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Quicki note on "Normalization"


Doctordick

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That would be normalization from a philosophic perspective.

 

Hi Anssi, I am answering your e-mail as a hypography post because I know that the hypographic notes allow things which I am afraid e-mail may not render correctly. Plus that, the information might be useful to anyone trying to follow my work.

 

> From: Anssi Hyytiäinen

>

> I'm not familiar with how the wave function

> normalization arose in

> standard quantum physics, or what people generally think it

> means, so I

> don't know what those philosophical problems are. Can

> you elaborate on that?

 

The issue is quite simple. In standard quantum mechanics, it is the equation which appears first. Its validity was originally argued from the mathematical work surrounding the varied possible ways of expressing classical mechanics. From that perspective, the solution (and that would be the “wave function”) was to be a function which satisfied the differential equation represented by Schrödinger's equation.

 

Here I might insert some facts which to me are rather beside the point but to professional physicists are paramount. I have only talked about Schrödinger's equation (commonly referred to as “wave mechanics”) but there was once a competitive theory called “matrix mechanics” where the various differential operators were expressed instead by matrices and the fundamental underlying expression was a “matrix” equation.

 

Paul Dirac, one of truly great mathematical physicists, proved that “wave mechanics” and “matrix mechanics” were actually mathematically equivalent. In 1939 he also introduced a notation of his own called the “bra”, “ket” notation. Put a “bra” (normally written <eigenvalues|) and a “ket” (normally written |eigenvalues>) together around an "operator" and you have a “bracket” (<a|operator|b>); get it? The “bra” corresponds to [imath]\Psi^\dagger[/imath], the “ket” corresponds to [imath]\Psi[/imath] and the bra-ket corresponds to the integral over all possibilities thus to the actual expectations for the results expected from whatever is represented by that operator.

 

If you want to see “matrix mechanics”, check out the matrix representation in terms of bra's and ket's. The bra's and ket's you see there are merely labels to the rows and columns of a matrix used in matrix mechanics. The elements of the matrices are the direct expectations of possible results.

 

Now quantum mechanics is called quantum mechanics because the possibilities are most often “quantized”. These “quantized” results arise from specific solutions called “eigenvalues” (“Eigen” is the German word for “real”). A good example of such quantization is angular momentum. If the Schrödinger wave function is given in polar coordinates; r, theta and phi; (the electron around a nucleus for example), and you add 360 degrees to the angle theta, the square of the resulting value of the wave function must be the same (you are talking about the same point in space. This is just like the vibration of a string on a stringed instrument (its displacement at each tied down end has to be zero). We are talking about fixed wave lengths of the function. Only certain frequencies are allowed.

 

In quantum mechanics, the presumed actual state of systems is presumed to be a sum over these “eigenstates” (often referred to as a superposition of states). When you go to measure the actual value of some measurement, you obtain one of these “eigenvalues” and then the universe proceeds to evolve as if that were the only state in the superposition. My approach is to simply find a function which fits the past as I have defined it (what you could refer to as those eigenvalues) so the issue of “superposition” is a totally fictitious mechanism used to yield your expectations. By the way, this gets you around the philosophical problems of the “Bell inequalities”.

 

But let us get back to the original question about “normalization”. Normalization is the adjustment of the magnitude of the Schrödinger wave function such that the integral over all possibilities yields unity (a result required by the definition of probability). The same problem exists in matrix mechanics and Dirac notation except that it is sort of brushed under the rug by the notation (normalization does not overtly appear as a problem but it is still arises when you try and work out some esoteric matrix elements).

 

The normalization arise because one is looking for solutions to the Schrödinger equation and one can often find solutions to that equation which are not normalizable; that is, one obtains infinities which are difficult to eliminate. I approach the problem from entirely the other side of the coin. When I open the field to “any function which will yield the same probability of your expectations”, I am not looking for a solution to an equation; I am looking for a function which yields your expectations, quite a different thing. From the collection of all possible mathematical functions, [imath]\vec{\Psi}(\vec{x},t)[/imath], (an expression of a way of getting from one set of numbers, [imath]\vec{x},t[/imath] to a second set of numbers, [imath]\vec{\Psi}[/imath]) one can always generate [imath]\vec{\Psi}^\dagger \cdot \vec{\Psi}[/imath] which will be a number greater than or equal to zero. If one integrates that function over all possibilities one will obtain a positive definite number bounded by zero and infinity. All one need do is divide the original function, [imath]\vec{\Psi}(\vec{x},t)[/imath], by the square root of that number. This will essentially normaliz the function (the mathematical results can now be interpreted as a probability).

 

There are only two problems there: division by zero is undefined and division by infinity yields zero. Division by zero is never required as, if that integral is zero, the original unnormalized [imath]\vec{\Psi}(\vec{x},t)[/imath] is just fine as its magnitude can clearly be interpreted as a probability (all it says is that the probability of any set of arguments is zero and there is no real problem with that). Division by infinity yields zero which means that the probability of any specific argument is zero; a quite reasonable result if the number of possibilities for the arguments is infinite. If this is the case, then one needs to work with a range of possibilities and compare the result for that range with the result for some alternated range. If you are comparing two ranges, there is no need to "normalize" the function.

 

The only thing of significance here is that the result can be interpreted as a probability. The whole philosophical problem of normalization simply vanishes.

 

From that starting point, I deduce that the function [imath]\vec{\Psi}(\vec{x},t)[/imath] must obey my fundamental equation so there can not be any “problem of normalization”. I might further comment that most of the real problems with normalization occur because of the presumptions of “hard entities”, entities of non zero dimensions where the wave function can not penetrate the entity. If you look at my fundamental equation, the interaction term is a Dirac delta function with a range of zero thus that problem can not arise. One could say that the problems in classical wave mechanics arise because their presumptions are false.

 

At any rate, these problems do not arise in my interpretation.

 

Have fun -- Dick

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I would like to first give a note of caution. Quantum physics is a very vast and complicated matter, although the most basic formalism can be "condensed" so to speak, one must be careful of trying to draw conclusions without having gone through a lot of mathematical tools. Mostly, the notoriously counterintuitive aspects and the various schools of "interpretation" are an even more confusing topic and full of pitfalls too. The meaning of much of the terminology has come to be very varied by there being many differing points of view and with subtleties going missed in comunication. While the formalism offers a precise language for computing results and describing experimental outcomes, any discussion of interpretaions and implications about reality lacks the same standard of precisely defined meanings and is hence subject to severe difficulties, even amongst academics with respectable grounding in the topics. It is very easy to fall into argumentative fallacies and even unwittingly circular arguments.

 

That said, I'd like to draw Anssi's attention to these interesting links. The first is a very lucid analysis of Bell's work and its implications; it is not easy going but I can say I've a high esteem academically for Abner Shimony (with whom I even had an interesting and very pleasant chat when I was a young student, after he had delivered a talk at the Padova uni's physics dept.) and I found this article to be of a great excellence in standard. The second is about the intricate matter of decoherence (which, in the complexity of debate I mentioned above, is sometimes considered an "alternative" to the Copenhagen interpretation whereas my point of view is just that the CI has eveolved and been refined over time). I don't know this author but there is no mistake in the use of formalism and the first stretch of article can be helpful as a summary introduction to it, although I found some of the terminology such as the classification of states differs from what I had aquired in my courses, textbooks and other literature but is reasonably well defined; from the argumentative I never found quite enough time to analyse and digest the final part (the actual aim of the article) where some things are stated a bit summarily and not argued all that much in detail and rigour. For this reason I don't vouch for it quite as much as for the first.

