I think the issue is that this function is a probability distribution for position measurements, if it was a spatial function that simply described some sort of classical extended object or charge distribution it would be easily accepted.PeroK said:if the position of an electron is described by a spatial function, then it doesn't exist to the same extent and the theory of the electron is incomplete
Well, this is in part the case. A pure probability distribution wouldn't be much of an issue here either if it could be always interpreted within classical probability theory, but we instead introduce quantum probabilities for that. The deviation from Kolmogorovs probabilities leaves us entirely blank of a solid interpretation - because we now cannot attribute those probability distribution to purely represent our lack of knowledge about the system as we would have classically. Instead it leaves the gate wide open for a huge variety of vastly different interpretation that just don't seem to be consistent with each other. That big confusion is kind of what makes up the core of the problem.CelHolo said:I think the issue is that this function is a probability distribution for position measurements, if it was a spatial function that simply described some sort of classical extended object or charge distribution it would be easily accepted.
Not that the former is actually a problem but that's where the issue originates I think.
That's a good point. The difference in QM is quite deep.CelHolo said:I think the issue is that this function is a probability distribution for position measurements, if it was a spatial function that simply described some sort of classical extended object or charge distribution it would be easily accepted.
Not that the former is actually a problem but that's where the issue originates I think.
The inability of human intelligence to agree on an interpretation of QM does not, by itself, invalidate the theory. No more than the debate over the existence of complex numbers undermines the pure mathematics.Killtech said:Instead it leaves the gate wide open for a huge variety of vastly different interpretation that just don't seem to be consistent with each other. That big confusion is kind of what makes up the core of the problem.
I don't think there is a problem with the validity of the theory at all. It is just it's messy formulation which sparks the issue which we cannot make sense of. What's worse is that all that complain about it are unable to write it down formally what they are actually requesting / how a theory needs to be formulated to be easily make sense of.PeroK said:The inability of human intelligence to agree on an interpretation of QM does not, by itself, invalidate the theory. No more than the debate over the existence of complex numbers undermines the pure mathematics.
There just isn't such a probability space, one way of characterising the difference in quantum probability is the absence of such a space. So demanding it be formulated seems fruitless.Killtech said:I don't think there is a problem with the validity of the theory at all. It is just it's messy formulation which sparks the issue which we cannot make sense of. What's worse is that all that complain about it are unable to write it down formally what they are actually requesting / how a theory needs to be formulated to be easily make sense of.
... ah god, like just work out the damn actual and correct Kolmogorov probability space for QT / QFT and we are done with this nonsense.
Given that complex probability amplitudes are at the root of the non-classical aspects of QM, then this debate echoes the original debate about complex numbers. Scott Aaronson has a neat anecdote about this when he was troubled by why nature chose the complex numbers and got talking to some maths grads. They just laughed and said "because the complex numbers are algebraically closed, of course".Killtech said:... ah god, like just work out the damn actual and correct Kolmogorov probability space for QT / QFT and we are done with this nonsense.
The very issue with this statement is that Kolmologovs theory is in no way restricting. My biggest issue with understanding the need for quantum probabilities was that Kolmogorovs theory is actually able to produce any kind of distributions and correlations (well fine, there is a restriction to Borel sets for it cannot handle Banach-Tarski stuff, but QFT is harmless and has no such thing). In its raw form probability theory doesn't even have a concept of locality so Bell-stuff isn't in any way special for PT.CelHolo said:There just isn't such a probability space, one way of characterising the difference in quantum probability is the absence of such a space. So demanding it be formulated seems fruitless.
The rest of your response was hard for me to understand but it's easy to show that the CHSH inequality follows from assuming that the four observables being measured are random variables on a single sample space as Kolmogorov probability would. This was shown in the 80s by Tsirelson and is covered in textbooks on quantum probability and information. It's nothing really to do with "burdening" Kolmogorov probability with "classical particle understanding". Thus QM violating these constraints indicates it's not a Kolmogorov theory.Killtech said:The very issue with this statement is that Kolmologovs theory is in no way restricting. My biggest issue with understanding the need for quantum probabilities was that Kolmogorovs theory is actually able to produce any kind of distributions and correlations (well fine, there is a restriction to Borel sets for it cannot handle Banach-Tarski stuff, but QFT is harmless and has no such thing). In its raw form probability theory doesn't even have a concept of locality so Bell-stuff isn't in any way special for PT.
