I think I just became a QBist ?

[strangerep]

[...] it may be a mistake to venture into C* algebra too far

I think about this in the context of the question (borrowing part of your phrase): "what is the mathematical content of the principle that the laws of physics are the same for all observers, if there is no unique official representation of global spacetime ? "

 

[marcus]

I guess the good (and also the bad) thing about the C* embodiment of this idea is that it backs away the idea of a global geometry and focuses entirely on the algebra of observables. It focuses on actual measurements.

I believe it was von Neumann who observed that you can formulate QM without a Hilbert space of states. If you HAD a Hilbert space you could take the "von Neumann" algebra of observables on it and then pick one state, and throw away the rest of the Hilbert space. That chosen state provides a positive linear functional on the algebra (expectation value of the observable evaluated on that state).

So now you have an abstract algebra (which happens to have an adjoint or * operation) and a positive functional on it.

That is just as good a place to start a quantum theory as the conventional Hilberspace is. And there is a Gelfand NaimarkSegal construction that recovers an equivalent Hilbertspace. So it seems like nothing has changed it is all pure mathematical fiddlesticks.

But starting with a C* algebra with a positive functional (a "state") defined on it nevertheless proved to be a fertile new approach.

One odd advantage: in usual QG there's no preferred idea of time BUT R. thinks that to do thermodynamics and to do statistical mechanics you NEED a global time at least as an occasional point of reference HOWEVER in the C* formulation something like a global time emerges from the positive linear functional called the STATE. It also uses the adjoint or * that comes with the abstract algebra.

 

[marcus]

I think about this in the context of the question (borrowing part of your phrase): "what is the mathematical content of the principle that the laws of physics are the same for all observers, if there is no unique official representation of global spacetime ? "

You know more and think deeper than I do. I'm interested to see how this thread goes. Right now I have to go for a walk up this grassy tree grown hill near the house, , it overlooks the Bay. It is 5:03PM Pacific time and getting dark already. If I don't go I get more like a vegetable. Back later

 

[strangerep]

You know more and think deeper than I do.

Rubbish.

Depending on how the "algebra of observables" sub-theme of this thread develops, I might get to prove that it's rubbish.

 

[Demystifier]

Demy, what can you mean by "search for a resolution"?

Searching for a new description, new equations, which better fits nature as we see it.

 

[marcus]

Searching for a new description, new equations, which better fits nature as we see it.

It sounds like what you had in mind, then, was not a final theory but an incremental improvement.
Thanks for the clarification.

Quote by audioloop
...but NATURE is more than equations.

It certainly is, but that constatation alone cannot resolve any problem one might have with the equations. Perhaps it can give someone a reason not to search for a resolution, but a reason not to search for a resolution is not a resolution.

As an experiment, let me try this substitution using what you say you meant by "resolution":
Perhaps it can give someone a reason not to search for a better fit, but a reason not to search for a better fit is not a better fit.

I was puzzled by this exchange. I assume that equations are just description in an evolving artificial human language which hopefully will get better over time (if people keep trying). And I assume that as such the equations are DISJOINT from the reality. Nature is not merely "more" but actually other than our current most reliable description---reality is not to be confused with the description.

I do not see how this could be imagined to be a reason to stop trying to find a better description. AFAICS there is no reason not to keep striving for simpler/more reliable/more accurate/more beautiful models.

So I did not understand what you said about "Perhaps it can give someone a reason not to search for a resolution…"

If you simply mean incrementally improved accuracy etc then how could what Audioloop said give someone a reason not to improve the description?

Also it seemed to me that in your post you were hinting at some mysterious "ontological" connection between our human equations and the reality: that the description really was connected somehow with true Being---that the equations "knew more" than we do.

Let me also say a few words on the Mermin's essay.

I think all this can be reduced to the following question:
Who is more clever, the physics equations, or the physicists who invented them?

If physicists are more clever, and equations merely represent a part of all things which they understand, then Mermin is right: Equations are nothing but a part of our description of our knowledge about the world, not the reality. If so, then there is no problem of now, no problem of interpretation of quantum mechanics, etc.

