Conservation Of Inherent Ignorance!

[Qfwfq]

Perhaps Anssi you shouldn't worry too much about the formal meaning of number of dimensions, it's really just a matter of how vector spaces are abstractly defined on top of the definition of field. Indeed, in the next thing you ask about:

So, I suppose,

 

[math]\frac{d}{da}\Psi=ik \Psi[/math]

 

is stating that the output of [imath]\Psi[/imath] can change along with the shift parameter [imath]a[/imath], in the manner that that rate of change can be expressed as a product between an imaginary number [imath]ik[/imath] and the original output?

 

So, it's an imaginary number because it would be invalid to see that derivative as a product between a real number and [imath]\Psi[/imath]...?

It is much more helpful to think of the complex numbers as a 2D space, so real and imaginary values are at right angles to each other. If you recall that the tangent at a point of a circumference is at right angles to the radius in the same point, you should be able to interpret that differential equation like the rate at which a point is going around in a circular motion.

 

Hmm, there's something here that I still don't quite understand...

Sorry, I made a hash, thinking of concepts out of step with the equations under discussion and not spelling it out. It seems you have understood if you disregard the confusion I led you into:

 

The summation is indeed necessary, but in order to understand the factor becoming unity (which I held to be your difficulty) it is enough to think the change in [imath]a[/imath] or each [imath]z_i[/imath] is the same and consider first as if there is only one [imath]z[/imath], then the full case with several [imath]z_i[/imath].

 

Right okay, but my interpretation of how the "ik" ends up not having any effect on "P" via [imath]P=\vec{\Psi}^\dagger\cdot \vec{\Psi}[/imath], does that look correct to you?

Well, I'm not sure what you want to actually state here, but [imath]P=\vec{\Psi}^\dagger\cdot \vec{\Psi}[/imath] means that [imath]P[/imath] depends only on the modulus (since it is equal to the modulus squared). This is equivalent to saying that only its phase depends on those variables.

 

The phase just relates to a point on the circumference. Dick's use of a value [imath]k[/imath] amounts to assuming the phase being linear in the parameter. Mathematically, the arbitrarity of assigning values to these variables can make this seem not to lose generality, but at the current clarity of the presentation I still hold doubts about how far this could carry into quantum physics without a need for a further postulate based on experience.

[AnssiH]

Perhaps Anssi you shouldn't worry too much about the formal meaning of number of dimensions,

 

My thoughts exactly. :)

 

it's really just a matter of how vector spaces are abstractly defined on top of the definition of field. Indeed, in the next thing you ask about: It is much more helpful to think of the complex numbers as a 2D space, so real and imaginary values are at right angles to each other. If you recall that the tangent at a point of a circumference is at right angles to the radius in the same point, you should be able to interpret that differential equation like the rate at which a point is going around in a circular motion.

 

Ah, right, DD explained this concept to me earlier and it's coming back to me now. I took a look at the multiplications of complex numbers at http://www.clarku.edu/~djoyce/complex/mult.html and yeah, multiplying a complex number by an imaginary number yields a rotation, which does not change the modulus, so it preserves shift symmetry in P.

 

Where-as multiplying by a real number would yield changes to the modulus, i.e. would not preserve shift symmetry to the P.

 

I think I got it straight now.

 

Sorry, I made a hash, thinking of concepts out of step with the equations under discussion and not spelling it out. It seems you have understood if you disregard the confusion I led you into:

 

The summation is indeed necessary, but in order to understand the factor becoming unity (which I held to be your difficulty) it is enough to think the change in [imath]a[/imath] or each [imath]z_i[/imath] is the same and consider first as if there is only one [imath]z[/imath], then the full case with several [imath]z_i[/imath].

 

Okay, so then I guess I had struck on the correct interpretation initially, that the summation is necessary. Then, the intermediate derivatives are necessary for the chain rule of the partial derivatives to hold. I won't dwell on the details more now, I can believe the validity of that chain rule on the basis that it's a well known rule, and now I feel like I have a pretty good idea of the mechanism behind the rule.

 

Well, I'm not sure what you want to actually state here, but [imath]P=\vec{\Psi}^\dagger\cdot \vec{\Psi}[/imath] means that [imath]P[/imath] depends only on the modulus (since it is equal to the modulus squared).

 

Yes, I feel like I understand it now.

 

Thank you for your help!

 

This is equivalent to saying that only its phase depends on those variables.

 

The phase just relates to a point on the circumference. Dick's use of a value [imath]k[/imath] amounts to assuming the phase being linear in the parameter. Mathematically, the arbitrarity of assigning values to these variables can make this seem not to lose generality, but at the current clarity of the presentation I still hold doubts about how far this could carry into quantum physics without a need for a further postulate based on experience.

 

That's the question isn't it.

 

What I'm doing right now is that I'm trying to undersand better those details, which I took on faith the first time around. But having walked through it once, I must say it is quite plausible how it all falls together, all things considered.

 

Just to cherry pick few things to keep in mind;

 

All the defined entities that exist in our explanation of reality, can be seen as a method of representing some recurring aspects of some "noumena". (They must be in some shape or form based on some recurring aspects of something)

 

We don't know how "some recurring aspects of some noumena" are translated into "the defined entities" that exist in our explanation of that noumena. Including the defined entities that exhibit quantum behaviour.

 

This analysis is (among other things) a mathematical examination to the relationship between "universal aspects of explanations", and "the definitions behind quantum mechanically behaving entities". (including space and time definitions)

 

Examining that path in detail, it should become clear that it amounts to a very strong implication towards saying, that there's absolutely no real reason to think of our defined entities as quite "realistic" (i.e. as "persistent entities in-themselves"), while there is all the reason in the world to think of them as extremely accurate representation of "some recurring aspects of some noumena".

 

I am quite aware of the paradoxical spatial/temporal nature of quantum entities (and I'm aware there are many ways to see that issue ontologically, none quite satisfying), and that's exactly the thing. If you manage to see just why these entities should be viewed more appropriately as simply a representation of "some recurring aspects of something", it should also make it clear exactly why you could take the most obscure "delayed choice quantum eraser entanglement experiment" you can think of, and yet those defined entities must do exactly what quantum definitions say they would do in all those different circumstances.

 

I could say that the key is in realizing, that the translation between "some recurring aspects of some noumena" and "the defined entities (of a Bell experiment)" is probably not very straightforward, and the effect that an observation has to our expectations is partially hidden inside that translation. That is why there is no reason to think of that observation as having any effect on the actual underlying circumstance itself. It's just that our representation of that circumstance is such, that upon receiving more information, that representation of the circumstance MUST change in seemingly non-realistic ways (in spatial and/or temporal manner, depending on the particular flavour of your chosen representation form).

 

Conversely, if you think that those entities that we represent reality with, actually do have a real persistent identity to them over and beyond us having defined noumena that way (i.e. that they translate to actual reality in quite straight-forward fashion, spatially and temporally etc), then certainly they seem to behave in mysterious ways...

 

Actually, it wouldn't be wrong at all to say that Bell experiments are a strong experimental indication towards the validity of this analysis.

 

Just food for thought.

 

-Anssi

[Qfwfq]

...multiplying a complex number by an imaginary number yields a rotation, which does not change the modulus, so it preserves shift symmetry in P.

 

Where-as multiplying by a real number would yield changes to the modulus, i.e. would not preserve shift symmetry to the P.

 

I think I got it straight now.

Well, not quite. You can have a factor wich is real valued and doesn't change the modulus; there are exactly two of them which are plus and minus one. You can also have an imaginary factor which does change the modulus: any excepting plus and minus the imaginary unit. You can have a factor which is neither real nor imaginary, a complex factor in general changes the modulus if its own is other than one; it changes the phase if it isn't pure real. If it is pure imaginary, it changes the phase by exactly a quarter turn.

 

Think about the term [imath]Ae^{i\varphi}[/imath] and see it as a point on the circumference of radius [imath]A[/imath]. As [imath]\varphi[/imath] varies, the point is just going around. The exponential factor changes the phase of [imath]A[/imath] and not its modulus; among possible values of [imath]e^{i\varphi}[/imath] are those two real and two imaginary ones (these are [imath]e^0=1[/imath], [imath]e^{i\pi}=-1[/imath], [imath]e^{i\frac{\pi}{2}}=i[/imath] and [imath]e^{-i\frac{\pi}{2}}=-i[/imath]).

 

Where you get confused is probably in relating the above to real and complex values of the exponent and also to what I posted about the derivative and the tangent. It is the pure imaginary value of the exponent that conserves the modulus, whereas a real component gives a modulus other than one. In general [math]e^{a+ib}=e^ae^{ib}[/math] and you can compare this to the above expression.

 

If the exponent is dependent on a real parameter and you follow through with the rules of derivation, can you see what I meant about the differential equation? You likely find it confusing because it takes a lot of getting used to, if you've never been through a calculus course and done adequate exercises.

 

Examining that path in detail, it should become clear that it amounts to a very strong implication towards saying, that there's absolutely no real reason to think of our defined entities as quite "realistic" (i.e. as "persistent entities in-themselves"), while there is all the reason in the world to think of them as extremely accurate representation of "some recurring aspects of some noumena".

