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QM and the problem of the 'middle'

  1. Apr 28, 2010 #1
    Note: I fully understand that the nature of following essay is of a sufficiently philosophical nature, so as to possibly warrant its movement to another subforum. But as I understand it, the philosophy section is supposed to be about non-scientific questions, whereas the following is concerned with the theoretical aspects of quantum theory at its most fundamental level. I grant that it is always the moderator's right to move any thread to a more suitable place, but it is my understanding that failing such kinds of conceptual discussions, then theoretical physics will only lose sight of the very same critical and reflective spirit that brought it into existence in the first place.

    Perhaps the single most important character of what we may call 'quantum mechanical thought' is that it seriously asks about the nature of the 'middle.' This 'middle' is currently asked about vis-a-vis the state of Nature as she subsists in between moments of observation. But as we look deeper into this question, we will find that it is indeed nothing new, and that, in point of fact, the problem is not really so much of a problem after all.

    We can first begin to trace this problem (in the modern sense) with Newton's investigations into a method to quantify the slope of a curve at a given point. Thus, the idea of the 'infinitesimal' was born, and it allowed a way for mathematicians to apply a rigid methodology to what had previously been a kind of nebulous artistic technique.

    By dividing an unbroken curve into many smaller segments, the idea of the mathematical differentiation and integration was able to gain acceptance. It was in this way that we were able to get a handle on the question of the nature what goes on 'in the middle' between two points that are connected by a curve.

    Or was it?

    Thinking logically about it, we can see that instead of just two points to worry about, there are now many, many points to worry about that are each boundaries of their own 'local' curves. This just means that thinking of these interior points as being the limits of 'sufficiently small' segments is merely a 'cheat' that allows us to approximate the natures of given curves. But at the same time, this kind of cheating is necessary if humanity is to be able to get along with the business of making approximate, real world calculations.

    Over time, the success of the Newtonian calculation procedure opened up the possibility of thinking that cheating was not really happening, and that Nature just might be of exactly the same nature as the calculation procedures themselves. But this possibility of thought could not truly be actualized unless and until people started trying to comprehend the way in which calculation applies to Nature, herself, and not merely in terms of her various practical manifestations.

    This possibility started to be realized by the later part of the 19th century with the investigations of the kinetic theory of gases and of the related issue of thermodynamical equilibrium. For, these questions were asking of the dynamics of the most elemental of physical objects, and given that these 'elements' could not be directly perceived, it was possible to ask whether the empirically proven statistical methods should serve as some kind of 'final authority' or whether there should be some deeper theory that allows the behavior of Nature to be sensible on the smallest of levels. We can understand the 'infinitesimal spaces' of which Boltzmann concerned himself in developing his ideas of statistical mechanics to be the first explicit attempt to superimpose the Newtonian mathematical technique directly atop a 'picture' of Nature at her most elemental level.

    Planck's goal, however, was in trying to find a way of applying the second law of thermodynamics to this very same level, within the context of Maxwell's theories of the electromagnetic phenomena; the end result being that he had to divide not space--but time--into infinitesimal segments. For, it is pure radiant energy that is here at issue, and the only way that this can be quantified is to speak in terms of cycles per unit of time (frequency; Hz if the unit==1s).

    So we can see here that it was not by some fluke that Planck proposed his revolutionary 'quantum of action,' which is simply a constant, that, when multiplied by frequency, will yield a 'physically relevant' measure of energy content. In other words, the use of this constant was absolutely necessary if the world of EM and the world of matter were to become conjoined, thus allowing for continuing progression in the theoretical understanding of Nature.

    But at the same time, there was a reckoning that eventually had to be made. And that was just this: Are we going to think of the results of these 'merely logical' differentiation techniques as equivalent with Nature's fundamental constitution, or are we going to finally admit to ourselves that our techniques can only possibly be 'mere approximations,' with the inevitable conclusion being that human beings, at the most fundamental level, will always remain completely in the dark?

    And as the years went by following Planck's discovery, new thinkers began to devote themselves to answering the question of the ultimate form of matter. The Bohr model of the atom was a preliminary stop on the path that ultimately ended in the Schrodinger wave equation, which is a physical variation on the theme that had earlier been introduced by Laplace, with his equation for the 'standing-wave' spherical harmonics that occupy bounded spaces.

    But a man named Heisenberg put an end to all of the jubilation with the reintroduction of the 'dreaded' Planck constant within his relations that determined under what conditions certain kinds of of measurements could be known. In other words, the wave equation, as a continuously evolving function of space and time, given that the question of radiant energy content could only make sense when it was restricted by discontinuities in the timeline, and given furthermore that all questions in physics ultimately reduce to this selfsame notion of energy content, it became necessary--in order to keep a hold of the physicist's dream of the 'perfect knowledge of Nature'--to regard the Schrodinger equation itself as evolving in discrete intervals of time.

    So here is the obvious problem. In such a 'picture,' there cannot any longer be such thing as motion. That is, because physical 'action' only exists at idealized points in time, the only thing that can be said is that the state of the 'enduring middle' is always completely in question. And the way that this ontological question mark was erased was when Max Born understood the 'middle' to consist of nothing more than the chance that a certain 'action' would ensue, with the next obvious problem being that if all 'middles' are states that can only be determined in the statistical sense, then what can ever possibly be said about Reality, as she subsists?

    After all of this, we only have to return to the very beginning when Newton developed his technique of 'getting a handle on' (i.e. calculating) 'middles.' What we can say, then, is that all of the seemingly unanswerable physical questions that have followed Newton's invention could easily have been understood in light of the idea that it has never been Nature herself that has been at issue, but rather the way that we can understand the calculation techniques that are merely applied to Nature, vis-a-vis the way that she is empirically measured/quantified. For, the only way that we can possibly put Nature to use is by way of the quantification procedures, that, of themselves, necessarily exclude any concepts that deal in the idea continuity.

    So, it has been our 'wildly successful' ability to put Nature to effective use that has ultimately deluded us into thinking that she does indeed, at the most fundamental level, resemble the techniques with which we use to quantify her. And here is how all of the difficulties can be finally overcome: Were it not for Nature's ultimately continuous essence, then the very idea of measurement itself collapses, for the simple reason there are no longer any 'things' that are substantial enough to do any measuring or to be measured. This is simply to say that at the deepest theoretical level, the only way that a foundational physical theory can in fact be brought into fruition is by first simply positing (postulating) the existence of some continuously subsisting 'thing' that may be formed and fashioned in some dependable way (i.e. mathematics).

    And it is from this necessary foundational theoretical posture that I started to develop https://www.physicsforums.com/showpost.php?p=2692724&postcount=60" of the modes in which substantial forms can be said to subsist and inter-relate in the ways that are so obvious to our common sensibilities.
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
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