (random) process: collections or sequences of random variables that represent the state of a particle over different points in time. While not representing the enigmatic quantum state as more commonly envisioned, it should be seen as no different from how stochastic processes are widely used to describe the behavior of many other real physical systems in the natural sciences.

    A motivation for deflating the wave function's status as a representation of some specific physical state is that we can restore some intuitive aspects of "realism" with regard to particles: during an experiment, particles do have definite properties at a given point in time, we just do not know which states they are in unless we measure them because of the random nature of their behavior. The famous wave-particle duality then becomes completely deflated given that quantum mechanics just becomes about particles with definite states which behave according to probability distributions given by the wave function.

    In orthodox interpretations, treating the wave function as a physical state is accompanied by the introduction of the collapse postulate in order to reconcile, and provide a mechanism that transitions between, the indefinite properties of the unobserved quantum state and the definite properties we observe with measurement. The statistical approach obviously has no requirement for this: on the one hand, particles have definite properties both when unobserved and measured, intuitively conforming to our sense of "realism"; on the other hand, the wave function does not represent a single given particle anyway, just probabilities regarding particle behavior under particular conditions. Without physical collapse, we don't need a special role played by observation or measurement that needs further explanation concerning when and why collapse occurs - i.e. the measurement problem. Nor do we have to deal with various ambiguities and difficulties regarding relativistic causation, which are especially salient when applying collapse to entangled pairs of particles. The emergence of the classical world is also in principle less complicated given that particles always have definite properties; it can be noted that limits where quantum mechanics approximates classical behavior can be derived without any reference to collapse.



    2. Bell violations are direct consequences of non-commutativity.


    An obvious question for any interpretation is: how does it approach the infamous Bell violations? Works by a number of people have indicated that the violation of Bell inequalities by a set of observables is equivalent to the absence of a joint probability distribution that encompasses all of those observables. One notable example of this work is Fine's theorem; from this, it can be inferred that Bell violations are consequences of non-commutativity, which will be defined shortly.


    --- --- ---
    (Some references for Fine's theorem)

    Hidden variables, joint probability, and the Bell inequalities

    https://scholar.google.co.uk/scholar?cluster=2543155278787880428&hl=en&as_sdt=0,5&as_vis=1

    Joint distributions, quantum correlations, and commuting observables

    https://scholar.google.co.uk/scholar?cluster=8813695518940155915&hl=en&as_sdt=0,5&as_vis=1

    --- --- ---


    Also in a similar vein:


    --- --- ---
    George Boole's 'conditions of possible experience' and the quantum puzzle

    https://scholar.google.co.uk/scholar?cluster=16366977415123888164&hl=en&as_sdt=0,5&as_vis=1

    Possible Experience: From Boole to Bell

    https://scholar.google.co.uk/scholar?cluster=301320604491795906&hl=en&as_sdt=0,5&as_vis=1

    --- --- ---



    Fine's theorem specifically demands the following as equivalent:


    "(3) There is one [global] joint distribution for all observables of the experiment, returning the experimental probabilities.

    (4) There are well-defined, compatible joint distributions for all pairs and triples of commuting and non-commuting observables.

    (5) The Bell inequalities hold."



    The Kochen-Specker theorem stipulates that (4) from above is impossible in quantum mechanics due to its Hilbert space structure. More specifically, (4) is violated simply because in quantum mechanics there is always a presence of non-commuting pairs of observables and these cannot have valid pairwise joint probability distributions under usual assumptions.

    Pairs of observables without joint probability distributions can be said to be incompatible. When we try to define joint probability distributions for these incompatible pairs of observables, their distributions violate the rules of probability, notably the law of total probability which equates marginal probabilities to sums of joint probabilities:


    https://en.m.wikipedia.org/wiki/Law_of_total_probability


    This prevents the resultant probabilities from describing a conventionally valid probability distribution (though I suppose this doesn't necessarily stop someone using unconventional rules of probability). In contrast, compatible pairs of observables do have valid joint probability distributions.

    Non-commutativity just means that the order of applying a pair of quantum measurement operators affects the measurement results for that pair: essentially, measurements on non-commuting observables disturb each other. On the contrary, commuting pairs of observables will not disturb each other: the outcome of one observable in the pair will not be affected by the measurement of the other, and so the measurement order has no effect.

    Since (4) doesn't hold, we see that (5) doesn't either. The fact that a quantum system generates profound correlations to the extent of Bell violation is equivalent to the fact that it does not have a global joint probability distribution (also by violating the law of total probability), which is caused by the presence of incompatible pairs of variables that do not commute. Without a global joint probability description, the statistics of Bell experiments can only be described using the multiple separate joint probability spaces that describe each of the compatible pairs.

