Wikipedia talk:Requests for mediation/Zeno's paradoxes/Archive 1

Observations by Paradoctor

• Zeno's paradoxes is on 148 watchlists, and is viewed ~ 1000 times each day.
• Of the 1677 edits to the article, 247 (15%) are by JimWae, and 142 (8%) by Steaphen, that's 23% together.
• The three talk pages there comprise as of now 527k of text, give or take a few blank lines and the stray duplicate section. Of these discussions, only 126k, less than 24%, do not involve Steaphen.
• Steaphen's first edit was on 4 November 2006, three years ago. First discussion with JimWae two days later.
• Of Steaphen's 576 edits to Wikipedia overall, only two are not directly or indirectly related to Zeno's paradoxes and the talk page discussion there.
  • Correction: I overlooked half a dozen edits to this EAR.
• All of Ansgarf's 94 edits so far are either to the article or to discussions with Steaphen, or to the mediation page.
• I tried twice to calm down things. (Please note that I was not the only one.)

Paradoctor (talk) 14:20, 10 November 2009 (UTC)

Opinions by Paradoctor

• Even by a pretty generous account: The SEP entry alone has a much better set of references than our article.
• If you're masochistic enough to check, you'll probably find that neither of the involved parties ever quoted or cited the literature. I did see couple of (IMO incorrect) claims about what Zeno said or argued for.
• Under the same caveat as above, the involved parties stayed largely civil.
• Steaphen considers himself a "Belief Doctor®", which to me implies that his main occupation is convincing others of what he considers the right belief(s).

Addendum: Since Steaphen questioned the level of diligence in forming my opinion. (click "[show]") ->

• A Wikipedia search yields no results for "belief consultant" and three hits for "belief doctor", all your edits.
• I did read more about your life, which was decisive for my judgment.
• Quotes from above-mentioned page

These quotes establish sales as your main strength, for which "Belief Doctor®" is an apt metaphor, akin to spin doctor in political "sales".

• Talk page quotes

• In my opinion, this is enough to justify the assertion that you consider yourself a "Belief Doctor®". Your remark "despite the initial sting and whinnying, folk are, in my professional opinion, the better for it" is all the confirmation I need. I exercise my right to be treated by a doctor of my own choice.

Paradoctor (talk) 00:10, 11 November 2009 (UTC)

• For whatever is sacred to you's sake: Do not let yourself get dragged into discussions about the article's subject here. The only way of staying sane with paradoxes in general, and Zeno's dittys in particular is to stay glued to the literature. This is a difficult topic, about which some of the brightest minds in human history have disagreed about. Entire libraries have been written about this subject, so the chances of pulling something original or at least substantially correct from your own mind are less than slim. The chances of it being uncontroversial are less than zero.
• I'm no Buddhist, but DGAF has saved me considerable grief on this one.

Paradoctor (talk) 14:20, 10 November 2009 (UTC)

Criticism by Steaphen (click "[show]") ->

Ah, so now comes the personal attacks. Previously I provided a response to your criticism of my seeking "convincing others". I have not sought to criticise you, other than in reply to your criticisms. Again, how has my background any relevance to the issue at hand .. that of the inapplicability of applying infinite-series to Zeno's Paradoxes?

As I explained to JimWae, let's leave any further criticisms or opinions for the mediators. Cheers, Steaphen (talk) 00:23, 11 November 2009 (UTC)

Absolutely. Paradoctor (talk) 00:34, 11 November 2009 (UTC)

Thank you, Paradoctor. In the meantime, please remove the copyrighted material that you quoted above. Thanking you in advance. Cheers, Steaphen (talk) 01:17, 11 November 2009 (UTC)

I'm confident that these quotations are within acceptable limits. I do not consider them to be personal attacks, and Wikipedia is not censored. If you have further arguments, I'll gladly consider them. Failing that, and if my reply does not satisfy you, the next step would be to ask for editor assistance. Regards, Paradoctor (talk) 01:40, 11 November 2009 (UTC)

Paradoctor, I note that you have declined my request to remove the copyrighted material. Also, you have posted details of my background to this subject when it served no purpose to the issue at hand (that being the inapplicability of infinite-series to solving Zeno's Paradoxes). Steaphen (talk) 02:00, 11 November 2009 (UTC)

• I try to restrain myself, but if I let that one slide, I just as well might gnaw off my own leg: Steaphen's item 4: "reasonable" ... "to not draw the conclusion".

Wikipedia talk:Requests for mediation/Zeno's paradoxes/Archive 1/auxiliary box Also, the ellipses (...) make the paragraph look like a quotation. Is it?

My comments have been painfully researched.

