Insights The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

[AlexCaledin]

From Physics and Philosophy by Werner Heisenberg

... one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena. This is in fact not surprising since the concepts of natural language are formed by the immediate connection with reality; they represent reality. It is true that they are not very well defined and may therefore also undergo changes in the course of the centuries, just as reality itself did, but they never lose the immediate connection with reality. On the other hand, the scientific concepts are idealizations; they are derived from experience obtained by refined experimental tools, and are precisely defined through axioms and definitions. Only through these precise definitions is it possible to connect the concepts with a mathematical scheme and to derive mathematically the infinite variety of possible phenomena in this field. But through this process of idealization and precise definition the immediate connection with reality is lost. The concepts still correspond very closely to reality in that part of nature which had been the object of the research. But the correspondence may be lost in other parts containing other groups of phenomena.

 

[lightarrow]

Yes, and in 1926ff we learned that this is a misleading statement. The explanation of the photoelectric effect on the level of Einstein's famous 1905 paper does not necessitate the quantization of the electromagnetic field but only of the (bound) electrons.

https://www.physicsforums.com/insights/sins-physics-didactics/

I didn' want to be the one to say that and I was pretty sure you or Arnold would have corrected me
Thanks.
--
lightarrow

 

[Lord Jestocost]

...superfluous philosophical balast

Bohr and Heisenberg were confronted with simple materialistic views that prevailed in the natural science of the nineteenth century and which were still held during the development of quantum theory by, for example, Einstein. What you call “philosophical ballast“ are at the end nothing else but attempts to explain to Einstein and others that the task of “Physics” is not to promote concepts of materialistic philosophy.

 

[stevendaryl]

I'm not quite clear on why it is that if "we can never make deterministic predictions about the results of quantum experiments" that this implies non-reality, as opposed, for example, to a system that is chaotic (in the sense of having dynamics that are highly sensitive to slight changes in initial conditions) with sensitivity to differences in initial conditions that aren't merely hard to measure, but are inherently and theoretically impossible to measure because measurement is theoretically incapable of measuring both location and momentum at the scale relevant to the future dynamics of a particle.

Well, Bell's theorem was the result of investigating exactly this question: How do we know that the indeterminacy of QM isn't due to some unknown dynamics that are just too complicated to extract deterministic results from? The answer is: As long as the dynamics is local (no instantaneous long-range interactions), you can't reproduce the predictions of QM this way.

The use of the word "realism" is a little confusing and unclear. But if you look at Bell's proof, a local, realistic theory is one satisfying the following conditions:

1. Every small region in space has a state that possibly changes with time.
2. If you perform a measurement that involves only a small region in space, the outcome can depend only on the state of that region (or neighboring regions--it can't depend on the state in distant regions)

Why is the word "realism" associated with these assumptions? Well, let's look at a classical example from probability to illustrate:

Suppose you have two balls, a red ball and a black ball. You place each of them into an identical white box and close it. Then you mix up the two boxes. You give one box to Alice, and another box to Bob, and they go far apart to open their boxes. We can summarize the situation as follows:

• The probability that Alice will find a red ball is 50%.
• The probability that Alice will find a black ball is 50%.
• The probability that Bob will find a red ball is 50%.
• The probability that Bob will find a black ball is 50%.
• The probability that they both will find a black ball is 0.
• The probability that they both will find a red ball is 0.

If you consider the probability distribution to be a kind of "state" of the system, then this system violates locality: The probability that Bob will find a red ball depends not only on the state of Bob and his box, but also on whether Alice has already found a red ball or a black ball. So this is a violation of condition 2 in my definition of a local realistic theory.

However, the correct explanation for this violation is that classical probability is not a realistic theory. To say that Bob's box has a 50% probability of producing a red ball is not a statement about the box; it's a statement about Bob's knowledge of the box. A realistic theory of Bob's box would be one that describes what's really in the box, a black ball or a red ball, and not Bob's information about the box. Of course, Bob may have no way of knowing what his box's state is, but after opening his box and seeing that it contains a red ball, Bob can conclude, using a realistic theory, "The box really contained a red ball all along, I just didn't know it until I opened it."

In a realistic theory, systems have properties that exist whether or not anyone has measured them, and measuring just reveals something about their value. (I wouldn't put it as "a measurement reveals the value of the property", because there is no need to assume that the properties are in one-to-one correspondence with measurement results. More generally, the properties influence the measurement results, but may not necessarily determine those results, nor do the results need to uniquely determine the properties).

