What theories address the fundamental questions about quantum mechanics?

[A. Neumaier]

Explain please why this post was intended as a joke. And explain again please why you don't take back your post. If this is about some kind of laughing matter, I wouldn't mind a laugh myself. Please, explain.

Axioms form the foundations of a theory or discipline. They summarize in a compact way the assumptions that need to be made in order to be able to derive everything else from it.

Given that, it should be easy for you to realize that what you proposed could at best be regarded as a joke, if not as a sign of basic incompetence.

With your current state of knowledge (as displayed by the few postings you made so far) you are better advised in this forum to learn from it and to ask questions rather than to propose answers (which are not likely to be well-received).

Remember that the web forgets nothing. People will forever be able to read about your follies, even if you don't recognize them now as such...

To learn more about the meaning of axioms in science, read http://en.wikipedia.org/wiki/Axiom

 

[dextercioby]

An axiom is a postulate. My sentance was a postulate And since this thread is about axioms, I decided to share mine.

which was... ''Non-locality is a quantum phenomena. Non-locality should not have descriptions for macroscopic bodies. For large enough systems, locality is preserved. ''
.

1. How do you define non-locality in a concise and understandable manner ?
2. What does <For large enough systems> mean ?

a) An axiom must not have vague or unprecise statements.
b) How do you relate your statement (assumingly cured from vagueness) to the the other axioms which form the mathematical and experimental nucleus of the theory ?
c) Is it logically independent from the axioms in my post or the ones proposed by A.Neumaier ? If not, then what other axioms would have to join it to become a set equivalent (or probably superior) to the ones already presented ?

 

[QuantumClue]

1. How do define non-locality is a concise and understandable manner ?
2. What does <For large enough systems> mean ?

a) An axiom must not have vague or unprecise statements.
b) How do you relate your statement (assumingly cured from vagueness) to the the other axioms which form the mathematical and experimental nucleus of the theory ?
c) Is it logically independent from the axioms in my post or the ones proposed by prof. Neumaier ?

1) 1. How do define non-locality is a concise and understandable manner ?

I ask how one defines a subject with is mostly mathematical in nature? The only definition one can honestly make about non-locality is the philosophical arguements which naturally occur from it. I will proceed to write some of these down if you wish.

2) 2. What does <For large enough systems> mean ?

This is the same vague interpretation I adopt for the Copenhagenistic interperation for systems which no longer exhibit wave functions which are visible. If an interpretation that is one of the oldest to formulate quantum mechanics cannot explain the cut-off or how to properly define it, I don't know how you can expect me to.

a) An axiom must not have vague or unprecise statements.

Who says? The Copenhagen interpretation makes many axioms which are to current, vague.

b) How do you relate your statement (assumingly cured from vagueness) to the the other axioms which form the mathematical and experimental nucleus of the theory ?

I don't see how a nucleus comes into the question of my axiom

c) Is it logically independent from the axioms in my post or the ones proposed by prof. Neumaier ?

Of course it is based on logical assertions. It is also quite clear it is independant of your discussion before, as I made clear, I saw this thread was on axioms of quantum mechanics, so I decided to post mine.

 

[dextercioby]

So your statement has more of a philosophical value. That settles it, I guess.

 

[QuantumClue]

Axioms form the foundations of a theory or discipline. They summarize in a compact way the assumptions that need to be made in order to be able to derive everything else from it.

Given that, it should be easy for you to realize that what you proposed could at best be regarded as a joke, if not as a sign of basic incompetence.

With your current state of knowledge (as displayed by the few postings you made so far) you are better advised in this forum to learn from it and to ask questions rather than to propose answers (which are not likely to be well-received).

Remember that the web forgets nothing. People will forever be able to read about your follies, even if you don't recognize them now as such...

To learn more about the meaning of axioms in science, read http://en.wikipedia.org/wiki/Axiom

Axioms form the foundations of a theory or discipline. They summarize in a compact way the assumptions that need to be made in order to be able to derive everything else from it.