 

Bell's Theorem (Stanford Encyclopedia of Philosophy)

Decoherence (Technical Notes)

 

Enjoy. :shrug:

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That would be normalization from a philosophic perspective.

When my cursor read that line yesterday, I thought, 'Oh well, this isn't about quantum physics.'

Imagine my surprise today when I clicked on this post by accident!

 

I can't add much, but I bet this link will be helpful!

 

ScienceDirect - Computer Physics Communications : VNI 3.1 MC-simulation program to study high-energy particle collisions in QCD by space-time evolution of parton-cascades and parton-hadron conversion

 

or just google renormalization.

...or renormalization "quark-gluon plasma"

for a different perspective....

 

Lunchtime: gotta run

 

~ :shrug:

 

Klaus Kinder-Geiger 1962-1998

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Hi Qfwfq, I was surprised to see your post and appreciate the fact that you still read some of my stuff. I have taken the trouble to read the references you have suggested and, for the most part, they have nothing to do with my proof nor my deductions of various physics expressions. Particularly in view of Anssi's mathematical background; I suspect he will be unable to follow most of what is there; however, there are a couple of points made in the article on Bell's theorem which I think need to be emphasized, at least with regard to how they impact what Anssi and I are talking about.

 

From section 2, Proof of a Theorem of Bell's Type

 

“What Bell's Theorem shows is that Quantum Mechanics has a structure that is incompatible with the conceptual framework within which Bell's Inequality was demonstrated: ...”. Underlying this statement is the assumption that the physical interpretation of reality is valid; that physical interpretation is the “conceptual framework” which stands behind most everyone's mental picture of reality.

 

5. The Communication Loophole and its Remedy

 

“The counting rates agreed well with the predictions of Quantum Mechanics and violated one of Bell's Inequalities.” Which could be taken as very strong evidence that something is wrong with Bell's theorem.

 

Also, in the same section, one has:

 

“Furthermore — and this is the feature which seems most to have captured the imagination of physicists — this experiment achieved much greater separation of the analyzers than ever before, thereby providing the best reply to date to a conjecture by Schrödinger (1935) that entanglement is a property that may dwindle with spatial separation.” What they miss is the fact that “entanglement” is a hypothetical explanation of their experiment which maintains that “physical interpretation of reality” I refer to above. I suspect you are the only person who comprehends that this is exactly the issue which I am complaining about. Under my analysis, there is no cause and effect presumed; my fundamental equation does not require cause and effect as it is no more than the consistency requirements which must be obeyed by a flaw free explanation.

 

From section 7, Philosophical Comments,

 

“It is not, however, a demonstration that quantum mechanics is nonlocal, much less (as some proclaim) that nature is.” If you read through my work, you will discover that I have, at no time, defined “local”. At one point Qfwfq brought up the issue of locality

Yes, but one nitpickin' detail: constant K is the specific case of global phase shift, the shift symmetry (or any one that's on P) doesn't imply this, it may be local.
A problem which I tried to address in my next post:
The issue here is that the indices [imath](x_1.\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n [/imath] and [/imath] t)[/imath] are nothing more than arbitrary numerical labels used to refer to ontological elements. They constitute an undefined language containing the information to be explained. In any logical deduction based upon those ontological elements, nothing can be introduced which violates the arbitrariness of those assignments (what I believe Anssi refers to as semantics) as, if you make an assumption which violates that arbitrariness, it amounts to asserting you know something about what the assignments mean. I have essentially defined only one basic concept; I have defined what I mean by time. Now if you were to define what you meant by a term, as I did with my definition of “time”, that would be another story: i.e., you could use the concept “local” but only after you had defined what you meant by the term. The issue is that you cannot talk about ontological elements being “local” without providing me with a method of determining which ones qualify as local, the point being that, your definition must be applicable even under the arbitrary reassignment of all of those labels. You should understand here, that I can talk about position on the x axis because that is nothing more than a representation of arbitrary label: that is to say, the labels can be arbitrarily shuffled throughout the collection of ontological elements without violating that definition.
The only issue of significance here is that the final explanation, no matter what that explanation might be, is interpretable in a manner such that the ontological elements on which that explanation is built must behave in a manner (those numerical labels) which constitute a solution to my fundamental equation.

 

The only really intelligent statement in the article is the quote from Zeilinger, “If we accept that the quantum state is no more than a representation of the information we have, then the spontaneous change of the state upon observation, the so-called collapse or reduction of the wave packet, is just a very natural consequence of the fact that, upon observation, our information changes and therefore we have to change our representation of the information, that is, the quantum state. “ Which is one hundred percent consistent to what I am presenting.

 

However, that statement is dismissed with the cavalier assertion,“Especially it scants the fact that the quantum state probabilistically controls the occurrence of actual events.” The fact they say! On what basis is that “a fact”? That is an assumption; a fundamental assumption of everyone's explanation. What they omit to say is that their explanation explains what they know, not what the future: i.e., what they do not know.

 

This reminds me of an exchange I had with a young fellow a number of years ago. I read a post which complained about the fact (in the opinion of the author) that modern probability theory was wrong. Since probability theory is part of the “mathematical structure I take as sound (i.e., leave to others)” and one of the most basic things in my presentation, I was concerned that something basic in my attack could be wrong.

 

He was a math major (with little or no graduate work) who had been hired by a computer disk drive manufacture to mathematically analyze failure rates of their production. What is important here is to realize that actual failure is extremely rare (we have millions upon millions of successful performance for relatively long times before a failure occurs). The results are way out on that bell curve of probability. What he found out, after years of analyzing these failures, was that the calculations he did from standard theory consistently gave the wrong answers. He came across a rather simple correction which yielded results consistent with “experiment” (real failure rates).

 

He had arrived at his adjustment by a method which seemed logical to him and, when it worked, he tried to write it up and get it published. He was rejected by everyone and, as far as I know, has still not been published. All the authorities simply assert that he is making a mistake in his calculations somewhere after all, making calculations concerning very rare events is a complex affair and he must obviously be leaving out some subtle factor somewhere.

 

I suggested he publish the experimental results together with the simple correction which yielded good answers as a phenomenological solution to a common industrial problem. With that kind of approach, I suspect he might have gotten published, but he had no interest in doing that. What he wanted was recognition that he had discovered an error in probability theory. So he was cutting off his nose to spite his face (so to speak). Who am I to complain as I suspect many would accuse me of the same thing.

 

At any rate, what he found to be a successful attack (as explained from a coin tossing perspective) was to presume that the probability of a head/tail was not universally invariant but rather that, as the string of heads (or tails) became extremely large, the probability of the opposite occurrence rose. Of course, true or false, neither his nor the standard presumption bears on my work as all I am concerned with is that the probability be given by [imath]\vec{\Psi}^\dagger \cdot \vec{\Psi}[/imath], not exactly what procedure is to be used to define that function.