Bell's notion of realism is sort of the opposite of the idea that our observations create reality. Reality determines our observations, not the other way around.

 

[stevendaryl]

Bohr and Heisenberg were confronted with simple materialistic views that prevailed in the natural science of the nineteenth century and which were still held during the development of quantum theory by, for example, Einstein. What you call “philosophical ballast“ are at the end nothing else but attempts to explain to Einstein and others that the task of “Physics” is not to promote concepts of materialistic philosophy.

What's funny (to me) about the anti-philosophy bent of so many physicists is that many of them actually do have deeply-held philosophical beliefs, but they prefer to only use the word "philosophy" to apply to philosophies that are different from their own.

 

[vanhees71]

From Physics and Philosophy by Werner Heisenberg

... one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena. This is in fact not surprising since the concepts of natural language are formed by the immediate connection with reality; they represent reality. It is true that they are not very well defined and may therefore also undergo changes in the course of the centuries, just as reality itself did, but they never lose the immediate connection with reality. On the other hand, the scientific concepts are idealizations; they are derived from experience obtained by refined experimental tools, and are precisely defined through axioms and definitions. Only through these precise definitions is it possible to connect the concepts with a mathematical scheme and to derive mathematically the infinite variety of possible phenomena in this field. But through this process of idealization and precise definition the immediate connection with reality is lost. The concepts still correspond very closely to reality in that part of nature which had been the object of the research. But the correspondence may be lost in other parts containing other groups of phenomena.

Well, I think the opposite is true. With the refined means of the scientific effort we come closer and closer to reality. Our senses and "natural language" are optimized to survive under the specific "macroscopic" circumstances on Earth but not necessarily to understand realms of reality which are much different in scale than the one relevant for our survival like the microscopic scale of atoms, atomic nuclei, and subatomic/elementary particles or the very large scale of astronomy and cosmology. It's very natural to expect that our "natural language" is unsuitable to describe, let alone in some sense understand, what's going on at these vastly different scales. As proven by evidence the most efficient way to communicate about and to some extent understand nature on various scales is mathematics, and as with natural languages to learn a new language is never a loss but always a gain in understanding and experience.

 

[Auto-Didact]

As for the axiomatic treatment a la Ballentine, I believe the others have answered that adequately, but I will reiterate my own viewpoint: that is a mathematical axiomatization made in a similar vein to measure theoretic probability theory, not a physical derivation from first principles.

@bhobba I feel I need to expand on this by explaining what exactly the difference is between a formal axiomatization as is customarily used in contemporary mathematics since the late 19th/early 20th century and a derivation from first principles as was invented by Newton and is practically unaltered customarily used in physics up to this day. I will once again let Feynman do the talking, so just sit back and relax:


I hope this exposition makes things somewhat more clear. If it doesn't, well... here is just a little more elaboration explaining why physics is not mathematics (NB: especially regarding that the measurement process being described is part of physics and a scientific necessity not just some afterthought)

Spoiler

For those who really can't get enough of this, these videos are part of the lecture The Relation of Mathematics and Physics, which are part of Feynman's seven part Messenger lectures on the Character of Physical Law. These were intended for the public but in my opinion they should be compulsory viewing for all physics students.

 

[bhobba]

... one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena.

To be fair he did not write that in light of future developments that shows the exact opposite to an even greater degree than was then known. But even then they knew the work of Wigner and Noether that showed it most definitely is NOT true. It can only be expressed in the language of math.

If you think otherwise state Noether's theorem in plain English without resorting to technical concepts that can only be expressed mathematically. Here is the theorem: Noether's first theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.

Mathematical concepts used - diferrentiable symmetry and action. If you can explain it in plain English - be my guest.

Thanks
Bill

 

[bhobba]

I feel I need to expand on this by explaining what exactly the difference is between a formal axiomatization as is customarily used in contemporary mathematics since the late 19th/early 20th century and a derivation from first principles as was invented by Newton

Newton - first principles - well let's look at those shall we:
Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...

What utter nonsense, and there is zero doubt Feynman would agree. I know those vireos you posted very well and they say nothing of the sort.

With all due respect to Newton, who as Einstein said was really the only path a man of the highest intellect could take in his time, from our vantage its nonsense - things have moved on - a lot.