Thank you for the lesson professor, but I quite understand these things. I made an assertion which was brisk. It should have been your duty to address the right questions to obtain the correct answers, instead of making wild claims on the post or the poster.

Given that, it should be easy for you to realize that what you proposed could at best be regarded as a joke, if not as a sign of basic incompetence.

Actually no. From your rude outburst had me in confusement. Especially your retort, when you could not back your own claim up, or when I asked you to show an example of a macroscopic body exhibiting the nature of non-locality.

With your current state of knowledge (as displayed by the few postings you made so far) you are better advised in this forum to learn from it and to ask questions rather than to propose answers (which are not likely to be well-received).

It is not wise to make assertions on posters you quite clearly recognize as newcomers to the site. My knowledge on physics, professor is hardly something of the know to you.

Remember that the web forgets nothing. People will forever be able to read about your
follies, even if you don't recognize them now as such...

Are you basing my confrontation with you, as perhaps something I should be ashamed about. I am not ashamed of anything I have posted here. I have explained technical posts like differences between Majorana and Weyl fields, and also an explanation on the Transactional interpretation. I am not ashamed one bit.

To learn more about the meaning of axioms in science, read http://en.wikipedia.org/wiki/Axiom[/QUOTE]

Patronizing me again. It is only a sign of your own insecurities, professor.

 

[QuantumClue]

So your statement has more of a philosophical value. That settles it, I guess.

No I explained reasons why my axiom holds. I said it becomes philosophical when you want to discuss something like the definition of something, when it is purely a mathematical conjecture. If you want a definition of non-locality, you look for the philosophical interpretations which have been drawn by different scientists. You will also find each scientists either share the same interpretation, or will prefer another postulation.

My axiom has underlying assertions that it is a quantum phenomenon, which is associated to the similarity of the wave function and quantum tunnelling as being also quantum phenomena. After a certain threshold, the wave function cannot be viewed, and quantum tunnelling after the same threshold cease to be operative for large enough systems. On the same arguement, you do not witness non-locality at macroscopic levels. It is purely a quantum phenomena.

Then I asked the professor to explain why the statement was wrong, or intended to be a joke. Remember?

 

[dextercioby]

OFF-TOPIC NOTE:

I don't want this thread to turn into a/another battlefield with personal remarks. Not to mention rude/offending. This is a moderated forum, after all, so it could only cause harm to the participants. So please, attack the words and not the person.

 

[QuantumClue]

OFF-TOPIC NOTE:

I don't want this thread to turn into a/another battlefield with personal remarks. Not to mention rude/offending. This is a moderated forum, after all, so it could only cause harm to the participants. So please, attack the words and not the person.

That is very noble of you. But a bit late.

I will of course try and remain as civil as possible.

 

[dextercioby]

No I explained reasons why my axiom holds. I said it becomes philosophical when you want to discuss something like the definition of something, when it is purely a mathematical conjecture.

But an axiom of quantum mechanics, seen as a theoretical science, cannot have a philosophical content, but an operational and a mathematical one. Namely it introduces/defines concepts, links these through logical connectors and uses its defining property to made deductions, or theorems.

What mathematical conjecture are you talking about ?

If you want a definition of non-locality, you look for the philosophical interpretations which have been drawn by different scientists. You will also find each scientists either share the same interpretation, or will prefer another postulation.

I don't want to venture into philosophy. I'd rather stick to physics and mathematics. Interpretations of a theory are already in the realms of philosophy. I don't venture there, I'm just asking you to state an axiom which meets the standard requirements of mathematics.

My axiom has underlying assertions that it is a quantum phenomenon, which is associated to the similarity of the wave function and quantum tunnelling as being also quantum phenomena. After a certain threshold, the wave function cannot be viewed, and quantum tunnelling after the same threshold cease to be operative for large enough systems. On the same arguement, you do not witness non-locality at macroscopic levels. It is purely a quantum phenomena.

