AlexL

Members
  • Content count

    59
  • Joined

  • Last visited

Everything posted by AlexL

  1. This is a belated comment to the following exchange: I should have asked first what is Harriman’s definition/description of (the method of) induction and only then of the problem of induction. From your quote from LL, I suspect he means by induction something different from what I do. In my understanding, induction (or inductive reasoning, or inductive inference) is stating that a property is common to all members of a class after finding out that it is true without exception of a (limited) number of members of that class. Such a generalization is a notoriously invalid leap - from the logical point of view - in the sense that the conclusion can, but must not be true. Harriman must mean something completely different by the word “induction”, because he states that : - the induction is valid, and that - “the "problem of induction" ... is to identify the method of induction” Within my definition of the inductive reasoning, there is no way to guarantee the validity of the generalization only from the validity in a number of cases. The latter can only suggest the general validity as a hypothesis, perhaps a very useful one in the everyday life, but inconclusive in sciences, in particular in physics. Alex P.S. In order to prove, or at least justify, the validity of the general statement, one has to know at least something or maybe a lot, about the class, its members and their properties. If the objects are purely conceptual, for example mathematical objects, as their properties are given, we a priory know everything about them, and can prove general statements about them from particulars. This is the mathematical induction, and is in fact a logical deduction. If the object are real, the proof, or justification, is very roundabout and can be very sophisticated; the method is in essence the scientific method, which consists in elaborating a theory about that class of objects. That theory will have to be discovered - invented, in fact; it will operate with new concepts, with properties which are not directly visible in the initial facts, etc. This, the invention of a theory is, in my view, the leap from particulars to universal. It presupposes creativity and cannot, therefore, be formalized.
  2. I am completely baffled! Why is nobody simply quoting Harriman's definition/description of the problem of induction from "The Logical Leap"?? Don't tell me there is none: those who have the book should just look, there should be just one or two phrases, somewhere on the very first pages. Sasha
  3. Einstein and Modern Physics

    Regarding Einstein's political stand there is a caveat, which I mentioned on this forum before - see here. Sasha
  4. Happy Birthday to AlexL

    Thanks a lot Betsy. Sasha
  5. A Quantum Question

    Strictly speaking, the "wave" which describes a quantum system does not propagate through space, at least not through the space through which the system itself moves. Namely, the system moves through the physical space, but the "wave"function which describes that system is defined over, and "moves" through, an abstract "configuration space". For example, the "wave"function of a system of two particles "moves" through an abstract, 6-dimensional, space. For a one-particle system, although the two spaces involved are both 3-dimensional, they are different in nature (one is physical, the other mathematical). Moreover, the "wave"function is not real-valued, and cannot, therefore, describe a true wave, similar to a sound or electromagnetic wave; that is why I prefer to write "wave". Keeping the above facts in mind will help avoid some of the misconceptions which plague the already difficult subject of quantum mechanics. Sasha
  6. The Soaring Romanticism of Ennio Morricone

    A beautiful song by Morricone: Quattro Vestiti Lyrics is here. Alex
  7. Whose side would she take?

    I heard about this story a couple of years ago, but it is even older, starting 2002 or so. It provoked quite a stir in the leftist circles, and a new wave of enthusiasm and hope :-) A quick search for "Argentina abandoned factories" results in a lot of links; here are two: Recovered Factories / South America, Wikipedia Workers in Argentina Take Over Abandoned Factories, NYT, July 8, 2003 Here is a more recent story: Fired workers take over chocolate factory in Argentina. Here the author's conclusion: Don't expect a serious analysis: all are about how capitalism (?) failed and the workers are rescuing themselves. Moreover, the absence of follow-ups about individual stories suggests that on the longer run they are not quite as successful as the enthusiasts hoped. And then there is the legal aspect of confiscating property from the owners. Alex
  8. Looking for Russian Speaker

    I do read Russian; it is my English that is not so good. If you don't find a better option, I'll be glad to help. Sasha
  9. The Theory of Elementary Waves

    And I started by examining the Schrödinger "wave" equation. You wrote: "your thesis doesn’t affect the validity of the TEW". This is plausible only if you believe that the SE is completely irrelevant for the TEW. From what I've read about TEW, it was my understanding that it is, although I never saw, unfortunately, a (Schrödinger-like?) equation for an elementary wave written down in the TEW literature (I don't have the recent TEW book, however). Alex
  10. The Theory of Elementary Waves

    Maybe am I not answering your question? Did I misunderstand it? Could you rephrase it? Is my answer to simple(istic)? Too complex? I don't know your context... Alex
  11. The Theory of Elementary Waves