"the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes"PeroK said:Given that complex probability amplitudes are at the root of the non-classical aspects of QM, then this debate echoes the original debate about complex numbers. Scott Aaronson has a neat anecdote about this when he was troubled by why nature chose the complex numbers and got talking to some maths grads. They just laughed and said "because the complex numbers are algebraically closed, of course".
https://www.scottaaronson.com/democritus/lec9.html
You should maybe look at CHSH a little deeper. It's achieving it's purpose very well, but what it is going beyond a pure Kolmogorov assumptions and introduces a concept of hidden variables and specifically the property of them being local. It's core is coming up with a workable definition of locality that allows handling in a very general context to provide a framework for experiments to check the assumption of locality. And it perfectly achieves that goal.CelHolo said:The rest of your response was hard for me to understand but it's easy to show that the CHSH inequality follows from assuming that the four observables being measured are random variables on a single sample space as Kolmogorov probability would. This was shown in the 80s by Tsirelson and is covered in textbooks on quantum probability and information. It's nothing really to do with "burdening" Kolmogorov probability with "classical particle understanding". Thus QM violating these constraints indicates it's not a Kolmogorov theory.
Just like Special and General Relativity teach one that geometry must be generalised, so as well quantum theory teaches one that probability theory must be generalised. I don't see the demand for QM to have a Kolmogorov formulation as sensible, any more than GR should have a Euclidean formulation.
All of your posts seemed to be based on something other than an understanding of QM. Ultimately, the reason QM was adopted in the first place and the reason it's still the only game in town 100 years later is that it explains the body of 20th century experimental physics.Killtech said:"the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes"
Ugh... that quote is taken from your link. Like, no. What we measure is real because our measurement devices measure in real numbers. Well actually in finite numbers and Incidence counters even in integers. That's what spans the space of predictions we need to correctly describe. How we do it is up to us but of course we always take the best tools for a job. Probability amplitudes however are intrinsics of a theory, which is neither directly nature, nor directly our observation of it. All it is, is being useful... and we found that out long ago that combining the phase and amplitude of fields makes the calculus very convenient regardless weather we deal with classical fields or wave functions. It's just deeply inherent to everything related to sine/exp functions (and therefore naturally PDEs related to them). Sorry, there is just nothing special about complex numbers other then how they relate to other mathematical constructs from which they derive their situational convenience.
Oh, and in case you were wondering, there is no kind of restrictions that would prevent you to use a complex space as a underlying state space of a probability space. Kolmogorov doesn't bother at all how you calculate your probabilities as long as they are measurable functions (i.e. those cannot do Banach Tarski stuff) - this is what you call a random variable. In fact Kolmogorov actually allows you to make your state space not even of anything related to numbers at all if you fancy it. It just has to be well defined enough to produce a set in terms of Zermelo-Fraenkel. So if you think complex numbers are in any way restricting you from using classical PT, well then you are mistaken.
Um, you do know that the CHSH inequalities are violated in actual experiments (which confirm the predictions of QM), right?Killtech said:You should maybe look at CHSH a little deeper. It's achieving it's purpose very well
Really? Put the Hilbert space of QT states as your state space of your probability space. Then using linear operators together with Borns rule gives you a measurable function i.e. a valid definition of random variable.CelHolo said:But the non-commutative complex algebra of quantum observables does prevent you from using classical probability theory since it prevents realising the observables as random variables on a common probability space.
Yeah of course! I do know that physics exhibits a non local properties.PeterDonis said:Um, you do know that the CHSH inequalities are violated in actual experiments (which confirm the predictions of QM), right?
Yes.Killtech said:Have you actually ever read what the axioms of Kolmogorov even are?
Tsirelson proved you can derive the CHSH inequalities just from the assumption of a common probability space in the 80s. I think you're charging ahead in "dismantling" QM without having a decent command of the material.Killtech said:what it is going beyond a pure Kolmogorov assumptions and introduces a concept of hidden variables and specifically the property of them being local
Kolmogorov has not the slights concept of locality. The question of locality cannot be decided within that framework alone. You have to define it somehow, which adds additional assumptions.CelHolo said:Tsirelson proved you can derive the CHSH inequalities just from the assumption of a common probability space in the 80s. I think you're charging ahead in "dismantling" QM without having a decent command of the material.