This part is completely as in 110% wrong.

Then I asked the professor to explain why the statement was wrong, or intended to be a joke. Remember?

He was harsh and offensive on you, but at least I give him credit on one part: please, be humble and come here to learn, so seek answers rather than offer solutions when you don't posess the necessary knowledge of the topics being discussed.

 

[QuantumClue]

But an axiom of quantum mechanics, seen as a theoretical science, cannot have a philosophical content, but an operational and a mathematical one. Namely it introduces/defines concepts, links these through logical connectors and uses its defining property to made deductions, or theorems.

What mathematical conjecture are you talking about ?



I don't want to venture into philosophy. I'd rather stick to physics and mathematics. Interpretations of a theory are already in the realms of philosophy. I don't venture there, I'm just asking you to state an axiom which meets the standard requirements of mathematics.



This part is completely as in 110% wrong.



He was harsh and offensive on you, but at least I give him credit on one part: please, be humble and come here to learn, so seek answers rather than offer solutions when you don't posess the necessary knowledge of the topics being discussed.

1) But an axiom of quantum mechanics, seen as a theoretical science, cannot have a philosophical content, but an operational and a mathematical one. Namely it introduces/defines concepts, links these through logical connectors and uses its defining property to made deductions, or theorems.

Philosophy is used when making interpretations of science. You seem to be denying we don't draw speculations on the meaning of mathematics.

2)What mathematical conjecture are you talking about ?

Bells Inequalities. This where the idea of non-locality is drawn from.

3)I don't want to venture into philosophy. I'd rather stick to physics and mathematics. Interpretations of a theory are already in the realms of philosophy. I don't venture there, I'm just asking you to state an axiom which meets the standard requirements of mathematics.

So would I. I am a undergraduate of physics, so I am very interesting in drawing the mathmatical side of things.

4)This part is completely as in 110% wrong.

It ironic, saying something is 110% wrong, when it is even wrong to speculate 110% even exists.

Would you please elaborate on how my contentions above are incorrect?

5)He was harsh and offensive on you, but at least I give him credit on one part: please, be humble and come here to learn, so seek answers rather than offer solutions when you don't posess the necessary knowledge of the topics being discussed

Oh please.

How have I displayed I am not humble? His ignorant outburst was uncalled for. This was even picked up on by a separate member. It's an often attitude to pass the buck, which is quite evidently what you are doing now. It is also a typical troll behaviour.

 

[Careful]

after all, so it could only cause harm to the participants. So please, attack the words and not the person.

Words are merely the mask of the person. In some cases, it is more important to read what is not responded to than to notice a few idle sentences meant to divert the attention from the unspoken word. To avoid this and out of sincere respect for the full range of thougts of the person, I respond to everything within a single message.

 

[dextercioby]

Philosophy is used when making interpretations of science. You seem to be denying we don't draw speculations on the meaning of mathematics.

But before going into philosophy, science needs to be formulated. I think that an axiomatization must be as much as possible subjective-free.

Bells Inequalities. This where the idea of non-locality is drawn from.

So non-locality is mere consequence of Bell's inequalities. But Bell's inequalities can be derived from the standard postulates (1st post in this thread). So, logically, non-locality of quantum phenomena results from axioms already stated. So why would it postulated, if it can be proved ??

So would I. I am a undergraduate of physics, so I am very interesting in drawing the mathmatical side of things.

You don't really show it, probably because you haven't been <exposed> to serious mathematics yet. To meet your desire, let's hope you will.

It ironic, saying something is 110% wrong, when it is even wrong to speculate 110% even exists.

Of course the wrong percentage was meant to be ironic.

Would you please elaborate on how my contentions above are incorrect?

I retract my statement, yours it 100% correct.

 

[QuantumClue]

I retract my statement, yours it 100% correct.

