yes, but macroreality is no indefinite.Hurkyl said:I mean reluctance to accept indefiniteness -- that we can do physics well (or even merely adequately) when the states of our physical theory has objects for which allegedly physical questions O=a don't have definite true/false values, and especially when we continue to use such objects after an observation of O.
But this is the premise of the entire class of decoherence-based interpretations. Decoherence-upon-measurement even has the exact same mathematical form as collapse-upon-measurement, but without interpreting the probabilities as ignorance of the system
More ambitious approaches hope for macroscopic decoherence to be an emergent property of unitary evolution. The relative state interpretation (i.e. many worlds) studies unitary evolution directly and its effect on subsystems. Bohmian mechanics likewise keeps the indefiniteness of the wave-function, but shows its (definitely located) particles tend towards the distribution of the wave-function.
Even interpretations that aren't decoherence-based can allow for this indefiniteness. For example, Rovelli's paper on relational quantum mechanics analyzes the Wigner's Friend thought experiment and arguesto the effect that Wigner's analysis would be
My friend has opened the box and remains in an indefinite state, but one entangled with Schrödinger's cat. Their joint state collapsed to a live cat when I asked him about the results.and Wigner's friend's analysis would be
I opened the box and saw a live cat! I told Wigner when he asked.and both analyses would be equally valid. (actually, I'm not entirely sure if RQM is decoherence-based or collapse-based or agnostic about it. Really, I didn't like the paper other than this point of view on the Wigner's friend thought experiment, and don't remember the rest at all)
I liken the rejection of indefiniteness to the person who studies Newtonian mechanics but rather than setting up an inertial reference frame, instead carefully solves sets up coordinates in which the observer is always at the origin and at rest, and refuses to understand the laws of mechanics presented in any other coordinate system. After all, when he looks around, he always sees things from his perspective; working with a coordinate chart centered elsewhere would be nonphysical and meaningless!
Hmm, I do not see why there should be any reluctance to accept such indefiniteness.Hurkyl said:I mean reluctance to accept indefiniteness -- that we can do physics well (or even merely adequately) when the states of our physical theory has objects for which allegedly physical questions O=a don't have definite true/false values, and especially when we continue to use such objects after an observation of O.
Well, this part is rather unclear. First, are you redefinig "probability" without giving new definition or what?Hurkyl said:But this is the premise of the entire class of decoherence-based interpretations. Decoherence-upon-measurement even has the exact same mathematical form as collapse-upon-measurement, but without interpreting the probabilities as ignorance of the system
It's not clear to me what you mean by indefiniteness. If you just mean that exactly what one perceives is relative to one's viewpoint, then ok. But physical science has to do with publicly discernible/countable phenomena. In what way might these phenomena of public historical record be considered indefinite?Hurkyl said:I mean reluctance to accept indefiniteness -- that we can do physics well (or even merely adequately) when the states of our physical theory has objects for which allegedly physical questions O=a don't have definite true/false values, and especially when we continue to use such objects after an observation of O.
mainly because evolution equation (Schrodinger or whatever) is deterministic, so every experiment, idealized as the evolution equation applied to the system + the instrument should be deterministic.
one can never know the exact state of the instrument, and that adds an apparent randomness to the final state of the system.
an experiment is an interaction that makes the system leave the actual state (in contrafactual definiteness language, leave its properties) and forces it to go to some random (from the point of view of the scientist, not from the one of god -of whatever- that knows the exact state of the instrument) state
Consider first ordinary classical mechanics. We have a phase space X representing all possible states of some system under study, and an observable like the "x-coordinate of the third particle" is a function on X: to each element of the phase space it assigns a real number. An ordinary interpretation of ordinal classical mechanics would imply that the 'state of reality' corresponds to some point in X, and questions like "What is the x coordinate of the third particle?" make sense as questions about reality and have precise, definite answers.ThomasT said:It's not clear to me what you mean by indefiniteness.
These are very good points, I almost agree with you. The only difficulty is that deterministic equation of evolution is not enough to call the theory deterministic. One also needs quantity that fully describes physical state of the system, with no reference to probability.