    1. But I do not deny that the solutions of the Schroedinger equation do represent something real ! The only question was how is the reality represented by these solutions. Is it represented directly, as is the case with elastic or electromagnetic waves, or in some different way? In the case of the elastic waves the solution of the corresponding equation is the value of the displacement from the equilibrium position as a function of time and place. As you see, the solution delivers directly a physical property of the phenomenon. The waving take place in the elastic medium, and this medium exists in the ordinary space. All this is also valid for the electromagnetic waves, where the oscillating properties are the electric and magnetic fields. The displacement, respectively the electric and magnetic field components, are real numbers, as all physical, that is measurable, properties must be. In stark contrast, the solutions of the Schroedinger equation are complex numbers, they depend in general on more than three coordinates, and have a number of other nasty properties. Therefore, they are not at all similar to the ordinary waves. Neither the real part, nor the imaginary part has any physical meaning. In order to obtain from this solutions the physical quantities which describe the phenomenon, for example the quantities which characterize the position of the system, the momentum, energy and their evolution in time (those are the typical characteristics looked for in classical mechanics), we have to resort to more sophisticated operation on this solutions. For example, in order to determine some kind of a trajectory of the system (the "average position"), we have - to compute the complex conjugate of the solution - to multiply it with the solution itself - to multiply the result by "x" - and to sum (integrate) the result over the full configuration space. - and repeat everything for all the other coordinates. The result is guaranteed to be real, as it should be for a physical characteristic of a physical system. For the momentum it is similar, just slightly more complicated. [see here for an example: the free fall of a submicroscopic particle, with a depiction of the (complex) solution of the corresponding SE, and the representation of the "average position". The (complex) phase of the "wave" in different points of the space is represented by color codes. As you can see, this "wave" does not make much sense - by itself.] This shows that the solutions of the SE are indeed interpreted as representing something real, but the way in which the representation takes place is indirect, and unusually complicated. 2. Now about the solutions of the SE being interpreted as "wave-like". The key word here is "like". The submicroscopic entities are neither waves, nor particles. they are sui generis entities, and would therefore deserve a new name. I have seen the name "quanton" being sometimes used. Such entities display, in certain special cases, particle-like properties, and in others wave-like properties. For example: the electron can "diffract" - by a crystal lattice (your example), but two of the same electrons can collide - like particles. And when they diffract, the diffraction pattern depends on the mass and spin of the electron - typical particle-like characteristics! What an electron really is, is told by the quantum theory, which can be interpreted realistically, without the pragmatism and subjectivism of the Copenhagen interpretation. "Particles" and "waves" are but classical analogies, inevitable at the beginnings of the quantum theory, when they had some heuristic value. I will simply copy/paste an apt analogy attributed to Levy-Leblond and Balibar, 1984, which illuminates the situation: A cylinder presents both circular and rectangular features, but it is neither a circle nor a rectangle. And saying that the circle and the rectangle are mutually complementary will not help understand what a cylinder is - whereas exhibiting a solid cylinder or the corresponding mathematical formula will help. Yet it is true that, in exceptional circumstances - namely when seen along its axis - a cylinder looks as if it were a circle; and in others - namely when looked at from the side - it appears as a rectangle. Alex
  12. The Theory of Elementary Waves

    And you assumed, and wrote, that I did it in bad faith: "taking my statements out of context to suit your own purposes" means exactly this. There could have been many other explanation for what I chose to quote and what I chose to omit, but you, without knowing nothing about my character or about the content of my mind, decided and declared that I am dishonest. Alex
  13. The Theory of Elementary Waves

    Sorry Dean M. Sandin, the more precise formulation of my thesis is the one here, where I specify: Alex
  14. The Theory of Elementary Waves

    While the subject interests me very much, as do your remarks - some of them questionable, in my view - of epistemological nature, I do not think that the premises of a rational discussion between two of us are present: you do not know me enough, and you are not able to read my mind, so that your accusation of bad faith on my part are baseless.Alex
  15. The Theory of Elementary Waves

    I am not quite sure what your answer means, exactly, with regard to my thesis the solutions of the time-dependent Schrödinger equation cannot be interpreted as real waves, because the mathematical structure of this equation prevents this. for which I brought a number of arguments. Therefore, the questions which I am asking are: do you agree with the above thesis?, only in part?, which part?, which argument(s) are false and why? These question are clear, precise and specific, as are my arguments, so please be specific. Please note that my arguments are neutral with respect to the direction of the waves ("waves", in my view), so the direction is not an issue in my thesis. Alex
  16. The Theory of Elementary Waves