 

But there is an interesting observation to be made here. If the explanation is to explain the past (what we know) then it would be unreasonable to expect extremely long sequences when such sequences are absent in “what we know”. The most reasonable expectation is that the future will not change the statistical nature of the past: i.e., if the past does consist of a 50/50 division and you are currently seeing an overwhelming sequence of one result, your expectations of the opposite result should eventually rise. Now Qfwfq, how does that interpretation of your expectation jibe with “local reality”? This picture would require an explanation where events in the past (what you know) actually influencing the future outcome of statistical events and that is about as non-local as one can get. :lol:

 

Finally, I would comment that the article on “decoherence” is really concerned with reducing the quantum mechanical solution to the classical view of phenomena: i.e., it is a defense of one's world view as being consistent with quantum mechanics. Essentially, both of these articles are concerned with interpretation of quantum mechanics and the mental picture commonly referred to as one's world view.

 

I guess what I am saying here is that these two articles are quite valuable if your interest is to see how the physics community views the connection between quantum mechanics and common experience but actually have little bearing on my presentation (other than the fact that quantum mechanics can be so interpreted).

 

Qfwfq, I have no intention of belittling your contribution; I just think Anssi will have a lot of trouble following the details of what is being said there. Suffice it to say that there exists little argument upon how the results are to be explained; most all physicist would agree with the procedures used. It is only the interpretation of the procedures which generate any philosophical difficulties.

 

And, Essay, I do not understand what you have in mind.

 

Have fun -- Dick

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And, Essay, I do not understand what you have in mind.

 

hehe ...yes; if I had a nickel for every time.... No, I think surely it's me that doesn't understand what is being talked about.

I suppose at best this link could have been pertinent, but at worst it could still be of serendipitous interest. :lol:

 

I only dabble in this quantum stuff, but several years ago I ran across this memorial book:

RHIC physics and beyond : Kay Kay Gee Day; Upton, New York, October 1998 / editors Berndt Müller, Robert D. Pisarski. Publisher Woodbury, N.Y. : American Institute of Physics, c1999. LC call# QC787.L5 R43 1999

(AIP Conference Proceedings ; No. 482).

 

Well, I felt it gave me a better sense of how baryonic matter renormalizes (reconstitutes itself?) after being forced into a wave state. Or, if that doesn't make sense, how about: ...after being forced into a highly perturbed quantum state (with the suggested "parton" being the "transition state" during renormalization). I thought it would be a sort of different perspective on this subject (esp. for Anssi, who I suspect is more interested in the conceptual side...), but for all I really know this stuff may be completely unrelated to your subject, if not what your purpose or focus is;

so, if so.... ~Nevermind.... ~ :hihi:

 

~Kay Kay Gee (1962-1998)

"One day you find, ten years have got behind...."

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I do agree that Essay is not in keeping with the point and perhaps even slightly hit-and-run-ish.

 

Er, Dick, I really only meant to offer Anssi something possibly helpful toward his understanding of the matters of quantum mechanics, which you are introducing him to. :lol: I do fear that you read Shimony much too hastily and prejudiciously to properly understand and discuss it. At least you got to see that you're not the first to say what you quoted of Zeilinger; indeed neither was he the first aware of it. To the contrary it is essential to the very logic on which the so-called collapse or reduction of the wave packet is argued by also supposing two requisites of the method used to observe the eigenvalue. Shimony's "caviler (cavalier?) assertion" is perhaps not so well put but it really stands for something that would be longer to spell out and discuss and which is also the essence of criticism towards Bohm's interpretation.

 

I will definitely say that you have misunderstood here:

“It is not, however, a demonstration that quantum mechanics is nonlocal, much less (as some proclaim) that nature is.” If you read through my work, you will discover that I have, at no time, defined “local”. At one point Qfwfq brought up the issue of locality
Yes, but one nitpickin' detail: constant K is the specific case of global phase shift, the shift symmetry (or any one that's on P) doesn't imply this, it may be local.
Here I must say you're comparing totally different things, Bell and Shimony's article discuss local realism whereas the quote of me was talking about a local symmetry as opposed to a global one.

 

At any rate, what he found to be a successful attack (as explained from a coin tossing perspective) was to presume that the probability of a head/tail was not universally invariant but rather that, as the string of heads (or tails) became extremely large, the probability of the opposite occurrence rose.
He was aware of the fact that the events being dealt with couldn't be considered independent, this is a fundamental assumption for many an analysis concerning probability. It is not an assumption of the very notion of probability or of its axiomatic definition. It holds for repeated outcomes of a roulette wheel, rolling dice of coin flipping but I'm not in the least surprised if it doesn't hold exactly for the disk failures the guy was analyzing; actually I'm more surprised by the idea that engineers were not considering cumulative aspects.

 

The most reasonable expectation is that the future will not change the statistical nature of the past: i.e., if the past does consist of a 50/50 division and you are currently seeing an overwhelming sequence of one result, your expectations of the opposite result should eventually rise. Now Qfwfq, how does that interpretation of your expectation jibe with “local reality”? This picture would require an explanation where events in the past (what you know) actually influencing the future outcome of statistical events and that is about as non-local as one can get. :hihi:
In order to reply, I should be more certain of your meaning but apparently you're talking about the old paradox which induces many people to place their money on lottery numbers which have not come ot for much more than average; they are delusional because they don't understand the binomial distribution or the notion of conditional probability, the distinction between probability before each outcome and information after it. So, what exactly is the point you are asking me to address?

 

I guess what I am saying here is that these two articles are quite valuable if your interest is to see how the physics community views the connection between quantum mechanics and common experience but actually have little bearing on my presentation (other than the fact that quantum mechanics can be so interpreted).
As I said, I simply offered something helpful for Anssi. He might also find some of the first chapters of vol. 3 of the Feynman lectures interesting; one thing adressed therein shows why the words you quoted from Zeilinger do not suffice to solve the difficulties consequent from the quantum description of reality. Put in a nutshell: if interference is observed in the double-slit experiment and we conjecture that the photon, as a plain simple corpuscle, did go through one of the two holes although we don't know which, how does "the other" hole cause the destructive interference (influence where the photon is detected)?

 

I think however that Anssi should read these things himself and he alone decide whether or not they are too difficult for him to understand. :beer-fresh:

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So this is more wave/particle duality, Copenhagen Interpretation, Heisenberg... maybe?

===

 

By way of an apology, may I offer the Table of Contents for RHIC Physics and Beyond, the above cited monograph

on Relativistic Heavy Ion Collision physics.

(...had thought p.53 & p.113 might seem relevant; but anyway...)