However, the function Psi describes the state in a probabilistic way. I do not think there is a way to understand Psi as a specification of a physical state. The only thing we know about it is that it gives probabilities.
It seems that if one wants to have deterministic theory, one also has to introduce additional quantitities.
...that the phenomenon in question, whatever it may be, is genuinely random. That is to say, the exact, actual result has no identifiable cause...
The HUP strikes at the heart of classical physics: the trajectory. Obviously, if we cannot know the position and momentum of a particle at t[0] we cannot specify the initial conditions of the particle and hence cannot calculate the trajectory...Due to quantum mechanics probabilistic nature, only statistical information about aggregates of identical systems can be obtained. QM can tell us nothing about the behavior of individual systems. ….QUOTE]
what the quotes means: unlike classical physics, quantum physics means future predications of state [like position, momentum] are NOT precise.]
But why does this situation pop up in quantum mechanics? because of our mathematical representations.
[scattering, mentioned below, happens to be a convenient example of our limited ability to make measurements of arbitrary precision. ]The basic ideas are these: HUP [Heinsenberg uncertainty principle] is a result of nature, not of experimental based uncertainties. From the axioms of QM and the math that is used to build observables and states of systems, it turns out that position and velocity (and also momentum) are examples of what are called "canonical conjugates" [a function and its Fourier transform]; They cannot be both be "sharply localized". That is, they cannot be measured to an arbitrary level of precision. It is a mathematical fact that any function and its Fourier transform cannot both be made sharp.
The wave function describes not a single scattering particle but an ensemble of similarly accelerated particles. Physical systems [like particles] which have been subjected to the same state preparation will be similar in some of their properties but not all of them. The physical implication of the uncertainty principle is that NO STATE PREPARATION PROCEDURE IS POSSIBLE WHICH WOULD YIELD AN ENSEMBLE OF SYSTEMS IDENTICAL IN ALL OF THEIR OBSERVABLE PROPERTIES.
A few cornerstone mathematical underpinnings:
The wave function describes an ensemble of similarly prepared particles rather than a single scattering particle. A wave function with a well defined wavelength must have a large special extension, and conversely a wave function which is localized in a small region of space must be a Fourier synthesis of components with a wide range of wavelengths. We cannot measure them both to an arbitrary level of precision. A function and its Fourier transform cannot both be made sharp. This is a purely a mathematical fact and so has nothing to do with our ability to do experiments or our present-day technology. As long as QM is based on the present mathematical theory an arbitrary level of precision cannot be achieved. The HUP isn't about the knowledge of the conjugate observables of a single particle in a single measurement. that the uncertainty theorem is about the statistical distribution of the results of future measurements. The theorem doesn't say anything about whether you can measure both at the same time. That is a separate issue. A single scattering experiment consists of shooting a single particle at a target and measuring its angle of scatter. Quantum theory does not deal with such an experiment but rather with the statistical distribution of the results of an ensemble of similar results. Quantum theory predicts the statistical frequencies of the various angles through which a an ensemble of similarly prepared particles may be scattered.
What we can't do is to prepare a state such that we would be able to make an accurate prediction about what the result of a position measurement would be, and an accurate prediction about what the result of a momentum measurement would be.
Physical systems which have been subjected to the same state preparation will be similar in some of their properties but not all of them. The physical implication of the uncertainty principle is that NO STATE PREPARATION PROCEDURE IS POSSIBLE WHICH WOULD YIELD AN ENSEMBLE OF SYSTEMS IDENTICAL IN ALL OF THEIR OBSERVABLE PROPERTIES.