    The non-commuting pairs are therefore the root of Bell violations, something that has been emphasized by some recent physicists including proofs in the case of the CHSH inequality for the necessity and sufficiency of non-commutativity for Bell violation.


    --- --- ---
    Get rid of nonlocality from quantum physics

    https://scholar.google.co.uk/scholar?cluster=11575548674791370584&hl=en&as_sdt=0,5&as_vis=1

    Making sense of Bell's theorem and quantum nonlocality:

    https://scholar.google.co.uk/scholar?cluster=6010274925746687086&hl=en&as_sdt=0,5&as_vis=1

    Nonlocality claims are inconsistent with Hilbert-space quantum mechanics:

    https://scholar.google.co.uk/scholar?cluster=18053424246858448382&hl=en&as_sdt=0,5&as_vis=1

    In praise of quantum uncertainty:

    https://scholar.google.co.uk/scholar?cluster=4615841789462490335&hl=en&as_sdt=0,5&as_vis=1

    Experimental Counterexample to Bell's Locality Criterion:

    https://scholar.google.co.uk/scholar?cluster=4769324801739580243&hl=en&as_sdt=0,5&as_vis=1

    --- --- ---



    It is worth noting briefly that in any Bell experiment, the non-commuting pairs of observables that cause the Bell correlations are always locally related to each other in the sense of being properties of the same particle. Therefore, we cannot explain Bell correlations as being a direct result of disturbances between non-commuting observables acting across spatially separated locations. On the contrary, the spatially separated pairs of observables in these experiments are always pairwise compatible and this is typically interpreted as suggesting that non-locally separated observables cannot disturb each other in ways that violate speed-of-light limits (non-signalling).

    It might also be worth noting that the link between non-commutativity and Bell-type violations also seems to occur in classical systems, most notably in classical polarization optics. Bell-type violations have also been derived in the context of Brownian motion as a consequence of Heisenberg-like uncertainty relations. An important distinction from quantum violations is that none of the classical examples involve nonlocal correlations between spatially separated variables: i.e. they are local intrasystem violations. While clearly not quantum, this perhaps adds more evidence that Bell violations are clearly a formal necessity due to non-commutativity, regardless of the system.


    --- --- ---
    Quantum Mechanics and Classical Optics: New Ways to Combine Classical and Quantum Methods:

    https://scholar.google.co.uk/scholar?cluster=9708108079894379453&hl=en&as_sdt=0,5&as_vis=1


    Entanglement in Classical Optics:

    https://scholar.google.co.uk/scholar?cluster=9687012103438601910&hl=en&as_sdt=0,5&as_vis=1


    Brownian Entanglement:

    https://scholar.google.co.uk/scholar?cluster=11916823875626356065&hl=en&as_sdt=0,5&as_vis=1

    --- --- ---



    3. Heisenberg's uncertainty principle and non-commutativity are generic properties of stochastic processes.


    First, it can be noted that generally, canonical non-commuting variables in quantum mechanics are those that correspond to cases of generalized coordinates (e.g. position) and generalized momentum in Hamiltonian mechanics. The major exception is the mutually non-commuting angular momentum operators along x, y and z axes (which can then be generalized to spin observables as seen in Bell experiments). Though deriving their commutation relations requires the use of the regular canonical commutation relations for position and momentum, this non-commutativity is essentially inherited from a generic non-commutativity that affects all descriptions of 3D rotation (The SU(2) or SO(3) group). It is also the root of Bell-type violations in classical polarization optics. Even with everyday objects, you can see that successive rotations along different planes from the same starting positions will result in different ending positions if you perform those same rotations in different orders: the different planes of rotation just don't commute.

    From non-commutativity, Heisenberg's uncertainty relations can be derived. These relations dictate that the variance or uncertainty of measurement for one observable of a non-commuting pair is inversely related to the uncertainty for the other observable in that pair. In the statistical interpretation, we can interpret this purely in terms of probability distributions that are realized by the long run relative frequencies of outcomes. For instance: if, over many repeated iterations of some experimental context, the measured position of a particle tends to be bunched up in one location, then the repeated measurements of momentum will give values be dispersed in all directions.

    There is a very simple example of this which can be described in classical optics. If we send a beam of light through a slit, the width of the slit (denoting position) is inversely related to the size of the angle or spread of directions (denoting momentum) by which the light exits the other side of the slit. In the (statistical) quantum description, this pattern is predicted when repeatedly sending single photons one by one through the slit. Importantly, it can be gleaned from the example that the Heisenberg uncertainty relation is not about measurement itself, but the experimental context which constrains the behavior of the particles. If the experimental context necessitates a particular spread of position measurements (e.g. because of the width of the slit), then this constrains (i.e. disturbs a la non-commutativity) the spread of momentum measurements, and vice versa.

