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I have been trying to work out how to prove theat Quatum Superposition is contradictory rather than just contraintuitive, as claimed in the propaganda put out by the QS evangelists. One of the difficulties is that their arguments are actually rather vauge when you try to analyse them.
What is worse is that if you accept the QS contradiction, then any resulting contradictions simply become "evidence" to support the original position.

I think I have managed to identify the central flaw in their argument. As the QS argument is actually an argument by analogy, it has to be approached the same way:


If we apply the same logic to solving a simple equation that the Copenhagen Interpretation of Quantum Mechanics applies to solving the Wave Equation, we would conclude that an unknown point on a line is a superposition of all points on the line, which would then collapse to a single point when solve the equation.

Stating this in Set Theory form, they claim that an unresolved solution to an equation is the set of all possible solutions, which then collapses to being one member of the set when the equation is solved.

This is clearly wrong - while the unresolved solution can be any one of the possible solutions in the set, it remains a solution and does not become the set (I am ignoring cases where the solutions are also sets).

While a line can be considered to be the superposition of all points on the line, it is incorrect to claim that an unknown point on a line is the superposition of all points on the line. A point is a point, while a line is a set of points.

Going back to QS, it is clear that they are treating the unresolved Quantum State of an electon as being the set of all its possible states. This is contradictory.

In the point on the line example, the superposition of all the solutions is the line. If my logic is correct, then it may also be possible to identify what the superposition of all electron quantum states really applies to. Obviously it is something to do with all possible states of electron "orbitals" around an atom rather than an individual electron.


Can anyone see any holes in this, or a better way of stating it?

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I hope you didn't get a hernia trying to create the above analogy. ;-)

I have a lot of problems with the standard explanations of QM. I find what you wrote equally convoluted. I don't see that it proves or disproves anything.

That one side of an equation contains nonsense does not mean one can refute it with nonsense.


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I seem to recall that in P.A.M. Dirac's book "The Principles of Quantum Mechanics" he says that supperposition is a reasonable assumption. I don't have my copy with me so I can't give a page reference right off the top.

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The universe isn't Newtonian. Get over it.

Whatever you propose must match empirical observation. If you find a mistake in quantum field theory, you are wrong. Ditto Special and General Relativity. There are no contradictions, there are no paradoxes, there is not a single empirical falsification overall. That the two theories are incompatible where they overlap is part of their charm.

Now go look up where quantum field theory and Relativity contradict and why there is no observation to settle the dispute.


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http://www.mazepath.com/uncleal/qz3.pdf
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Pretty close to the mark Al with one caveat.

We know that those theories are not complete. We know, further, that additional observations must demonstrate some inconsistencies.

They will, however, be evolutionary ... not revolutionary ... so your basic premise is valid.


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dr_rocket said '.... in P.A.M. Dirac's book "The Principles of Quantum Mechanics" he says that supperposition is a reasonable assumption.'

This is interesting as just about everyone else says that QS is "Contra-Intuitive" and talk about "Quantum Weirdness".
---------

Uncle Al said "... Whatever you propose must match empirical observation."

I am not proposing anything, merely pointing out what appears to be a fundamental logic error in the case for Quantum Superposition. The Scientific Method only requires empirical observation to test an hypothesis which is logically consistent. If the hypothesis has failed the logical consistency test there is no point progressing to observational tests.

However the requirement to test a hypothesis by empirical observation is relevant, as this does not appears to have been done for Quantum Superposition (there are some circular arguments to do with entanglement but these prove nothing, and the non QS interpretation handles them without breaking conservation of information).
If there are any observations which support Quantum Superposition, surely these would be refered to by anyone writing about QS? I have not come across any references to experimental evidence in Physics texts, Science history, biographies and science magazine articles dealing with Quantum Theory.

Please note that I am not talking about Quantum Mechanics - only the Quantum Superposition component of the Copenhagen Interpretation. Therefore I do live in a Quantum universe rather than a Newtonian one - its just not a Quantum Superpostional Universe (unless someone comes up with some good evidence).
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DA Morgan is convinced that QS can evolve to overcome its inconsistencies (yet in a previous post he seemed to be agreeing that it was nonsense?).

While theories which are basically right can evolve to become more accurate or be extended to become more general, theories with fundamental flaws require revolutionary change.

I suspect that some of the lack of progress in String Theory, etc, may be related to bad assumptions in the Copenhagen Interpretation.