Well, thank you bhobba and ThomasT, and I certainly agree with the implication that the value is not as much in the answer each of us arrives at, as it is in the tensions between the possible answers, around just what is this amazing relationship between us, our environment, and our mathematics that tries to connect the two. I suspect answers like this will continue to be moving targets, as much as what physics is will itself continue to be a moving target. It is not just physics theories that change, but physics itself. Although we may fall into thinking that the modern version is what physics "is", that doesn't seem to do justice to the remarkable evolutionary resilience of this animal. To me, its most remarkable attribute is the way the accuracy and generality of its predictions converges steadily, yet the ingenious ontologies it invokes to achieve this convergence of accuracy do not converge at all.bhobba said:Ken is a wonder all right - his clarity of thought is awe inspiring and an excellent counterpoint to guys like me that side with Penrose and believe the math is the reality in a very literal sense.
Ken G said:... which is exactly the reason that people thought the Newtonian paradigm was correct long before we discovered quantum mechanics...
Jazzdude said:Since the resulting discussion could become speculative at some points and I want to respect the forum rules, I have moved the blog elsewhere. If you have comments and would like to discuss you are invited to do it there. In any case I am looking forward to your feedback.
Zmunkz said:It therefore seem to me a fair conclusion that reality is, at bottom -- fundamentally if you prefer -- probabilistic. And I think we must concede that even while admitting QM is unlikely to be the final say in our understanding of particles.
Ken G said:...The reason it can't be probabilistic is that probabilistic theories are, almost by definition, not rock-bottom theories
Ken G said:A much more natural conclusion seems to be that Bohr was right-- physics is what we can say about nature, and never was, nor ever should have been, a "rock bottom" description.
...
Physics is all about creating a language that let's us talk about reality, so there is no such thing as a reality outside of physics that we could ever try to talk about intelligibly in a physics forum. Terms like "probabilistic" or "deterministic" are mathematical physics terms-- they have no meaning outside that context.
Ken G said:The reason it can't be probabilistic is that probabilistic theories are, almost by definition, not rock-bottom theories (probabilities reflect some process or information that is omitted on purpose, and probabilities are generated as placekeepers for what is omitted-- that's just what they are whenever we understand what we are actually doing).
jfy4 said:To me it means there is a black curtain.
It's not so much that I'm claiming it has to be true for everything, rather, I'm saying it is true every time we understand why our theory is probabilistic. So we can classify all our probabilistic theories into two bins-- one includes all the ones that we understand why a probabilistic theory works, and the other includes all the ones we don't understand. In that first bin, in every case the probabilistic theory works because it is a stand-in for all the processes the theory is not explicitly treating (flipping coins, shuffling cards, all of statistical mechanics and thermodynamics, etc.). In the second bin is just one thing: quantum mechanics.Zmunkz said:You've outlined an interesting way of looking at this. Could you possibly elaborate on the above quotation? I'm trying to understand why by definition probabilistic theories cannot be foundational. I can see in the macro sense (something like flipping a coin for instance) probabilities are a stand-ins for actual non-probabilistic phenomenon... but I can't quite convince myself this analogy carries to everything.
Yes, I agree this is well-worn territory. In a sense I am siding with Einstein that "the Old One does not roll dice," but I am differing from him in concluding, therefore, that straightforward realism is the only alternative. In fact, what most people call realism, I call unrealism-- it requires a dose of denial to hold that reality uniformly conforms to our macroscopic impressions of it, when the microscopic evidence is quite clear that it does not. So if there are no dice to roll, and if there is also no precise reality where everything has a position and a momentum and the future is entirely determined by the past, then what is left? What is left is the actual nature of reality. That's realism, if you ask me.This is the classic realist vs. instrumentalist debate. Looks like you fall on the instrumentalist side -- I am not sure if I can meet you there, although you make the case well.
I agree with you about the curtain, but I find the implications less disturbing. It reminds me of the way Hoyle found the Big Bang to be disturbing-- he could not fathom an origin to the universe, anything but a steady state was disturbing. But I always wondered, why wasn't a steady state disturbing too, because of how it invokes a concept of a "forever" of events? We invoke "forever" to avoid a "start", or we invoke a "start" to avoid a "forever", yet which is less disturbing? I ask, why are we disturbed by mystery?jfy4 said:To me it means there is a black curtain. Some might say then "your assuming there is something going on behind the curtain, and that's hidden variables". I say "no", there doesn't even have to be something deterministic going on behind the curtain, but there is a curtain nonetheless, and when physics is revealed it is always random. To be told that all we will ever get to see is what the curtain reveals is disturbing.