BTW I know those video's from the Character of Physical Law by Feynman very very well. But reviewed it again. He is simply saying what I am saying - you can write QM purely as a mathematical system - no problem. But to apply it you need to map the things in the math to what you are applying it to. In QM its so easy you don't even have to spell it out in beginner or even intermediate textbooks - its simply left up in the air. It is assumed you know what an observation is etc. That's why they can study QM without any of the difficulties of interpretation - ie shut up and calculate. You can go a long way dong just that. But, just like what probability is in probability theory, if you want to delve deeper and understand it what it means when you apply it, you run into a morass. For example, exacty what is an observation. Since observations, supposedly anyway - its never spelled out in such treatments - occur here in the macro world how do you explain that macro world with a theory that assumes it's existence in the first place. They are only some of the many issues if you look deeply enough. To answer them we have interpretations. But it's wise to study them after you have at least done QM to the intermediate level - eg Griffiths would be an example - but Vanhees who teaches this stuff knows a better book whose name I can't recall - but anyway it's unimportant - the important thing is you need to study the 'intuitive' treatment before delving into the deep issues. BTW that's one reason Ballentine is so good - he does not skirt those issues. You may or may not agree with him - but he does not skirt them. However it is an advanced book you study after intermediate books like Griffiths.

Thanks
Bill

 

[Auto-Didact]

Newton - first principles - well let's look at those shall we:
Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...

What utter nonsense, and there is zero doubt Feynman would agree. I know those vireos you posted very well and they say nothing of the sort.

With all due respect to Newton of course who as Einstein said was really the only path a man of the highest intellect could take in his time.

But things have moved on.

Thanks
Bill

You somehow manage to twist and misunderstand everything I say. Nowhere did I imply that we still use the same first principles that Newton used, I said that physicists still use derivation from first principles as invented by Newton, i.e. we still use the method, which Newton invented, of mathematically deriving physical laws from first principles. Before Newton there simply was no such approach to physics and therefore no true inkling of physical law; in this sense it can be said that Newton invented (mathematical) physics.

In the video Feynman makes crystal clear that the physics approach to mathematics and how mathematics is used in physics to derive laws from principles and vice versa, is as far from formalist mathematician-type axiomatic mathematics as can be.

 

[bhobba]

You somehow manage to twist and misunderstand everything I say. Nowhere did I imply that we still use the same first principles that Newton used, I said that physicists still use derivation from first principles as invented by Newton,

And I could also say the same thing.

Didn't you get what was being inferred - we do not use the same methods as Newton because they do not work. We can't elucidate those 'first principles' you talk about, even for such a simple thing as what time is.

The modern definition of time is - its what a clock measures.

Wow what a great revelation - but as a first principle - well its not sating much is it beyond common sense - basically things called clocks exist and they measure this thing called time. It does however have some value - it stops people trying to do what Newton tried - and failed.

Want to know what the 'first principles' of modern classical mechanics is:

1. The principle of least action.
2. The principle of relativity.

Now, if what you say is true then you should be able to state those in your 'first principles' form. I would be very interested in seeing them. BTW 1. follows from QM - but that is just by the by - I even gave a non rigorous proof - see post 3:
https://www.physicsforums.com/threa...fication-of-principle-of-least-action.881155/

You will find it doesn't matter what you do, you at the end of the day end up with very vague, or even when looked at deeply enough, nonsensical statements. That's why it's expressed in mathematical form with some terms left to just common sense in how you apply it. In fact that's what Feynman was alluding to at the end of the second video you posted. Physics is not mathematics but is written in the language of math. How do you go from one to the other? Usually common-sense. But if you want to go deeper then you end up in a philosophical morass that we do not discuss here.

Thanks
Bill

 

[Auto-Didact]

And I could also say the same thing.

Didn't you get what was being inferred - we do not use the same methods as Newton because they do not work. We can't elucidate those 'first principles' you talk about, even for such a simple thing as what time is.

The modern definition of time is - its what a clock measures.

Wow what a great revelation - but as a first principle - well its not sating much is it beyond common sense - basically things called clocks exist and they measure this thing called time. It does however have some value - it stops people trying to do what Newton tried - and failed.