Well if the professor will not explain his arguement, perhaps you will? Put your money where your mouth is, explain how my paragraph was incorrect. Saying it ''just is'' is about as helpful as an ashtray on a motorcycle.

 

[dextercioby]

Well if the professor will not explain his arguement, perhaps you will? Put your money where your mouth is, explain how my paragraph was incorrect. Saying it ''just is'' is about as helpful as an ashtray on a motorcycle.

It's ok, it's nothing to debate/refute about your paragraph, except probably that wavefunctions can never be viewed, felt, nor measured. They are only mathematical objects, just like the sign + in this phrase is. As for quantum tunelling, it's deduction of a set of axioms whose applicability to macroscopic objects is incredibly well approximated by the number 0. As for the so-called non-locality, if proven experimentally, it's probably a consequence of a set of axioms whose applicability to macroscopic objects is unbelievebly well approximated by the number 0.

 

[QuantumClue]

It's ok, it's nothing to debate/refute about your paragraph, except probably that wavefunctions can never be view, felt, nor measured. They are only mathematical objects, just like the sign + is.

Then what was your retort about, saying it was 100% wrong? It seems like you are now contradicting your first statement.

And by the way, we can view the wave function, or effects thereof: http://www.dailymail.co.uk/sciencet...-mechanics-shown-work-visible-world-time.html

 

[dextercioby]

And by the way, we can view the wave function, or effects thereof: http://www.dailymail.co.uk/sciencet...-mechanics-shown-work-visible-world-time.html

Experimentalists observe phenomena, they measure physical quantities. We can never view, nor measure wave functions/density operators as they are simply mathematical tools to describe reality. I think of a quantum states as being a part of reality.

We will always measure (or determine from numerical analysis of experimental tests of quantum mechanics) probabilities or spectral values of self-adjoint operators, because, as it follows from the axiomatization I proposed in post 1 of the thread, they are the only items assuring the connection between mathematics (functional analysis) and experiment.

 

[QuantumClue]

Experimentalists observe phenomena, they measure physical quantities. We can never view, nor measure wave functions/density operators as they are simply mathematical tools to describe reality. I think of a quantum states as being a part of reality.

We will always measure (or determine from numerical analysis of experimental tests of quantum mechanics) probabilities or spectral values of self-adjoint operators, because, as it follows from the axiomatization I proposed in post 1 of the thread, they are the only items assuring the connection between mathematics (functional analysis) and experiment.

There are scientists who take the superpositioning principle of wave mechanics as a physical phenomenon quite seriously, and not merely a mathematical artefact as you are applying it soley to. And this is what they observe in the link I showed you. Then it is evident we can view a wave function [of] matter.

 

[dextercioby]

Here is an axiom system fully covering current mainstream quantum mechanics and quantum field theory (but not various speculations beyond the standard model). It covers both the nonrelativistic case and the relativistic case.

There are six basic axioms:

A1. A generic system (e.g., a 'hydrogen molecule')
is defined by specifying a Hilbert space K whose elements
are called state vectors and a (densely defined, self-adjoint)
Hermitian linear operator H called the _Hamiltonian_ or the _energy_.

A2. A particular system (e.g., 'the ion in the ion trap on this
particular desk') is characterized by its _state_ rho(t)
at every time t in R (the set of real numbers). Here rho(t) is a
Hermitian, positive semidefinite (trace class) linear operator on K
satisfying at all times the conditions
trace rho(t) = 1. (normalization)
[/url]

1. Is it apparent to me, or you introduce two different description of states, one through <state vectors> and the other through <states $\rho (t)$> ? Are they both necessary, thus independent of each other ?
2. How are these two these axioms used to describe the physical states of a helium atom ?
3. How does A2 apply to the simplest possible system, the nonrelativistic free massive particle ?

 

[DarMM]

This is exactly what I was thinking. Separable spaces are easier to work with. That's why we try using a separable space first.