However, there are good reasons to believe that equations are more clever than the physicists who invented them. In other words, equations know a lot which their inventers do not. For example, Dirac new nothing about positrons when invented the Dirac equation, and the inventers of quantum electrodynamics new nothing about 10 digits of the quantity g-2.

So, as equations seem to know more than their inventors, it is hard not to take the equations seriously and believe that they represent something more than merely our current incomplete knowledge about the world. Of course, with such an attitude, there is a problem of now and there is a problem of interpretation of quantum mechanics, because the equations we currently know do not provide a direct answer.

 

[atyy]

Another paper with comments on what might be beyond quantum theory.

http://arxiv.org/abs/quant-ph/0102043
Causal and localizable quantum operations
David Beckman, Daniel Gottesman, M. A. Nielsen, John Preskill
"From this perspective, the existence of causal operations that are not localizable comes as a surprise. We seem to have the freedom to relax the rules of quantum theory by allowing more general operations, without encountering unacceptable physical consequences. Nontrivial support for this notion is provided by the semigroup property of the causal operations. It is reasonable to insist that the operations allowed at a given time ought not to depend on the previous history of the system; since the composition of two causal operations is causal, a theory that admits more general causal operations than those allowed in local quantum theory could adhere to this proviso."

 

[Demystifier]

Also it seemed to me that in your post you were hinting at some mysterious "ontological" connection between our human equations and the reality: that the description really was connected somehow with true Being---that the equations "knew more" than we do.

What I meant is the following. Sometimes, equations fit reality much better than we expected (e.g., prediction of positron by the Dirac equation). When this happens, it is hard to resist temptetation to believe that equations are somehow more clever than their inventors, and consequently, that equations are not ONLY the description, but also something "real" or "ontological".

 

[Paulibus]

...it is hard to resist temptation to believe that equations are somehow more clever than their inventors, and consequently, that equations are not ONLY the description, but also something "real" or "ontological".

A mysterious something "real"? Sounds a bit contra-eponymous to me!

I suspect that you are inclining to a belief that I've found shared by many mathematicians; that equations (and mathematics generally) are something 'found', which one discovers. I prefer to think that mathematicians spend their time inventing a clever language --- not unrelated to music and the game of chess --- and that physicists, as more pedestrian folk, carpenter away at describing discovered reality with this language. Happily it takes two to tango!

 

[Demystifier]

A mysterious something "real"? Sounds a bit contra-eponymous to me!

I suspect that you are inclining to a belief that I've found shared by many mathematicians; that equations (and mathematics generally) are something 'found', which one discovers. I prefer to think that mathematicians spend their time inventing a clever language --- not unrelated to music and the game of chess --- and that physicists, as more pedestrian folk, carpenter away at describing discovered reality with this language. Happily it takes two to tango!

So you and me have different views on the Wigner's "Unreasonable Effectiveness of Mathematics in the Natural Sciences":
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

 

[TrickyDicky]

What I meant is the following. Sometimes, equations fit reality much better than we expected (e.g., prediction of positron by the Dirac equation). When this happens, it is hard to resist temptetation to believe that equations are somehow more clever than their inventors, and consequently, that equations are not ONLY the description, but also something "real" or "ontological".

A mysterious something "real"? Sounds a bit contra-eponymous to me!

I suspect that you are inclining to a belief that I've found shared by many mathematicians; that equations (and mathematics generally) are something 'found', which one discovers. I prefer to think that mathematicians spend their time inventing a clever language --- not unrelated to music and the game of chess --- and that physicists, as more pedestrian folk, carpenter away at describing discovered reality with this language. Happily it takes two to tango!

So you and me have different views on the Wigner's "Unreasonable Effectiveness of Mathematics in the Natural Sciences":
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

Hamming's explanations of the unreasonable effectiveness of math seem quite reasonable to me.
My own view is that as always it is tempting to evoke some mystery, that's just human nature, but it is not really hard to find examples, that are so far not contradicted by observations , of physical arrangements that dissolve any mystery wrt the effectiveness of math in physics.