I'm under the impression that you consider these matters as if all physicists embraced a Bohmian vision of quantum physics (which clings to the idea of a corpuscle and it having a trajectory) and you consequently think of this as being the only reason people are troubled by certain things. This is very far from how it is, I can never get it across to you. In fact, ever since the Copenhagen School and the great disputes between Einstein and others, the brunt of quantum physicists have discarded all hidden variables ideas, of which Bohm's interpretation is an example. I don't know what to say, what effort to make in reaching you, without ending up only in further misunderstanding; the most frustrating parts are where you try to make me understand your views but you are only raining on wet ground.

 

That is why there is no reason to think of that observation as having any effect on the actual underlying circumstance itself.

I actually don't think of it that way, and the conscious observer idea is obsolete. What does play a role is the interaction that makes "observation" at all possible and that's where things get complicated. The trouble is, though, the very meaning of the word observation and, in the end, we could even say it isn't such a different thing from the above mentioned interaction, only that there is a mighty chain of them before an ape has had what we call a perception of something. This chain toward the macroscopic is where decoherence plays the important role.

 

It's just that our representation of that circumstance is such, that upon receiving more information, that representation of the circumstance MUST change in seemingly non-realistic ways (in spatial and/or temporal manner, depending on the particular flavour of your chosen representation form).

This amounts to claiming that von Neumann projection is a matter of our "chosen representation" of reality. I really don't see any chance of how Dick's presentation can show this.

 

Actually, it wouldn't be wrong at all to say that Bell experiments are a strong experimental indication towards the validity of this analysis.

Here I totally disagree. They definitely do make hidden variables and Bohmian views unpalatable. They support quantum formalism even under aspects where its non-local nature is most striking. I don't see any manner in which they support Dick's presentation (nor does it add any cherry to the top of the cake) and it is mistaken to think that discarding the "persistent entities" can be sufficient for clarifying and solving everything. Edited January 17, 2011 by Qfwfq
mistake corrected

[AnssiH]

Well, not quite. You can have a factor wich is real valued and doesn't change the modulus; there are exactly two of them which are plus and minus one. You can also have an imaginary factor which does change the modulus: any excepting plus and minus the imaginary unit. You can have a factor which is neither real nor imaginary, a complex factor in general changes the modulus if its own is other than one; it changes the phase if it isn't pure real. If it is pure imaginary, it changes the phase by exactly a quarter turn.

 

Think about the term [imath]Ae^{i\varphi}[/imath] and see it as a point on the circumference of radius [imath]A[/imath]. As [imath]A\varphi[/imath] varies, the point is just going around. The exponential factor changes the phase of [imath]A[/imath] and not its modulus; among possible values of [imath]e^{i\varphi}[/imath] are those two real and two imaginary ones (these are [imath]e^0=1[/imath], [imath]e^{i\pi}=-1[/imath], [imath]e^{i\frac{\pi}{2}}=i[/imath] and [imath]e^{-i\frac{\pi}{2}}=-i[/imath]).

 

Yup. I believe I understand what you are saying.

 

I should have phrased it, "multiplying by a real number could yield changes to the modulus" (which wouldn't preserve shift symmetry in P). And that's why the derivative is [math]\frac{d}{da}\Psi=ik \Psi[/math].

 

Where you get confused is probably in relating the above to real and complex values of the exponent and also to what I posted about the derivative and the tangent. It is the pure imaginary value of the exponent that conserves the modulus, whereas a real component gives a modulus other than one. In general [math]e^{a+ib}=e^ae^{ib}[/math] and you can compare this to the above expression.

 

If the exponent is dependent on a real parameter and you follow through with the rules of derivation, can you see what I meant about the differential equation?

 

Yup, I think so. Because [math]\frac{d}{da}\Psi=ik \Psi[/math] states that the shift parameter is allowed to yield a rotation to the probability vector in the complex plane. The actual value of ik would essentially state the rate of change, i.e. rate of rotation, with respect to [imath]a[/imath]

 

You likely find it confusing because it takes a lot of getting used to, if you've never been through a calculus course and done adequate exercises.

 

Most definitely. And after I've walked through some issue once, I forget it quickly. This is the second time I'm looking at this particular issue of interpreting multiplications of complex numbers like rotation in a complex plane, so it was quite a bit faster this time to bring it all back.

 

I'm under the impression that you consider these matters as if all physicists embraced a Bohmian vision of quantum physics (which clings to the idea of a corpuscle and it having a trajectory) and you consequently think of this as being the only reason people are troubled by certain things.

 

Hmmm, I don't understand why you have that impression. Like I said, I'm aware there are many ways to see these issues. About physicists, I'm sure many like to avoid making ontological arguments anyway. I'm sure they'd also appreciate understanding why quantum mechanics are valid in epistemological sense.

 

I actually don't think of it that way, and the conscious observer idea is obsolete. What does play a role is the interaction that makes "observation" at all possible and that's where things get complicated. The trouble is, though, the very meaning of the word observation and, in the end, we could even say it isn't such a different thing from the above mentioned interaction, only that there is a mighty chain of them before an ape has had what we call a perception of something.

 

Yes. In terms of DD's epistemological analysis, observation is of course treated simply as an event of gaining new information about some situation (or perhaps more accurately, having interpreting something in terms of your world view). Of course there are quite readily apparent obstacles when following down that road, and we could discuss those obstacles.

 

Different people like to think of those obstacles in slightly different ways, so tell me, how would you express in your own words, the problem with treating observation as nothing more but an event of gaining more information about some circumstance.

 

This amounts to claiming that von Neumann projection is a matter of our "chosen representation" of reality. I really don't see any chance of how Dick's presentation can show this.

 

I don't know what's a von Neumann projection so I'm not sure what you are referring to.

 

Here I totally disagree. They definitely do make hidden variables and Bohmian views unpalatable. They support quantum formalism even under aspects where its non-local nature is most striking.

 

I thought that's what I said. Even the most obscure experiments must produce results according to quantum formalism. DD's analysis just explains why our representation of reality acts that way. It doesn't explain what reality is like of course.

 

Also I don't see this as a hidden variable explanation, at least not in the sense I usually understand them. At any rate, we could discuss the issues that actually appear to prevent treating observation as simply "new information". That is in many senses the heart of the whole mystery anyway.

 

-Anssi

[Qfwfq]

I don't know what's a von Neumann projection so I'm not sure what you are referring to.

I think I've mentioned it before but I'll repeat, maybe even a bit more in detail.

 

The so-called von Neuman projection is just the ideal case of the so-called collapse. it is the ideal case because one supposes that (at least immediately after the measurement) the system is in an eigenstate of that observable, with that eigenvalue and that, for the rest, the state is changed as little as possible. These assumptions certainly do not hold for all ways of making a measurement. It is, however, the same idea that you talk about: gaining more information about the circumstance. Note though that other information might be lost and there are cases in which this happens of necessity; denying this would be in contradiction of Heisenberg's principle.

 

I thought that's what I said. Even the most obscure experiments must produce results according to quantum formalism. DD's analysis just explains why our representation of reality acts that way. It doesn't explain what reality is like of course.

 

Also I don't see this as a hidden variable explanation, at least not in the sense I usually understand them. At any rate, we could discuss the issues that actually appear to prevent treating observation as simply "new information". That is in many senses the heart of the whole mystery anyway.

This is the kind of thing that shows you really don't follow what I say. The Book of Psalms does not preach Atheism, you need to understand the whole thing. First I said what those results do imply, then I said what they don't imply, and I had not taken Dick's presentation to be a hidden variables interpretation. Edited January 18, 2011 by Qfwfq
dumb typo

[AnssiH]

This a the kind of thing that shows you really don't follow what I say. The Book of Psalms does not preach Atheism, you need to understand the whole thing. First I said what those results do imply, then I said what they don't imply, and I had not taken Dick's presentation to be a hidden variables interpretation.

 

Okay, then I have no idea why you brought it up.

 

What I said was just a reaction to your comment, that imply you can't see how the quantum dilemma could possibly be resolved by any universal considerations.

 

Well, you probably agree that if you think of each observed state of the system like a "snapshot" of its underlying information (instead of thinking of them in the common terminology of fundamental particles), there's nothing mysterious in becoming able to connect different "snapshots" together with some set of rules (i.e. being able to draw predictions). All you need is a function that properly expresses those rules.

 

I.e. you probably agree that the mysteries only arise when you start to consider the additional ontological beliefs; when the representation form of those "snapshots" just is such that things start to look odd one way or another.

 

So, if it can be shown that, certain universal aspects of explanations lead to the universal validity of exactly those rules that stand behind quantum mechanical formalism, what would you make of that?

 

-Anssi

[Qfwfq]

Okay, then I have no idea why you brought it up.

You said that Bell experiments are a strong experimental indication towards the validity of Dick's analysis and I disagree; I said what they do and don't imply.

 

...you can't see how the quantum dilemma could possibly be resolved by any universal considerations.

I don't think Dick's presentation does it.