    We can also see (Old Edit: ignore this paragraph; do not think this intuition is correct) in an intuitive sense how this might lead to pairwise incompatibility, precluding a valid joint probability distribution. Just as the statistics of the global joint probability distribution referred to earlier can only be represented in multiple separate probability spaces or contexts, it seems that joint probability distributions for position and momentum might in principle only be represented validly within distinct experimental contexts (e.g. different widths of slit) which each ascribe mutually exclusive sets of variances / spreads to the different observables. (New edit: having thought about it, I am pretty sure this paragraph is actually correct. Some experimental set up might be constituted of two variables A and B, each with marginal probabilities that will be realized in the experimental outcomes. There will be incompatibility when the law of total probability (LTP) is violated so that p(A) will not be the same as [sum p(A, B)] when A is considered jointly with B, perhaps under some specific measurement setting. This means B is disturbing p(A). [sum p(A, B)] is still a marginal probability but the question is: for what? Skipping some explanation for brevity, It will just be a marginal probability for A in some specific context involving B that must be somehow different to our original p(A) where no contexts have been explicitly differentiated in the experimental set up. For position-momentum, we might see the disturbance as linked to the Heisenberg Uncertainty - since the variance of one observable is inversely related to the other, their marginal probability distributions are necessarily constrained / altered by each other. The marginal distribution of one of the non-commuting pairs will depend on the specific distribution of the other, disturbing the notion of any context independent marginal probabilities. The contextual joint probabilities are then always dependent on how particular experimental contexts constrain position/momentum and so there would be no possible joint probability that we can construct just using p(A) and p(B) taken at face value from the experimental set up. Any experimental set up which subsumes or fails to differentiate multiple different contexts for non-commuting observables will have marginal probabilities which fail to produce a single valid joint probability distribution for those observables that attempts to generalize across all of those different contexts simultaneously... Only joint probabilities in individual contexts induced by disturbances.

    Andrei Khrennikov has a whole series of papers informative on this, talking about the link between the law of total probability, interference and experimental contexts. The following is just one example:


    https://scholar.google.co.uk/scholar?cluster=4642651957428255714&hl=en&as_sdt=0,5&as_vis=1 )



    We can now look at specifically why position and momentum do not commute and have particular uncertainty relations. When looked at in terms of the path integral formulation, the non-commutativity in quantum mechanics can be derived directly from the fact that the particle trajectories are non-differentiable. This can be seen as a direct result of the erratic, zig-zagging nature of the paths, embodying the inherently random, probabilistic nature of measurement outcomes in quantum mechanics.


    https://en.m.wikipedia.org/wiki/Path_integral_formulation (Section: path integral in quantum mechanics; canonical commutation relations)


    This property seems to be directly inherited from the Wiener process / integral that the path integral formulation is related to by Wick rotation.


    https://en.m.wikipedia.org/wiki/Wick_rotation

    Note: Where is the Commutation Relation Hiding in the Path Integral Formulation?
    https://scholar.google.co.uk/scholar?cluster=11872738296616463941&hl=en&as_sdt=0,5&as_vis=1



    The Wiener process is a very broadly applicable stochastic process, perhaps most well known in physics as a model for Brownian motion which describes the random behavior of a particle suspended in a medium (i.e. liquid or gas). The evolving probability density function for the Brownian motion of a particle can then be described by a diffusion equation. Interestingly, the Schrodinger equation is also related by Wick rotation to a diffusion equation so that the Schrodinger equation can effectively be seen as a diffusion equation with a complex constant or describing a diffusion process in imaginary (related to complex numbers) time.

    Paths realized by Wiener processes are also characterized by the same kinds of random jumps, rendering them non-differentiable. This non-differentiability is well known, leading to the construction of tools such as stochastic calculus designed specifically to deal with this non-differentiable nature. Consequently, we can actually derive non-commutativity properties for classical Wiener processes in a similar way as in the quantum case:


    Ito’s stochastic calculus and Heisenberg
    commutation relations:

    https://www.sciencedirect.com/science/article/pii/S0304414910000256



    Given that the Heisenberg uncertainty relations can be derived from non-commutativity, it is then no surprise that analogous uncertainty relations are actually well documented in diffusion processes. Not only can these be derived from the same kind of non-differentiability but it can be shown that this seems to apply generically for a broad range of stochastic systems. Examples, subsumed into this also include hydrodynamics and well known uncertainty relations in statistical thermodynamics:


    --- --- ---
    Generalization of uncertainty relation for quantum and stochastic systems:

    https://www.sciencedirect.com/science/article/abs/pii/S0375960118303633

    Classical uncertainty relations and entropy production in non-equilibrium statistical mechanics:

    https://scholar.google.co.uk/scholar?cluster=6026419417934600498&hl=en&as_sdt=0,5&as_vis=1

    Non-quantum uncertainty relations of stochastic dynamics:

    https://scholar.google.co.uk/scholar?cluster=12722751213412558053&hl=en&as_sdt=0,5&as_vis=1

    --- --- ---



    Given that quantum mechanics is clearly a special case of stochastic systems where non-commutativity and uncertainty relations occur, this hints that they are just a direct result of the random, probabilistic nature of quantum mechanics.