You might find this interesting, but there is a somewhat justifiable reason not to use them. For a non-separable Hilbert space the fact that a Lie group has a representation on the Hilbert space doesn't imply that the Lie Algebra has a representation. So even though rotations might be represented by a group of unitary operators, angular momentum wouldn't be a well defined operator.

 

[dextercioby]

You might find this interesting, but there is a somewhat justifiable reason not to use them. For a non-separable Hilbert space the fact that a Lie group has a representation on the Hilbert space doesn't imply that the Lie Algebra has a representation. So even though rotations might be represented by a group of unitary operators, angular momentum wouldn't be a well defined operator.

Can you post or send a reference to a mathematical proof for that ? Thanks!

 

[A. Neumaier]

1. Is it apparent to me, or you introduce two different description of states, one through <state vectors> and the other through <states $\rho (t)$> ? Are they both necessary, thus independent of each other ?
2. How are these two these axioms used to describe the physical states of a helium atom ?
3. How does A2 apply to the simplest possible system, the nonrelativistic free massive particle ?

1. The state vectors are called so conventionally, without having to be states - they are just calculational tools. The physicall state is rho(t) and carries the information about experimental behavior. To remove the confusion, just replace Axiom A1 by the following improved version.

A1. A generic system (e.g., a 'hydrogen molecule') is defined by
specifying a Hilbert space K and a (densely defined, self-adjoint)
Hermitian linear operator H called the _Hamiltonian_ or the _energy_.

2. Here you need also Axiom A4. with three particles (alpha, e, e'). But e and e' are indistinguishable, so only symmetric functions of the labels e and e' are observable. H is given by the standard atomic Hamiltonian one can find in any textbook.

3. H= p^2/2m.

 

[DarMM]

Can you post or send a reference to a mathematical proof for that ? Thanks!

In the theory of representations of Lie groups on Hilbert spaces, the separability property allows you prove the existence of a representation of the Lie algebra. However without separability you cannot complete the proof, so there is no guarantee that the Lie algebra has a representation. There are several example theories where this is the case.

(In fact it was an issue in Loop Quantum Gravity at one point I believe, but I don't know much about that subject.)

There isn't really a proof, since it is a description of what occurs in a case where another proof (representations on separable Hilbert spaces) fails.

 

[A. Neumaier]

In the theory of representations of Lie groups on Hilbert spaces, the separability property allows you prove the existence of a representation of the Lie algebra. However without separability you cannot complete the proof, so there is no guarantee that the Lie algebra has a representation.

a) Is there a simple explicit example of this situation?

b) What about the converse: Does a unitary representation of a Lie algebra by self-adjoint operators always generate unitary representation of a Lie group?

 

[dextercioby]

[...]just replace Axiom A1 by the following improved version.

A1. A generic system (e.g., a 'hydrogen molecule') is defined by
specifying a Hilbert space K and a (densely defined, self-adjoint)
Hermitian linear operator H called the _Hamiltonian_ or the _energy_.

Alright, agreed.

2. Here you need also Axiom A4. with three particles (alpha, e, e'). But e and e' are indistinguishable, so only symmetric functions of the labels e and e' are observable. H is given by the standard atomic Hamiltonian one can find in any textbook.

I'm not satisfied with this answer. The question was about the description of states, not of observables. The states in your formulation are described by the density operator rho(t). So my question remains: how do you describe the the states of that system using this operator ?

3. H= p^2/2m.

Hmmm...No answer provided to my 3rd question.

 

[dextercioby]

In the theory of representations of Lie groups on Hilbert spaces, the separability property allows you prove the existence of a representation of the Lie algebra. However without separability you cannot complete the proof, so there is no guarantee that the Lie algebra has a representation. There are several example theories where this is the case. [...] There isn't really a proof, since it is a description of what occurs in a case where another proof (representations on separable Hilbert spaces) fails.

So you can't back up your statement with a proof. With all due respect, I'll just then disregard it.