 

Well, you probably agree that if you think of each observed state of the system like a "snapshot" of its underlying information (instead of thinking of them in the common terminology of fundamental particles), there's nothing mysterious in becoming able to connect different "snapshots" together with some set of rules (i.e. being able to draw predictions). All you need is a function that properly expresses those rules.

This isn't what the problem is.

 

I.e. you probably agree that the mysteries only arise when you start to consider the additional ontological beliefs;

No, I think the problem is the belief in causality (as opposed to specific ontological things). The problem is very subtle anyway and I think you don't understand it exactly.

 

The "rules" you mention are already known, only there are two aspects which seem at first glance to contradict each other. The subtle reason they don't truly contradict is that they don't apply to the same kind things, but this shows how these two kinds have a markedly different nature, with one of them being much less known and understood. Some people are bent on finding out more about it, just like folks have striven to improve understanding of many other things. It could even lead to discovering something interesting, just like the solutions to some past problems opened up whole new frontiers. I really don't agree that Dick's views solve this problem, nor that they have any other use.

 

So, if it can be shown that, certain universal aspects of explanations lead to the universal validity of exactly those rules that stand behind quantum mechanical formalism, what would you make of that?

If Dick could prove his claims conclusively I would make quite a bit of it. Since he can't and I believe it can't be proven, I don't make much of it at all. I don't think either of you understand how much of your considerations are already included in quantum physics, so there's nothing surprising if a choice or two makes it possible to arrive at Dirac's equation. If you refuse to admit these choices are further assumptions, there's not much more I can say. Edited January 18, 2011 by Qfwfq
slight revisions

[AnssiH]

You said that Bell experiments are a strong experimental indication towards the validity of Dick's analysis and I disagree; I said what they do and don't imply.

 

Well then I should just say that I agree with your comments about what they do and don't imply, and I guess your disagreement just meant you don't see any connection between DD's analysis and Bell experiments. I didn't expect you to just magically see any explicit connection after I mention the subject, don't worry. Like I said, just food for thought.

 

It is very difficult for me to follow what you are implying with the rest of the post, but I'll give it a try.

 

Well, you probably agree that if you think of each observed state of the system like a "snapshot" of its underlying information (instead of thinking of them in the common terminology of fundamental particles), there's nothing mysterious in becoming able to connect different "snapshots" together with some set of rules (i.e. being able to draw predictions). All you need is a function that properly expresses those rules.

This isn't what the problem is.

 

Since I did not suggest "this is what the problem is" anywhere in there, I suppose that is your way of saying "Yes I do agree".

 

I.e. you probably agree that the mysteries only arise when you start to consider the additional ontological beliefs;

No, I think the problem is the belief in causality (as opposed to specific ontological things). The problem is very subtle anyway and I think you don't understand it exactly.

 

The "rules" you mention are already known, only there are two aspects which seem at first glance to contradict each other. The subtle reason they don't truly contradict is that they don't apply to the same kind things, but this shows how these two kinds have a markedly different nature, with one of them being much less known and understood.

 

I believe you are rephrasing the same issue I was referring to; that the rules in themselves are unproblematic if you just view them as "what connects different observed states together in valid manner".

 

The problems arise when the "rules don't apply to the same kind of things", yes I'm okay with putting it like that, if you want. You could say, it's as if nature manifests itself to our observation differently than it acts in the absence of our perception, why not put it that way. It's the same thing I've been trying to refer to.

 

But, since the rules themselves are already unproblematic, how is this problem not a case of "mysteries arising when you start to consider the additional ontological beliefs"?

 

Are there some aspects to those "different kinds of things/realms" that you are convinced to be a more or less straight representation of reality (i.e. any of the aspects that refer to properties over and beyond the rules that already connect different observed states together in valid manner)?

 

Some people are bent on finding out more about it, just like folks have striven to improve understanding of many other things. It could even lead to discovering something interesting, just like the solutions to some past problems opened up whole new frontiers.

 

Of course, I agree with that completely. It is entirely possible that people find better and/or more useful ways to express expectations. DD's analysis is not in the same category with people finding better theories, it is not in any sense the be-all-end-all ultimate theory of everything, just like universal turing machine is not the ultimate computer program for everything.

 

It is epistemological analysis about explanations, that's all. In principle, it should be possible to analyze the epistemological aspects of any theory of reality, if you manage to express its assumptions properly in the terminology of DD's analysis. The point is just to pull out the consequences of those assumptions and the self-coherence constraints (the symmetries).

 

The reason he is talking about no-assumptions is because the expression of the universal constraints (what he calls the fundamental equation) can't contain assumptions that may invalidate some explanations. It wouldn't be the universal constraints in that case.

 

If Dick could prove his claims conclusively I would make quite a bit of it. Since he can't and I believe it can't be proven, I don't make much of it at all. I don't think either of you understand how much of your considerations are already included in quantum physics, so there's nothing surprising if a choice or two makes it possible to arrive at Dirac's equation. If you refuse to admit these choices are further assumptions, there's not much more I can say.

 

Oh there are certainly further assumptions! No one is saying there aren't, and in fact DD is multiple times commented there are assumptions, and so have I. Assumptions deliberately made to end up with such and such representation form.

 

The questions is, are they assumptions that would be valid only in the case that the underlying information was of some specific kind? I.e. does actual reality have to lend itself to that assumption? Or is it always possible to translate any recurring activity into a representation form where those particular assumptions just so happen to exists. (i.e. is it always valid to interpret things in such and such manner)

 

That question can't really be answered very easily, without being able to investigate the most fundamental aspects of that translation, and obviously those aspects are not the easiest things to investigate...

 

-Anssi

[Qfwfq]

Well then I should just say that I agree with your comments about what they do and don't imply, and I guess your disagreement just meant you don't see any connection between DD's analysis and Bell experiments. I didn't expect you to just magically see any explicit connection after I mention the subject, don't worry. Like I said, just food for thought.

Then on what grounds do you claim it wouldn't be wrong to make that statement? I still maintain that Dick's analysis adds no cherry to the top of the cake, no added value. I see it only having less utility than the full quantum formalism.

 

It is very difficult for me to follow what you are implying with the rest of the post, but I'll give it a try.

Yeah, I can see that, it seems it's never worth the effort, trying to reach you.

 

Since I did not suggest "this is what the problem is" anywhere in there, I suppose that is your way of saying "Yes I do agree".

It was my way of saying that what I quoted isn't mistaken... it is only superfluous to state it, and you were leading up to something untenable.

 

I believe you are rephrasing the same issue I was referring to; that the rules in themselves are unproblematic if you just view them as "what connects different observed states together in valid manner".

It is terribly hard to be sure of this when we simply don't possess a common language, sufficient to discuss the whole thing, and the conclusions we draw do not agree.

 

But, since the rules themselves are already unproblematic, how is this problem not a case of "mysteries arising when you start to consider the additional ontological beliefs"?

Yeah, you always bring it around to ontological beliefs; I keep finding it non sequitur. The "rules" needed a kind of "sorting out" so to speak. This does not mean they remain "unproblematic" because their striking distinction in nature (or of properties) is and remains troublesome, much as it needn't be seen as a real contradiction. It is a problem to solve, which people are working on.

 

Are there some aspects to those "different kinds of things/realms" that you are convinced to be a more or less straight representation of reality (i.e. any of the aspects that refer to properties over and beyond the rules that already connect different observed states together in valid manner)?

It is hard to glean your meaning across the gap in our languages, but I wouldn't quite put my opinion into those words. I would rather say there is certainly something that remains to be understood and that the non local aspects, especially with the highlights of Bell inequality violations, show that it can't be a simple matter of applying quantum formalism to the details of the events that play the role of measurement.

 

It is entirely possible that people find better and/or more useful ways to express expectations.

Better than what? This isn't the point at all and you couldn't disagree if only you more fully knew the comparison between Dick's presentation and standard quantum formalism.

 

The reason he is talking about no-assumptions is because the expression of the universal constraints (what he calls the fundamental equation) can't contain assumptions that may invalidate some explanations. It wouldn't be the universal constraints in that case.

But I've said I don't consider his FE to be as universal as the initial premises, to which he claims to add nothing else, and.....

Oh there are certainly further assumptions! No one is saying there aren't, and in fact DD is multiple times commented there are assumptions, and so have I.

Which ones are you referring to? The choice of Lie algebra? Perhaps even the restriction to the phase being linear in the shift parameter [imath]a[/imath], which gives the simple value [imath]k[/imath]?

 

I any case, if you put it this way, I don't get you and Dick making some claims in the past, especially those with the word tautology in them, regarding the whole of scientific knowledge.

 

The questions is, are they assumptions that would be valid only in the case that the underlying information was of some specific kind? I.e. does actual reality have to lend itself to that assumption? Or is it always possible to translate any recurring activity into a representation form where those particular assumptions just so happen to exists. (i.e. is it always valid to interpret things in such and such manner)

 

That question can't really be answered very easily, without being able to investigate the most fundamental aspects of that translation, and obviously those aspects are not the easiest things to investigate...