— Ansgarf

Footnote: my comments have not been painfully researched -- I make them up as I go along. Much more fun, doesn't take much effort, and means I don't have to remember stuff ... I rely on quantum superpositioning principles, in that whatever I write, will be in effect right. Does take a bit of getting used to though (as any half-decent writer will appreciate :)

— Steaphen Pirie

My first reflex was to point out that it is "painstakingly" rather "painfully". But I think there is nothing I can say that would help. Paradoctor (talk) 16:07, 3 December 2009 (UTC)

It seems to me that it should indeed say "painstakingly", but my comment was commented on, before I could fix it. But it was also painful. Ansgarf (talk) 07:13, 5 December 2009 (UTC)

I'm afraid you're missing the point. Paradoctor (talk) 17:07, 5 December 2009 (UTC)

Reply by Steaphen to Paradoctor's observations and opinions

Dear Paradoctor, Thank you for the statistics. Interesting.

• A few corrections, or qualifications concerning your points. It is, in my opinion, disingenuous of you to say that I try to convince others of what is right. The mere fact that you have written here demonstrates that you attempt to do the same. It's called having an opinion.
• But more to the point, I ask questions that few others ask, it seems. As for "DGAF" my question is why then GAF for writing here. Again, highly disingenuous. If you're seeking to mollify things, you won't help by being hypocritical.
• As for staying sane, please speak for yourself. I'm comfortable with Zeno's Paradoxes, and with paradoxes in general. I wrote a whole book on them "Awkward Truths" about how paradox is central to life; about how they give us surprise and predictability, creativity that rides order and structure. Wonderful experiences can be had by enjoying paradox. I don't share your fears. Please don't bring them to this forum.
• Furthermore, I don't quite understand your reference to the original literature, if most of my edits have been to question what is currently being said that goes against scientific principles. In other words, if the article were to say something like, "according to historical records, Zeno said "blah, blah, blah" and from that others have attempted to use "mathematical model T" to resolve the paradoxes, but have now been shown to be invalid due to experimental evidence (examples a, b,c )" then there would have been far less edits.
• Finally, this issue is indeed controversial, but that is no reason to run away and wave the white flag. It deserves better treatment given its central place and importance in philosophical thought. It deserves far more discipline than has been shown. And it begs the question: What do you believe? Do infinite-series solve the paradoxes? If you believe they do, how do you reconcile them with the evidence that indicates otherwise? If you believe they don't, then fine. We're in agreement. Then all that's left is deliberations as to what is really going on. That's a whole different article, or book, or life. But my first question would be, "do you believe infinite-series resolve Zeno's Paradoxes?". To respond that you don't know, begs the question, "why then bother posting here?".

As a footnote, I would invite you to be more diligent when describing or referring to me. If you were to read my bio, you would find that I am, among other things, a "belief consultant". As for being The Belief Doctor®, that's my Registered Trademark, like "Coca-Cola" is for Amatil or whoever owns it. It's handy for marketing, identification and gives a quick conceptual insight into what I do (which is to heal and improve 'bodies of belief' in all areas of life). Sometimes that 'doctoring' involves "giving a shot to the arm", but despite the initial sting and whinnying, folk are, in my professional opinion, the better for it.

• Paradoctor, what exactly is the point of stating when I first made a post concerning this topic? What on Earth has that got to do with the issues being raised? As for being on a gazillion watch lists, so what? If fundamental violations of intelligent inquiry and scientific-method have been committed and remain intact, how is it that no one has previously spoken up? Have those who are on these watch lists been asleep, frightened, or too busy constructing white flags to offer intelligent critiques of the accepted dogmas that are, in the face of ample experimental evidence, no longer credible or tenable?Steaphen (talk) 21:23, 10 November 2009 (UTC)

• • Knowing the date of your first post establishes your behavior as long-term. The page statistics are a reminder that we are not alone in here, and that our actions potentially influence tens of thousands of readers. Paradoctor (talk) 00:18, 11 November 2009 (UTC)

• • • So what are you suggesting? That even though there may be great merit in the content of what one says, if the style or personality of the presenter doesn't quite suit you, that you can criticise the content, or disregard it? And this is supposedly helping to solve a physics problem, by bringing personality into it?

• • • Paradoctor, I think it best we leave further commentary for the mediators. Cheers, Steaphen (talk) 00:31, 11 November 2009 (UTC)

Steaphen's Resources and preparations for Formal Mediation Case

• Note to Ansgar and JimWae (the other two involved parties) -- you are both welcome to include your own resources and counter-arguments. However, please do so in your own sections. Please do not add comments or opinions to this section.

Facts and supporting evidence that the deterministic basis upon which infinite series solutions are reliant is untenable:

1. An experimental test of non-local realism:
   "Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affect by actions in spacelike separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned."

   Conclusion: in particular "we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations".

