• [deleted]

To All,

The measurement problem in quantum mechanics is the unresolved problem of how (or if) wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the process under examination. Whatever that "something" may be does not appear to be explained by the basic theory.

To express matters differently (to paraphrase Steven Weinberg [1][2]), the Schrödinger wave equation determines the wavefunction at any later time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities? As a general question: How can one establish a correspondence between quantum and classical reality?[3]

CIG Attempt at explanation (www.cigtheory.com)

Wherein it is stated "actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the process under examination.":

YES, according and consistent with CIG, the "did something" was to slow the "real" probabalistic wave function and to collapse it. To observe interferes sufficiently and truly so that the probability (in all actuality there is a new and real spatial volume that was created as a result of the motion of the particle) collapses into the defined observation (customarily on the screen in the double slit, or before that if obbservation posts are placed in between the slits and the screen. Anytime the wave slows, it will become the smaller identifiable particle. Prior to observation, it travels at great speeds and its spatial qualities are manifested. It has become its larger spatial self. The correspondence between quantum and classical reality relies on the fact that quantum is in motion and classical is zero %"c". Quantum is classical at zero velocity. MTS

THX

doug (www.cigtheory.com)

    • [deleted]

    The above, above CIG Attempt at explanation (www.cigtheory.com)

    , was taken from WIKI, which I meant to credit.

    I am attemting to explain away the measurement problem.

    I hope that you follow my rationale. It may require a full read and total understanding of CIG Theory. (www.CIGTheory.com)

    Don't forget the marshmallows...

    THX

    doug

    doug,

    The so-called measurement problem in quantum mechanics has been solved. Please read the first chapter of this book:

    Joy Christian

    Image 1

    • [deleted]

    Not only is time important, but scale is crucial too.

    The other morning I was about to leave my homr for work, as I looked out of the window to see what weather like, I noticed while looning up at Orion, the image I observed was I dentical to the diffraction grating image on the head page of this article. when I moved my head left, to a point where there was no net curtain, the star I was looking at reverted back to a "point like" white dot? The fact fine net curtain can reproduce this effect macroscopically, has got me thinking about scale and distance.

    This effect is no different to the quantum douvle slit experiment, go find a fine mesh and try for yourself, the bigger the mesh (slit), the more pointlike the image, you can actuall perform the double slit experiment on a macro scale yourself :) !

      • [deleted]

      Sorry this was my post above.

      7 days later
      • [deleted]

      time has no physical dimension,

      time is a mathematical dimension of change running in a 3D quantum vacuum.

      see my papers in Physics essays - AIP

      Amrit Sorli

      20 days later
      • [deleted]

      Very recently there have been unexpected advances in understanding dark energy. In fact if the claim of the Egyptian Scientist M. S. El Naschie is correct, then there is no more a mystery regarding dark energy. El Naschie's solution is disarmingly simple and was presented at two conferences which were almost entirely devoted to his work. The first was held in Bibliotheca Alexandrina early October 2012 and the second was in Shanghai a week or so ago. On both occasions El Naschie presented a revision of Einstein's theory leading to an equation very similar to that of Einstein's namely Energy equals mass x the square of the speed of the light. However unlike Einstein's equation, the result is divided by 22. His explanation of 22 is as follows: As in the old string theory of strong interaction, space time of relativity should have been considered 26 dimensional. Taking 4 only is what Einstein did and that is how he got his famous result. Nevertheless Einstein ignored 22 dimensions. This is a scaling factor following Nottale's theory as argued by El Naschie. Even in simpler terms, he reasons that Einstein knew only one elementary messenger particle namely the photon. He knew nothing about the other 11 messenger particles of the standard model which were not known in 1905. Adding 11 super partners it turned out that Einstein did not know about an additional 22 elementary particles. These are the particles needed to explain the missing dark energy. In this way El Naschie was able to show that 95.5% of the energy of the Universe is missing. Alternatively this energy was never there to start with because space time is a fractal and although it looks puffed up it boils down to very little similar to cotton candy. In addition the compactified 22 dimensions are the cause for the negative pressure which increases the acceleration of the Universe's expansion. He claims to have tested his theory using 25 different methods including Witten's M-Theory and reached the same result. Even more importantly this result agrees completely with observation. In other words mathematics and physics have been substantiated by measurement which led last year to the award of the Nobel Prize to the 3 team who obtained this incredible measurement and data. Click on this link to get more info re the above (under news) http://www.msel-naschie.com/ and also http://mohamed-elnaschie.blogspot.com/.