Say there is a constant and uniform physical entity, call it universe (this is a quite typical assumption in physics and in science in general, think of the constancy of physical laws throughout the universe, the homogeneity assumption...).
Now this particular physical arrangement will have certain constant relationships within its elements, will follow certain particular patterns and evolution, particular properties and magnitudes that will allow to define mathematical equations that will differ from other conceivable particular physical entities.

In as much as it is possible for humans(and perhaps this is indeed a mystery) to develope a symbolic language that allows to play with relationships between elements such as mathematics, it should come as no surprise that we are able to model at least partially some of the traits of the assumed homogeneous and constant physical entity. Of course most conceivable mathematical objects will not correspond to the physical entity, but humans obviously select of all the conceivable infinite set those that are more practical in their environment which happen to be those closer to the properties of the physical entity assumed. This selection process is often unconscious which lends itself to atttribute to the math language itself some magical properties.
It follows quite easily from this that mathematical objects have no reality of their own other than how closely they resemble the properties and structure of the physical entity in case.
It is not automatic either that human ingenuity will eventually find the more fitting equations dscribing the universe, but it suggests that it is certainly possible. The only evidenc is that so far it has only found equations like the EFE, Schrodinger's, Dirac's... that give very good approximations but that aren't obviously completely correct(given their incompatibility) in the sense of modelling a single physical entity coherently, but are good enough to model it partially.

Whether the particular mathematical object "manifold" is capable of accomplishing the modelling of the universe that I refer to above or we need a different object/s as has been suggested in this thread is an interesting debate IMO.

 

[strangerep]

I feel that the "Nature is more than equations" subdiscussion is hijacking my thread.

I created a https://www.physicsforums.com/showthread.php?t=731870 where those discussions can continue, and I've asked the Mentors to move relevant posts into the new thread. Please continue that subdiscussion there instead of here.

 

[marcus]

I feel that the "Nature is more than equations" subdiscussion is hijacking my thread.

I created a https://www.physicsforums.com/showthread.php?t=731870 where those discussions can continue, and I've asked the Mentors to move relevant posts into the new thread. Please continue that subdiscussion there instead of here.

That seems like a good idea. QBism is interesting in and of itself. We could try to stay focused on QBism in this thread and let the other discussion gravitate to the other thread.
QBism is new to me and I'm not confident I understand its main thrust. Mermin seems to be a really effective advocate so I will assume it is "what Mermin says".

I liked the article very much that you linked in post #33:

Looks like N.D.Mermin is still thinking about this stuff...

N. D. Mermin,
QBism as CBism: Solving the Problem of "the Now",
Available as: http://arxiv.org/abs/1312.7825
...

He communicates the gist of CLASSICAL QBism and he uses it to solve the problem of NOW.
We are talking about aninterpretation of Quantum Mechanics that solves several problems that hound other interpretations and also has a classical correlative that solves a chronic classic irritation that festers around the "block universe" idea.

So it might be fun to quote a paragraph or two of that paper you mentioned in post #33

 

[marcus]

==quote Mermin page 2==
“Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.”
The issue here is not that the simultaneity of two different events in different places depends on frame of reference. The issue is that physics seems to have nothing whatever to say about the local Now at a single event.⁸ This apparent silence is a puzzle even without the relativity of simultaneity. Physics, both pre- and post-relativistic, deals only with relations between one time and another. Nevertheless a local present moment — the Now — is immediately evident as such to each and every one of us. My experience of the Now is a primitive fact. It simply can’t be argued with.⁹ Sum; ergo Nunc est. How can there be no place in physics for something as obvious as that?
My Now is a special event for me as it is happening. The Now is distinguished from all the other events I have experienced by being the actual current state of affairs. I can distinguish it from earlier events (former Nows) which I merely can remember, and from…
==endquote==
He says that the trouble is caused by our making two mistakes:
==Mermin excerpts page 3 and page 4==
The problem of the Now will not be solved by discovering new physics behind that glowing point. Nor is it solved by dismissing the Now as an “illusion” or as “chauvinism of the present moment.” It is solved by identifying the mistakes that lead us to conclude, contrary to all our experience, that there is no place for the Now in our physical description of the world.
III. The mistakes
There are two mistakes. The first is our deeply ingrained unwillingness, noted above, to acknowledge that whenever anybody uses science it has a subject as well as an object. It is the well-established habit of each of us to leave ourself — the experiencing subject —completely out of the story told by physics.^12,13
The second mistake is the promotion of space-time, from a 4-dimensional diagram that we each find an extremely useful conceptual device, into what Bohr called a “real essence”. My diagram enables me to represent events from my past experience, together with my possible conjectures, deductions, or expectations for events that are not in my past, or that escaped my direct attention. By identifying my abstract diagram with an objective reality, I fool myself into regarding the diagram as a 4-dimensional arena in which my life is lived.
==endquote==
Beautiful!