    There have also been some attempts to derive uncertainty relations directly from the probability density functions of stochastic processes in a comparatively generic manner. Here, probability densities (analogous to generalized coordinates/position) are contrasted with the probability gradient or flow/dynamics (analogous to generalized momentum) in the context of systems characterized by random behavior. These can also be described in terms of the Fourier transform in the same way as can be done for quantum position-momentum uncertainty relations:


    --- --- ---
    Indeterminacy relations in random dynamics:

    https://scholar.google.co.uk/scholar?cluster=6176854777283805481&hl=en&as_sdt=0,5&as_vis=1

    Information dynamics: temporal behavior of uncertainty measures:

    https://scholar.google.co.uk/scholar?cluster=6481107725040031189&hl=en&as_sdt=0,5&as_vis=1

    Parcels and particles: Markov blankets in the brain:

    https://scholar.google.co.uk/scholar?cluster=13034249073504028456&hl=en&as_sdt=0,5&as_vis=1

    A free energy principle for a particular physics:

    https://scholar.google.co.uk/scholar?cluster=10954599080507512058&hl=en&as_sdt=0,5&as_vis=1

    --- --- ---



    The author of the bottom paper has given an interesting possible intuition for thinking about why these types of uncertainty relations might exist generically:


    "Intuitively, if the probability mass of a particular state is concentrated around one point in phase-space, then the flow must [be vigorously rebuilding gradients – in all directions – to counter the dispersive effects of random fluctuations]. This means that the flow is as dispersed as the fluctuations. Conversely, if flow is limited to a small range, random fluctuations would disperse particular states over state-space. In short, the dispersion of states and their flow must complement each other at a nonequilibrium steady-state."


    As an example: if you want to stop a droplet of some liquid dissolving in a glass of water, you will want forces to act on the liquid particles from all directions to keep them within a small vicinity. If force is applied solely from one direction without counteracting forces from all of the others, the liquid droplet will still be able to disperse everywhere else except from where the force came from. It would be impossible to keep the liquid particles all in one place if the forces acting on them are all acting in / from a single precise direction. Conversely, the liquid particles could never disperse across a broad range of positions if there were forces acting from every possible direction gathering them up.


    The author also expresses this similarly in the more specific context of thermodynamics which also has well known thermodynamic uncertainty relations:


    "Intuitively speaking, random fluctuations always increase the entropy through dispersing the ensemble density, while flow decreases entropy by ‘rebuilding’ probability gradients (i.e., where probability currents flow towards regimes of greater density). In other words, random fluctuations disperse states into regimes of high surprisal (and implicitly thermodynamic potential), while gradient flows – due to forces – counter the implicit dispersion."



    4. Do we need to give up realism, locality or free choice?


    As has been said, the wave function does no more than describe long run relative frequencies which manifest as compatible, non-signalling joint probability distributions between the spatially separated measurements of a Bell experiment. The wave function does not describe individual particles whose superpositions physically collapse either. When combined with the fact that the Bell violations are formally rooted in locally non-commuting variables which are necessitated by stochastic systems, it is tempting to think that Bell nonlocality is more or less just a strange statistical artifact that signifies the absence of global joint probability distributions (or conditions of possible experience according to Boole). This may explain why nonlocality seems to co-exist happily with non-signalling even though they prima-facie contradict each other. Therefore, even though there are definitely nonlocal correlations in quantum mechanics, we seem to be able to explain them away locally without a need to refer to spooky nonlocal forces that act between individual particles and violate speed-of-light limits. Given that the non-commutativity of locally related observables can be naturally explained as a consequence of stochasticity, there also does not seem to be a need to appeal to distant causes in the past that are influencing measurement settings a la superdeterminism, i.e. giving up free choice.

    It seems that giving up realism may be what is preferable: giving up the notion that particle states have pre-existing values. Under a statistical interpretation, we can retain definite properties of particles at every point in time during any run of an experiment without contradicting ideas of contextuality, incompatibility or the notion of irrealism. This is because the wave function and superposition is about probability distributions describing long run frequencies, not individual particles. The idea that particles do not have definite pre-existing states prior to measurement is then simply replaced by, or rather, shifted toward the notion that non-commuting variables do not have meaningful joint probability distributions for their long run frequencies that are independent of the particular experimental context. Therefore, even though realism is given up in a way compatible with the requirements of Bell's theorem, particles can still retain their definite properties as individuals in a realist way.