------------

Finally, I agree the logic is somewhat convoluted, and while some of this may be due to my wording, etc, most of it is due to the convoluted nature of the QS argument.
By the way DA, the analogy was quite easy to produce - all I did was take the QS logic and apply it to solving a simple equation. I tried to use the QS terminology as much as possible, except for the reference to set Theory.

I am dissapointed that no one who replied so far actually tried to adress the logic of my argument. Maybe I should be encouraged that they did not spot any obvious logic errors, even though it is as convoluted, and they don't seem to have been trying very hard.

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I didn't say what you think. QS is QS is QS. I said current theory will evolve to overcome inconsistencies in its explanation.

You can not argue with QS. We observe it.

What is open to argument is our explanation as to what it is we are observing and why.

Peter wrote:
"By the way DA, the analogy was quite easy to produce - all I did was take the QS logic and apply it to solving a simple equation."

This may be what you think you did. But it is not what this reader read.

Find fault in your argument? I didn't see that you had one. What you wrote looked to me something like:

Why does a mouse when it spins?
Because the higher the fewer!

There was no substance I could find to refute. Thus I referred to your analogy as needing oxycodone.


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QS is an idea.

You can't observe an idea, but you can argue for or against it.
You can even argue against a belief, but what you can't argue against is unreasoned faith.

Even though you can't observe an idea, you can observe phenomina which either support or refute the idea. DA keeps refering to observation, but so far he has failed to produce any. Where is this experimental evidence which supports the QS hypothesis?
I don't think that there is any, otherwise we would have been bombarded with it.

------------------------------------

Lets consider a little bit of Science history.

The Ether was also an idea in which Scientists beleived without any reservation. Sound and Water waves need a physical medium, so by analogy, everyone thought that Electromagnetic waves needed a medium too. They thought that their logic alone was sufficient proof for the Ether and never even considered the need for experimental verification.
When two of them ran an experiment designed to measure the effect of the Earth's motion through the Ether on the speed of light in different directions, they failed to find any. As a result, the experiment became famous and the idea of the Ether faded away.

Quantum Superposition is an idea which does not seem reasonable or obviously true, and most of its strongest proponents like to stress this (based on the volume of "Quantum Weirdness" articles in Science magazines, they even seem to glory in it.).
One of the early promoters of QS boasted to reporters that he regularly "believed three impossible things before breakfast".
Despite its counter-intuitive nature and the lack of any supporting experimental evidence, the QS Hypothesis was quickly accepted and acclaimed as a proven Theory. While some Physicists argued against QS, they were up against a large, vocal and influential group, and so they gradually fell silent under the pressure.

All that is generally remembered of the debate now is a snide putdown, the posturing of "three impossible things", and "Shroedingers Cat".
This is in stark contrast to other major Scientific paradigm shifts, where the main evidence and arguments for and against the new and old models have been preserved.
This failure to safegaurd the evaluative evidence suggests that the debate was fundamentaly ideological/philosophical, rather than Scientific.

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My error: I misread what you wrote. I think QS a remarkable demonstration of our lack of ability to understand a natural phenomenon and little else.


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Hi Peter Bmn,

I think that there is some deep confusion here. I thought my reference to Dirac might clear it up, but it seems not. One must keep in mind that Dirac was the first to propose quantum mechanics in the essential form that is now used.

QM notions were originally introduced Planck and then Einstein. This was followed by a provisional QM developed by Neils Bohr using Rutherford's idea of the nuclear atom with some hints from spectroscopy. This theory was further developed by Wilson and Sommerfeld, but was rather limited in its scope. It was clearly realized that the theory was limited and this gave an impetus to develop a better quantum theory. This was done first by Heisenberg in his Matrix Mechanics, which he further developed in conjunction with Born and Jordan. (Bohr, Heisenberg, Born and Jordan essentially "were" the Copenhagen school.) Shortly afterward, Schrodinger, expanding on De Broglie's ideas, developed his version of quantum theory known as Wave Mechanics.

This was an uncomfortable situation - having two theories developed from completely different approaches, yet describing the same thing. It was Schrodinger who realized that the two theories were just different representations of the same underlying base. It was Dirac that first sorted it all out and came up with the "operators on Hilbert space" idea. His approach was further developed by von Neumann and many others and eventually leads to quantum field theory and so on.