   From the article, "it is reasonable to consider the violation of local realism a well established fact" -- infinite-series rely on "local realism" as they require point-for-point, local, real points traversed. In light of this experimental evidence, and the clear conclusions drawn, there are insufficient grounds for assuming that infinite-series solutions, reliant on localism and realism are valid or tenable. The application of infinite-series to the movement of objects (Zeno's arrow, runner, tortoise etc) requires that at every position and point in time, those objects remain physically real and local. They necessarily must remain local due to the deterministic correlations of actual position with the calculated position. Similarly, by using infinite-series the objects must remain entirely 'real' (tangible, measurable, observable) at any and every point.

   The evidence and quantum theory has shown the assumptions of locality and realism to be invalid. For infinite-series solutions to meaningfully resolve the paradoxes, experimental evidence would need to show how localism and realism (upon which infinite-series are entirely reliant) can be substantiated. Based on the available evidence, infinite-series solutions are not able to meaningfully resolve the paradoxes (not even as a "proposed solution").

This research does not constitute "original research", it is merely revealed here to demonstrate that the assumptions upon which various statements on the main page of the article "Zeno's Paradoxes" are asserted, cannot be supported (even theoretically), or verified by experimental evidence.

Specifically, the statement "using ordinary mathematics we can ..." (on the main page) is unsupportable conjecture that has little relevance or application to resolving Zeno's Paradoxes.

Note to Ansgar and JimWae: you may wish to review Fig. 3 (of the referenced article An experimental test of non-local realism) which displays the "Experimental violation of the inequalities for non-local hidden-variable theories (NLHV) and for local realistic theories (CHSH)"

It should be evident to even the lay reader that infinite-series are based on a local realistic (CHSH) model, which according to the evidence is clearly not within any reasonable range of error, in regards to the data. In fact the CHSH (infinite-series) model (flat-line) reveals an almost complete lack of correlation with the data (strikingly, Fig.3.b. reveals an extraordinarily similar lack of correlation as would be typical of how little a flat-earth view correlates with the curved/round earth).

For any reasonable thinker who reviews the data, infinite-series solutions are theoretical models that, even though they offer crude approximations sufficient for practical use by engineers, provide no credible resolution to Zeno's Paradoxes.

2. There is simply no evidence that infinite-series can be meaningfully applied point-for-point to the movement of objects (be they particles, people or planets). Nor are there any Reliable Sources confirming as much.

   However ...

   Calculus has been, and remains highly useful in describing the trajectories of satellites, falling bodies, planets, growth of bacterial populations, the rates of change in chemical reactions, and the statistical distributions in the social sciences -- to name a few of its applications.
   

   But in none of those applications does calculus provide exact, precise descriptions or predictions of the movement of large bodies, or the rate of growth of populations etc. It is only in relatively crude terms that calculus is useful, when the scale of perceived movement or collective change is well above quantum increments and scales.
   

   Zeno deliberations concerns the finer detail of movement, below that of the relatively large scales handled by calculus (Newtonian physics). [This is due to calculus being based on the inferred summations of collective points/particles/people, and cannot therefore fully predict or explain the actual behaviour of an individual quantum/particle/person. Those who argue otherwise are simply not seeing the trees for the forest.]

   In view of the evidence - as provided in An experimental test of non-local realism which clearly demonstrates how a local-realistic (Newtonian/infinite-series) model fails at small scales - we are only justified in saying "Using ordinary mathematics we may calculate when Achilles will approximately overtake the tortoise." But we may not say, with any credulity or substance that we can calculate when the runner will precisely overtake the tortoise. To do so is simply bad science, based on crude approximations that fail close scrutiny, application or analysis.

3. Respondents to this site seem to believe that quoting theorems (such as Ehrenfest's Theorem) that involve "expectation values" and "rules of thumb" are in some way able to add merit to the absolute-deterministic application of infinite-series to the physical movement of objects. Infinite-series do not involve "expectation values" or "rules of thumb" -- they state categorically, clearly and precisely a 1:1, point-for-point correspondence between predicted physical values and actual physical values, which through quantum research is known to be plain and simply wrong. Infinite-series cannot be meaningfully applied to solve Zeno's Paradoxes.
4. It is frequently argued that the mathematics of infinite-series is correct, when applied to Zeno's Paradoxes. However, there has been no evidence that shows, or Reliable Sources who claim, that infinite-series can be applied point-for-point to the actual movement of physical objects, such as runners, arrows etc.

   In other words, despite the efficacy of "ordinary mathematics" in providing crude approximations that have proved useful to engineers and many scientists, an exact correlation of the mathematics with actual physical movement has not been demonstrated or substantiated.

   The assumption of point-for-point calculations of position and speed of objects relies on a CHSH (local realistic) model that is (see point 1 above) not able to be correlated with the facts.