Want to know what the 'first principles' of modern classical mechanics is:

1. The principle of least action.
2. The principle of relativity.

Now, if what you say is true then you should be able to state those in your 'first principles' form. I would be very interested in seeing them. BTW 1. follows from QM - but that is just by the by - I even gave a non rigorous proof - see post 3:
https://www.physicsforums.com/threa...fication-of-principle-of-least-action.881155/

You will find it doesn't matter what you do, you at the end of the day end up with very vague, or even when looked at deeply enough, nonsensical statements. That's why it's expressed in mathematical form with some terms left to just common sense in how you apply it. In fact that's what Feynman was alluding to at the end of the second video you posted. Physics is not mathematics but is written in the language of math. How do you go from one to the other? Usually common-sense. But if you want to go deeper then you end up in a philosophical morass that we do not discuss here.

Thanks
Bill

I'm not sure that you understand that I am saying that our first principles are all literally mathematical statements - all our first principles are observational facts in the form of mathematical statements, the best example is the principle of general covariance.

This changes nothing of the fact that the physicist's method of doing mathematics and of deriving new laws looks almost nothing like the modern mathematician's axiomatic style of doing formal mathematics as is customary since Bourbaki; the gist of mathematics used in physics was maybe 'modern' in the 18th/19th century.

Derivation from first principles of physics is the de facto physicist technique of discovering physical laws and theories from principles based on observation in the form of mathematical statements. Derivation from first principles is however not rigorous mathematical proof based on axioms, nor will it ever be: these are two different methods of using mathematics, that is my point.

tl;dr mathematicians and physicists tend to use mathematics in completely different ways due to different purposes, this is a good thing.

 

[bhobba]

the best example is the principle of general covariance.

You know the principle of general covarience is wrong don't you (or rather is totally vacuous as first pointed out by Kretchmann to Einstein - and Einstein agreed - but thought it still had heuristic value)? But that is best suited to the relativity forum.

Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.

Is that what you mean?

Then yes I agree. My two examples of the modern version of classical mechanics would fit that as well.

But I am scratching my head about why the principles I gave from Ballentine would not fit that criteria?

Thanks
Bill

 

[PeterDonis]

Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.

Isn't that what "the principle of general covariance" means?

 

[bhobba]

Isn't that what "the principle of general covariance" means?

Not according to Ohanian:
https://www.amazon.com/dp/0393965015/?tag=pfamazon01-20

There has been long debate about it:
http://www.pitt.edu/~jdnorton/papers/decades.pdf
Ohanian (1976, pp252-4) uses Anderson’s principle of general invariance to
respond to Kretschmann’s objection that general covariance is physically vacuous. He
does insist, however, that the principle is not a relativity principle and that the general
theory of relativity is no more relativistic than the special theory (~257). Anderson’s
ideas seem also to inform Buchdahl’s (1981, Lecture 6) notion of ‘absolute form
invariance’.

Its Anderson's principle of invarience which technically is - The requirement that the Einstein group is also an invariance group of all physical systems constitutes the principle of general invariance.

I will need to dig up my copy Ohanian to give his exact definition of the two - ie invarience and covarience. What I posted is his definition of invarience which I will need to contrast to his definition of covarience. That will take me a couple of minutes - but need to go to lunch now. I will see if I can do it now, otherwise it will need to wait until I get back.

Added Later:
Found it - from page 373 of Ohanain - the Principle of General covarience is:
All laws of physics shall be stated as equations covarient with respect to general coordinate transformations.

The difference is, as Kretchmann showed (and others if I recall), any equation can be bought into covarient form, but invarience is stronger - the content of the law itself must be invariant under coordinate transformations - not just its form.

I think if anyone wants to pursue it further the relativity forum is the best place.

Thanks
Bill

 

[Auto-Didact]

You know the principle of general covarience is wrong don't you (or rather is totally vacuous as first pointed out by Kretchmann to Einstein - and Einstein agreed - but thought it still had heuristic value)? But that is best suited to the relativity forum.

Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.

Is that what you mean?

Then yes I agree. My two examples of the modern version of classical mechanics would fit that as well.

But I am scratching my head about why the principles I gave from Ballentine would not fit that criteria?

Thanks
Bill

I learned GR from MTW, since they use the term general covariance it was what stuck with me.

Ballentines "derivation" is very much an axiomatic formalisation/deduction similar to using the Kolmogorov axioms to formalise probability theory. His "derivation" feels nothing at all like say deriving Maxwell's equations from experimental observations, like deriving Einstein's field equations from Gaussian gravity, or even like deriving the covariant formulation of electrodynamics from respecting the Minkowski metric. The key takeaway here is that Ballentine's 'principles' contain no actual observational content whatsoever, making them (mathematical) axioms not (physical) principles.