    And I mean exactly what I say: the solution themself, as such, the function <psi>, depending on time and a number of coordinates, cannot be a physical wave field, that is cannot describe directly a physical, a real wave. The solutions of the SE are purely mathematical objects, they do indeed describe the system and its evolution, but do not directly describe a physical property; physical properties are always real numbers (or functions). The physical properties of a system are "extracted" from the <psi> function, namely through more or less complicated constructs (various bilinear forms), which always result in real numbers. It could be that these constructs manifest some "oscillating" properties, but this is something completely different from a similar claim about <psi> itself. Therefore, my claim that Argument #1 implies my thesis that "the solutions of the (time-dependent) Schrödinger equations (SE) cannot be interpreted as real waves" stands exactly as stated. This being the case, all the talk about "interference" and "diffraction" of the Schrödinger "waves" is to be meant not literally, but analogically, figuratively, metaphorically, if not even allegorically. Any analysis and argument based on these metaphores is at most a qualitative and inductive one, must be very well scrutinized and finally replaced ba the real thing - the analysis (qualitative, quantitative) of the solutions of the Schrödinger equation for the specific problem and with specific initial and boundary conditions. Alex
  17. The Theory of Elementary Waves

    Sorry for the belated answer. First, a secondary point: Regarding (a) ,(c ) & (e): various interpretations of the QM formalism have different attitudes: for some the waves are real, for others not. See for example the table http://en.wikipedia.org/wiki/Interpretatio...nics#Comparison. Of course, I will not count how many are for and against, I will rather gauge the strength of the arguments listed above :-) Regarding (d). I prefer to go step by step: before discussing the direction of the waves, I want to make sure they do really exist. Alex
  18. The Theory of Elementary Waves

    This "amelioration" of yours to the #3 shows that you misunderstood me: the inductive part is completed after #1, and as soon as the formalism is in place with #2, the stages #3 and the following ones are truly mathematical deductions/theorems. In the case of the QM, for #3 we have e.g. the continuity relation, the Heisenberg dispersion relations (improperly called "Heisenberg uncertainty principle"), various conservation laws as implied by invariance w.r.t. certain symmetries, and so on. #4 means, in the case of classical mechanics (for a change), the mathematical study of e.g. free particle motion, motion under a constant force (or force field, like electric or gravitational), under a central force (again gravitational or electric), harmonic oscillator, all these using the 2nd Newton law introduced at #2, etc. I also think that, instead of glossing around the double slit experiment, ERP, half-dead cats, Bell inequalities and all these complex matters at a mostly qualitative and figurative level, it would have been much more productive to figure out how the existence of the elementary waves could be experimentally proven. The entire TEW holds or fails with this. Alex
  19. The Theory of Elementary Waves

    1. The discovery of the atoms and molecules allowed to find the limits of continuum theories, that is the limit of the modeling of fluids, gases, solids as mathematical continuums. Note that this has nothing to do with the modeling of the ordinary space - which was our subject; the model for it was and remained the Euclidean continuum. 2. differentials and integrals presuppose a continuum (with respect to the respective variables); in a discrete model for the ordinary space, e.g. lattice models, we have finite differences, respectively sums. 3. In the formalisms of QM and QED we have differentials and integrals; if one claims that the ordinary space is in fact discrete, the mathematical formalism of the QM and QED is a priori out. We can still keep this formalism unchanged only after proving that the discreteness is irrelevant in the context, possibly for greater distances (or solid angles) and/or as an approximation. We cannot just take it over tacitly. Alex
  20. The Theory of Elementary Waves

    A remark on the question of the continuity of the ordinary space in the context of the TEW. It is not the case that TEW is noncommittal on this question. TEW presupposes, at least implicitly, that the ordinary space, where the events take place, is a continuum. Here is why. One assumption of TEW is the validity of (most of?) the formalism of the quantum mechanics, and the latter presupposes that the ordinary space is a (3-dimensional) continuum which is modeled by a 3-dimensional Euclidean space. If, at some future time, TEW will give up on this hypothesis, it will also have to drop the whole mathematical formalism of the QM, as well as of QED, including Feynman diagrams (otherwise the fallacy of the stolen concept will be committed). Alex
  21. The Theory of Elementary Waves

    takes care, in a synthetic way, of your objections. Alex
  22. The Theory of Elementary Waves