   In summary, there is no evidence or Reliable Sources FOR (The assumption) and substantial evidence AGAINST the assumption of the relevance and applicability of point-for-point calculations (using infinite-series) of position and speed of moving objects.

   Thus the statement "using ordinary mathematics we can calculate" when a runner overtakes a tortoise is conjecture without substance or basis in fact, and represents a biased point of view (POV).

5. The de Broglie wavelength of an object (e.g. Zeno's arrow) is :$\lambda ={h}/{p}$ (where p = momentum). This is a mathematical expression relating position and momentum to probabilities. It's a mathematical expression that is unrelated to any need for measurement. Actual experimental evidence confirms the wave nature of physical objects (experimentally verified for C₆₀F₄₈, a fluorinated buckyball with a mass of about 1600 u, composed of 108 atoms).
   
   This mathematical expression, independent of the need for any measurement reveals the deeper probabilistic non-deterministic nature of physical reality.
   
   The infinitesimal precision of the object's position or any part thereof (as required by infinite-series solutions) requires that $\lambda$ approaches zero (since the de Broglie wavelength of the object indicates the range of possible positions and momentums of the object).

   From the Wikipedia entry Matter wave "given the enormous momentum of a person compared with the very tiny Planck constant, the wavelength of a person would be so small (on the order of 10⁻³⁵ meter or smaller) as to be undetectable by any current measurement tools".

   However, the infinite-series solutions require that the precise and exact location and speed of Zeno's runner can be calculated.

   For this to be applicable to a runner (even for a heavy runner, at considerable speed) $\lambda$ must approach zero (to ensure a short sharp pulse with infinite precision, exactly matching that of infinite-series). However as $\lambda$ approaches zero, p (momentum = mass x velocity) approaches infinity. Thus, to precisely predict (calculate) a runner's location at some arbitrary point in time t (as is expected using Newtonian mechanics/infinite-series), requires the object to have infinite mass, and/or infinite velocity.

   Despite the fact that the calculated wavelength for a runner, tortoise or arrow might be immeasurably small (short), it is still some finite wave-length. This finite-wavelength categorically conflicts with the necessarily infinitely-short wavelength required by infinite-series. This undeniably rules out infinite-precision/infinite-series predictions of when the runner will overtake the hare.

   The inability to calculate (even in theory) when the runner will (precisely) overtake the hare is not due to clumsy scientists, with fat fingers using blunt measuring instruments.

   Many respondents on the talk page confuse the inability to experimentally measure the speed and location of objects as being a limitation of technology. Quantum theory requires that the uncertainty is an aspect of deep reality, and is unrelated to whatever apparatus or means is used to measure or observe the object. Quantum Theory describes deep levels of physical reality, independent of the process of measurement. Quantum theory describes the reality, not the means to verify it. This is apparently the source of the confusion by those who assert that infinite-series can resolve Zeno's Paradoxes -- a case of confusing menus, forks and meals.

   Based on this simple analysis, infinite-series cannot be meaningfully applied to Zeno's Paradoxes.

6. It would be entirely reasonable to assume the Earth is flat, judging by the data we see with our eyes ... the flatness of the area local to our position. If we were by the sea, we might see a small curvature, but sufficiently small to not draw the conclusion that ... the whole Earth was actually round.

   Similarly, we may use Newtonian mechanics for large things, not paying much attention to the "small curvature" of the evidence, as highlighted by Zeilinger et al., in their experiment An experimental test of non-local realism.

   But their evidence is clear.

   "Flat-line"/CHSH infinite-series models (see An experimental test of non-local realism do not fit the facts. Flat-line (infinite-series) models, like flat-earth theories, appear correct, but are shown through the evidence to be incongruent with actual reality.

   We may continue to believe in a 'flat-earth' but that won't stop it from being round.

7. Some respondents attempt to frame the issue of Zeno's Paradoxes purely within a mathematical context, citing esoteric 'dense time-space' theoretical models, which are, from cursory searching, not mentioned by competent physicists. Physicists, those who are at the 'coal face' in terms of resolving Zeno's Paradoxes in the minutia, instead use models such as CHSH which can be experimentally tested, thus working theory in with reality, not avoiding it by citing esoteric theories with no tested basis in reality.
8. Recapping what has already been well covered before: [1]

9. There are some who believe, somewhat naively, that the results of quantum experiments using entangled pairs of photons only applies to entangled photons. However, as many (if not all) competent physicists appreciate, the fact of nonlocal correlations, proven through the use of entangled pairs, reveals the deeper framework for all matter, and energy. Hence why Dr Nick Herbert wrote that "Whatever reality may be, it must be non-local. Since Clauser’si experimental verification of Bell’s theorem, we know that any correct model of reality has to incorporate explicit non-local connections. No local reality can explain the type of world we live in. Furthermore, since Bell’s result is based on experimental facts, it is independent of whether quantum theory is correct or not."