This of course is not to say that there aren't any first principles in QM, there definitely are, for example most famously Heisenberg's uncertainty principle, which is an experimental observation; a proper physics derivation of QM from first principles should contain a first principle like this, not some semantically (NB: I forgot the correct term) closed statement like the Born rule.

 

[fresh_42]

Before Newton there simply was no such approach to physics and therefore no true inkling of physical law; in this sense it can be said that Newton invented (mathematical) physics.

Why doesn't Kepler (1619) count? Because his laws certainly satisfy:

Derivation from first principles of physics is the de facto physicist technique of discovering physical laws and theories from principles based on observation in the form of mathematical statements.

In my opinion it has been simply a matter of the time he lived in. Several parallel developments in mathematics and physics took place and developed in a mathematical handling of physical laws. To reduce this complex process to a single person or even book is which I find disrespectful towards all others who have been involved in it. It is an oversimplification and irregular reduction of history.

 

[PeterDonis]

Not according to Ohanian

Looks like a variance in terminology, then. As @Auto-Didact mentions, MTW uses the term "general covariance" to mean what you are using the term "general invariance" to mean. (And since I also learned GR from MTW, I would use "general covariance" to mean that as well.) So you and he actually agree on the physics; you're just using different words.

 

[Auto-Didact]

Why doesn't Kepler (1619) count? Because his laws certainly satisfy:

In my opinion it has been simply a matter of the time he lived in. Several parallel developments in mathematics and physics took place and developed in a mathematical handling of physical laws. To reduce this complex process to a single person or even book is which I find disrespectful towards all others who have been involved in it. It is an oversimplification and irregular reduction of history.

Many modern mathematicians/scientists tend to mistake what is heritage for what is history. Coincidentally, Feynman also explained this difference: "What I have just outlined is what I call a ‘physicist’s history of physics’, which is never correct… a sort of conventionalized myth-story that the physicist tell to their students, and those students tell to their students, and it is not necessarily related to actual historical development, which I do not really know!". I quote Unguru “to read ancient mathematical texts with modern mathematics in mind is the safest method for misunderstanding the character of ancient mathematics".

From actual history, we know that Kepler did not yet have the full tools of Vieta's (elementary) algebra nor Descartes' analytic geometry, i.e. our conception of a formula was literally a foreign concept to his mind, while it is widely known that Newton directly self-studied Descartes which enabled him to invent calculus, i.e. those prerequisites were central to inventing mathematical physics and it was Newton and only Newton who did so; all other physical theories were subsequently modeled after Newton's paradigmatic way of doing mathematical physics using differential equations.

Addendum: In fact, it is known that Kepler even fudged his statistical analysis of the orbits to end up with his laws. His laws of course are not general enough to be called fundamental laws of physics, while Newton's clearly were; we still to this day say Newton's laws are limiting cases to GR. Still, you have a point that Keplers laws were stated using mathematics, just not in the mathematical physics way we state fundamental laws today. This is mostly because Kepler's laws are just a mathematical encoding of experimental phenomenology, i.e. they are principles, perhaps even fundamental ones. Much of the same can be said for Galileo's work.

 

[fresh_42]

From actual history, we know that Kepler did not yet have the full tools of Vieta's (elementary) algebra nor Descartes' analytic geometry ...

... and Newton didn't have differential geometry. This underlines my point of view as a matter of historical developments and doesn't contradict it. Newton wasn't the one and only, but rather one in a long row before and after him, many of them mathematicians by the way, who contributed to physics. It is as if you say before Euclid there wasn't geometry, or before Zermelo there wasn't sets. It is still a rough oversimplification. To distinguish heritage and history at this point is hair splitting. This might make sense in philosophy as you called Wittgenstein as your witness, but not here. Still, why shouldn't Kepler count? And this is only the easiest example I've found without digging too deep into years of date.

Anyway, this is a discussion which a) belongs in a separate thread and b) in a different sub-forum. I'll therefore end my participation in it now, the more as I have the feeling you try to convince by repetition instead of argumentation.