I said nothing whatever about the Kolmogorov axioms. I was responding to your claim about the CHSH inequality. It seems odd to say that that inequality is "achieving its purpose very well" when it makes predictions that are falsified by experiments.Killtech said:now do you know that Kolmogorovs theory is not local??
Oh, sorry. I though the idea of the inequality was to provide a tool to decide the question that Einstein has put up via an experiment. It's achieving its goal by deciding/settling the problem, no?PeterDonis said:I said nothing whatever about the Kolmogorov axioms. I was responding to your claim about the CHSH inequality. It seems odd to say that that inequality is "achieving its purpose very well" when it makes predictions that are falsified by experiments.
Yes. They're simply constraints on any four binary random variables sharing a common probability space.Killtech said:CHSH and Tsirelson deal with the concept of locality. You cannot take that part away from those and expect them to hold anyway. Or do you actually claim that those have nothing to do with locality?
If you mean that experimentally showing that the CHSH inequality is violated rules out certain types of models, sure, that goal has been achieved. But the claims you are making don't appear to be about ruling out certain types of models. You appear to have some specific type of model in mind that is not ruled out and that somehow "explains" QM without all the problems that other people see. If you do, you should give a specific reference that tells us what that model is, so we have a basis for discussion. For example, if you think some version of "Kolmogorov theory" does the job, give us a reference that explains what that theory is and what predictions it makes.Killtech said:I though the idea of the inequality was to provide a tool to decide the question that Einstein has put up via an experiment. It's achieving its goal by deciding/settling the problem, no?
Oh boy. The whole point of the exercise is the assumption that the quantum systems in Alice and Bobs lab cannot communicate. But if that isolation restriction (which is trying to represent the core property of distance) is lifted, then there is just nothing preventing the violating the inequality by as much as possible, even beyond Tsirelson's bound. If the system in Alice's lab can tell Bob's what it settled for during its measurement and before Bob's system was measured, then of course it can conveniently change itself to whatever it needs to to produce any desired distribution.CelHolo said:Yes. They're simply constraints on any four binary random variables sharing a common probability space.
Break that common probability space into that of a two step stochastic process - i.e. deviate from the assumptions made for CHSH but which is still perfectly fine within Kolmogorovs framework.CelHolo said:I think you just don't know the mathematics, it's quite easy to derive the CHSH inequalities from the assumption of a common probability space. See Streater's Lost Causes in theoretical physics for a full explanation.
As I have already asked you once, please give a reference for the specific model that you have in mind. You can't just wave your hands. Either there is a valid reference describing a specific model with the properties you keep claiming, or there isn't.Killtech said:Break that common probability space into that of a two step stochastic process - i.e. deviate from the assumptions made for CHSH but which is still perfectly fine within Kolmogorovs framework.
Pushed to it's limit, neither the light nor the electron is ontic. They are all "things" we merely theorize from our perceptions. At one time there were different theories explaining those same perceptions, e.g. when the Greeks thought of vision as rays that reached out from one's eye. This seems to point to Quine's concept of ontologies as whatever entities are assumed in one's theory of the world.vanhees71 said:Well, if ontology is about what Kant called "Ding an sich" (I don't know, how to translate Kant into English), then it's something not subject to the natural sciences, because the natural sciences are about nature as can be objectively observed. Objectively means the observations must be reproducible and independent from the individual making the expression.
Take, e.g., classical electrodynamics and the electromagnetic field. Is the classical electromagnetic field ontic, providing an "ontology of light"? I don't know, because if one thinks about it, it's just a mathematical framework describing the phenomena of emission of "light" (e.g., the Sun as a thermal light source) and its registration at some distant place. We never directly observe the field but just its action on some matter. Usually it's the photoelectric effect which provides a signal in a detector (photoplate, CCD cam, the retina of our eyes etc). So "is light really" the electromagnetic field or is it the photo electron ejected from matter which then leads to a "signal" we can preceive?
I think an answer to this question is pretty irrelevant from the point of view of the natural sciences. It's simply easier to talk about the electromagnetic field about some "thing" with a kinematics and dynamics in its own right as if it were something like a substance though for a substance it doesn't have a typical "substance-like" (charge-like) conserved quantity. It basically has been introduced by Faraday (based on his experience with experiments and observations) and then brought in a mathematical form by Maxwell to have a concise way to talk about these electromagnetic phenomena.