   Similarly the experiment by Zeilinger et al, reveals that through the use of entangled photons, a local-realistic model for explaining the deeper framework of physical reality, including all physical objects, be they small or large, micro-sized or macro-sized, is clearly untenable.

   The experimental evidence clearly demolishes any validity for local-realistic models (and some elements of nonlocal realistic models) for explaining deep reality. As result, it becomes almost surreal to see respondents continuing to argue for said models as some sort of valid framework for explaining the movement of physical things (such as runners, arrows and the like) through all scales of increment. All this despite there being NO evidence to meaningfully apply infinite-series point-for-point to the movement of physical objects. None whatsoever.

   The poor analysis of the experimental evidence, and the erroneous conclusions drawn as a result by respondents on this website seriously undermines the credibility of Wikipedia as a reliable resource. Which is quite a shame, given it started with good intentions.

   Those who are naive or afraid may continue to believe in a 'flat-earth' but that won't stop it from being 'round'.

10. Perhaps this list of questions will assist the mediator(s), given the content on this page:

    1. Is there any evidence of anyone having successfully applied or correlated point-for-point, infinite-series to describe, predict and experimentally verify the movement of any physical object?
    2. Are there ANY Reliable Sources willing to affirm that we can, in theory, apply, point-for-point infinite-series to the actual real movement of physical objects (irrespective of size).
    3. Can those Reliable Sources explain how that object (irrespective of its size) moves point-for-point through quantum scales of movement, since by definition, infinite-series solutions requires any object to traverse ALL points along some arbitrary path, including point increments at and below the Planck length?
    4. Can those Reliable Sources also explain how infinite-series and the "simple ideas of geometry" upon which they are reliant, supersedes quantum theory when considering the movement of objects (such as runners, arrows and tortoises) at AND below the Planck length?
    5. Hands up all those physicists name Brian ... sorry, all those physicists who assert that we can apply infinite-series solutions to precisely, repeatedly and accurately predict the movement of physical things, through all scales of increment.

Steaphen (talk) 14:18, 10 December 2009 (UTC)

• Footnote: my comments have not been painfully researched -- I make them up as I go along. Much more fun, doesn't take much effort, and means I don't have to remember stuff ... I rely on quantum superpositioning principles, in that whatever I write, will be in effect right. Does take a bit of getting used to though (as any half-decent writer will appreciate :)

A comment on entanglement

The observed fact that entanglement is incompatible with locality is not contended. The reference An experimental test of non-local realism argues that certain local and realistic models are not suitable to describe entanglement. This is not contended either. The result presented in the article for entangled particles question not only locality, but also certain intuitive features of realism; this further undermines Stephean's insistence on realistic interpretations, and questions his ridicule for instrumentalist interpretations.

That said, this is not the main problem with the reference in this context. The problem is that the reference does not claim that the obtained results are relevant to either Zeno's paradox or infinite-series mathematics. That it would, is purely Steaphens interpretation, especially since the article itself is using infinite-series mathematics throughout. Zeno's paradox on the other hand does not deal with entanglement, but refers to objects in a classic non-quantum way. The reference is therefore off-topic. It would be relevant to the article on quantum entanglement. Ansgarf (talk) 21:41, 2 December 2009 (UTC)

Ansgarf's (talk) statement

The problem with Steaphen's criticisms are numerous. The criticism is based on a misrepresentations of the content of the article, they are often off-topic, and as often based on factually wrong claims and category mistakes.

Misrepresentation

At the root of the contention are the following two observations:

1. The calculus solution to ZP assumes a dense model of time and space.
2. Some interpretations of QM propose a discrete model of time and space.

Neither of these facts is contended. Based on these facts however, Steahpen concludes that calculus and infinite-series solution are fundamentally wrong. He demands to

• remove any mention of calculus or infinite-series solutions as proposed solutions
• remove any mention that mathematics can be used to compute the trajectories of moving objects

These demands ignore the following:

• The article does not claim in any form that calculus and infinite series solve the problem for a discrete model of time and space. It offers for a discrete model another explanation. Namely that in that case there would be no infinite series of distances to begin with. (last paragraph)
• The article does not claim that the calculus solution solves all philosophical problems. It already acknowledges claims to the opposite. (third paragraph).

Zeno's paradox is a paradox of philosophy

Zeno's argument uses a mathematical argument to show that movement is an illusion. A purely mathematical treatment of Zeno's argument is therefore legitimate. For example:

• Zeno's paradox is not formulated for quantum systems. Zeno assumes that the position of an object is a point and not a distribution. It is therefore legitimate to use the same model when discussing the paradox.
• Zeno's formulation of the paradox does not assume a discrete model of space and time. He assumes that any distance can be divided in two. It is therefore legitimate to use the same model when discussing the paradox.
• In Zeno's formulation of the paradox does not assume that motion at small scales is different from motion at large scales. Motion was assumed to be of the same nature regardless of distance or scale. Zeno's did not argue that the character of motion changes at small scales, but he argued that motion can be divided into an infinite number of geometrically similar parts. It is therefore legitimate to use the same model when discussing the paradox.