 

[Auto-Didact]

... and Newton didn't have differential geometry. This underlines my point of view as a matter of historical developments and doesn't contradict it. Newton wasn't the one and only, but rather one in a long row before and after him, many of them mathematicians by the way, who contributed to physics. It is as if you say before Euclid there wasn't geometry, or before Zermelo there wasn't sets. It is still a rough oversimplification. To distinguish heritage and history at this point is hair splitting. This might make sense in philosophy as you called Wittgenstein as your witness, but not here. Still, why shouldn't Kepler count? And this is only the easiest example I've found without digging too deep into years of date.

Anyway, this is a discussion which a) belongs in a separate thread and b) in a different sub-forum. I'll therefore end my participation in it now, the more as I have the feeling you try to convince by repetition instead of argumentation.

I agree, this discussion is somewhat fruitless. Both Kepler and Galileo used mathematics, and in that descriptive sense could be said to be doing 'mathematical physics'. The problem is that mathematical physics has historically always referred to calculus/analysis/differential equation type physics namely classical physics without modern physics i.e. what you and I learned in undergraduate physics along with most physicists post-Newton in history. The curriculum of course over the years has become supplemented with more and more subjects from mathematics, probably most strikingly linear algebra which almost no physicist knew before almost halfway past the 20th century. In any case, we are literally arguing semantics, so I'll stop as well.

 

[atyy]

I agree with all of this except specifically that collapse is de facto not actually an interpretation of QM because orthodox QM has no collapse, orthodox QM being purely the Schrodinger equation and its mathematical properties. As I said above however QM as a whole is a mathematically inconsistent conjoining of the Schrodinger equation and the stochastic selection of the state from the ensemble which occurs empirically.

Collapse is therefore a prediction of a phenomenologic theory which directly competes with QM, but which has yet to be mathematically formulated. This theory should then contain QM as some particular low order limit, analogous to how Newtonian mechanics is a low order limit of SR.

Orthodox QM does have collapse.

 

[Auto-Didact]

Orthodox QM does have collapse.

After having written that I was going to edit and make the post more complete since I actually think so as well, I agree that state vector reduction is directly part of standard QM.

It however isn't part of what many physicists deem to be 'orthodox QM', namely a pure mathematical treatment of the Schrodinger equation.

Collapse theories with dynamics such as GRW or DP OR are theories competing with QM/beyond QM.

 

[atyy]

After having written that I was going to edit and make the post more complete since I actually think so as well, I agree that state vector reduction is directly part of standard QM.

It however isn't part of what many physicists deem to be 'orthodox QM', namely a pure mathematical treatment of the Schrodinger equation.

Collapse theories with dynamics such as GRW or DP OR are theories competing with QM/beyond QM.

And actually that's why I am not sure Ballentine's axiomatization is correct. Ballentine has a huge rant against collapse. I consider Ballentine among the worst books on QM fundamentals, and not even worth discussing. In contrast, Hardy's "5 reasonable axioms" derivation and others following his footsteps like the "informational" derivation by Chiribella and colleagues does also derive collapse.

 

[Auto-Didact]

And actually that's why I am not sure Ballentine's axiomatization is correct. Ballentine has a huge rant against collapse. I consider Ballentine among the worst books on QM fundamentals, and not even worth discussing. In contrast, Hardy's "5 reasonable axioms" derivation and others following his footsteps like the "informational" derivation by Chiribella and colleagues does also derive collapse.

I'd put it much stronger, I'm sure Ballentine's derivation is incorrect, because it isn't a real physical derivation because it makes no direct statement whatsoever about observations or experimental facts in the world.

Ballentine's axioms are both semantically closed mathematical statements/propositions, which implies any deductions made from them can have no empirical content but only mathematical content, meaning whatever can be deduced solely on the basis of them can never legitimately be called a physical theory. To paraphrase Poincaré, those axioms are definitions in disguise.

 

[atyy]

I'd put it much stronger, I'm sure Ballentine's derivation is incorrect, because it isn't a real physical derivation because it makes no direct statement whatsoever about observations or experimental facts in the world.

Ballentine's axioms are both semantically closed mathematical statements/propositions, which implies any deductions made from them can have no empirical content but only mathematical content, meaning whatever can be deduced solely on the basis of them can never legitimately be called a physical theory. To paraphrase Poincaré, those axioms are definitions in disguise.

I understand what you mean, but maybe that is too strong. After all, the standard axioms are also mathematical. The standard axioms of classical mechanics are also mathematical (the are all definitions in disguise).

Aren't all axioms definitions in disguise? I guess this goes into the tricky issue of the relationship between axioms and models (eg. standard and non-standard models of arithemetic). But I guess scientists use second order logic, so the model is unique.