Especially without the conceptual tools of information theory, such as entropy! :P

 

But of course you decree that it doesn't apply because you're talking about "undefined information" or whatever you want to call it. :doh:

 

Let's call it the poltergeist just to avoid the semantic oddities and I assume you wrote representation as synonymous to "explanation", as I even find it a better term (which should stir up less debate over the meaning of the word). If the analysis can be applied to a given representation of it, then information theory is relevant to this representation, eh? If it is what you and Dick call a valid explanation, it must have something to do with the poltergeist, somehow, eh? I can understand one having difficulty due to the fact that a representation might (likely) not be faithful, with some being more or less than others. Let's consider a set of valid ones; if they are all valid, they must share some kind of properties or aspects, eh? Would you say this means --for valid ones-- that those shared things could be attributed to the poltergeist? The more a given pair of them give you similar expectations, the more things they must share in comparison to those each of them has, eh? Would you say this has to do with how faithful they are? If OTOH some of them seem to be equivalent to each other, you would say that their differences don't seem relevant to the actual poltergeist, eh? So, once we re-label a class of equivalent ones as one and the same, we could say that the more faithful it is, the more its properties/aspects/etc. can be attributed to the polergeist, eh?

 

I hope this approach (suggested to me by Dick's recent example of the Egyptian alchemist, the modern chemist and the hypothetical founder of an even better representation) will be of help in getting over past difficulties in reaching you. I'm aware it has some weak spots, but this is partly from trying to keep it simple and it would be more effective to conceptually contemplate the set of classes of all possible ones and consider the "most faithful" classes.

[Bombadil]

The issue is actually quite simple. Since all circumstances can be represented by a collection of numerical labels and the probability of any circumstance can be represented by a number bounded by zero and one, the mechanism for coming up with the probability of a specific circumstance can be seen as a mathematical function (one set of numbers transformed into another set). In my logical examination, I wish to omit no mathematical relation from the collection under consideration (to omit a mathematical relation would be to make a presumption that there existed no explanation which required that relation). It is the fact that probability is bounded by zero and one (by definition) which yields a problem here.

 

But what about the possibility that an explanation exists that requires that such a relationship is not included in the function. Isn’t the way that you are setting up the problem requiring us to include the relationships that are implied by complex numbers in the final equation. Isn’t this the effect of using the relationship

 

[math] \frac{d}{da}\Psi=ik \Psi [/math].

 

The representation certainly allows for correlations in the various components of those abstract vectors. It turns out that a correlation totally analogous to complex numbers serves a very valuable purpose. It allows us to insert into the representation an internal correlation which identically satisfies the required shift symmetry without constraining the representation in any way. The only real constraint is that the transformation used to define [math]\vec{\Psi}^{\dagger}[/math] will leave [math]\vec{\Psi}^{\dagger}\cdot\vec{\Psi}[/math] positive definite

 

Then you are just trying to define P so that it is a bound function between 0 and 1 without constraining the possible forms that [math]\vec{\Psi}[/math] will take. I assume that we don’t mind if solutions show up down the line that would satisfy such constraints, we just don’t limit ourselves to only such solutions.

 

It is the explanation which defines the probability, not my logic. We are not talking about “actual probability” here, we are talking about our expectations which arise from the explanation we believe is valid: i.e., it is our expectations which the explanation provides, not the actual probabilities (those are fundamentally unknowable).

 

Then the expectations of something are not a function of probabilities but rather ones expectations are only a relationship of [math]\vec{\Psi}[/math]. So the probabilities are not only unknowable they also have no effect on any expectations? Then are our expectations more like an equivalence class of [math]\vec{\Psi}[/math]?

 

The derivative of [math]\Psi[/math] with respect to “[math]a[/math]” turns out to somewhat different from what we had earlier. If the abstract space was originally two dimensional (in which case the abstract dimensionality of the complex [math]\vec{\Psi}[/math] is unity), we have now the expression

 

[math]\frac{d}{da}\Psi=ik \Psi[/math]

 

If the abstract dimensionality of this complex [math]\vec{\Psi}[/math] is greater than one, the partial with respect to the shift parameter yields an independent parameter k for each direction in that abstract dimensionality. The same analysis suggests that shift symmetry in the various dimensional components of [math]\vec{\Psi}[/math] can be handled as independent symmetries; however, the power and consequences of that possibility will be brought up later (under the coming post on "A Universal Representation of Rules") as it is a field all unto itself. For the moment, I will concern myself only with the actual form of the constraint required by shift symmetry in one dimension: i.e., [math]\Psi[/math] will be handled as a one dimensional complex function.

 

Isn’t this really saying that we can see any [math]\vec{\Psi}[/math] as containing a set of complex exponents which have no effect on the value of P and can rotate in any way as long as the value of P remains constant at each point.

 

I’m having a hard time at seeing this as anything more then just a bunch of randomly rotating vectors of an unknowable length. Can this tell us anything about P or is this more like a smoothing property of P?

[Qfwfq]

Isn’t this really saying that we can see any [math]\vec{\Psi}[/math] as containing a set of complex exponents which have no effect on the value of P and can rotate in any way as long as the value of P remains constant at each point.

 

I’m having a hard time at seeing this as anything more then just a bunch of randomly rotating vectors of an unknowable length. Can this tell us anything about P or is this more like a smoothing property of P?

Pretty much, yes, that's what it is. They are rotating especially randomly if one doesn't make the restriction as he does in the OP:

However, now the lone terms have been combined as a complex number and the expression c+id can be represented by [math]Ae^{ika}[/math]: i.e., the correlations of interest I spoke of earlier have been extracted into the expression [math]e^{ika}[/math] (see common trigonometric relationships).

where one could as well write the expression [imath]e^{i\varphi(a)}[/imath] and the differential equation would become

 

[math]\frac{d}{da}\Psi=i\frac{d\varphi(a)}{da}\Psi[/math]

 

This of course requires a less simple analysis but it definitely satisfies the same requisite of probability not depending on the [imath]a[/imath] variable. What Dick does can be called the case of a linear (and homogenous) choice of the [imath]\varphi(a)[/imath] function.

Edited January 19, 2011 by Qfwfq
addendum

[AnssiH]

Then on what grounds do you claim it wouldn't be wrong to make that statement? I still maintain that Dick's analysis adds no cherry to the top of the cake, no added value. I see it only having less utility than the full quantum formalism.

 

On the grounds that you can see quantum behaviour as an expected feature of a specific representation form of any sort of recurring activity. I have no idea what your comparison with full quantum formalism is supposed to mean.

 

Yeah, you always bring it around to ontological beliefs; I keep finding it non sequitur. The "rules" needed a kind of "sorting out" so to speak. This does not mean they remain "unproblematic" because their striking distinction in nature (or of properties) is and remains troublesome, much as it needn't be seen as a real contradiction. It is a problem to solve, which people are working on.

 

We already established that the "rules" are not stating anything contradictory.

 

But your mental picture of them (or the entities associated with the rules) are stating something contradictory.

 

Whatever that additional contradiction is in the latter case, it has to do with your ontological beliefs. This is the very definition of ontological beliefs; it is some aspect of reality which is part of your representation of it, but not part of the information underlying your representation (i.e. an aspect you can't defend, but an aspect you have to use in order to represent the rules.

 

It is a pretty trivial statement, that the apparent quantum contradiction is due to incompatible set of ontological beliefs put together. The problem here is that those beliefs are very fundamental aspects of our representation of reality. So fundamental that people get an immediate negative reaction to any suggestion about questioning them. Let's say, there's no such thing a space where bunch of objects are floating around, but that is instead just your way to represent expectations of something completely different. Obviously a possibility; for all we know we have just managed to explain some information in a manner that produces valid expectations.

 

So, think again, what is it in your mental picture of quantum effects, that is not explicitly required by the "rules", but you are still convinced to be a feature of reality, and not a figment of your imagination? There are many options, and each constitutes an ontological belief. (And I don't mean that you explicitly believe them all to be true, I just mean they are necessary part of a representation of the rules)

 

Better than what? This isn't the point at all and you couldn't disagree if only you more fully knew the comparison between Dick's presentation and standard quantum formalism.

 

Better than quantum formalism.

 

I was not disagreeing with anything, if you look back to what I was responding to.

 

But I've said I don't consider his FE to be as universal as the initial premises, to which he claims to add nothing else, and.....Which ones are you referring to? The choice of Lie algebra? Perhaps even the restriction to the phase being linear in the shift parameter [imath]a[/imath], which gives the simple value [imath]k[/imath]?

 

Could you please just explain what is it with these choices that they restrict in the input data? I.e. what sorts of assumptions about the "nature of the data" they constitute. I.e. what sorts of explanations they rule out?

 

Of course there can be mistakes like that in there, but it's just not possible to do anything with your objections when you merely say "I think this constitutes a problem. Now prove me wrong". If you can just show what is it that goes awry, it would always be useful.

 

Just in case that you are simply thinking that his choice of lie algebra moves the eventual representation of the rules towards something that looks like quantum formalism, then yes, that is correct, and entirely deliberate. Obviously, that is what we are trying to achieve, to see the connection between the symmetries and quantum formalism. Does that move require the underlying data to be of specific kind?