Ok, that's all well and good you say, but where does superposition come in? In the first place the development of quantum theory was in response to several big glitches between experiment and classical theory. These include: anomalous specific heat, atomic stability, atomic emission spectra, the law of equipartition of energy, the photoelectric effect - the list goes on and on. It was these experiments that forced the introduction of quantum ideas including superposition. In particular, Dirac gives two examples in his:

P.A.M. Dirac (1902-1984)
The Principles of Quantum Mechanics (4th Ed.)
The Oxford University Press, 1958

in articles 1 through 3. These are the Young's Double Slit Experiment and the Photoelectric Effect. In article 4 he goes into quantum superposition at length using these examples as fodder. He explains that some kind of a vector space is required to deal effectively with the experimental facts.

The Hilbert space that he uses is a "souped up" vector space. Dirac's book is a model of clarity if you have the math. If not, the first part is non-mathematical and is largely in English. The best thing is that it gives a good account of what the motivation is for quantum theory. It is worth a read.

The point that I am trying to make here is that there is nothing contradictory or illogical about the superposition principle in QM. It is an odd concept and as Dirac points out you just have to get used to it.

In you original post you said" "... a simple equation that the Copenhagen Interpretation of Quantum Mechanics applies to solving the Wave Equation ..." I find myself wondering, specifically, what equation you are talking about? You say, further on that "This is clearly wrong". Since you are not specific this is not at all clear.

I'm not trying to be critical here. However, you ask "Can anyone see any holes in this, or a better way of stating it?" If you were to carefully state the arguement, perhaps I could find out what the problem is.

Dr. R.

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dr_rocket,

i congratulate you on a clear exposition of current dogma. There is, however, one problem I would like you to comment on. What does the single-particle Schrodinger equation describe when applying it to an electron: it MUST BE a single electron. Thus, all the possible solutions MUST EACH represent a single electron. If there is no electron in a specific allowed energy state, can that state manifest? I say NO IT CANNOT. So how is it possible that in free space one can superpose states, each of which is not an electron ("empty" states), and then equate the superpostion to a "single electron"? It is just
B(C)S again!! (without the C just as in superconduction; is it not?)

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Quote:
........
The fact that there is confusion and contradction with superpoosition understanding by pseudoscience crooks, does not mean that Quantum Theory itself has a problem as such.
It is abused by ignorant scoundrels, is anaother matter.

ES

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I think Relativity and QM have convincingly shown that the (so far) best explaantion of nature's behaviour is utterly incomprehensible to the human mind - Set Theory is just one formalisation of human thought, so it is not surprising that Set Theory makes contradictions emerge.
It is useless to apply logic to QS, because logic has been built up by man - and man is the product of evolution. The reasoning is the following: Evolution built a suitable animal - with the mental representations just useful to survive and reproduce. We cannot understand the "logic" of QS just as we cannot conceive or imagine a 4-D space. It was simply evolutionarily useless to be able to perceive 4 or more dimensions. Much in the same way we developed a "logic" that is suitable to survive. The logic (and Set Theory) are just refinements of our intuitional thought (the evolved one), and carry exactly the same limitations as the original ones. So, no wonder that we (and logic, and set theory) fail to "understand" QS, which then remains the best explanation.
When I (and Uncle Al above) say "best", I refer to Lakatos's definition of "best theory". I.e., it does not matter how crazy or illogical a theory appears, the only judge of its validity is experiment (see also Feynamn, etc.)

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Quote:
Originally posted by alessio toraldo:
I think Relativity and QM have convincingly shown that the (so far) best explaantion of nature's behaviour is utterly incomprehensible to the human mind -

When I (and Uncle Al above) say "best", I refer to Lakatos's definition of "best theory". I.e., it does not matter how crazy or illogical a theory appears, the only judge of its validity is experiment (see also Feynamn, etc.)
We must be careful not to go back to the dark ages when it was reasoned that man cannot comprehend because the god's doe not allow it. The statement that QM is utterly incomprehensible could just mean that we interpret it incorrectly. I believe the latter to be the case.

YES!! there is only one test for a theory and that is experiment. My theory on superconduction models experimental results which BCS cannot; however, my theory is still attacked to protect BCS: see the thread: modelling superconduction 2. Strange is it not?

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Get over it JB. No one gives a rip about protecting BCS. In fact if I could find anyone that thought you credible they'd be standing in-line trying to be your coauthor to be able to claim they were part of the new paradigm.

Your sour grapes have made whine ... not wine. What is stopping you from being accepted and successful is your attitude not whether you are right or wrong.


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Quote:
Originally posted by DA Morgan:
Get over it JB. No one gives a rip about protecting BCS. In fact if I could find anyone that thought you credible they'd be standing in-line trying to be your coauthor to be able to claim they were part of the new paradigm.