Zeno describes the movement of a hypothetical tortoise and a hypothetical runner, to show that motion is in theory impossible.

It is true that observable reality, and results from quantum mechanics in particular, might undermine some of these assumptions for actual runners and tortoises. However, this would not only undermine Zeno's formulation of the paradox, but it is also a separate issue. And the current article already deals with it separately.

Infinite-series in quantum mechanics

It is wrong to claim that all Interpretations of Quantum Mechanics describe the wave function as a real process. A fair number do not assume that the wave function is real. It is also not true that QM implies that only discrete models of time and space are correct. The Schroedinger equation itself is a continuous time partial differential equation, and the wave function its continuous time solution. It is also not true that QM shows that there you cannot use any mathematical/algebraic/geometric expressions to define the momentum and position of matter. The Schroedinger equation itself is a continuous time partial differential equation which does exactly that. It is also wrong to claim that there cannot exist a mathematical model based on infinite series mathematics that produces predictable results. Fact is, QM is itself a mathematical model, that has produced experimentally validated predictions, based on infinite-series continuous time solutions.

Furthermore, it is wrong that no physicist uses infinite series mathematics to describe trajectories of objects. Ever since the invention of calculus by Newton and Leibnitz to do exactly that, infinite-series mathematics have been used for the same purpose; it has been used by, among others, Maxwell, Boltzmann, Planck, Bohr, Einstein, Heisenberg, Schrödinger, Bohm, Dyson, Feynman,Higgs, Weinberg, 't Hooft and more recently by a physicist called Brian Cox [2].

Uncertainty

Uncertainty, and other arguments from e.g. De Broglie's wave length, are concerned with measurements of physical quantities. This means in particular

• The uncertainty principle does not apply to mathematical proofs and within mathematical models. The fact that geometric series converge is not subject to the uncertainty principle. Neither are any other theorems in calculus, an area of mathematics which is fundamentally based on infinite series. The trajectory of tortoises in mathematical models is defined mathematically precise. The expected value of a mathematical distribution is defined mathematically precise. Applying uncertainty to calculus solutions or other mathematical claims is a category mistake.
• All physical measurements are subject to the uncertainty principle. It has as much relevance to actual turtles and runners, as it has to the objects used by Galilei Galileo in his free fall experiments, or planetary orbits, or the position and height of the Eiffel Tower, or the top speed of a Volkswagen Beetle. It would be factually correct to mention in all these cases that their positions, height, length, speed, acceleration, temperature, etcetera are only approximately known. However, the suitable place to discuss uncertainty that arises from quantum mechanics is the article on the Uncertainty Principle.

QM and continuous motion

Finally, QM is consistent with classic descriptions of motion for non-quantum objects. The correspondence principle entails that you can use mathematics to compute trajectories of such objects. An arguably reliable source, Fred Alan Wolf, said the following on whether QM means that we should do away with classic descriptions of movement:

This does not mean that we should throw away all of our machines. Just the opposite is true. Our mechanical models work beautifully for large objects because of the smallness of Planck's constant. (Dr Fred Alan Wolf, Taking the Quantum Leap, Harper and Row, New York, 1989)

That QM is complementary with a continuous (akin newtownian) description of motion of larger objects is also known as Ehrenfest's Theorem. See also [3] or [4]. Every physical object - electrons, buckyballs or moons - are associated with a wave-function, which can be viewed as a probability distribution (Copenhagen interpretation). The centre of the wave can be used to define a point position, just as the centre of a classical object defines its position. Ehrenfest's Theorem does not assume that the wave is a point distribution, i.e. it does not assume determinism of the distribution. The theorem proves mathematically that the motion of the centre of a wave-packet as described in QM, coincides exactly with the solution of a continuous-time differential equation.

Summary

It is commonly accepted to use ordinary mathematics to describe motion of macroscopic objects. The mathematical fact that geometric series converge to a finite limit is not affected by the uncertainty principle, and the mathematical limit is precise and not approximate. The physical fact of the uncertainty principle affects all measurements of physical objects, and not just those of tortoises and runners. The appropriate place to discuss this fact is the article on the uncertainty principle. While the article should be improved - including the paragraphs mentioning QM - there is no reason to remove the mention of classic mathematical methods, or to qualify their application beyond what is already contained in the article. Ansgarf (talk) 13:58, 1 December 2009 (UTC)

Update: Ansgarf (talk) 08:15, 5 December 2009 (UTC)

Ansgarf's response on the issues

In addition to my statement, I'll address the issues that have been mentioned on the mediation page

• Issue 1

The article does not state that the infinite-series solution solves all aspects of Zeno's paradox. It only states that is answers one aspect of it (the limit of geometric series that appear in some descriptions of the paradox).