 

Contents:

01. Beyond the Parton Cascade Model: Klaus Kinder-Geiger and VNI / B. Muller

17. Schematic Model for Density Dependent Vector Meson Masses [et al.]

35. Heavy-Ion Collisions and Black Holes in Anti-de-Sitter Space / J. Ellis

53. Baryon, Charged Hadron, Drell-Yan and J/[Psi] Production in High Energy Proton-Nucleus Collisions / C. Gale....

69. Testing the Space-Time Structure of Event Generators / U. Heinz, U. A. Weidemann

85. Parton Structure through Two Particle Correlations in Au-Au at RHIC / R. S. Longacre

105. Initial Conditions for Parton Cascades / L. McLerran

113. Detailed Comparison between Parton Cascade and Hadronic Cascade at SPS and RHIC / Y. Nara, K. Geiger....

121. Physics Opportunities at RHIC and LHC [et al.]

142. Flash of Prompt Photons from the Early Stage of Heavy-Ion Collisions / D. K. Srivastava

157. Unraveling the Myth of Large p[subscript T] Hadron Spectra in High Energy Heavy-Ion Collisions / X.-N. Wang

167. Author Index

===

 

...Smashing Gold nuclei together at relativistic speeds, and modeling/theorizing about how the ensuing quark-gluon plasma renormalizes! What could be more exciting? ....and who could pass up page 35?

~ :turtle:

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Hi Qfwfq, I really want you to know that I appreciate your attention. In my opinion you are one of the most valuable people on this forum. You have impressed me with both your knowledge and your thoughtfulness and I sincerely hope that my continual dismissal of your comments don't lead you to think that I feel otherwise. At the moment, the two people I want to maintain contact with the most are you and Anssi. The two of you are like opposite sides of a very similar coin. Anssi understands exactly what conundrum stands behind my thoughts but lacks the mathematics and the understanding of modern physics necessary to appreciate my conclusions. You, on the other hand, clearly possess all the training and sophistication to follow my work (and have offered very good criticisms of the same when you have taken the trouble to look at it); however, your attention is almost always slightly askew of the central issue I am attacking. You and Anssi together have all the intellectual qualities I have been searching for but each of you seem to lack exactly what the other has.

 

I have been very slow to react to your post because I really don't want to upset you but somehow I want to communicate the issues you are overlooking. I am sorry that I keep harping on exactly those same issues; I am sure you find it rather unproductive. I keep hoping that sooner or later, something I say will click with you and the light will come on; that you will understand the foundation I am working with and thus the direction of my thoughts. Once perceiving exactly what I am talking about I feel sure that you would follow all of my comments without much difficulty at all. The most important point is that my work is divided into two very different and essentially unconnected issues, a point Buffy has, in many respects, referred to quite often. The first issue is the deduction of my fundamental equation. That is a pure consequence of the various definitions I try to express in A Universal Analytical Model of Explanation Itself. It is not a hypothesis but is essentially a proof. Perhaps not laid out as well as it should be, but a proof nonetheless.

 

The result is an explicit an n-body equation and, as I know you are well aware, no general solution to such an n-body equation has ever been achieved. I hope you appreciate the full generality of the notation [imath]\vec{\Psi}(\vec{x}_1,\vec{x}_2, \cdots,t)[/imath] as representing any possible relationship between the arguments and the probability of those arguments being realized: i.e., if a general solution to that n-body equation were ever to be found, it could certainly put into exactly that form.

 

We have two issues here. The first is that there must exist an interpretation of the undefined ontological elements behind any epistemological structure such that those references to the ontological elements obey my equation (that is true by construction). The second issue is very simple; is that information of any value? With regard to that question, I have found a very interesting fact. That fact can be stated as follows: if one presumes the availability of a solution which provides the probability for all the arguments but one, that self same equation can be seen as providing the behavior of that last argument.

 

There is no theory in either of those two statements; they are both facts not hypotheses. What is important is the form of the resultant two body equation (the two bodies being referred to here are the index under examination and the rest of the universe as a collection of indices). The form of the resultant equations is quite interesting. By some rather simple algebra (simple for anyone with a decent founding in advanced algebra) I have explicitly derived the fact that Schroedinger's equation is an approximation to my equation.

 

My comment that this removes all the philosophical difficulties from the problems of wave function normalization is no more than an assertion that the question is now being asked from the other direction. The equation and the definition of [imath]\vec{\Psi}[/imath] are now the fundamental inputs to the problem, not the solution being searched for. It is a totally different perspective and needs no justification beyond the proofs I have given.

Er, Dick, I really only meant to offer Anssi something possibly helpful toward his understanding of the matters of quantum mechanics, which you are introducing him to. :shrug:
I understand that and accept it. I originally made the post in answer to an e-mail from him. In a sense, I sort of got carried away but I thought he ought to know a little about the various notations used in quantum mechanics (I personally like the Schroedinger notation myself because it essentially hides very little). But I doubt Anssi will be able to follow much of either of the presentations you refer him to as they bring in issues with which I doubt he has any familiarity and at the same time have little to do with what I am trying to communicate. I just don't want him run off by the idea that he needs to know all of that information.
I do fear that you read Shimony much too hastily and prejudiciously to properly understand and discuss it.
Not really; the essence of my reaction was a general lack of interest in such things. Both those articles are very concerned with interpreting the issues brought up. That subject is simply outside my interest. As I said, I have proved “that there must exist an interpretation of the undefined ontological elements behind any epistemological structure such that those references to the ontological elements obey my equation”: i.e., the expectations for those indices. Proof that such an interpretation exists does not, in any way, imply that I can provide one but, in a very important sence, it removes the real significance of any explanation. That is why I often say that intelligent explanations are actually data compression mechanisms.
At least you got to see that you're not the first to say what you quoted of Zeilinger; indeed neither was he the first aware of it. To the contrary it is essential to the very logic on which the so-called collapse or reduction of the wave packet is argued by also supposing two requisites of the method used to observe the eigenvalue. Shimony's "caviler (cavalier?) assertion" is perhaps not so well put but it really stands for something that would be longer to spell out and discuss and which is also the essence of criticism towards Bohm's interpretation.
Again, you are bringing up issues outside my interest which have little or nothing to do with what I am trying to communicate. (Cavalier is, of course, the correct spelling; sorry about that. I was thinking in terms of the verb "to cavil". I suspect the words have very similar sources.)
I will definitely say that you have misunderstood here:Here I must say you're comparing totally different things, Bell and Shimony's article discuss local realism whereas the quote of me was talking about a local symmetry as opposed to a global one.
You miss a very important point (Anssi, maybe you can do a better job of explaining that fact than I do). The issue is that any term used in the description of any solution, or constraint of that solution, must be defined. The mechanisms used to communicate are as much a part of the problem being solved as are the numerical representation of the problem (in fact they must, in their entirety, be included in the numerical representation of the problem). Otherwise, you are presuming the validity of a very substantial portion of the problem being examined without putting significant portions of that problem up to examination. Anssi, I know you understand exactly what I am saying there; how about a little assistance.

 

Finally, Chris, you have totally misunderstood my interaction with the fellow and his disk drive statistics. I am not supporting his suggestion that probability theory is wrong. I got in touch with him for the simple reason that my entire work is dependent upon a clear understanding of probability and I wanted to know exactly what his complaint was. It was quite clear to me that his complaint had utterly nothing to do with what stood behind my work so that issue was totally cleared up. I had not examined his work (I do not claim to be an expert in any mathematical structure of probability theory) I was merely giving him advice on the path he should take without making any pronouncement on the validity or error of his work.