 

I any case, if you put it this way, I don't get you and Dick making some claims in the past, especially those with the word tautology in them, regarding the whole of scientific knowledge.

 

If it sounds confusing, don't worry about it. You will know what he actually means by it if you every happen to follow through the thing.

 

Let's call it the poltergeist just to avoid the semantic oddities and I assume you wrote representation as synonymous to "explanation", as I even find it a better term (which should stir up less debate over the meaning of the word). If the analysis can be applied to a given representation of it, then information theory is relevant to this representation, eh?

 

I am not following at all. I don't know what it means that the analysis is applied to a given representation (i.e. given explanation?). Do you mean if we can draw out the relationship between FE and some definitions of some explanation (like the deductions DD's done)?

 

Information theory applied to those definitions is not the same thing as deducing those definitions, obviously... Or are you saying something about entropy that is universal to all explanations? Yes I suppose something like that could be expressed, and yes I suppose some interesting relationships could be covered that way perhaps. I can't think of how it's related to DD's analysis. I.e. I have no idea why you are bringing it up, I am just guessing you have seen something that implied some connection.

 

If it is what you and Dick call a valid explanation, it must have something to do with the poltergeist, somehow, eh?

 

I'm afraid "poltergeist" contains semantic oddities as well, but okay I'll use it.

 

The representation has got something to do with those aspects of the "poltergeist" that can be seen as recurring activity of some sort. I.e, it represents that recurring activity in some manner.

 

I can understand one having difficulty due to the fact that a representation might (likely) not be faithful, with some being more or less than others. Let's consider a set of valid ones; if they are all valid, they must share some kind of properties or aspects, eh?

 

Well as long as they produce correct expectations, they are all valid, by the definition of "valid".

 

Apart from that, of course they can look very very different from each others. Their definition of space, its dimensionality and other properties can be very different. Some can include fundamental concepts that others don't. The fundamental set of entities can very easily be different. For the representation form, anything goes, as long as it represents the actual recurring activity in some manner.

 

Would you say this means --for valid ones-- that those shared things could be attributed to the poltergeist?

 

No, of course not.

 

If it was actually possible to exhaustively investigate every single possibility to represent the "poltergeist", and we could find that some properties appear in every single valid representation, then we could say that it is a necessary property of a representation of the poltergeist. We still could not say if the poltergeist contains that property in itself, or if it's just the need to represent its future that forces that property onto any appropriate representation (i.e. any representation capable of predicting its future)

 

I'm not saying that just to throw in some idle philosophy babble to confuse the conversation. I'm saying it because of what I said about the ontological beliefs in our mental picture of a Bell experiment; consider that there are properties to that mental picture that are necessary to represent our expectations, while they are not necessary aspects of reality.

 

If you understand what I mean by that, maybe my earlier posts make more sense now.

 

The more a given pair of them give you similar expectations, the more things they must share in comparison to those each of them has, eh? Would you say this has to do with how faithful they are?

 

No. Even if all the different representations produce exactly equally accurate expectations, I could not defend their "faithfulness" (ontological correctedness?) by their commonly shared aspects. Maybe the most commonly shared aspects are rather the simplest ways to represent the future behaviour of the poltergeist. How could I tell.

 

If OTOH some of them seem to be equivalent to each other, you would say that their differences don't seem relevant to the actual poltergeist, eh?

 

Yes.

 

So, once we re-label a class of equivalent ones as one and the same, we could say that the more faithful it is, the more its properties/aspects/etc. can be attributed to the polergeist, eh?

 

I thought by "more faithful" you meant it is closer to the actual real nature of the poltergeist. But if you did, then your above sentence just would mean "the more faithful it is, the more faithful it is".

 

If by "more faithful" you rather mean it produces better expectations, then your earlier use of it doesn't make sense to me.

 

At any rate, if we had a representation that produces more accurate expectations, we could still only say it is more accurate way to represent the expectations about the poltergeist, but not necessarily more accurate to the nature of the poltergeist itself. To say it is more accurate representation of the poltergeist itself, is to make undefendable ontological assumptions.

 

Everything I'm stating in the above in so convoluted manner (I'm sorry but I feel like I'm responding to a very convoluted question), can be reduced to one very simple and well known principle. The prediction-wise accuracy of a representation is not a defense of its ontological correctedness. It is just a defense of its usefulness as a prediction tool. Your question suggests you think ontological correctedness is the same thing as prediction-wise accuracy. I am in doubt of your ability to recognize which aspects of your personal representation of reality, are actually ontological assumptions, simply because they are necessary part of representing your expectations.

 

-Anssi

[Qfwfq]

Anssi, put a bit more thought into your replies. For one, if you don't know what I meant by a representation being faithful, you could waste less bandwith by just asking me first. Sorry if I hadn't specified it. For another, there is the usual misunderanding about ontological beliefs.

 

A representation of something is said to be faithul if the mapping is one to one (or more concisely bijective) and in my discussion, considering that some might be less faithful I meant there might be redundancies. I waqs only trying to get over the fact that we can't just assume the mapping is bijective, given a specific representation of whatever poltergeist is being examined.

 

Your usual pestering about ontological assumptions/beliefs being undefendable, stressing the impossibility of knowing what the poltergeist actually is, are quite superfluous. Why do you think I'm calling it the poltergeist?

 

I think you should at least try to avoid misunderstandings.

 

On the grounds that you can see quantum behaviour as an expected feature of a specific representation form of any sort of recurring activity. I have no idea what your comparison with full quantum formalism is supposed to mean.

And you're so convinced of those grounds, aren't you? Even granting that, it doesn't support your statement. Note that I did not discuss the comparison, I said it would be helpful if you were able to make it. I don't have enough time to learn Finnish, try to make an effort at understanding English.

 

We already established that the "rules" are not stating anything contradictory.

Neither did I deny it. But, therefore, it is odd that you say:

But your mental picture of them (or the entities associated with the rules) are stating something contradictory.

since we said that the matter is only contrdictory at first glance. So it doesn't follow that ontological beliefs are getting into my way. Wanna know what I think? I suspect that there isn't any cause-effect propagation between the two events that constitue the outcomes, despite the fact that results refute the correlation being due to a common cause originating from the departure of the pair of particles. This implies the explanation can't be within the spacetime that we ordinarily observe. Pure speculation, of course, but I have long been pondering some ideas about this conjecture. The alternative, of cause propagating along spacelike paths, would have other implications and some are already working on such investigations. But in any case I don't find Dick's presentation useful to the matter.

 

Better than quantum formalism.

How are you making the comparison? Tell me exactly where you believe the advantage lies and let's see if it is an actual advantage, lacking in quantum formalism. I hadn't taken you to be disagreeing with anything.

 

Could you please just explain what is it with these choices that they restrict in the input data? I.e. what sorts of assumptions about the "nature of the data" they constitute. I.e. what sorts of explanations they rule out?

What do you want me to explain? Group theory, representations, Lie groups and algebras and their role in theoretical physics? Quite a mouthful for a post. The trouble is:

Of course there can be mistakes like that in there, but it's just not possible to do anything with your objections when you merely say "I think this constitutes a problem. Now prove me wrong".

Don't forget the onus of proof is on who makes the claim, you can't dismiss objections on grounds of your lack of understanding of topics that are essential. It works the other way around, you don't show me that your judgement is adequate when you claim it's better than quantum formalism.

 

Just in case that you are simply thinking that his choice of lie algebra moves the eventual representation of the rules towards something that looks like quantum formalism, then yes, that is correct, and entirely deliberate. Obviously, that is what we are trying to achieve, to see the connection between the symmetries and quantum formalism. Does that move require the underlying data to be of specific kind?

How about this: We don't so easily expect Acrobat Reader to open a file that is an Excel spreadsheet; we don't so easily expect Excel to open an Autocad project; we don't so easily expect Word to open an Access database file. If you deliberately choose a certain format, you are requiring the file to be compliant with it. If you deliberately choose the equation to be Dirac's, you are requiring the data to be a solution of it.

 

Now, if you admit that, then you are not supporting the claim that quantum behaviour is a necessary consequence of the initial essential premises and nothing else, nor the the FE is universal.

 

If it sounds confusing, don't worry about it. You will know what he actually means by it if you every happen to follow through the thing.

Oh, I won't worry about it, because it did not sound confusing. It only sounded like you and Dick are not supporting those claims. I happen to have followed through the thing already, enough to understand why Dick obtains the equations he does: by deliberately making those choices. You say that means quantum physics and even all science is a tautology?

 

I don't know what it means that the analysis is applied to a given representation (i.e. given explanation?). Do you mean if we can draw out the relationship between FE and some definitions of some explanation (like the deductions DD's done)?

I mean the representation isn't the poltergeist; the map isn't the territory, the representation is a mathematical construct, a bunch of numbers that you can call data and you can't tell me that it makes no sense to reason on it with information theory.

 

If it was actually possible to exhaustively investigate every single possibility to represent the "poltergeist", and we could find that some properties appear in every single valid representation, then we could say that it is a necessary property of a representation of the poltergeist.