• Issue 2

My comments have been painfully researched. While I wish that Steaphen would stop his intransigent behaviour, I see no need to prohibit people from making statements on the talk pages that are wrong or might be wrong. In principle every opinion on the talk pages should be permitted, as long as it is on topic, and not ad-hominem.

• Issue 3

It is actually not Wikipedia policy to ask for references to common textbook knowledge that is unlikely to be challenged. Given however that Steaphen is challenging it, I am happy to provide a textbook reference to the effect that infinite-series mathematics can be used to describe moving objects: Advanced Engineering Mathematics, by Edwin Kreysig [5]. It gives plenty of examples of how to model moving objects with infinite-series mathematics.

To address the question whether QM is consistent with a classic descriptions of motion, here another textbook reference on Ehrenfest's theorem [6]. Note that this reference states in its conclusion that "the centre of a wave-packet always moves like a classical particle".

• Issue 4

Whether QM is a complete theory is a topic of debate since the paper "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" by Einstein et al [7]. Quantum theory and relativity have not yet been integrated, but nevertheless all of the best descriptions use calculus to describe motion. How to use calculus to describe the physical motion see Kreysig. How to derive a classic description of motion from quantum mechanics see Ehrenfest's theorem. A general model for continuously evolving probability distributions, using infinite-series mathematics, are Continuous-Time Markov Processes. See also [8] and [9]

• Issue 5

All statements about positions of objects can be correlated with observable experiments. There have been repeatedly experiments proposed to Steaphen. Well known examples of successful predictions, based on calculus solutions, of movement of physical objects are planetary orbits, ballistics, satellites, falling objects, trajectories in particle accelerators.

It is true that physical experiments may falsify a particular mathematical model. However, that does not disprove the underlying mathematics, but the used model. Failure of newtwonian mechanics to predict the orbit of Mercury, for example, did not mean that the used calculus was imprecise, but that the model was incomplete; it did not include relativistic effects. Imprecision in the model of moving tortoises are caused by imprecision in parameters and initial conditions, such as speed and starting position. This imprecision is however not caused by a fundamental uncertainty of calculus or infinite series. The geometric series $\sum 1/2^{n}$ converges to 2, not to approximately 2. Mathematical theorems on calculus and infinite series are not experimental proofs, but logical derivations, and thus not subject to uncertainty we see in physical experiments.

• Issue 6

This issue refers to the following comment [10] on the talk page. It is true that uncertainty principle is a fundamental property, and not just imprecision of measurement, but Jim's comment on the talk page was appropriate in the context.

• Issue 7

Steaphen is referring to the second comment in this edit [11]. My comment actually said the opposite from what Steaphen claims in Issue 7. In the sentence "It just shows that you hope to expect a mechanical world down there" the word "you" referred to Steaphen. Issue 7 seems to be based on a misunderstanding, since we both seem to agree that one should not expect that naive notions from classical mechanics on a quantum level. This resolves the issue. Ansgarf (talk) 11:30, 3 December 2009 (UTC)

Responses by JimWae

Steaphan's comments included in this series of posts indicates a complete lack of awareness regarding the difference between simple algebra & calculus. The point about "Using simple mathematics we can calculate..." is to point out that calculus is NOT needed to determine the point at which Achilles catches the tortoise (nor is infinite series). If we are given each runner's speed and the amount of the head start, then using simple math (6th grade level or less) we can determine the relative position of each runner at every second. With the numbers in the article, Achilles "catches" the tortoise sometime between whole number values for the seconds. Algebra (9th grade math or so) can be used to calculate the specific (fractional) time & distance at which Achilles catches the tortoise. To say it is a "specific" time and distance is not the same as saying we can determine the time & distance to an infinite degree of precision. Each runner's speed is already a rounded-off value, as is the head-start. Most people understand that speeds, distances, and times are not usually given to an infinite degree of precision. I have a proposed solution to this impasse, but I wish first to determine whether settling this one point will settle the controversy, and if Steaphan will be content if the solution does not result in including his beliefdoctor thesis in the article--JimWae (talk) 05:52, 11 December 2009 (UTC)

I must also repeat: The paradoxes are not about whether or not we can find a precise point in space and time at which Achilles is located. (In fact, the arrow paradox depends on the arrow having a precise location at a precise point in time.) Zeno paradoxes do not stand or fall based upon whether we can model motion mathematically to calculate some points along the way. Zeno's paradoxes are based on the impossibility of completing an infinite number of tasks.--JimWae (talk) 06:05, 11 December 2009 (UTC)