And solipsism is out of the question because there are a multiplicity of observers/agents who moreover can communicate among themselves.
==Amusing footnote laughing at the solipsism charge, on page 3==
11 It is not obvious to a distinguished philosopher of science, who recently had this to say about an unpublished, unarXived talk on the Now that I gave at the Perimeter Institute in 2009 [a video is at http://pirsa.org/09090077]: “A distinguished quantum theorist insisted that the past is just a model we invent to make sense of present evidence and not to be taken literally. . . .The time snobs’ chauvinism of the present moment slides easily into solipsism.” [Huw Price, Science 341, 960-961, 30 August 2013.] The QBist (CBist) recognition that the subject in science is as important as the object often elicits charges of solipsism, even though the multiplicity of subjects (agents) and their ability to communicate with each other is a crucial and explicit part of both the general QBist story and the particular CBist application I describe here, particularly in Section V below.
==endquote==

No time to finish or edit. Have to go to supper. It is 7:25 PM Pacific.
Now I'm back. So the two (actually classical) points he wants to make are:
1. What matters is the information exchanged between two subsystems. If one happens to be called an "observer" don't discount the observer. Even a rock can have a NOW. "I am, therefore it is now." Sum, ergo nunc est
2. The 4D blocky picture is a useful conceptual device but don't let that fool you into accepting it as "ontology". BTW events are not POINTS. That's a radical idealization. Events have extension and so do clocks. And reading a clock takes time…etc etc.

I think that's what he's saying in section III. It's an entertaining lively provocative paper. I think there are some strategic ideas here that could simplify both our view of basic physics and our frustrating attempts to interpret quantum mechanics.

Mermin says he is not sure what CBism (a term he coined for the classical correlative of QBism) actually stands for! He thinks maybe it stands for "Classical Bohrism". Why not? I'm certainly good with that.

I think it is possible that there is a RIGHT interpretation of Quantum Mechanics. What a surprising idea! since we are used to a menu of them, each one inedible in its own way.


 

[strangerep]

[...Mermin quote...]
Beautiful!

Yes. I enjoy his writing style.

But I wonder about all this "personal experience of Now" stuff -- in the context of Atyy's remarks about psychological time. I don't experience an event until slightly after the signals have entered my brain and been processed far enough to register in my conscious mind. One needs some background on the pre-conscious and conscious, but the science of psychology+neurology seem still very far from a detailed model of brain->mind.

So, for purposes of physics, I retreat to the simplicity of some form of automated sensing system, recording incoming signals on (some equivalent of) a spatially sequential tape. And "ideal systems" instead of "observers". Then a notion of interaction (i.e., recorded communication) in terms of coalescence and splitting of ideal systems seems doable. E.g., a photon (ideal system 1) is absorbed by a atom (ideal system 2). Then there is only one ideal system: the atom in an excited state. Later, they probably split into 2 ideal systems again, but now they're correlated. This relates to the Mermin footnote you quoted, i.e.,

[...] the multiplicity of subjects (agents) and their ability to communicate with each other is a crucial and explicit part of both the general QBist story [...]

 

[TrickyDicky]

I feel that the "Nature is more than equations" subdiscussion is hijacking my thread.