First, for me the observation overrides any theoretical concern. If it is not there, how can you measure a phase shift? Second, does not the path integral method effectively give the least action result? If so, the same action determines the phase shift of the wave, does it not?meekerdb said:If it's real how do you explain that the same result can be obtained by Feynmann's path integral method?
When orthodox QM is presented in instrumental form, just as a set of practical rules for computing probabilities of measurement outcomes, it's perfectly consistent. But I see inconsistencies when the orthodox guys start to make a philosophy out of it, i.e. when they try to explain what those rules mean at a deeper level. (The very first inconsistency that many of them commit is that they use philosophy to argue that one should not do philosophy.) Anyway, if some of my demands are too excessive, I would like to know what those demands are.PeroK said:This leaves us with two possibilities:
1) QM is manifestly incomplete - and anyone who believes in orthodox QM must lack something in terms of the intellectual capability to think logically. I.e. they embrace an obvious contradiction.
2) You place excessive demands on a fundamental theorem of nature that, from a matter purely of logical consistency, are not required. I.e. there is no inconsistency, only your perception that this particular fundamental theory of nature is deficient.
My understanding of this thread in broad terms is that orthodox QM does not demand that all measurables have well-defined values at all times and that you believe that this makes QM incomplete and inevitably leads to philosophical inconsistencies.Demystifier said:Anyway, if some of my demands are too excessive, I would like to know what those demands are.
I can well understand that. It's impossible to be totally aphilosophical (since, as you point out, even arguing to keep philosophy out of physics is a philosophy in itself). From my point of view, the whole debate about ontology is a quagmire from which it may be impossible to emerge. I would say - and this is more than "shut up and calculate" - that even if the philosophical questions that QM raises are unanswerable, then this could equally be seen as a warning against expecting too much from a philosophical analysis of natural science.Demystifier said:But I see inconsistencies when the orthodox guys start to make a philosophy out of it, i.e. when they try to explain what those rules mean at a deeper level. (The very first inconsistency that many of them commit is that they use philosophy to argue that one should not do philosophy.)
This was dealt with long ago by Bill Unruh and others. It's impossible to directly measure the quantum state, just as it is impossible to directly measure any set of probability distributions, what they actually do is measure a POVM with postselection.Ian J Miller said:then how do you account for the following paper: Lundeen, J. S., Sutherland, B., Patel, A., Stewart, C., Bamber, C. 2011. Direct measurement of the quantum wavefunction
One must be more careful to formulate things right. It is an indication that we don't do this properly, because we always start from scratch. I come more and more to the conclusion that there's no way to make progress, but here's one more try:Demystifier said:So you are saying that the state always exists, while values of the observables exist only when they are measured, is that right? But it creates a lot of additional questions:
The quantum formalism is the result of many observations and experimental facts. There is no sensible way to answer such "why questions" in the natural sciences, which figure out as precisely as possible how Nature behaves but never can answer why she behaves the way she does. Discussions concerning this quesions touch the realm of religion and are not subject of the natural sciences.Demystifier said:1. Why do values not exist before measurement?
Measurements are interactions between the measurement device and the measured object. The dynamics is described by quantum (statistical) theory.Demystifier said:2. How the values know that there is a measurement out there?
It's given by a concrete measurment apparatus.Demystifier said:3. What's the precise definition of measurement?
The construction of measurment devices is based on the known natural laws as any technical development. The "primitive concepts" behind this constructions thus are the corresponding theories describing them.Demystifier said:4. Can measurement be derived from something more fundamental, or is measurement a primitive concept?
Of course the state of the measured system changes due to the interaction with the measurement device. Whether or not the system persists to exist, i.e., can be in a meaningful way separated from the measurement device an/or "the environment" depends on the specifics of the measurement device. Thus this is a question to be answered theoretically using the theory but it cannot be answered by inventing some new fundamental postulate of the theory.Demystifier said:5. Does a value (randomly created in a measurement) have influence on the state?