 

As I have said many times, my only assertion is that any explanation must be consistent with what is known and no more: i.e., it must be “flaw-free”. You, on the other hand, immediately jump in to providing an explanation for his problem. This is exactly the difficulty I have with your approach to my work. You either have utterly no interest in the question I am attacking or you simply do not understand what I am doing. I would like to believe your difficulty is the second circumstance as the first is just not an intelligent position.

 

My position is very simple; whatever the explanation is, it must be consistent with information upon which it is based: i.e., if, never in the history of the world, has a repetitive sequence of some specific event achieved a one sided outcome beyond certain limits, it is quite reasonable to expect a current run to terminate sometime before that limit is achieved. Whether one has a theory which provides some such limit or whether one simply says this is no more then the simple fact that the probability is getting so small that the probability I will see such a longer run is very small and may be ignored. What you have to recognize is that both propositions are “theories” and not “facts”. The only question of interest to me is, “does the theory fit the facts”; any theory which does so is possibly correct (and that would include theories not yet proposed).

As I said, I simply offered something helpful for Anssi. He might also find some of the first chapters of vol. 3 of the Feynman lectures interesting; one thing adressed therein shows why the words you quoted from Zeilinger do not suffice to solve the difficulties consequent from the quantum description of reality.
That is because you are looking for “an explanation”. I am not. All I am saying is that, if you use the definitions I lay out, any flaw-free explanation of the information available to you requires that your expectations are solutions to my equation. As Buffy says, this says absolutely nothing about reality and she is quite right. It is the simple consequence of the fact that your “flaw-free” explanation must conform to the data on which it is based.

 

What you seem to miss is the fact that the meanings of the words you use to describe your explanation are part of the explanation; i.e., understanding the explanation requires understanding the language used to express that explanation. That process itself involves assumptions beyond your ability to even express. The only solution is to work with the global generalization of the problem from the perspective I have given as the problem is otherwise totally beyond solution. By guess and by golly (the historic approach) just is not a valid attack.

Put in a nutshell: if interference is observed in the double-slit experiment and we conjecture that the photon, as a plain simple corpuscle, did go through one of the two holes although we don't know which, how does "the other" hole cause the destructive interference (influence where the photon is detected)?
You bring up another “conjecture”. None of these conjectures have anything to do with my proof.

 

I once asked a fellow if he had ever tried to describe what he would expect the universe to look like if there were absolutely no rules and everything was nothing but statistically random. He refused to even consider the issue because “he knew that could not be possible”. When I pressed him on the issue his defense was that “white noise could not produce ...” some technical thing or another. I was quite astonished that he was so simple minded that he thought a circumstance he had never seen (white noise doing whatever he was suggesting) would be a sufficiently probable occurrence in a statistically random universe that its absence in his experience was sufficient to conclude the universe was not statically random. He apparently did not understand the need to do statistical examination of his expectations.

 

All I am doing is looking at an arbitrary distribution of (???? - whatever it is that makes up what we know of reality) and simply saying that any explanation must provide expectation consistent with what is known. If that is false, it certainly isn't a very good explanation. If you define arrangements you know (which are less than the entire universe) then those arrangements must occur in conjunction with elements that are not part of those specifically defined arrangements. To expect utterly no correlation in a finite collection of such information is about as ridiculous as I can imagine.

 

Having sufficient probability of seeing any specific arrangement often enough to be led to come up with a definition of that arrangement (i.e., name it) and then say that no other collections of elements in the universe can possibly have any correlation with those defined arrangements is simply unsupportable. In fact, I have proved that, if you have expectations for the rest of the universe (what ever those expectations might be) reasonable expectations for a single index on a single element must essentially obey Schroedinger's equation. It is a simple proof and no more.

 

Think of the black body spectrum. That spectrum is entirely defined by self consistency and nothing else under two very simple rules. First, if a collection of entities in a gas are in a stable state, the number scattering into a specific state must exactly equal the number scattering out of that state. And, second, if the energy emitted by such scattering is quantized, the black body spectrum is uniquely defined. That is a fact and not a conjecture. It follows directly from conservation of energy and momentum.

 

My work is as solid as is that proof and as easy to follow, if anyone would take the trouble to follow it.

 

Have fun -- Dick

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Hi guys, I didn't notice this thread here until yesterday, and had no time to reply until now :shrug:

 

First, I should clarify that originally I was just looking to find out what sorts of philosophical problems normalization has brought up in standard quantum physics. I know about the philosophical problems regarding interpreting QM, although I'm not familiar with the mathematical formalism of QM.

 

I suppose the answer to my question was essentially:

 

The normalization arise because one is looking for solutions to the Schrödinger equation and one can often find solutions to that equation which are not normalizable; that is, one obtains infinities which are difficult to eliminate.

 

So, am I right to look at Schrödinger's equation as a constraining equation to the behaviour of possible wave function(s)? The problem then being that some otherwise valid solutions cannot be normalized? If I picked that up correctly, I'm still not quite sure what sorts of philosophical problems that brings up exactly...

 

I do understand why there are no philosophical problems with DD's approach. Or let's be more careful and say; I cannot see any philosophical problems with it.

 

I would like to first give a note of caution. Quantum physics is a very vast and complicated matter, although the most basic formalism can be "condensed" so to speak, one must be careful of trying to draw conclusions without having gone through a lot of mathematical tools. Mostly, the notoriously counterintuitive aspects and the various schools of "interpretation" are an even more confusing topic and full of pitfalls too. The meaning of much of the terminology has come to be very varied by there being many differing points of view and with subtleties going missed in comunication. While the formalism offers a precise language for computing results and describing experimental outcomes, any discussion of interpretaions and implications about reality lacks the same standard of precisely defined meanings and is hence subject to severe difficulties, even amongst academics with respectable grounding in the topics. It is very easy to fall into argumentative fallacies and even unwittingly circular arguments.

 

I understand exactly what you are cautioning me about, and I'd claim that I don't very easily make hasty conclusions based on some specific interpretation on QM, or based on some specific view of reality in general. I have seen those unwittingly circular arguments many times, and I see them as unwittingly circular exactly because I look at the different views just as different "self-coherent sets of concepts" cast onto the exact same raw information... An issue usually known as "semantics".

 

I've referred to human worldview as "semantical worldview" exactly because whatever the raw input information is, there always exists many very different ways to interpret its meaning. Different QM interpretations are clear examples of this, but let it be said that this issue is not limited to QM interpretations. Any world model that is built onto raw information whose explicit meaning is unknown, will have that same semantical nature to it, because alternative and equally valid models can always be built (i.e. models that fit the known data just as well). However you perceive the raw data, is an interpretation according to your own worldview. By some mechanism you come to interpret the data in terms of "~objects floating around in space"

 

Heh, I actually googled "semantical worldview" to see if others have used the term, and amusingly, the first result is to my own old post where I explain what I mean by "semantical worldview", after using the term in a thread where people discuss what "local realism" means to them exactly, in the context of Bell's Theorem.

 

You miss a very important point (Anssi, maybe you can do a better job of explaining that fact than I do).

 

Well, without getting into who meant what with "locality" in what context, I guess I could just continue with some commentary about how your analysis relates to that semantical nature of our worldviews.