The "subdiscussion" started in page three of "your thread" about a week ago as a comment by Demystifier on the Mermin's paper subject of the thread, and continued by Marcus and others in page 4 without you or anyone apparently considering it as hijacking. If it hadn't been for Marcus insistence on clarifying Demystifier's "Nature is more than equations" comment about Mermin's paper I don't think the "subdiscussion" would have gone further than a casual post,-on topic as it was meant as a comment on the thread's subject-.
Of course you are entitled to feel hijacked whenever you wish but it puzzles me that you didn't feel it in the previous pages of the thread.

 

[marcus]

If it hadn't been for Marcus insistence on clarifying Demystifier's "Nature is more than equations" comment about Mermin's paper I don't think the "subdiscussion" would have gone further...

My fault then. Sorry about accidentally getting us off track. Hope we can get back down to business.
I'm eager to understand more about the QB interpretation of QM.

 

[marcus]

Here's Strangerep's original post:

Just finished a first reading of this paper:

C.A.Fuchs, N.D.Mermin, R.Schack,
"An Introduction to QBism with an Application to the Locality of Quantum Mechanics",
http://arxiv.org/abs/1311.5253

Abstract:
==quote==
We give an introduction to the QBist interpretation of quantum mechanics. We note that it removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades. As an example, we show in detail how it eliminates “quantum non locality”.
==endquote==

Interesting that it has ideas that remind me of Rovelli's Relational QM and Relational EPR (which I find appealing), though Rovelli is not cited in the FMS paper.

I like it because (imho) it cuts through a lot of the widespread BS that wafts around QM.

(I mention the FMS paper here in BSTM, rather than the quantum forum, since it's a bit off the mainstream.)

So can someone summarize what the QBist interpretation of QM is and briefly say how it removes the ...pseudo-problems that have plagued quantum foundations for nine decades?

I believe it actually does do that, and am eager to get a better grasp of it.

 

[atyy]

So can someone summarize what the QBist interpretation of QM is and briefly say how it removes the ...pseudo-problems that have plagued quantum foundations for nine decades?

I believe it actually does do that, and am eager to get a better grasp of it.

I dislike all the expositions by Mermin on this topic. I do find one idea attractive in QBism. That idea is that collapse is like Bayesian updating. Bayesian coherence is a standard term in Bayesian inference. This is a very old idea that is hinted at in Cohen Tannoudji, Diu and Laloe's text, and mentioned in the recent text of Wiseman and Milburn.

Here is an example of Bayesian "coherence" in standard statistical usage: http://mlg.eng.cam.ac.uk/mlss09/mlss_slides/Jordan_1.pdf.
Are You a Bayesian or a Frequentist?
Michael I. Jordan

All solutions to the measurement problem introduce new postulates from which the Born rule or projection postulate are derived. For example, Bohmian mechanics introduces non-local hidden variables. Many-worlds introduces branching realities. Both are successful in the sense that the additional postulates are more natural.

Qbism introduces the new postulate "Principle of Reciprocity: Posteriors from Maximal Ignorance Are Priors" from which the projection postulate is derived. If you believe the new assumption is "natural", then it solves some aspect of the measurement problem.

The postulate is stated on p17 and p23 (Eq 130) of:
http://arxiv.org/abs/1301.3274
Quantum-Bayesian Coherence: The No-Nonsense Version
Christopher A. Fuchs, Ruediger Schack
Rev. Mod. Phys. 85, 1693–1715

For comparison, here's the different but related approach of Leifer and Spekkens, which I like:
http://arxiv.org/abs/1107.5849
Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
M. S. Leifer, R. W. Spekkens

Leifer and Spekkens compare their approach with QBism:
"It follows that in the conditional states framework, the steering effect is merely belief propagation (updating beliefs about one system based on new evidence about another) and does not require any causal influence from one to the other. This interpretation has been advocated previously by Fuchs [22]."