I would never suggest that "the fact that measurements are approximate suggests QM is irrelevant". My point is that the uncertainty within measurements made regarding race-courses has a far more significant bearing than QM on how precise our calculations can be - and that it would be ludicrous to introduce QM as the main factor of uncertainty in such calculations. --JimWae (talk) 06:13, 11 December 2009 (UTC)

PS: Steaphan has made additional edits to the projects page. It is my understanding that once the mediator has accepted, we are not to alter that page, no?--JimWae (talk) 06:59, 11 December 2009 (UTC)

Revert

Can we revert the main page on the mediation to what it was when it was accepted for mediation [12]. I agreed to respond to the issues raised on that page at that time. And I responded to those issues in the meanwhile. I did not agree to discuss Steaphen's changing views. For example, at that time Steaphen found the idea to describe the position of a particle as probability distributions ridiculous. Now he seems to accept it. It is his his good right to change his mind. But the appropriate place to discuss it is here. Unsigned comment by user:Ansgarf 2009-Dec-11

• Yes, please --JimWae (talk) 07:18, 11 December 2009 (UTC)

Ansgar, be my guest (to revert the page to as it was).

I've now removed the following updates from the front page, and present it here, for submission to the mediator(s).

It is largely irrelevant as to whether the following is included on the front page or otherwise.

There are competent physicists who affirm that we cannot precisely "calculate" the location of anything, no matter what its size or circumstance. Even the moon is accepted as having a wave-function which requires that we cannot exactly calculate its location and momentum (speed) (at and below Planck scale increments). The argument that we can "arrive at a specific time" is not even 'bad science' or any form of science. Such statements fail to observe the basic principle of the scientific-method.

The comments by various respondents on this site have degenerated into the unimaginably absurd. Case in point: JimWae said that

"The uncertainty in finding the point at which Achilles catches the tortoise comes more than 2 dozen magnitudes of distance before QM enters the picture. QM is an issue at around 10⁻³⁵ metres. We measure distances on a racecourse to a certainty of - at the very best - about 5 millimetres. Stopwatches at races record differences only as small as 1/100 second, whereas QM enters as an issue at about 10⁻⁴⁴ seconds. We do not have instruments than get anywhere near the theoretical limits of QM, and introducing QM as the primary uncertainty in a race is absurd."

If we analyse JimWae's comments, he suggests that to solve movement of racehorses, for example, we may theoretically use mathematics/algebra/calculus/geometry to plot their exact location and speed, irrespective of whatever distances they move, including at and below the Planck length. According to JimWae, we can only measure to around 5mm, therefore QM is irrelevant to the issue of Zeno's Paradoxes? He appears to misunderstand QM, in that reference to the requirement for actual measurement is not dictated by the Quantum Theory. The mathematical expressions stand independent of experimental evidence for them. It just so happens that every experiment (and there have been many tens of thousands of them) have not once disproved Quantum Theory. Hence why many physicists readily accept it to be the most successful physical theory, in history.

JimWae and Ansgar both appear to think that it is valid to apply geometric/algebraic/mathematical expressions to some phenomenon, even when there is overwhelming evidence revealing that it is invalid to do so. The Uncertainty Principle disallows application of any mathematical/algebraic/geometric expression to precisely define (to infinite precision) momentum and position of physical matter. The Uncertainty Principle requires that we may only approximate the location and speed of objects, irrespective of whatever mathematical/algebraic/geometric expression is used. This has nothing to do with the failure of measurement. It is simply reflecting the deeper non-deterministic nature of reality. If there are any Reliable Sources who can assert otherwise, they're welcome to state as much.

The statement "using ordinary mathematics we may calculate" requires perfect determinism (requiring INFINITE precision through INFINITE orders of magnitude below the Planck length), and that any such calculation is reflected in fact. The statements in contention and under scrutiny in this mediation have not been of the kind "Using ordinary mathematics we may approximate ...". Instead they have stated categorically, "we may calculate", with perfect determinism, requiring absolute correspondence with reality: no such absolute correspondence has been observed in actuality. Furthermore, the Uncertainty Principle requires that we may not even do so theoretically, by any mathematical/geometric/algebraic means whatsoever. The Quantum Theory and the experimental FACTS work together to reveal infinite-series/ordinary mathematics cannot precisely calculate an objects position and momentum, time and energy. The statement "using ordinary or simple mathematics we can calculate" is so fundamentally and deeply in error, as to be on par with "using ordinary mathematics we may calculate the number of angels on pinheads" ... both statements show an equal lack of correspondence with observable reality, and are therefore about as useful, meaningful or rational.

At what point does Wikipedia rein in unsupported, speculative and demonstrably erroneous suppositions of editors?

Steaphen (talk) 20:14, 11 December 2009 (UTC)