 

[DarMM]

So you can't back up your statement with a proof. With all due respect, I'll just then disregard it.

Perhaps I didn't explain myself well. It isn't the type of statement which has a proof. For example take the theorem that every operator is bounded on a finite dimensional Hilbert space. The analogue of my statement is that not every operator is bounded in an infinite dimensional Hilbert space. You don't prove this, you just give examples, since it is just description of what happens when another theorem doesn't hold.

For an example see Appendix C of:
Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, José Mourão, and Thomas Thiemann;Quantization of Diffeomorphism Invariant Theories of Connection with Local Degrees of Freedom, J. Math. Phys. 36, 6456

 

[A. Neumaier]

I'm not satisfied with this answer. The question was about the description of states, not of observables. The states in your formulation are described by the density operator rho(t). So my question remains: how do you describe the states of that system using this operator ?

This is specified in Axioms A2 and A3. There are lots of Hermitian, positive semidefinite, linear trace class operators rho_0 on the 3-particle Hilbert space K of the helium atom satisfying trace rho_0=1. Solving the initial value problem for d/dt rho(t) = i/hbar [rho(t),H] with rho(0)=rho_0 produces as many states satisfying at all times the conditions trace rho(t) = 1.

Note that the state at time t _is_ the operator rho(t), by definition.

Hmmm...No answer provided to my 3rd question.

The same holds for your third question.

 

[A. Neumaier]

Perhaps I didn't explain myself well. It isn't the type of statement which has a proof.

Actually, any counterexample _is_ a proof. All that was missing was the reference.

 

[DarMM]

Actually, any counterexample _is_ a proof. All that was missing was the reference.

Oh yeah!

 

[Fredrik]

Please, do comment, if possible, both on my set and on Arnold's one.

I was planning to do this today, but this morning I decided that I wanted to write down my own set of axioms before I comment on someone else's. I started by writing down a few general thoughts about axioms (instead of the actual axioms), and it turned into a detailed examination of the concepts of "state", "observable", and "measurement" that I'm still not done with. So even though I spent a few hours on this today, I still haven't written down a single axiom, or read any of yours or A.N.'s.

The only thing that's perfectly clear to me right now is that what's been bothering me about the axioms of QM can't be fixed by choosing a different set of axioms. All the significant problems I have are with the concepts of "state", "observable" and "measurement", and those parts of the identification of mathematical and real-world concepts that aren't even mentioned in the axioms.

I will continue to think about this tomorrow, and I intend to post my thoughts here when they're coherent enough to sound like an actual argument. I hope that will be tomorrow, but I can't promise anything.

 

[bg032]

In addition to these formal axioms one needs a rudimentary
interpretation relating the formal part to experiments.
The following _minimal_interpretation_ seems to be universally
accepted.

MI. Upon measuring at times t_l (l=1,...,n) a vector X of observables
with commuting components, for a large collection of independent
identical
(particular) systems closed for times t<t_l, all in the same state
rho_0 = lim_{t to t_l from below} rho(t)
(one calls such systems _identically_prepared_), the measurement
results are statistically consistent with independent realizations
of a random vector X with measure as defined in axiom A5.


Note that MI is no longer a formal statement since it neither defines
what 'measuring' is, nor what 'measurement results' are and what
'statistically consistent' or 'independent identical system' means.
Thus Axiom MI has no mathematical meaning. That's why it is already
part of the interpretation of formal quantum mechanics.

However, the terms 'measuring', 'measurement results', 'statistically
consistent', and 'independent' already have informal meaning in the
reality as perceived by a physicist. Everything stated in Axiom MI is
understandable by every trained physicist. Thus statement MI is not
for formal logical reasoning but for informal reasoning in the
traditional cultural setting that defines what a trained physicist
understands by reality.