    5. Underlying causes of indeterminacy?


    The main benefits of a statistical or stochastic interpretation is that there is no measurement problem and some realism is restored in the sense that particles have definite properties. It is also arguably the most straightforward way of interpreting the math of quantum mechanics without injecting any additional ontology into the formulas; after all, the Schrodinger equation is just a complex (number) diffusion equation, diffusion equations describing the behavior of stochastic processes. At the same time, this leaves a lot to be desired in terms of explanation: it might be asked why exactly particles behave non-deterministically, perhaps hinting at some underlying cause yet to be discovered. A deterministic explanation would not necessarily be ruled out, in the same way that stochastic models of Brownian motion are in principle explainable in a classical, deterministic way through collisions between a Brownian macro-particle and the micro-particles that constitute the medium it is suspended in. Given how Brownian motion is related to the behavior of Brownian particles suspended in some background medium, we might ask if there is something analogous in quantum mechanics which can provide the type of underlying explanation we might want. Potential hypotheses could relate to quantum foam or random fluctuations in the underlying spacetime and quantum vacuum fields.
  • tim wood
    9k
    The idea that particles do not have definite pre-existing states prior to measurement is then simply replaced by, or rather, shifted toward the notion that non-commuting variables do not have meaningful joint probability distributions for their long run frequencies that are independent of the particular experimental context. Therefore, even though realism is given up in a way compatible with the requirements of Bell's theorem, particles can still retain their definite properties as individuals in a realist way.Apustimelogist

    This is provocative. If I understand it, it can be restated as Bell's inequality being violated in the experiment - and it seems evident that therefore some particle pair(s) must be the the particles violating. But they cannot be identified! Thus it would seem to be a necessary conclusion that the violation is strictly an artifact of the statistics. That is, it occurs in the aggregate but not identifiably for any individual. Which is just as strange! I draw the inference that there is something else going on, but no one yet knows what that is.
  • Apustimelogist
    425


    Not quite, If I am understanding you correctly. Its saying that because quantum mechanics under this interpretation is solely about long run statistics of many repeated occurrences, realism is not about the indefiniteness of individual particles, it is about entire probabilitu distributions. These probability distributions are realized by those many repeated occurrences or experimental runs, each involving a particle with definite properties at any given time.

    Fine's theorem proves that a Bell violation is just equivalent to a lack of joint probability distribution. It doesn't matter why there is a lack of joint probability distribution, it doesn't matter exactly what forces are acting on the system and why, as long as there is a lack of joint probability distribution in this setting, Bell inequalities will be broken as a formal requirement. It is in that way that it is an artifact of statistics; the violation is very real, just that it is an artifact of the lack of joint probability distribution. This lack of joint distribution is caused in quantum mechanics by non-commuting observables and I believe this non-commuting nature is just a necessary fact of certain types of randomly behaving systems like quantum mechanics seems to describe.
  • tim wood
    9k
    These probability distributions are realized by those many repeated occurrences or experimental runs, each involving a particle with definite properties at any given time.Apustimelogist
    Exactly so. Particle-pair by particle-pair. As each is measured, the question is asked, "Was anything wrong with that measurement?" And the answer is always, no, nothing wrong. Yet at some point the inequality is violated. And in this description there is no mention of joint probability distributions or non-commuting observables - and it seems to me that the mention of them, providing no useful information, becomes irrelevant (I'm wearing my ignorance on my sleeve, here).

    In violating the inequality, I am under the impression that they still conform, are consistent with, the other probability described by the sin^2 (θ/2). That is to say, that while Bell's order is out, a different order is in. And so far, I do not think anyone knows how that order works.

    As the emitted particles speed to the detectors, whether their spins are determined or fuzzy seems not to matter, because at the detector they have a definite spin, and somehow still the total count is bounded. And that is some mystery! It can't be just luck every time: thus it seems reasonable to me to suppose that something is at work.

    It may be said that Bell's inequality just "falls out" as a natural consequence of the structure implied by the classical assumptions made about the particles - that their spin is determined and persists. It must be that there is a different "structure" yet to be discovered out of which "falls" as a natural consequence what is actually observed. Which would preserve reality, locality, logic, and the speed-of-light limit and dissolve all the mystery. .
  • flannel jesus
    1.7k
    It must be that there is a different "structure" yet to be discovered out of which "falls" as a natural consequence what is actually observed. Which would preserve reality, locality, logic, and the speed-of-light limit and dissolve all the mystery.tim wood

    I'm pretty sure physicists call that structure quantum mechanics, because quantum mechanics explicitly predicted the results we do in fact see.