 

[Fra]

Here is where my viewpoint not just diverges away from standard philosophy of science, but also from standard philosophy of mathematics: in my view not only is Pierce's abduction necessary to choose scientific hypotheses, abduction seems more or less at the basis of human reasoning itself. For example, if we observe a dark yellowish transparant liquid in a glass in a kitchen, one is easily tempted to conclude it is apple juice, while it actually may be any of a million other things, i.e. it is possibly any of a multitude of things. Yet our intuition based on our everyday experience will tell us that it probably is apple juice; if we for some reason doubt that, we would check it by smelling or tasting or some other means of checking and then updating our idea what it is accordingly. (NB: contrast probability theory and possibility theory).

I was away yesterday, but in short. I agree with you on abduction. Indeed the human brain seems to be designed so that It encodes not a record to events, but it abduces the "best rule" and store that. This is what our memories are not always accurate, but are tweaked. Best rule, means the rule to best predict the future give the constraints of our limited capacity of storage and processing power. I don't dig up references now but this is supported by some neuroscientis working on understanding human brain.

After all this is perfectly natural and intuitive for anyone that understands evolution. The motivation for the brain to develop this behaviour is simply survival.

As inferences are general abstractions, there are analogies between inferences executed by the human brain, and the physical inferences executed by subatomic sys tems. But with that said, i am usually careful to mix the discussions as anyone who is not on the same page so to speak, are with highest possible certainly going to misunderstand things grossly, and think we are suggesting that the human brain of consciousness have a role to play in fundamental physics and measurement. This is not so.

/Fredrik

 

[Auto-Didact]

I understand what you mean, but maybe that is too strong. After all, the standard axioms are also mathematical. The standard axioms of classical mechanics are also mathematical (the are all definitions in disguise).

Aren't all axioms definitions in disguise? I guess this goes into the tricky issue of the relationship between axioms and models (eg. standard and non-standard models of arithemetic). But I guess scientists use second order logic, so the model is unique.

The difference is that in the case of the axioms for classical mechanics the content of every mathematical statement can be at least in principle connected to an observational statement, either through the principles involved, through the laws derived or through the postulates stated. On the other hand, Ballentine's mathematical statements upon closer inspection have only mathematical content, just look:

Ballentine has two axioms

1. Outcomes of observations are the eigenvalues of some operator.
2. The Born Rule.

As for your other question, probably, but I'm no logician/mathematician, so in my doing of mathematics I tend to avoid anything axiomatic or Bourbaki-esque like the plague. Then again I do like the word bijective :p

 

[atyy]

The difference is that in the case of the axioms for classical mechanics the content of every mathematical statement can be at least in principle connected to an observational statement, either through the principles involved, through the laws derived or through the postulates stated. On the other hand, Ballentine's mathematical statements upon closer inspection have only mathematical content.

As for your question, probably, but I'm no logician/mathematician, so in my doing of mathematics I tend to avoid anything axiomatic or Bourbaki-esque like the plague. Then again I do like the word bijective :p

So you are really talking about the informal motivation for Ballentine's axioms? I think by your ideas, even the orthodox axioms would be "wrong", but it would be better to say they are not well motivated. On the other hand, Hardy's axioms (equivalent to the orthodox axioms) are presumably better motivated.

 

[Fra]

but it's not a good way to learn quantum theory since their writings tend to clutter the physics with superfluous philosophical balast which confuses the subject more than it helps to understand it.

While i absolutely get your point, that to learn quantum theory, what the mature says, how to apply it etc, can probably be easiest done studying the cleaned up writings, where the historical context and the logic used to construct the theory is left out, as it unavoidable contains detoures and wrong turns.

But wether its wise to decouple the state of science from its historical inference is a question of wether you seek knowledge or understanding, just like Feynman said in the video in post#82 or Auto-Didact.

I seek understanding in order to progress knowledge, this is for me the fun part. Applications tend to bore me. I want to do new things. Once i understand them i loose interest. But this is just me.

I have read both kind of books, i also love the rigour of pure mathematics books. It is a different world though, thinking always in terms of what can be deduced from the given axioms, or the more fuzzy problems of understanding our world. And one does not exclude the other. because solving fuzzy problems with deductive tools simply does not work, because you can not even define the problem, and are then led to the fallacious conclusion that they are not worthy thinking about.

/Fredrik