Your sour grapes have made whine ... not wine. What is stopping you from being accepted and successful is your attitude not whether you are right or wrong.
And you call yourself a scientist? If Newton was evaluated on his "attitude" instead of his "Principia", we would have lost valuable physics. Thank God there were no D A Morgan's alive during that time. I find that you are the one with the attitude. You have not contributed anything to the discourse that is scientifically valuable. Try and argue science instead of becoming uptight on your perceived "attitudes" in other people.

BTW what type of a person would like to become a co-author to a paper that he/she did not contribute anything to? This is another problem, like peer review, which have to be looked at in depth. The integrity of science is under attack.

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Actually I do. A belief system apparently subscribed to by a a couple of universities and a few publishers of peer reviewed journals I might add.

You've got your ego so wound around the axle you can't even tell when someone is trying to help you.

The reason I am suggesting a coauthor is that you need someone else to make a contribution. JAG, for example, could have made a substantial one if you allowed it. And you need someone who isn't going to be calling an editor an idiot. That might be the biggest contribution of all.


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Quote:
Originally posted by DA Morgan:
Actually I do. A belief system apparently subscribed to by a a couple of universities and a few publishers of peer reviewed journals I might add.

You've got your ego so wound around the axle you can't even tell when someone is trying to help you.

The reason I am suggesting a coauthor is that you need someone else to make a contribution. JAG, for example, could have made a substantial one if you allowed it. And you need someone who isn't going to be calling an editor an idiot. That might be the biggest contribution of all.
I am sure you are intelligent enough to realise that I will not respond to such nonsense. JAG is also intelligent enough to make a follow-up contribution by writing his own papers on the subject instead of requiring coattails. Let us just accept that the way you see scientific practise, I will always find unacceptable. I can assure you that it falls outside the accepted moral rules that Sigma Xi has drawn up about co-authoring.

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Hi Alessio,

You said: "I think Relativity and QM have convincingly shown that the (so far) best explaantion of nature's behaviour is utterly incomprehensible to the human mind ..."

I have to take issue with this statement. In the first place the theories mentioned are not explanatory. They are, in fact, descriptive theories. This is especially true of QM in the form of matrix mechanics. Heisenberg made it a point to avoid explanations. He was worried that Bohr's "stationary electron orbits" were unobservable in principle. His whole thing was to develope a calculus of observables. Special relativity is a description of the consequences of measuring position and time by operational means. The general theory of relativity is description of the geometry of space in the presence of matter and energy. These theories explain nothing while each describes a part of Nature.

The remarks about set theory and logic are either irrelevant or unfounded. The arguement concerning evolution and human capabilities is plainly specious, not to say, bordering on pretentious. To see this note the use of the word "built". There is too much vague baggage associated with this term.

You say: "We cannot understand the "logic" of QS just as we cannot conceive or imagine a 4-D space."

Maybe "we" cannot but, I know several mathematicians and scientist who would disagree with you on this. Some are so good at it that they might be called multidimensionally adroit.

As I recall Imre Lakatos wrote mostly about mathematics and philosophy. I don't recall a single scientific paper in his collected works. It seems that this non-scientist was attempting to find a middle ground between Karl Popper and Thomas Kuhn and thier concepts of how scientific changes take place. While I have the highest respect for these three great thinkers, I believe that Planck, Bohr, Heisenberg, Dirac, Schrodinger etc. have much more to say on the subject and are far better qualified.

QM is a logical response to the facts of experiment. The mathematics involved is quite rigorous and not by any means the most abstract there is. This indicates that the physicists response to the demands of experiment are rational. QM is quite logical and can be dealt with by rational humans. The idea that QM is counterintuitive or defies comprehension is based on uninformed expectations.

I disagree with you on several points, but please do not take this as a form of disrespect. I am using your expressions as "grist for the mill" wink

Dr. R.

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That might sound weird after 3 years - it's only now that I realised somebody replied to my post.
Briefly - it is entirely clear that you do not know anything about philosophy of science. Let alone about Lakatos, which clearly you did not read a line of. Moreover, you're trapped in a notoriously empty distinction, the one between "description" and "explanation".
Moreover, the opinion I expressed is definitely founded. Many philosophers of science accept it as a standard view.
Your disquieting statement that "Lakatos did not ever publish a scientific paper" does not need any further comment - apart from classifying it as a (not very elegant) version of the middle-ages principle of authority.
Incidentally, I am not a philosopher of science.
Please study more about what you are willing to speak about before "disrespecting" others.

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