Yeah, I kinda said at the end that this is a stronger approach, albeit more idealistic, after suggesting a path by which maybe it isn't so strictly necessary.

 

We still could not say if the poltergeist contains that property in itself, or if it's just the need to represent its future that forces that property onto any appropriate representation (i.e. any representation capable of predicting its future)

So if something is a necessary property of any representation of a specific poltergeist, how is it not due to some property of that poltergeist? Any consequence of the requisite of predicting its future can't be specific, it would have to hold for any poltergeist of which it is possible to predict the future. This doesn't match up with properties of valid and not valid representations.

 

consider that there are properties to that mental picture that are necessary to represent our expectations, while they are not necessary aspects of reality.

Either it is a perfectly unbroken symmetry (the reason I babbled about equivalence classes) or there must be a way of representing the poltergeist that does without it.

 

Your doubts and disagreements after this point are due to the misunderstandings about ontological beliefs and the word faithful.

[AnssiH]

Anssi, put a bit more thought into your replies. For one, if you don't know what I meant by a representation being faithful, you could waste less bandwith by just asking me first. Sorry if I hadn't specified it. For another, there is the usual misunderanding about ontological beliefs.

 

Sure, just one thing I've been meaning to say. Your continuous accusations of me not following the conversation are a bit tiring. Your posts are not always perfectly clear either, and you should understand that from my perspective it also looks as if you are not making a good attempt to follow what I'm trying to say.

 

A representation of something is said to be faithul if the mapping is one to one (or more concisely bijective) and in my discussion, considering that some might be less faithful I meant there might be redundancies. I waqs only trying to get over the fact that we can't just assume the mapping is bijective, given a specific representation of whatever poltergeist is being examined.

 

By "faithful", you mean by what degree the defined entities of a representation are bijective to the...

...undefined information under the representation?

or

...actual reality behind the undefined information?

 

Either way, of course we can't just assume the mapping is bijective. Why do you bring this up?

 

Going back to;

 

If it is what you and Dick call a valid explanation, it must have something to do with the poltergeist, somehow, eh? I can understand one having difficulty due to the fact that a representation might (likely) not be faithful, with some being more or less than others. Let's consider a set of valid ones; if they are all valid, they must share some kind of properties or aspects, eh? Would you say this means --for valid ones-- that those shared things could be attributed to the poltergeist? The more a given pair of them give you similar expectations, the more things they must share in comparison to those each of them has, eh? Would you say this has to do with how faithful they are? If OTOH some of them seem to be equivalent to each other, you would say that their differences don't seem relevant to the actual poltergeist, eh? So, once we re-label a class of equivalent ones as one and the same, we could say that the more faithful it is, the more its properties/aspects/etc. can be attributed to the polergeist, eh?

 

A representation being bijective to the undefined information underlying the representation would just mean there are no defined entities that persist from one moment to the next (because without definitions, every bit of new information is exactly that, entirely new information).

 

That is essentially what DD refers to as the "what is, is what is" explanation, but it is not a characteristic of any representation that can express useful predictions.

 

If you meant to refer to a representation being bijective to the actual reality behind the undefined information, then that is exactly what I refer to as "ontological correctedness of the representation", and my earlier response stands.

 

I think you should at least try to avoid misunderstandings.

 

These comments are exactly what I find so tiring...

 

Let me just add multiple quotations so we are staying on track;

 

Anssi:

Actually, it wouldn't be wrong at all to say that Bell experiments are a strong experimental indication towards the validity of this analysis.

 

Qfwfq:

Here I totally disagree. They definitely do make hidden variables and Bohmian views unpalatable. They support quantum formalism even under aspects where its non-local nature is most striking.

 

Anssi:

I thought that's what I said. Even the most obscure experiments must produce results according to quantum formalism. DD's analysis just explains why our representation of reality acts that way. It doesn't explain what reality is like of course.

I don't see this as a hidden variable explanation.

 

Qfwfq:

First I said what those results do imply, then I said what they don't imply, and I had not taken Dick's presentation to be a hidden variables interpretation.

 

Anssi:

Okay, then I have no idea why you brought it up.

 

Qfwfq:

You said that Bell experiments are a strong experimental indication towards the validity of Dick's analysis and I disagree; I said what they do and don't imply.

 

Anssi:

Well then I should just say that I agree with your comments about what they do and don't imply, and I guess your disagreement just meant you don't see any connection between DD's analysis and Bell experiments. I didn't expect you to just magically see any explicit connection after I mention the subject, don't worry.

 

Qfwfq:

Then on what grounds do you claim it wouldn't be wrong to make that statement?

 

Anssi:

On the grounds that you can see quantum behaviour as an expected feature of a specific representation form of any sort of recurring activity.

 

Qfwfq:

And you're so convinced of those grounds, aren't you? Even granting that, it doesn't support your statement.

 

So, dissecting that crazy amount of quotations, I essentially asserted that Bell experiments can be seen as an experimental indication towards the validity of DD's analysis.

 

Yes, I am very much convinced that they can be viewed that way, given that, I am, as we speak, capable of viewing them that way.

 

I assume we both realize there are also many other ways to view Bell experiments, i.e. we both realize this is in no way suggesting an explicit proof.

 

You started to talk about what Bell experiments imply about hidden variable explanations, but said that this was not because of having assumed that DD's analysis is one.

 

So am I to take your assertion as, "since this is what they imply about hidden variable explanations, they can't imply anything about DD's analysis, even though it is not a hidden variable explanation"?

 

Or, should I take your assertion as simply, "no, Bell experiments cannot possibly make any implications about DD's analysis"?

 

If so, I still have absolutely no idea why you are saying that, and my only explanation to your comment is that you are not seeing any connection there. In which case, I am not going to attempt to spell it out. Rather, I am reverting back to my response "I didn't expect you to just magically see any explicit connection after I mention the subject".

 

Next confusion;

 

Qfwfq:

I still maintain that Dick's analysis adds no cherry to the top of the cake, no added value. I see it only having less utility than the full quantum formalism.

 

Anssi:

I have no idea what your comparison with full quantum formalism is supposed to mean.

 

Qfwfq:

Note that I did not discuss the comparison, I said it would be helpful if you were able to make it. I don't have enough time to learn Finnish, try to make an effort at understanding English.

 

I don't usually include things like that last sentence into quotes. This time I did just so you can see that you are really making a lot of accusations of me not following you. Trust me, I am making an effort.

 

That being said, after some head scratching, I came to conclude that "I said it would be helpful if you were able to make it" was written there because you mixed up different threads of our conversation; I believe it is meant to refer to your comment that I should be able to compare the results of DD's analysis and full quantum formalism better.

 

Just to return to this thread, I said I don't understand your comparison because it is much like comparing, let's say "Facebook" with "Universal Turing Machine".

 

QM is a physics theory, DD's analysis is an analysis about symmetries. They exist in different categories.

 

Yes, QM has more utility in very many ways. And yet, DD's analysis is about QM.

 

it is odd that you say:since we said that the matter is only contrdictory at first glance.

 

It sounds like you are saying what I said, semantics aside.

 

Or, do you not agree that something needs to change in our mental picture of a quantum behaviour, for the contradiction to go away?

 

I would imagine that "second glance" implies exactly that; a change in our mental picture.

 

Hence, do we not agree, that the situation can be expressed exactly like I did? While the rules are already self-coherent, our mental representation of those rules contains facets that are contradictory.

 

Yes, I can express the same thing by saying, that the contradiction is "only apparent". No, I do not believe that reality in itself is contradictory, only our idea of it.

 

Keep in mind that some undefendable facets are necessary, just so we can actually have a useful mental representation of those rules. The rules just by themselves can be thought of as the best known method of making predictions about the information underlying our representation.

 

Wanna know what I think? I suspect that there isn't any cause-effect propagation between the two events that constitue the outcomes, despite the fact that results refute the correlation being due to a common cause originating from the departure of the pair of particles. This implies the explanation can't be within the spacetime that we ordinarily observe. Pure speculation, of course, but I have long been pondering some ideas about this conjecture.

 

Then I would expect you to be interested of putting much more effort into trying to understand his definitions, and then following the analysis. Many of your responses reflect clear misunderstandings about the fundamental aspects of his analysis, and I'm sure a lot of things seem non-sensical due to that.

 

Rule of thumb, if you see a painfully obvious problem in the middle of seemingly confusing explanation, the chances are, you are interpreting it wrong. At that point, try to make an interpretation that makes sense, and you may pick up what he was trying to say.

 

Ultimately, it does amount to implying exactly that there is no cause-effect propagation at all, nor is there any dual nature to nature itself. That dual nature is found entirely from our methods of drawing predictions from recurring patterns of undefined information.

 

And it's all happening without making any arguments about what reality is or is not like. There are definitions that we have chosen to use as very fundamental aspects of our representation of reality. Essentially, they are the means of categorizing recurring activity. If all of those definitions required for quantum behaviour can be seen as a categorization method applicaple to any sort of recurring activity, then quantum behaviour can be seen as a feature of the method we are currently employing in tracking and representing recurring features of reality.