Gleason's theorem is a theorem about the theories of physics that can match observations, yet the "curtain" is an image about the connection between theories and reality. I think that is what you are not following there-- you are not distinguishing our theories from the way things "really work." I realize this is because of your rationalistic bent, you imagine that things really work according to some theory, and our goal is to either find that theory, or at least get as close as we can. That's a fine choice to make, rationalists abound who make that choice, and some get Nobel prizes pursuing it. But it's why you won't understand non-rationalists who don't think the world actually follows theories, because theories are in our brains, and the world is not beholden to our brains, only our language about the world is. The world is doing something that closely resembles following theories, but every time we think we have the theory it follows, we discover not just that the theory has its domain of applicability, but much more: we discover that the ontological constructs of the theory are completely different in some better theory. Why would we imagine that will ever not be true?bhobba said:I must say I can't follow that one. To me probabilities are simply the result of stuff like Gleason's Theorem which shows determinism is not compatible with the definition of an observable.
Contextuality is like determinism or probability, it is an aspect of a theory. We must never mistake the attributes of our theories for attributes of reality, or else we fall into the same trap that physicists have fallen for a half dozen times in the history of this science. When do we learn?There are outs but to me they are ugly such as contextuality - of course what is ugly is in the eye of the beholder.
I think that's a lovely way to explain why observables are associated with operators, which is probably the most important thing one needs to understand to "get" quantum mechanics (that and why the basis transformations need to allow complex inner products, and I know you have some nice insights into that issue as well). Also, we can agree that the job of a physics theory is to connect reality to the things we can observe about it. But none of this tells us why a description of reality that connects our observables with mathematical structures that predict those observables has to be what reality actually is. There is a weird kind of "sitting the fence" between objectivism and subjectivism that is required to hold that stance-- you invoke subjectivism when you build the theory from the need to give invariant observables (rather than from some more fundamental constraint on the quantum state itself), yet ally with objectivism when you promote the resulting quantum theory to the level of a description of reality. If you instead simply say it is a description of how we observe reality, hence how we interact with reality, hence how we give language to our interaction with reality, then you arrive finally at Bohr's insight that physics is what we can say about reality.And observables to me are very intuitive since they are the most reasonable way to ensure basis invariance. Suppose there is a system and observational apparatus with n outcomes yi. Write them out as a vector sum yi |bi>. Problem is the yi are not invariant to a change in basis and since that is an entirely arbitrary man made thing it should be expressed in such a way as to be invariant. By changing the |bi> to |bi><bi| we have sum yi |bi><bi| which is a Hermitian operator whose eigenvalues are the possible outcomes of the measurement and basis invariant.
Ken G said:Gleason's theorem is a theorem about the theories of physics that can match observations, yet the "curtain" is an image about the connection between theories and reality. I think that is what you are not following there-- you are not distinguishing our theories from the way things "really work." I realize this is because of your rationalistic bent, you imagine that things really work according to some theory, and our goal is to either find that theory, or at least get as close as we can. That's a fine choice to make, rationalists abound who make that choice, and some get Nobel prizes pursuing it. But it's why you won't understand non-rationalists who don't think the world actually follows theories, because theories are in our brains, and the world is not beholden to our brains, only our language about the world is. The world is doing something that closely resembles following theories, but every time we think we have the theory it follows, we discover not just that the theory has its domain of applicability, but much more: we discover that the ontological constructs of the theory are completely different in some better theory. Why would we imagine that will ever not be true?
Ken G said:Yes, the goal of science is to penetrate the shroud of mystery, but it's not to remove the shroud, because behind one shroud of mystery is always another. We are not trying to pull down that "curtain" you speak of, because there will always be a curtain, and there is supposed to be a curtain-- our goal is to get past as many curtains as we can. That may sound disturbing, but isn't it more disturbing to imagine an end to the curtains?