It seems to me that the MI collocates your system of axioms in the context of the Copehagen interpretation, where a macroscopic classical realm, including notions such as measuring apparatuses, is assumed to exist independently of the the quantum realm. For me this is unsatisfactory, because it implies that two different and independent theories, namely classical and quantum mechanics, are necessary in order to explain our empirical perceptions. I would like a formulation of QM (which is arguably more fundamental then CM) in which mathematical elements clearly corresponding to our empirical experience of a classical evolution (e.g., trajectories) were present.

 

[Fredrik]

It seems to me that the MI collocates your system of axioms in the context of the Copehagen interpretation, where a macroscopic classical realm, including notions such as measuring apparatuses, is assumed to exist independently of the the quantum realm. For me this is unsatisfactory, because it implies that two different and independent theories, namely classical and quantum mechanics, are necessary in order to explain our empirical perceptions. I would like a formulation of QM (which is arguably more fundamental then CM) in which mathematical elements clearly corresponding to our empirical experience of a classical evolution (e.g., trajectories) were present.

People always read too much into the fact that the state of a measuring device at the end of a measurement can for all practical purposes be described classically. It doesn't mean that measuring devices follow a different set of rules than microscopic systems. It just acknowledges that we wouldn't consider a device that's in a superposition of quantum states to have measured something.

 

[A. Neumaier]

The only thing that's perfectly clear to me right now is that what's been bothering me about the axioms of QM can't be fixed by choosing a different set of axioms. All the significant problems I have are with the concepts of "state", "observable" and "measurement", and those parts of the identification of mathematical and real-world concepts that aren't even mentioned in the axioms.

All this cannot be part of the axioms at all. To understand what axioms are, consider the axioms for projective planes:

The points form a set P.
The lines form a set L.
There is an incidence relation I subset P x L.
Say x in l. or l contains x if (x,l) in I.
Any two distinct points are in a unique line.
Any two distinct lines contain a unique point.

That's all. The axioms say everything needed to work with projective planes.

Although no explanation is given of the meaning of the concepts of ''point'', ''line'', ''incidence''. This is not part of the _axioms_ but part of their _interpretation_ in real life. And indeed, here all the philosophical problems appear...

The purpose of an axiom system is precisely to separate the stuff that is problematic but peripheral from the stuff that is essential and allows rational deductions.

My axioms in the section ''Postulates for the formal core of quantum mechanics'' of Chapter A1 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#postulates give such a clear separation (and also explain some things about their interpretation).

 

[A. Neumaier]

It seems to me that the MI collocates your system of axioms in the context of the Copehagen interpretation, where a macroscopic classical realm, including notions such as measuring apparatuses, is assumed to exist independently of the the quantum realm.

Far from that.

MI is what _every_ interpretation I know of assumes (and has to assume) at least implicitly in order to make contact with experiments. It relates the axioms not to a hypothetical classical realm but to a nonphysical entity: the social conventions of the community of physicists.

Indeed, all interpretations I know of assume much more, but they differ a lot in what they assume beyond MI.

 

[Fra]

Although no explanation is given of the meaning of the concepts of ''point'', ''line'', ''incidence''. This is not part of the _axioms_ but part of their _interpretation_ in real life. And indeed, here all the philosophical problems appear...

In this decomposition, also the PHYSICAL problems appear there. After as long as it's purely axiomatic, it's pure mathematics, not only do you shave off the philosophy, but also the physical content.

The purpose of an axiom system is precisely to separate the stuff that is problematic but peripheral from the stuff that is essential and allows rational deductions.

AFAIK most real life problems and physics, are not something where deductive reasoning is used. Deductive reasoning is within pure mathematics.

I would like to claim that actually most relevant (non-idealized) problems in the real world required reasoning and decision making based upon incompelte information. Ie. it's some form of inference, but not deductive logic. Most some evolving inductive evolving logic.

Deductive logic is extremely efficient and precise, and useful, but it's also somewhat "sterile" and inflexible, lacking traits that are needed in most real situations.

/Fredrik