    Fun fact, the Schrödinger equation is deterministic! It's a deterministic mathematical equation that determines how the wave function evolves. Quantum physics is still math, like any other physics. It's still structured, it's not just a bunch of physicists around a hookah pipe.

    It seems you reject qm for what it is out of hand - perhaps, given its incredible track record for successful predictions, you could give it more of a chance than that.
  • tim wood
    9k
    I'm pretty sure physicists call that structure quantum mechanics, because quantum mechanics explicitly predicted the results we do in fact see.flannel jesus

    Hmm. Let's see. Bell's inequality arises out of what is believed to be the reality that the particle wrt to settings of a, b, and c degrees exists in one of eight possible spin states. As if to say, if that is how it is, then there must be certain constraints on the results of the tests. That is, first reality, then consequences of the reality.

    Now, I don't think QM works that way. If it does, what's the reality? There has to be one, yes? Theories and formulas are devised after the fact that fit experimental results, but they are not the machine itself; they are not causative. And believing that they are leads to a belief in magic. "Entanglement" might be a working name for it, but no one knows how that works, do they? And my guess is that whatever entanglement might be - in terms of reality - there must be a lot more to it than just lousing up Bell predictions. So our question becomes, underlying reality, yes? No?
  • flannel jesus
    1.7k
    Now, I don't think QM works that way.tim wood

    Sure it does. The op of this thread is trying to come up with an alternative of taking the wave function as ontologically real - which implicitly points to the fact that in many approaches to quantum mechanics, the wave function IS real, it is casual, it evolves deterministically over time via the Schrödinger equation, etc. So yeah, qm can absolutely work that way.
  • Apustimelogist
    425


    It is proven under Fine's theorem here:

    https://scholar.google.co.uk/scholar?cluster=2543155278787880428&hl=en&as_sdt=0,5&as_vis=1

    That Bell violations are equivalent to the absence of joint probability distribution for all variables which is equivalent to the presence of incompatible joint probability distributions caused by non-commuting variables.

    That is suggesting that Bell violations are caused by non-commuting variables and this is a completely formal result; in other words, it does not matter why the variables do not commute, they will cause Bell violations so long as they fulfil the formal conditions that characterize non-commuting observables. Quantum mechanics fulfils these exact criteria; in having non-commuting variables it will have Bell violations as a necessary mathematical consequence. That is absolutely sufficient for the "mystery", without requiring a physical explanation since the relation between Bell violations and joint probability distributions is completely formal, even if it looks really really bizarre.

    The something that is "at work" is the non-commutativity in the spin measurements (it causes the absence of global joint distribution) which has a natural local explanation in that 1) canonical position-momentum commutation is a generic feature certain kinds of random dynamic systems, even classical ones 2) 3d descriptions of rotation inherently have non-commuting properties for formal reasons which you can actually demonstrate for yourself by applying successive rotations in different orders even to your own hand.
  • tim wood
    9k
    So what is the reality? In a way you're telling me that cars run on gas. Absolutely no argument. But they require actual, real gas, not formulas and theories about gas. So what is the reality that enables the formulas?
  • flannel jesus
    1.7k
    I'm not sure I agree with that framing at all. In fact I think it's distinctly the likely to be the case that the base layer of reality IS something like a mathematical structure, or a computational structure.

    In other words, you're saying math exists only to describe the things you accept as real, but I think math is the reality, and the things you like to think of as real are a consequence of the math.

    What if every quantum object is just a numerical vector "moving" across a 3 dimensional (or more) array, and everything you know is just a consequence of these numbers interacting?
  • flannel jesus
    1.7k
    If you're curious about this idea that the basic structure of reality could be mathematical or computational, please check out Max Tegmarks mathematical universe hypothesis, and Stephen Wolfram's concept of the Ruliad.

    I personally don't think it's a coincidence that physics behaves in ways that are describable by functions. Galileo said mathematics is the language of the universe. Perhaps he was right?
  • tim wood
    9k
    but I think math is the reality,flannel jesus
    I invite you to think about your own remark and the difficulties of it. What if anything can you imagine that would make math more than, other than, just descriptive and give it causal efficacy?
  • flannel jesus
    1.7k
    Have you ever played a video game?
  • tim wood
    9k
    Alas, I have to go and cannot continue this except later. But yes, and also pin ball. Perhaps what might work is your definition of what mathematics is - because surely to be a cause it will have to be more than ideas.
  • flannel jesus
    1.7k
    I don't think I'm the best person to explain it, if I'm honest. Is this the first time you've come across the concept that mathematics is at the heart of the universe, rather than only a tool to describe it? Or were you already familiar with the concept before I said it?