"By contrast, our work takes quantum states to represent the beliefs of an agent about a spatio-temporal region and takes quantum operations to represent belief propagation; it has an epistemological flavor rather than an operational one. For instance, the notions that we deem to be most promising for making sense of the quantum formalism are those one finds in textbooks on statistics and inductive inference, such as Bayes’ theorem, conditional probabilities, statistical independence, conditional independence, and sufficient statistics and not the notions that are common to the operational approaches, such as measurements, transformations and preparations. In this sense, our approach is more closely aligned in its philosophical starting point with quantum Bayesianism, the view developed by Caves, Fuchs and Schack"

"Unlike the quantum Bayesians, however, we are not committed to the notion that the beliefs represented by quantum states concern the outcomes of future experiments. Rather, the picture we have in mind is of the quantum state for a region representing beliefs about the physical state of the region, even though we do not yet have a model to propose for the underlying physical states."

Of relevance to whether hidden variables are consistent with an "epistemic" approach are papers that support the existence of psi-epistemic hidden variables:

http://arxiv.org/abs/1201.6554
Distinct Quantum States Can Be Compatible with a Single State of Reality
Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph

http://arxiv.org/abs/1303.2834
Psi-Epistemic Theories: The Role of Symmetry
Scott Aaronson, Adam Bouland, Lynn Chua, George Lowther

There is a proof that maximally psi-epistemic hidden variables are forbidden:
http://arxiv.org/abs/1207.6906
How statistical are quantum states?
O. J. E. Maroney

 

[marcus]

I dislike all the expositions by Mermin on this topic. I do find one idea attractive in QBism. That idea is that collapse is like Bayesian updating...

I recall that the "updating" idea arose our discussion of the Rovelli Smerlak paper some time ago. Each observer has his own Hilbertspace to keep track of his information and updating is not something catastrophic that the world does, it is just something he does in his own file system to stay au courant.

You are on a different schedule from me, Atyy. You already understand QB interpretation and are starting to critique it and consider antecedents alternatives and improvements. I basically want to understand better, especially what Mermin is saying.

We have these two recent papers that Rep mentioned:
November FMS http://arxiv.org/abs/1311.5253
December Mermin http://arxiv.org/abs/1312.7825
That defines what QB is, for me, and what I want to concentrate on.

When Mermin talks about probability he refers to Bruno de Finetti:
[[That probabilities are personal judgments was put most forcibly by Bruno de Finetti, and if “B” has to stand for anything I would expand “QBism” to “Quantum Brunoism.”]]
I believe in this case it is the personal judgements of a rational bettor. What wagers would an ideal rational Bookie consider fair? He mentions is the concept of a "Dutch Book" which I suspect is where a good bookie writes down the odds at which to buy and sell bets.

 

[atyy]

I recall that the "updating" idea arose our discussion of the Rovelli Smerlak paper some time ago. Each observer has his own Hilbertspace to keep track of his information and updating is not something catastrophic that the world does, it is just something he does in his own file system to stay au courant.

You are on a different schedule from me, Atyy. You already understand QB interpretation and are starting to critique it and consider antecedents alternatives and improvements. I basically want to understand better, especially what Mermin is saying.

We have these two recent papers that Rep mentioned:
November FMS http://arxiv.org/abs/1311.5253
December Mermin http://arxiv.org/abs/1312.7825
That defines what QB is, for me, and what I want to concentrate on.

When Mermin talks about probability he refers to Bruno de Finetti:
[[That probabilities are personal judgments was put most forcibly by Bruno de Finetti, and if “B” has to stand for anything I would expand “QBism” to “Quantum Brunoism.”]]
I believe in this case it is the personal judgements of a rational bettor. What wagers would an ideal rational Bookie consider fair? He mentions is the concept of a "Dutch Book" which I suspect is where a good bookie writes down the odds at which to buy and sell bets.

No, if you read my post #89 it is my summary of QBism you asked for. I simply dislike Mermin's writing about it. I believe the review by Fuchs and Schack I linked to is a far better exposition of QBism. The statistical method of Bayesian inference I mentioned is based in large part on de Finetti's work, and the formal notion of Bayesian coherence I mentioned is de Finetti's. The Dutch Book example is a famous example illustrating Bayesian coherence.

 

[Dale]

It has been recommended that we close all the threads about QM interpretations in order to be coherent with the closure of the spawned thread.