 

It seems obvious to me that to identify reality in terms of any "elements" at all, is inherently and explicitly a feature of our world model building. We understand reality in terms of some defined objects. Different definitions yield different objects with different behaviour; just a different way to communicate the same raw data. I look at different (valid) worldviews essentially as different methods of mapping the same data (using different ontological entities to communicate the same data).

 

Since the explicit meaning of the raw data is unknown, and since it can always be interpreted in multitude of different ways, all the arguments about this or that element (existing only in some of those valid views) being ontologically real are somewhat moot; you can never prove such a thing, not without referring to arguments that are valid only in terms of some specific worldview.

 

What's nice about DD's analysis is that it is not by itself a set of ontological concepts. It is instead an analysis looking for consequences of modeling raw data whose meaning is unknown. I.e. whatever consequences are found, they have nothing to do with the ontological reality (the content of the data), but instead they are entirely epistemological features, springing into our worldviews from the process of classifying any data into intelligible "objects" in self-coherent manner. (I think it is rather interesting that the analysis seems to prove that relativistic time relationship springs from epistemological groundings completely)

 

Also still commenting on Bell experiments, in DD's analysis, quantum mechanical wave collapse occurs in our knowledge when new information comes in. Certainly a common interpretation of a delayed choice Bell experiment would seem to pose a problem, but that interpretation includes plethora of undefendable assumptions about reality. Looking at the raw data, there are no problems (remember, time and space are interpretations of the data), and without having any ontological preferences, it is quite possible to create ontological views that are coherent with Bell experiments & "epistemological wave function collapse".

 

In the end, what's important here is that DD's analysis is just a logical framework by itself, it gives us a clearer view of the logical groundings of such and such features in our comprehension of reality, and a clearer view on how our undefendable assumptions are tied to each others. Armed with that knowledge, maybe people would spend less time arguing over semantics (thinking they are talking about reality when they are talking about an interpretation of), and more time looking for other useful and simpler ways to model reality.

 

Oh, here's also my earlier attempt to explain what the analysis is about, in case you didn't see it. It's from slightly different angle, so it might be helpful:

http://hypography.com/forums/philosophy-of-science/11733-what-can-we-know-of-reality-28.html#post227884

 

-Anssi

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I suppose the answer to my question was essentially:
Pretty dammed close! In a nutshell, the issue is very simple: conventionally, the squared magnitude of the solution to the relevant “quantum mechanical” equation is the probability the specific defined events will be observed; on the other hand, in my analysis, the square root of the probability must be a solution to my fundamental equation. Although these seem to be quite similar constraints, they are, from a philosophical perspective, absolutely different.
Heh, I actually googled "semantical worldview" to see if others have used the term, and amusingly, the first result is to my own old post where I explain what I mean by "semantical worldview", after using the term in a thread where people discuss what "local realism" means to them exactly, in the context of Bell's Theorem.
Now I would call that strong evidence that you are an original thinker.
It is instead an analysis looking for consequences of modeling raw data whose meaning is unknown. I.e. whatever consequences are found, they have nothing to do with the ontological reality (the content of the data), but instead they are entirely epistemological features, springing into our worldviews from the process of classifying any data into intelligible "objects" in self-coherent manner.
That is exactly why I always refer to the process of developing epistemological constructs as inventing a data compression mechanism.

 

An excellent post Anssi. There is no question in my mind at all that you have any difficulty whatsoever understanding what the issue is here. I am very much looking forward to leading you through the whole magillah. I only hope I don’t lose you.

 

Have fun -- Dick

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So, am I right to look at Schrödinger's equation as a constraining equation to the behaviour of possible wave function(s)? The problem then being that some otherwise valid solutions cannot be normalized? If I picked that up correctly, I'm still not quite sure what sorts of philosophical problems that brings up exactly...
Well, you could put it in such words as a non-physicist, usually a Schrödinger equation is seen as being the description of dynamics for the quantum state. But, of course, this is a worldview, isn't it?

 

The solutions that aren't normalizable aren't a philosophical problem, if I haven't totally misunderstood what Dick means by them but I'm supposing he means the quasi-eigenstates in the case of continuous spectra. These are a mathematical problem but not an unsolved one; the strict treatment was outlined in my third year course on the formalism, just to show that applying the eigenvalue-eigenstate apparatus isn't BS. The eigenstate isn't an element of a Hilbert space, the math is more complicated but it has been worked out. :shrug:

 

I see them as unwittingly circular exactly because I look at the different views just as different "self-coherent sets of concepts" cast onto the exact same raw information... An issue usually known as "semantics".
Maybe that's even the same reason why Dick and I so often rant against each other without realizing that we're not actually contradicting the other but saying the same thing in different words! :doh:

 

Trouble is that I don't see how Dick's argument is conclusive and so I don't so far find it being a satisfactory wayout for the mysteries of modern physics. :hihi:

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Trouble is that I don't see how Dick's argument is conclusive and so I don't so far find it being a satisfactory wayout for the mysteries of modern physics. :shrug:
Which argument are you talking about, the validity of my fundamental equation (under the definitions I put forth), that Schroedinger's equation is an approximation to my equation or that solutions to that equation must obey special relativity? As far as I can see, your only problem can exist in the first issue as the deduction of Schroedinger's equation is trivial algebra and the form of the fundamental equation is exactly the same as the form of a many body equation for a classical photon gas; exactly the relationship from which special relativity is classically deduced.

 

If your problem is indeed with the proof of the validity of the fundamental equation, which one of these propositions do you find questionable?

 

1. That all epistemological constructs depend upon a specific set of ontological elements.

 

2. That these ontological elements are, prior to the existence of an epistemological solution, undefined.

 

3. That one may use numerical labels for these undefined ontological elements: i.e., that any language (and likewise, any statement in any language) can be reduced to a finite set of numerical labels.

 

4. That one's expectations (as provided by a specific epistemological construct) can be represented as a probability of experiencing a specific set of those ontological elements.

 

5. That epistemological constructs do not provide anything beyond one's expectations.

 

6. Acceptance of those five imply that any specific explanation of anything can be mapped into a mathematical function P(a specific set of numerical labels) which yields exactly what is known.

 

7. That any finite collection of results obtained from any mathematical function can be represented by a table of numerical labels for every set of arguments (which are also numerical labels): i.e., all possible mathematical functions can be represented by the notation [imath]\vec{\Psi}(\vec{x})[/imath].

 

8. That given such a function, one can always define a specific procedure for reducing such a function into a single positive definite number for each and every specific argument: i.e., one can define an inner product of the form [imath]\vec{\Psi}^\dagger \cdot \vec{\Psi}[/imath].

 

9. These three imply that, among all the possible functions [imath]\vec{\Psi}(\vec{x})[/imath], the one which yields [imath]P(\vec{x})=\vec{\Psi}^\dagger(\vec{x}) \cdot \vec{\Psi}(\vec{x})[/imath] must exist.

 

10. The above implies that any specific explanation of anything can be mapped into a specific function [imath]\vec{\Psi}(\vec{x})[/imath].