 

It is all quite mundane, it's just hard topic to discuss without explicitly pointing out that such and such features of our world view are not in fact "known features of reality", and that always gets people on their toes.

 

The alternative, of cause propagating along spacelike paths, would have other implications and some are already working on such investigations.

 

Obviously it is possible to generate a self-coherent representation of quantum behaviour; that is exactly what different quantum interpretations are. The only reason people have relatively low faith on them is that they contain assumptions that are very obviously undefendable. The less obvious the undefendable aspects are, the more convinced people tend to get. For instance, for most people, the undefendable nature of their conceptualization of "space" is not very obvious. In fact, they will fight you for it.

 

 

Qfwfq:

The subtle reason they don't truly contradict is that they don't apply to the same kind things, but this shows how these two kinds have a markedly different nature, with one of them being much less known and understood. Some people are bent on finding out more about it, just like folks have striven to improve understanding of many other things.

 

Anssi:

Of course, I agree with that completely. It is entirely possible that people find better and/or more useful ways to express expectations.

 

Qfwfq:

Better than what?

 

Anssi:

Better than quantum formalism.

 

Qfwfq:

How are you making the comparison? Tell me exactly where you believe the advantage lies and let's see if it is an actual advantage, lacking in quantum formalism. I hadn't taken you to be disagreeing with anything.

 

Sorry about another quote fest but I think it's the quickest way to resolve confusion. I was referring to future theories. I.e, better in that they make more accurate and/or more comprehensive predictions one way or another.

 

What do you want me to explain? Group theory, representations, Lie groups and algebras and their role in theoretical physics? Quite a mouthful for a post. The trouble is:Don't forget the onus of proof is on who makes the claim, you can't dismiss objections on grounds of your lack of understanding of topics that are essential.

 

As far as I can see, he is putting a whole lot of effort to discuss exactly why and how each step he makes does not require a specific nature to the underlying information itself. I don't know what to make of your accusations of not even trying to prove these things.

 

I don't know why you are mentioning the role of Lie groups (etc) in theoretical physics. He is aiming for a "representation of recurring activity" that is identical to theoretical physics, and he is trying to get there with definitions that are universally applicable. Thus the question, what is it in these choices that makes them require specific nature to the information itself?

 

Look at it this way. There are many mathematical tools in the physicist's toolbox. We all realize that the chosen tools play a role in the way the relationships are represented. In order to arrive at an identical representation, DD must use the same tools. All the tools he is using prior to arriving at the "fundamental equation" (or shall we call it "the universal constraints"), are used because they don't appear to constitute an assumption about what the undefined information is like. I.e. they are always valid, if the underlying definitions are fundamentally just a representation of a recurring activity.

 

You seem to complain that it is because he is using these tools, that he is arriving to the identical representations. Well yes, that is deliberate, but why is that a problem? He has also chosen to use numbers, and coordinate systems, and all kinds of things that are just as much playing a role in getting to identical representation. And likewise, they are not constituting an assumption about the underlying data itself.

 

That is why I said, you should be able to explain exactly, how does one or another choice constitute an assumption about what the underlying information actually is, as oppose to just constitute a categorization method of recurring activity.

 

How about this: We don't so easily expect Acrobat Reader to open a file that is an Excel spreadsheet; we don't so easily expect Excel to open an Autocad project; we don't so easily expect Word to open an Access database file. If you deliberately choose a certain format, you are requiring the file to be compliant with it. If you deliberately choose the equation to be Dirac's, you are requiring the data to be a solution of it.

 

The examples of file format do not compare because they are deliberately defined by whoever designed them.

 

As to get back to the topic of generating a representation of recurring activities, the choices that led to Dirac's equation are quite numerous, and you should be able to point out exactly at what point of that path, there is a choice that constituted a requirement for the underlying information to be of specific kind. I have not found it, and I have been looking very carefully.

 

I think your comment reflects a misunderstanding of some sort, I believe it's a misunderstanding about the role of undefined information, and how that leads to the fact that all we know "about" the information must be based on recurring activity of some sort, and nothing else.

 

Oh, I won't worry about it, because it did not sound confusing. It only sounded like you and Dick are not supporting those claims. I happen to have followed through the thing already, enough to understand why Dick obtains the equations he does: by deliberately making those choices. You say that means quantum physics and even all science is a tautology?

 

Like I've commented before, while I understand what he means by it, I would not put it like that because it will likely be understood wrong. It would be understood wrong exactly for the reason that there are choices to be made in order to get to exactly identical representation as modern physics.

 

It's a challenge to spell this out to anyone who has not picked it up by following the presentation carefully, but let's see if I can explain it.

 

On the high level, he means that the representation called "modern physics" doesn't reflect the true nature of the underlying information that the representation is based on. It just reflects a categorization method of some recurring activity in that information.

 

I'll spell out some details, let's view Schrödinger's Equation. The FE is tautologous to the symmetry arguments, but Schrödinger's Equation, in its specific form, is not strictly tautologous to FE. As in, you can't actually put an equal sign between the expressions.

 

But, there is a very real sense in which you can (and should) view the core of Schrödinger as tautologous to FE, and see the rest as merely semantical choices. His derivation makes this separation very explicit. The argument is;

 

The choices required to get from FE to Schrödinger, are all universally applicable definitions to any sort of underlying data. Out of very many possible definitions that would be universally applicable, we have "arbitrarily" chosen few that are useful in simplifying the representation of recurring activity.

 

In other words, Schrödinger amounts to a succint expression of "FE + arbitrary choices".

 

Now, for a reader who understands exactly where this is coming from, this reads clearly, that the exact form of Schrödinger's Equation is governed partially by self-coherence requirements that must always be present (FE), and partially by semantical choices, that further make the representation more succint.

 

As in, other arbitrary choices could have lead to a different representation of exactly the same information.

 

For a reader who is not up to speed with where all these choices came from and what the fundamental premise is, this comment about tautologous nature of modern physics only causes confusion because it might not make sense why would those "arbitrary choices" merely constitute some semantical aspects of some specific representation that merely obeys the self-coherence requirements, while expressing expectations, that are based on recurring activity of some sort.

 

That is exactly what your difficulty is in interpreting what he is saying.

 

In a nutshell, he says modern physics is tautologous to self-coherence requirements on the grounds that, those parts of its form that are not governed by the self-coherency requirements, appear to only amount to semantics, that are there to simplify the representation form.

 

I repeat, if that sounds confusing to you, don't worry about it. He points at that tautology as an attempt to simulate some thoughts, and perhaps align people to interpret his analysis more correctly, because it really requires proper understanding of his analysis, before that assertion makes sense.

 

I mean the representation isn't the poltergeist; the map isn't the territory, the representation is a mathematical construct, a bunch of numbers that you can call data and you can't tell me that it makes no sense to reason on it with information theory.

 

Like I've said, you can reason on a specific representation, yes, but you are not then analyzing the universal aspects of representations, you are analyzing that representation. That is different topic from what DD is doing.

 

And more to the point, even if you are referring to an analysis of universal aspects of representations, it just sounds like you are insisting that we'd discuss a different analysis? I've been trying to ask you to spell out what parallels you see in between. You seem to just respond that I should teach myself information theory and find out myself whether or not there are parallels. Are you saying, that you are just guessing there might be something useful there, without knowing what it might be? I.e, I don't understand at all why you are bringing it up.

 

So if something is a necessary property of any representation of a specific poltergeist, how is it not due to some property of that poltergeist?

 

By being necessary in order to represent any sorts of of expectations of recurring activity. For instance, to represent any expectations, we must express some defined entities that persistently exist in multiple "moments" of reality. But reality doesn't have to be like that. Reality doesn't need to be concerned about expressing its future. Reality doesn't have to define itself at all.

 

As a closely related issue, according to DD's analysis, for any recurring activity, it is always possible to generate an explanation where conservation of momentum is directly apparent. Which of course doesn't mean the poltergeist itself has got that property to it.

 

I said closely related, because on the other hand, for the same poltergeist, different valid explanations may take a form where conservation of momentum is not apparent. It may be hidden behind all kinds of convoluted definitions. At all times though, if the explanation really is valid, there exists a translation to the form where conservation of momentum is apparent.

 

I hope you realize it is extremely difficult to discuss these matters clearly in english language.

 

-Anssi

[Qfwfq]

It is true that the whole thing is tiring and I would like to avoid the exponential growth, especially when it isn't necessary nor useful.

 

By "faithful", you mean by what degree the defined entities of a representation are bijective to the...

...undefined information under the representation?

or

...actual reality behind the undefined information?

So far, you had led me to understand that the first thing is what you call the second thing; that's why I prefer to fancifully call it the poltergeist, take it as Kan'ts ding an sich, but of course you have so often ignored my recourse to that to. I'm the one that should be more clear in my posts?

 

Either way, of course we can't just assume the mapping is bijective.

That is exactly the kind of problem I was trying to get around, by arguing upon whole sets and classes of representations.

 

Why do you bring this up?

Because of you dismissing some previous points of mine.