    Well, I argued that, if particles can move in *any* direction (a fact which seems to be confirmed by, or at least compatible with, our everyday experience), then there must be an unlimited number of elementary waves, ready to "guide" the particles which could come from everywhere, at any time. Now, you (and other sources about TEW) seem to suggest that the primary, the commanding entities in the TEW are the elementary waves, and the particles have a subordinate status. If this is the case, it is in fact of no great importance whether all direction are potentially allowed or not for particles to travel along, because in fact the particles will only travel along those direction for which there are appropriate elementary waves available. If there is no wave for a specific direction, than no particle will travel along that direction. The waves ar the ones who dictate what is possible for a particle to do in a specific place and at a specific time. In this form, the argument has some initial plausibility, *if* such waves do exist and have the properties which this theory ascribes to them. But I have a problem with the various presentation of the TEW (1996, 2000's Chapter 1, JPL conference): the Elementary Waves are hypothesized, but their presumed fundamental properties are never listed and discussed in a systematic way. One can read, I read, here and there, that they are real, even classical, waves, that they move at the speed of light, that they posses momentum, energy and mass and the Schrödinger equation. This equation is never discussed: the Hamiltonian is not given, neither is the state function meaning and properties, interactions, conservation laws, etc. When the objects of a theory are not explicitly and clearly defined, no explanation can be either right or wrong and everyone has his chance in "explaining" even the more advanced points. And one mostly talks past one another. Physics has ceased to be a descriptive, qualitative science and became an exact, that is quantitative science several centuries ago. From a systematic presentation of a new theory of physics I expect 1. motivation for the need of a new theory, an inductive part which justifies the introduction of the new concepts and ideas, followed by 2. a presentation of the presuppositions/premises and of the mathematical formalism 3. deduction of the general properties 4. its application to a number of specific cases, discussion of validation by reality 5. discussion about limitations, future developments, etc. Unfortunately, the literature about TEW deals primarily with (1), and also attempts to check, qualitatively, if it can deal with more sophisticated matters, like relativity, quantum electrodynamics, etc. Alex
  23. The Theory of Elementary Waves

    Which means that the physical space is discrete, at least in the sense that the solid angles are quantized. OK, but this is a very bold and strong assumption, which, however, Dr. Little seems not to have made explicit himself. If this assumption is indeed necessary, before adding it, it must be checked if it is compatible with the rest of TEW's assumptions. It must also be checked if it is compatible with what we do observe in nature at our macroscopic level. Also, the full mathematical apparatus of QM - which TEW accepts - has to be adapted to this discretization of the space. Or this should be shown to be unnecessary.A rational physical theory is not a grab bag of arbitrary, ad hoc assumptions, growing in time by the necessity of answering various objections. I am not implying TEW is such a theory; I suppose (I didn't check) that Dr. Little checked the consistency of the assumptions he made himself. I still hope Dr. Little will accept to answer our questions, that are pertaining to the understanding of the very fundamentals of the TEW. Alex
  24. The Theory of Elementary Waves

    in the last paragraph should be: "TEW requires, therefore, an infinite number..." Sorry. Alex
  25. The Theory of Elementary Waves

    Let’s forget about energy for the moment and concentrate on simply counting of entities, thus largely leaving the quite complex realm of physics. I won’t count the elementary waves presumably existing in a small region of space, because I do not know how to do this. Instead, I will try to evaluate how many elementary waves does the Dr. Little’s TEW theory postulate to exist in that region of space. Then I will decide if this number alone makes TEW remain plausible or not. Please note that I am not counting here some real entities, but the number of entities whose existence TEW postulates. Essentially, I am counting (some of the) premises on which TEW rests. 1. I quoted Dr. Little as saying that TEW needs to assume (at least) one elementary wave for each possible spatial direction. Can we agree on this? 2. There is an infinity – a continuum, in fact - of possible spatial directions passing through a given point. Do you agree? 3. Therefore, Dr. Little TEW theory presumes the existence of an infinity of elementary waves. This is a simple syllogism; it has nothing to do with physics, it simply counts Dr. Little’s premises, as noted above. If you agree that the syllogism is correct and the premises are factually true, then the conclusion must be also true. If you don’t accept the conclusion, you must show that (1) and/or (2) are factually false, or that (3) does not logically follow from the premises. We now turn back to the physical realm. For TEW to be plausible, we therefore need to have an infinite number (actually, not potentially infinit!) of entities in a limited volume. I don't know about you, but this makes me extremely unconfortable. I would even venture to say that this denies by itself, from the start, any plausibility to TEW. Alex