    Good luck in whatever you're doing, I'll speak to you later.
  • Gnomon
    3.6k
    but I think math is the reality, — flannel jesus
    I invite you to think about your own remark and the difficulties of it. What if anything can you imagine that would make math more than, other than, just descriptive and give it causal efficacy?
    tim wood
    Slightly off-topic : If you will think of Mathematical relationships as A> a form of Information, and B> Information as "the power to enform a mind", plus C> Energy as the power to enform matter (as in E=MC^2), then the notion of a Real universe consisting of mathematical (structural) & informational (meaningful) relationships might begin to make sense. Of course, it's a great leap from Atomism & Materialism.

    Some of Tegmark's Mathematical Universe conjectures are preternatural & transcendent, but the notion that reality is fundamentally Mathematical & Informational is compatible with our modern knowledge of Nature via Physics. Below are a few other thoughts on Math (information) as the fundamental element of Reality. To answer your question, the Abstract Math form of Information may-or-may-not-be inert (depending), but the Energy form of Generic Information "gives it causal efficacy". :smile:

    The mass-energy-information equivalence principle :
    Landauer’s principle formulated in 1961 states that logical irreversibility implies physical irreversibility and demonstrated that information is physical. Here we formulate a new principle of mass-energy-information equivalence proposing that a bit of information is not just physical, as already demonstrated, but it has a finite and quantifiable mass while it stores information.
    https://pubs.aip.org/aip/adv/article/9/9/095206/1076232/The-mass-energy-information-equivalence-principle

    Mathematics : Greek máthēma (μάθημα), meaning "that which is learnt",[11] "what one gets to know",
    Note : Knowledge is Information ; hence Math is information.

    Is Information Theory Mathematics? :
    Yes, Information Theory is a branch of mathematics
    https://math.stackexchange.com/questions/1083862/is-information-theory-mathematics

    Is information the only thing that exists? :
    Physics suggests information is more fundamental than matter, energy, space and time
    https://www.newscientist.com/article/mg23431191-500-inside-knowledge-is-information-the-only-thing-that-exists/

    What is Information? :
    Abstract Information : the 1s & 0s of computer language. Existence = 1, Non-existence = 0

    Causal Information : Energy - e.g. the ratio between Hot & Cold. Energy is the causal power of Information. https://en.wikipedia.org/wiki/Information_causality
    https://en.wikipedia.org/wiki/Information

    Material Information : E=MC^2. Mass is Enformed Energy, and is an essential property of Matter. "the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing." https://www.pbs.org/wgbh/nova/einstein/ ... 2expl.html

    Shannon Information : The abstract ratio of One to Zero. It yields accuracy in computation, but omits any meaning or significance. Quantity without Quality. Like language, its utility is in its ability to mean anything you want to convey.
    https://informationphilosopher.com/index.30.en.html

    Organic Information : Living organisms are defined and organized by their "Information Molecule", which we call DNA. https://en.wikipedia.org/wiki/DNA

    Semantic Information : Meaning in a conscious mind; for example the relationship between Self and Other. It can be expressed mathematically as a numerical ratio, or emotionally as a positive/negative feeling.
    https://plato.stanford.edu/entries/info ... -Semantic/
    https://bothandblog6.enformationism.info/page16.html
  • tim wood
    9k
    No, not at all the first time. But anyone representing that the universe is mathematics, ought to offer a simple explanation of how that can be, and if nothing else, at least a cogent definition of what the term "mathematics" means in this context.

    My "model" of the universe is that it is made of matter and energy. Both these are real, and they interact. There appear to be rules that describe how these interactions will go, some known and some not known. And that's it. QM, then, would be just such a set of rules.

    Thank you for the references. I think if you read/listen to them critically, they omit just exactly the detail needed. For example, on the assumption that information is an efficient cause, then how can that work?

    My opinion is that the simplest explanation is that some mechanism lurks undiscovered, unexplicated.
  • flannel jesus
    1.7k
    There appear to be rules that describe how these interactions will gotim wood

    And you don't think those rules are defined in some way that's analogous to mathematics and/or computation?
  • flannel jesus
    1.7k
    ought to offer a simple explanation of how that can betim wood

    Well we have universes where the fundamental rules are defined by computation and mathematics, and those universes are called video games. Similarly, cellular automata universes like Conway's game of life.

    The things you call "matter" are in theory representable by numerical data (that's exactly how they're represented in video games and in physics simulations), and able to be manipulated by computations of mathematical rules - that's how every "universe" we've manufactured works, which at least gives us a potential analogy for how any universe might work - I'm not saying our universe definitely obviously works like that and you're wrong if you think otherwise (even though you're apparently that confident of your own position for some reason), I'm saying it's a potentially strong analogy to how our universe operates.
  • tim wood
    9k
    Yes. Absolutely.
    Well we have universes where the fundamental rules are defined by computation and mathematics, and those universes are called video games. Similarly, cellular automata universes like Conway's game of life.flannel jesus
    Sure, but those rules not efficacious, not efficient causes. Let's be very simple. Cars (mostly) run on gas. Well then, gas gas,.., gas. There's all the gas anyone could possibly want. But even all of it won't move a car even a fraction of an inch.