A closed system's dynamics is described by unitary time evolution. Attempts to extend QT beyond this standard formulation so far failed (or there are even counterarguments, e.g., by Susskind et al concerning the use of Lindblad equations generalizing the unitary time evolution of the standard theory).Demystifier said:6. If the answer to 5. is "yes", does this influence violate unitarity, linearity, locality and/or the Schrodinger equation?
likewise, why don't they take, any possible value, for example up and up.Demystifier said:So you are saying that the state always exists, while values of the observables exist only when they are measured, is that right? But it creates a lot of additional questions:
1. Why do values not exist before measurement?
2. How the values know that there is a measurement out there?
3. What's the precise definition of measurement?
4. Can measurement be derived from something more fundamental, or is measurement a primitive concept?
5. Does a value (randomly created in a measurement) have influence on the state?
6. If the answer to 5. is "yes", does this influence violate unitarity, linearity, locality and/or the Schrodinger equation
Demystifier said:But I see inconsistencies when the orthodox guys start to make a philosophy out of it, i.e. when they try to explain what those rules mean at a deeper level. (The very first inconsistency that many of them commit is that they use philosophy to argue that one should not do philosophy.)
Yeah I find this an odd question. To make scientific progress we had to realize that often most/all observables do not have a well-defined value. To me it would be like having a problem with GR because nobody has told you "why" spacetime is curved. Isn't QM a success because it correctly captures these new fascinating aspects of nature?vanhees71 said:The quantum formalism is the result of many observations and experimental facts. There is no sensible way to answer such "why questions" in the natural sciences, which figure out as precisely as possible how Nature behaves but never can answer why she behaves the way she does
Not exactly. I can accept a theory in which some values are not always defined, as far as the theory clearly specifies sufficient and necessary conditions for the values to become defined. The usual condition that it happens when those are "measured" is just not clear enough, unless one also makes a clear definition of measurement. It is this typical lack of clarity that makes it incomplete, which does not necessarily make it inconsistent. The inconsistencies usually appear in the second step, when people who are well trained in physics and math try to do philosophy.PeroK said:My understanding of this thread in broad terms is that orthodox QM does not demand that all measurables have well-defined values at all times and that you believe that this makes QM incomplete and inevitably leads to philosophical inconsistencies.
EPR started from the same postulate and, by assuming also locality, derived that QM is incomplete. I know that you disagree with EPR, but I don't see any consistent way to disagree with them given those two premises.vanhees71 said:An observable has a determined value, if with 100% probability a measurement of this observable results in this value.
But they said clearly what they mean by incomplete. In that sense QM is incomplete no question about it. Was that a useful definition?Demystifier said:EPR started from the same postulate and, by assuming also locality, derived that QM is incomplete. I know that you disagree with EPR, but I don't see any consistent way to disagree with them given those two premises.
I disagree with EPR, because local relativistic QFT is a model, where locality and indeterminism is fully consistently discribed. For me EPR is completely refuted by the demonstration of the violation of Bell's inequalities.Demystifier said:EPR started from the same postulate and, by assuming also locality, derived that QM is incomplete. I know that you disagree with EPR, but I don't see any consistent way to disagree with them given those two premises.
I don't understand in which part you disagree with EPR?vanhees71 said:I disagree with EPR, because local relativistic QFT is a model, where locality and indeterminism is fully consistently discribed. For me EPR is completely refuted by the demonstration of the violation of Bell's inequalities.
To be honest given the near century we've had of not needing such a theory while increasing our understanding of nature while remaining in the "EPR-incomplete" theory and all the no-go theorems against the EPR style theories, it's fruitless to keep seeking an EPR theory.vanhees71 said:Whether there is a then indeed necessarily nonlocal EPR-complete theory as "complete" in describing Nature as relativistic local QFT or not, I don't know
That's an utter nonsense. To agree with EPR means to agree that their assumptions logically imply their conclusions. No experiment can refute a validity of a logical argument. A logical argument can only be refuted by another logical argument. The logical assumptions of EPR are QM and locality, which you accept. Their logical conclusion is incompleteness, which is not refuted by experimental violation of Bell's inequalities.vanhees71 said:I disagree with EPR, because local relativistic QFT is a model, where locality and indeterminism is fully consistently discribed. For me EPR is completely refuted by the demonstration of the violation of Bell's inequalities.
Yes it was. When combined with the Bell's result, now we know that if we want to complete QM in this sense, we must abandon locality (in the EPR-Bell sense).martinbn said:But they said clearly what they mean by incomplete. In that sense QM is incomplete no question about it. Was that a useful definition?
