What theories address the fundamental questions about quantum mechanics?

[QuantumClue]

...

You seem to be retorting everyone else but me. Surely it is a requisit to reply to people if they talk to you, especially when you make wild assertions about the other posters work.

I asked you to show an example of a macroscopic body experiencing non-locality and I would take my comment back. If you can't do this, just say.

 

[A. Neumaier]

You seem to be retorting everyone else but me. Surely it is a requisit to reply to people if they talk to you, especially when you make wild assertions about the other posters work.

You are new to the forum and don't know the rules yet. Nobody is obliged to answer.

I asked you to show an example of a macroscopic body experiencing non-locality and I would take my comment back. If you can't do this, just say.

I told you that you post in the wrong forum, and I don't take back my comment.

You neither understand the purpose of this thread nor the meaning of the term ''axiom''.

 

[zenith8]

I only admitted that it is possible to treat entangled qubits with pilot waves.
But the paper you cited didn't verify your axioms. It featured no Lagrangian but a Hamiltonian, and it made use of Hilbert space.

Pretending that pilot waves avoid Hamiltonians and Hilbert space is just that - pretense.
It requires _all_ the standard stuff and in addition things that are superfluous for working with QM.

Poor prospects for a good axiom system.

Look, I admit I'm not fully engaging with your debate (and I apologize for this - I'm actually in the middle of writing a paper on a completely different subject and I'm just responding to your posts briefly everytime the computer goes beep without bothering to think too deeply or to do any research).

I'm not trying to claim that the deBB axioms are superior or inferior to those of orthodox QM for the purposes of practical calculations (though nor do I admit - without further consideration - the truth of any such claim on your part). My sole point is that it is possible to have fundamentally different sets of axioms than the ones proposed by the OP, and still have a theory which agrees with observations. I thought this might be an interesting point to make in the context of the thread.

And as I'm busy at the moment, let's agree to leave it there. Do get on with your other discussions.

 

[QuantumClue]

You are new to the forum and don't know the rules yet. Nobody is obliged to answer.



I told you that you post in the wrong forum, and I don't take back my comment.

You neither understand the purpose of this thread nor the meaning of the term ''axiom''.

Sir, do not patronize me.

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. ''


[Now]

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.

 

[A. Neumaier]

My sole point is that it is possible to have fundamentally different sets of axioms than the ones proposed by the OP, and still have a theory which agrees with observations. I thought this might be an interesting point to make in the context of the thread.

Look, it is not difficult to make extremely different axiom systems for any theory of your choice.

For example, look at the axiom systems for real numbers: They are all equivalent and yet totally different. Real numbers may be defined as
- numbers with infinite binary expansions
- numbers with infinite decimal expansions,
- nested sequences of intervals,
- equivalence classes of Cauchy sequences,
- pairs of sets forming a Dedekind cut,
- elements of a complete linearly ordered field,
and probably in several other interesting ways.

Thus a _different_ axiom system is not interesting in itself. To be interesting it must be _powerful_ - which means: simplify the subsequent theory.

Your axioms don't do that.

 

[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.