 

11. If two different people discover exactly the same explanation of a given specific set of ontological elements their explanation must be representable by exactly the same function [imath]\vec{\Psi}(\vec{x})[/imath]: i.e., for any given set of specific ontological elements, [imath]P(\vec{x})=\vec{\Psi}^\dagger(\vec{x}) \cdot \vec{\Psi}(\vec{x})[/imath] must yield exactly the same probability.

 

12. That result can not depend upon the actual numerical labels they happen to put upon those undefined ontological elements. Thus it follows that the function so defined must display any and all symmetries conceivable within that set of labels. (I actually suspect this is the one which bothers you the most.)

 

13. Shift symmetry can be reduced to equivalence with a partial derivative.

 

14. Given any set of known undefined ontological elements, there always exists a set of hypothetical ontological elements which, under the constraint

[math]\sum_{i \neq j}\delta(x_i -x_j)\vec{\Psi}(\vec{x})=0[/math]

 

(where [imath]\delta(x)[/imath] is the Dirac delta function) will allow only the known ontological elements to exist.

 

15. That the constrains on the three derivatives I obtain plus the Dirac constraint are identical to the implied constraints imposed by

[math]\left\{\sum_i \vec{\alpha}_i \cdot \nabla_i + \sum_{i neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\psi} = K\frac{\partial}{\partial t}\vec{\psi} = iKm\vec{\psi}.[/math]

 

together with

 

[imath][\alpha_{ix} , \alpha_{jx}] \equiv \alpha_{ix} \alpha_{jx} + \alpha_{jx}\alpha_{ix} = \delta_{ij}[/imath]

 

[imath][\alpha_{i\tau} , \alpha_{j\tau}] = \delta_{ij}[/imath]

 

[imath][\beta_{ij} , \beta_{kl}] = \delta_{ik}\delta_{jl}[/imath]

 

 

[imath][\alpha_{ix}, \beta_{kl}]=[\alpha_{i\tau}, \beta_{kl}] = 0 \text{ where } \delta_{ij} =

\left\{\begin{array}{ c c }

0, & \text{ if } i \neq j \\

1, & \text{ if } i=j

\end{array} \right.

[/imath]

 

This is a mere fifteen steps from absolutely no presumptions to the absolute truth of some very specific conclusions. Your doubt must arise in (or in between two or more of) these propositions. Please point out the statements which engender doubt and maybe a short note as to why.

 

That is, up to this point, the given equation is a direct consequence of the given definitions and, as Buffy has said a number of times, has nothing do with reality at all. It is no more than a constraint on the specific function which represents a specific self consistent explanation.

 

Or is it the fact that, although you might agree that the equation is valid under my definitions, you don't see the value of such a fact. If that is the case, then just stick around and I will show you what can be deduced from that equation. I might comment that, under the common interpretation of physics, I should be able to deduce absolutely nothing of value as what I have presented is a pure mathematical tautology and the only physics relationships which can be implied by such a tautology are tautological relationships. My real problem is that physicists just don't like to be told that their grand theories are tautologies.

 

Have fun – Dick

 

By the way Qfwfq, I will be out of touch with the internet from this coming Sunday until the fourth or fifth of December so you can take a couple weeks to decide what bothers you.

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Wow! That's the most concise and to the point summary I've seen you giving so far! ;) That's good. :(

Finally no bad squirrel decisions, no beating around the bush...

 

There are a few of the points I'll need to ponder and some that I do have doubts about so I'll be back with a more detailed critique when I can. :hyper:

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Well, you could put it in such words as a non-physicist, usually a Schrödinger equation is seen as being the description of dynamics for the quantum state. But, of course, this is a worldview, isn't it?

 

Hmm, I don't know. I mean, interpreting the meaning of Schrödinger equation is certainly up to one's worldview. But looking at DD's analysis, it suggests that Schrödinger equation is (almost) like a succint expression of those initial symmetries. I guess you could say; as long as you identify elements and their behaviour (from patterns in some raw data) in a way that does not violate those symmetries, Schrödinger equation is valid (at least approximately?).

 

Anyway, since I'm not familiar with the equation itself, I am interested of how people usually interpret Schrödinger equation - for historical reasons or otherwise - so can you elaborate on what it means that it describes the dynamics of the quantum state? You mean, along with a defined wave function, or even without?

 

Looking at the wikipedia page, I saw this: "The Schrödinger equation tells you the behaviour of [imath]\psi[/imath], but does not say what [imath]\psi[/imath] is."

 

So that's why I started thinking about "something that serves as a constraint to what the wave function can be"

 

The solutions that aren't normalizable aren't a philosophical problem, if I haven't totally misunderstood what Dick means by them but I'm supposing he means the quasi-eigenstates in the case of continuous spectra. These are a mathematical problem but not an unsolved one; the strict treatment was outlined in my third year course on the formalism, just to show that applying the eigenvalue-eigenstate apparatus isn't BS. The eigenstate isn't an element of a Hilbert space, the math is more complicated but it has been worked out. :)

 

I'm not entirely sure what you are saying... :I That there are solutions that are not normalizable but they can still be used to yield correct results? Something like that?

 

Maybe that's even the same reason why Dick and I so often rant against each other without realizing that we're not actually contradicting the other but saying the same thing in different words! :hihi:

 

Communication is hard when no one is using exactly the same terms with exactly the same meanings...

 

Trouble is that I don't see how Dick's argument is conclusive and so I don't so far find it being a satisfactory wayout for the mysteries of modern physics. :shrug:

 

Well, in one sense it doesn't explicitly say anything about the ontological reality. On the other hand it seems to shed light on what circumstances lead us to classify unknown data in such and such ways in our head.

 

I would like to know which parts of it seem valid to you. Do you find the derivation of Schrödinger equation valid, given the fundamental equation as a starting point?

 

As an additional commentary, seems to me that any attempt to understand the mysteries of modern physics must take into account our "methods of understanding", and explicitly understand that any identity we place on any "thing" is a matter of defining things that way, rather than a matter of measuring something "objectively". Objective measurement is something that does not exist because we always measure something that we have circularly defined in our head (and does not exist in different worldviews).

 

What I'm getting at is that reality does exist, but it seems rather mysterious or paradoxical to us in our head, so we must have made some bad assumtions somewhere. I.e. the mystery exist in our heads; maybe there is a problem in the very method we humans use to "comprehend" anything at all.

 

I think it's rather healthy to recognize that QM world seems mysterious because we first we assume certain identity on things (incl. spacetime), and consequently find out that those identified things don't seem to behave in very, let's say "intuitive manner". But at all times the mystery is seen in the behaviour of things we defined ourselves. We should think long and hard what does it even mean when we "identify elements as themselves".

 

-Anssi

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I do agree that quantum reality indicates that our "normal" notions are only the way we perceive things but not the way they are. It isn't easy to say what exactly is at fault, but I think our minds aren't designed to understand the actual reality; I also said this here. So the mystery is due to our inability to understand the ding-an-sich; as our observation gets closer to it, the phenomena are just plain counter-intuitive.

 

From the point of view of the physicist (without so much attention to ontology etc.) the Schrödinger equation just describes how the state changes over time, for a system represented by a given hamiltonian. That's what is meant by the dynamics of the quantum state. If you like, you can look up hamiltonian and lagrangian formulation of dynamics, including Nöther's theorem which is the cornerstone of modern reasoning by symmetries in mechanics.