 

A representation being bijective to the undefined information underlying the representation would just mean there are no defined entities that persist from one moment to the next (because without definitions, every bit of new information is exactly that, entirely new information).

 

That is essentially what DD refers to as the "what is, is what is" explanation, but it is not a characteristic of any representation that can express useful predictions.

If this were so, it would mean that, if only we knew the truth, there would be no grounds for expecting tomorrow morning to come, or even the next tick of the clock. It would mean there's no point in scientific research at all, nor in engineering, any kind of planning based on experience, absolutely nothing.

 

So, it seems that by "undefined information" you mean the "what is, is what is" explanation?

 

If you meant to refer to a representation being bijective to the actual reality behind the undefined information, then that is exactly what I refer to as "ontological correctedness of the representation", and my earlier response stands.

This would only be so according to a modern use of the word ontology, in which case you could not say ontological assumptions are inherently undefendable. This makes you repeated objection to me a moot point.

 

Let me just add multiple quotations so we are staying on track;

You leave the second quote (first of of me) just exactly as incomplete as it was the first time, despite me having pointed it out. That's called cherry-picking.

 

You started to talk about what Bell experiments imply about hidden variable explanations, but said that this was not because of having assumed that DD's analysis is one.

 

So am I to take your assertion as, "since this is what they imply about hidden variable explanations, they can't imply anything about DD's analysis, even though it is not a hidden variable explanation"?

 

Or, should I take your assertion as simply, "no, Bell experiments cannot possibly make any implications about DD's analysis"?

Including the part missing from that quote, I had said that what they imply is no grounds for the validity of Dick's analysis, simply because it does not follow of necessity from refuting hidden variables (or local realism). The experiments support QM aginst local realism, implying that the non local aspects inherent in the quantum description are a fact of reality, that's all.

 

That being said, after some head scratching, I came to conclude that "I said it would be helpful if you were able to make it" was written there because you mixed up different threads of our conversation; I believe it is meant to refer to your comment that I should be able to compare the results of DD's analysis and full quantum formalism better.

Or even in that same post and, since you wrote the word comparison it seemed you were thinking of both things. Could we get past these things? I really think that language has been a barrier too, I can tell because sometimes your use of English shows it and sometimes there's an added risk of ambiguity.

 

Just to return to this thread, I said I don't understand your comparison because it is much like comparing, let's say "Facebook" with "Universal Turing Machine".

 

QM is a physics theory, DD's analysis is an analysis about symmetries. They exist in different categories.

This shows me that you lack the competence necessary to make the comparison; von Neuamann and Wigner would never agree with that analogy. I'm aware that his analysis is about QM, but it adds nothing and is less useful. I'm also aware that his analysis isn't physics, but I also know that the general quantum formalism is only very slightly more about physics. What you refuse to understand is that, as a mathematical construct, it's initial premises are not much more restrictive. Also, it is very much about symmetries.

 

It sounds like you are saying what I said, semantics aside.

Semantics aside, it might even sound like the sentence "All apples are red." is saying the same thing as "All horseshoes are made of leather."

 

I wouldn't really say that something needs to change in our mental picture of a quantum behaviour for the contradiction to go away, if we forget about folks that can't get past the intuitive, classical notions. The fact is that the only reliable "picture" we currently know of is the quantum formalism itself and it is thought of as the best known method of making predictions.

 

Then I would expect you to be interested of putting much more effort into trying to understand his definitions, and then following the analysis.

Because you presume it is the way to go.

 

Rule of thumb, if you see a painfully obvious problem in the middle of seemingly confusing explanation, the chances are, you are interpreting it wrong. At that point, try to make an interpretation that makes sense, and you may pick up what he was trying to say.

You've no idea how much experience I've had in understanding things by looking for the interpretation that makes the most sense, how often it has been essential to my survival. You certainly don't show this ability when you complain about some of my replies, dimiss them as irrelevant and call them rather odd, when they are meant to stimulate a reflection on some aspect.

 

Ultimately, it does amount to implying exactly that there is no cause-effect propagation at all, nor is there any dual nature to nature itself.

I consider "dual nature" an archaic concept which the full mathematical formalism mkaes superfluous and what I said about cause-effect propagation only referred to the non local aspects.

 

For instance, for most people, the undefendable nature of their conceptualization of "space" is not very obvious. In fact, they will fight you for it.

I won't even fight an earthworm for it. I do however hold that it isn't just a subjective manner of representing things. At scales above Planck length and time, spacetime just looks the way Minkowski describes it, regardless of how we perceive the world, define entities and whatnot.

 

I was referring to future theories. I.e, better in that they make more accurate and/or more comprehensive predictions one way or another.

I disagree all the same.

 

There are certainly things to understand further, but if there were any possibility of passing the limits set by the quantum description, the world would not be the way it is. Forget about less essential things like permanent magnets and newfangled things like lasers, superfluidity and superconductivity, there is the more fundamental matter of properties of materials in general.

 

Look at it this way. There are many mathematical tools in the physicist's toolbox. We all realize that the chosen tools play a role in the way the relationships are represented. In order to arrive at an identical representation, DD must use the same tools. All the tools he is using prior to arriving at the "fundamental equation" (or shall we call it "the universal constraints"), are used because they don't appear to constitute an assumption about what the undefined information is like. I.e. they are always valid, if the underlying definitions are fundamentally just a representation of a recurring activity.

 

You seem to complain that it is because he is using these tools, that he is arriving to the identical representations. Well yes, that is deliberate, but why is that a problem? He has also chosen to use numbers, and coordinate systems, and all kinds of things that are just as much playing a role in getting to identical representation. And likewise, they are not constituting an assumption about the underlying data itself.

This is where you are totally out of depth, putting blind faith into Dick's statements and I'm just not falling for it. If you choose to agree with him in this, I can do nothing about it.

 

That is why I said, you should be able to explain exactly, how does one or another choice constitute an assumption about what the underlying information actually is, as oppose to just constitute a categorization method of recurring activity.

How about me repeating the question: What does it mean to say that one or another world view is valid? (I'm not asking you to explain it to me.)

 

The examples of file format do not compare because they are deliberately defined by whoever designed them.

That constitutes a discriminating factor? Consider this conjecture: The fundamental laws of physics, including the Dirac equation, are so because that's the way they are deliberately defined by the god who designed them. If you cannot prove this conjecture is false then you cannot discriminate between my example and Dick's choices restricting the kind of data on the above grounds.

 

I have not found it, and I have been looking very carefully.

Then demonstrate mathematically that the equations any other choices would lead to all have the same solutions as that FE and I'll have to admit to his claim of it being universal.

 

continued...

[Qfwfq]

I believe it's a misunderstanding about the role of undefined information, and how that leads to the fact that all we know "about" the information must be based on recurring activity of some sort, and nothing else.

You are actually saying that we can't determine any more than which formats the information (so far) does and which it doesn't fit.

 

The FE is tautologous to the symmetry arguments, but...

No, and the rest of that lesson is totally superfluous. You have no conclusive argument by which it is a purely semantic matter.

 

Like I've said, you can reason on a specific representation, yes, but you are not then analyzing the universal aspects of representations, you are analyzing that representation. That is different topic from what DD is doing.

This is a total misunderstanding of what I said, because what I quoted was a misunderstaning of what I previously had said. I was not relying on anything specific to a representation, I was saying something about any one of those in the analysis; they are all mathematical constructs, a bunch of numbers that you can call data and apply information theory to.

 

And more to the point, even if you are referring to an analysis of universal aspects of representations, it just sounds like you are insisting that we'd discuss a different analysis?

If I propose my design for a skyscraper, bridge or dam to be built in a populated area and the ministry rejects it as unsound, according to valid criteria, there's no use me telling them that those criteria have nothing to do with my analysis and therefore are irrelevant. It would be silly of me to ask them what parallels they see between them. They would certainly tell me I should learn engineering if I want to defend my design and claim that it is sound.

 

Which of course doesn't mean the poltergeist itself has got that property to it.

Which of course does mean there is no whatsoever use in studying the recurring data patterns. This whole lesson does not answer the question you quoted, unless you mean that the recurrences don't depend on the poltergeist at all, hence the data tells us nothing whatsoever about reality, not even in the sense mentioned earlier in this post, so it's useless trying to form expectations.

[Doctordick]

It is true that the whole thing is tiring and I would like to avoid the exponential growth, especially when it isn't necessary nor useful.

Qfwfq, have you ever heard of "the pot calling the kettle black!" Who is behind this "exponential growth in unnecessary" comments?

 

 

I have presented three posts giving (as clearly as I can) the derivation of my fundamental equation. Why don't you just read those three in order and, the moment you see a specific assertion I make that seems to you to constrain the information being evaluated in any way, point it out. Forget all this meaningless meandering and get down to specifics.

 

Unless you are willing to do that, I see no rational response beyond simply ignoring you.

 

Have fun -- Dick

 

Post #1 -- Laying out the representation to be solved.

Post #2 -- Conservation Of Inherent Ignorance!

Post #3 -- "a Universal Representation of Rules".

 

Sorry about the grammar of the titles but they don't allow editing titles.