    Maybe this:
    The things you call "matter" are in theory representable by numerical data, and able to be manipulated by computations of mathematical rulesflannel jesus
    Nothing was ever manipulated by rules, mathematical or otherwise. By the computations of rules - just how exactly does that happen? What I'm driving at that I hope you would notice, is that some action is implicit, but no account for any energy required to make it happen, or matter for it to happen to. Video games by themselves do absolutely nothing.

    I am trying to leave this simple and as intuitive as possible so that we may avoid if we can all sorts of tedious defining and clarifying. But just an example of what might be nice to steer clear of: to my way of thinking there is no such thing as information until and unless someone says it is. There is, then, a constitutive act required for information to become information, which subjectifies and classifies whatever the content of the information, and which as subject is what then becomes the information. And that information is not and cannot ever be the content itself.
  • flannel jesus
    1.7k
    Sure, but those rules not efficacious, not efficient causestim wood

    Why?
  • tim wood
    9k
    Do you mean why not? A rule (say) is an expression of something that must be the case, yes? No? As such it is an expression. And the expression of the rule is not the rule. And we could just as easily say that there is no such thing as a rule, or a law. There certainly seem to be things that happen (and maybe the "seems" is more important than it seems), but those the effect of some cause - and no cause is a rule, but rather we might say that rules are about causes - and what they cause.

    The sculptor is said to be the efficient cause of the statue, but that is not true. The efficient cause of the statue is the sculpting, which skilled action is usually given to be the province of the sculptor, but he has to sculpt before any statue "occurs."
  • flannel jesus
    1.7k
    but in the case of physics simulations, we literally have the source code. We know why things in those stimulations behave the way they do, and it's precisely because of the computations of formulas. It seems like you're just begging the question.
  • tim wood
    9k
    No. What makes the source code and simulations work?
  • tim wood
    9k
    Electricity (presumably).
  • flannel jesus
    1.7k
    and if I'm right, that the universe really is math at the fundamental level, then electricity is itself governed by math.

    You don't have to accept it as truth my man, I'm not trying to convince you it's the case. You asked some questions, I tried to answer them. Plenty of physicists think like this. It doesn't matter if you like it or not, I'm perfectly fine with you not thinking the universe is mathematical. It makes perfect sense to me.
  • tim wood
    9k
    We're at cross purposes. How is the math - or information - keeping in mind that it is neither energy or matter nor apparently anything other than what it is, an efficient cause? For it is either itself the cause you claim it to be, or something else not information is the cause. Nor is this a matter of likes or dislikes; and if it makes perfect sense to you, please share some of that sense.
    Manana.
  • flannel jesus
    1.7k
    Future states seem to have a mathematical relationship with past states. It might be because future states derive from applying mathematical laws or computations to those past states - that might be how the universe itself works. Or it might even be, as many physicists think, that time itself is an illusion, and future states and past states are all encoded together in one big mathematical object - and what we experience as the passing of time and the perception of casual chains might just be what it feels like to be inside that mathematical object.

    But in the end it actually is a matter of likes and dislikes. It's not like there's a known objective answer to the true fundamental nature of our universe right now, so if you feel strongly that it can't be mathematical, which you seem to do, it's not because you have scientific proof that it can't be. It's because you don't like it, it's because there's some aspect of it that doesn't sit well with you, that goes against the grain of your intuitions about how the world works. It goes exactly with the grain of my intuitions, so I think it's a compelling idea.

    The concept of Turing completeness provides the bedrock, for me, for the idea that we might be in a computational universe - that computation and/or mathematics are strongly analogous to the root nature of every thing and every event in this place. That makes sense to me.
  • tim wood
    9k
    It might be because future states derive from applying mathematical laws or computations tflannel jesus
    The problem in a word: "applying." I'll leave off if you indicate you see the problem. That is, if the world is code, or information, or a program, then what "applies" it?

    Btw I agree the universe operates on the basis of what we might very well call rules or laws - of course the universe has no need whatsoever of such terms or understandings; it just does the next thing, whatever that is. But of course our shared belief makes us both classicists, ,and QM when complete a classical theory. Which takes us back to the Bell particles in that whatever spin they have, they have it for a reason, which as yet we don't get. Or in the most general interpretation, Bell simply proved that there are at least some things we don't yet know.
  • flannel jesus
    1.7k
    no, I don't see a problem.

    I don't think there is any explicit problem with the idea. I think you may not like the idea for your own philosophical reasons, and I have no illusion that I'm capable of convincing you otherwise. I'm comfortable with that.
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