 

So that's why I started thinking about "something that serves as a constraint to what the wave function can be"
A source of confusion is in the fact that, in basic QM for describing things such as atomic orbitals, there are actually two Schrödinger equations: one is the "real" one and the other is just a descrition of energy eigenstates and is called the "steady state Schrödinger equation". Actually it's an eigenvalue equation, which can be derived from the true Schrödinger equation; it is used for deterimining what the energy eigenstates (the orbitals) are.

 

I'm not entirely sure what you are saying... :I That there are solutions that are not normalizable but they can still be used to yield correct results? Something like that?
Well let's say that the actual physical phenomena are normalizable states. For continuous spectra you don't really have an eigenstate but these are necessary for using the formalism; these aren't normalizable but an actual realistic state will be a distribution. I don't want to bury you in nerdish mathy jargon but I definitely see no philosophical problem.
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I do agree that quantum reality indicates that our "normal" notions are only the way we perceive things but not the way they are. It isn't easy to say what exactly is at fault, but I think our minds aren't designed to understand the actual reality; I also said this here. So the mystery is due to our inability to understand the ding-an-sich; as our observation gets closer to it, the phenomena are just plain counter-intuitive.

 

Yes... I definitely agree with that, and, I really would not want to sound pompous, but I think I have a pretty good idea of what the fault is.

 

It's that we understand reality as a set of entities in the first place. Entities, as in "physical objects", or as in "spacetime" (or whatever framework is necessary to give meaning to the behaviour of those "physical objects")

 

If you see "a flying ball" it means you have tacked identity on a pattern, you call it "a ball", and you can predict where it lands. You could also, just as an example, comprehend that situation as a stable moving space-warp-distortion-thingie without any real identity to the "ball" itself. That would mean you'd tack identity to "space" instead of to the "ball"; equally invalid.

 

Certainly there are survival benefits to being able to break reality into set of clearly defined "things" (that consequently exhibit some predictable behaviour; the definition kind of is the behaviour). We can make a quick and meaningful prediction about a "rock rolling down the hill towards me" because we have placed identity on the rock, and we have an idea about how rocks behave. (Or to put it another way; we recognize the rock by recognizing familiar "behaviour" or "pattern")

 

If you try to imagine reality where absolutely nothing has got any real identity to itself, you will fail. It is simply not possible to think, without thinking about some thing(s). Our subjective world works exclusively in terms of "things with identity". Do you know what I mean?

 

I guess it's because "things with identity" is so central to our thought processes, that most people will have very great difficulties understanding how ontological reality could possibly exist without having any identity to its components. We just always revert to thinking in terms of "entities", even when we know we first had to define those entities from the patterns (whose real source is not known). The point to notice here is that it is ontologically meaningless to say that the "ball" is the "same ball" from one moment to the next, because that is just a matter of defining "a ball".

 

(At this point I should also comment that all the "could be" arguments are somewhat moot because there's just no way of proving one way or another)

 

And that is what I mean by "fallacy of identity". Even the term "thing in itself" is a misleading misnomer; as soon as you invoke an idea of "a thing", you're lost.

 

And here's also why I find DD's analysis so reasonable. To an extent, you can look at it as a description of how data gets to be interpreted as "set of things which exhibit simple behaviour". Almost like a method of classifying data into simple "objects". With that tack, it is not too surprising to find epistemological reasons to our common interpretation (or perception) of reality. E.g. technically we could have classified reality in components that don't obey newtonian laws, but something more complicated with a lot of "special rules". But instead we have defined entities in such a way that newtonian laws are true... ...to those things we defined.

 

So on the context of quantum mechanics, seems to me that it really just starts to shine through how the identity of "things" is not a property of reality as much as it is a property of how we constructed our worldview. There is certain familiarity and repetition to the patterns that we see in QM, but placing uncalled identity on things (that we assume to exist in the situation) will cause trouble in a very concrete sense. That doesn't mean it wouldn't be possible to assume a clearly defined ontology; certainly it is possible to assume many. Just, there's no way to know.

 

From the point of view of the physicist (without so much attention to ontology etc.) the Schrödinger equation just describes how the state changes over time, for a system represented by a given hamiltonian. That's what is meant by the dynamics of the quantum state. If you like, you can look up hamiltonian and lagrangian formulation of dynamics, including Nöther's theorem which is the cornerstone of modern reasoning by symmetries in mechanics.

 

I spent quite a while browsing wikipedia, just had to dig in deeper and deeper in order to make any sense of the pages explaining hamiltonians. I learned something but not what I wanted to :I I would like to understand the formalism little better just to be able to communicate better, but it's a bit difficult to get a grasp of all that too quickly, at least with my math skills... And the limited time (actually it's already way too late for me to stay up as I'm typing this...) :/

 

-Anssi

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First, I will have very little time these days; I can't say as much as I'd like to.

 

If you try to imagine reality where absolutely nothing has got any real identity to itself, you will fail. It is simply not possible to think, without thinking about some thing(s). Our subjective world works exclusively in terms of "things with identity". Do you know what I mean?
Yup, I know what you mean Anssi!!!!

 

I guess it's because "things with identity" is so central to our thought processes, that most people will have very great difficulties understanding how ontological reality could possibly exist without having any identity to its components. We just always revert to thinking in terms of "entities", even when we know we first had to define those entities from the patterns (whose real source is not known). The point to notice here is that it is ontologically meaningless to say that the "ball" is the "same ball" from one moment to the next, because that is just a matter of defining "a ball".

 

...........................................

 

So on the context of quantum mechanics, seems to me that it really just starts to shine through how the identity of "things" is not a property of reality as much as it is a property of how we constructed our worldview. There is certain familiarity and repetition to the patterns that we see in QM, but placing uncalled identity on things (that we assume to exist in the situation) will cause trouble in a very concrete sense.

It's definitely hard to make head or tail of things this way, one tends to get into absurd ideas that are hard to discuss conclusively. Schrödinger for one came to believe that the actual reality is what his equation describes (the "waves" rather than the "particles") and so considered there to be no real problem in quantum physics. The famous cat gedankenexperiment was excogitated by other physicists to confront him with and snap him bach into a bit of healthy realism. The trouble is that, in some measure, the optical visual is the reality; it's all a matter of coherence and decoherence.

 

I spent quite a while browsing wikipedia, just had to dig in deeper and deeper in order to make any sense of the pages explaining hamiltonians. I learned something but not what I wanted to :I I would like to understand the formalism little better just to be able to communicate better, but it's a bit difficult to get a grasp of all that too quickly, at least with my math skills...
I know, it's not easy without the math but what you need is just an outline of things, an idea of what physicists and mathematicians are talking about when they use such terms. They are fundamental to gaining an insight of how the quantum formalism really works and I think you're needing to understand that better if you want to form a judgement that bears any weight. You need to start with something fairly brief and concise about classical (non quantum) analytical mechanics, then see how quantum formalism is built upon it. Trouble is, what is brief and concise either isn't introductory or isn't much to go by.

 

My time here is ending soon.

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