        22 days later
        • [deleted]

        by double slit experiment happens that by sending particles only through one slit interference pattern will appear because each particle moving in space creates also a wave of space which than pass the other slit.....and time here is just numerical order of motion of particle in a 3D spaceAttachment #1: Time_is_a_mesuring_system_derived_from...pdf

        4 days later
        • [deleted]

        Professor El Naschie's 'breakthough' is a little unbelieveable: Einstein's equation is easily derived from F=ma and you don't get a factor of 1/22.

        El Naschie recently lost a law suit against the journal Nature, criticised by the judge for having little consideration of the norms of sicentific pubishing, or respect of the ethics that underpin it, so he's in the scientific long grass now. There's even a blog watch of his activities.

        a month later
        • [deleted]

        Professor Caslav Brukner:

        I will refer not to the whole of your article, but only to "time dilation" or "relativistic time" We first should know what it is time

        I am going to be as concrete as possible; if you read the article you will realize why it can't be shorter. Mainly theoretical physicists are the most interested in "the nature of time" and they like to believe the subject is inherent to physicists and you will see it's no so.

        I will follow with an advice of somebody than most physicists in the world respect, Albert Einstein. "The whole of science is nothing more than a refinement of everyday thinking. It is for this reason that the critical thinking of the physicist cannot possibly to be restricted to the examination of the concepts of his own specific field. He cannot proceed without considering critically a much more difficult problem, the problem of analyzing the nature of everyday thinking.

        Our psychological experience contains, in colorful succession, sense experiences, memory pictures of them, images, and feelings. In contrast to psychology, physics treats directly only of sense experiences and of the "understanding" of their connection. But even the concept of the "real external world" of everyday thinking rests exclusively of sense impressions" "Ideas and Opinions" Einstein, pg.283 y 284, ISBN Nº 440-04150-150.

        I think this should be read slow, understanding each and every word of his thought about mind functioning, some times is as important as mathematics formulas.

        To make possible to comprehend this article, first you should believe possible that "The problem of time" can be solve. Second let the mind freer to the understanding of new things, for this, we should say that

        "time" has no definition, no empiric meaning, also can't be sense by any of our senses or by any man designed artifact, nobody can make a description or recognize "time". To make clearer this article we should keep in mind the last three lines through all the reading.

        If was any other word with those characteristics we immediately would say "time does not exist".

        why we don't say that, because since pre-Socratic Heraclito ,and after Socrates Plato and Aristoteles 2600 or 2300 years ago we are measuring what we call "time" and as physicist Sean Carroll said being quote by Lee Smolin "There is no question that time exists--we use it everyday," If we give this, as a reason of "time" existence. How he can be sure that exist, if he don't know what it is? The Carroll reason is, that he think he use it every day. Certainly for use, he meant measuring the so called "time". How he knows that what he is measuring is "time" and no something else? like movement ?

        Everybody knows movement, it has definition, empiric meaning. Everything with physical existence moves, from a galaxy to a subatomic particle. Movement origin is very much older and certain that "time". If the big-bang, happen, there was movement, life is possible because movement, our brain metabolism, which moves, is our mind that consider all movement we know of, that surround us. How we are not going to measure movement? We did it since the beginning of written history, but thinking that we were measuring "time".

        People think that with the clock movement we measure "time" and with it, comparatively we measure every other movement, change and transformation. A clock, to be one should have a "constant", "uniform" movement, if it is not so it's not a clock.

        The physical prove that we measure movement with movement consist that with a clock "constant" movement we measure fractions of "constant" earth rotation movement represented by clock dial numbers, as the hour, these are the reasons that this are "movements units" and no "time units"

        New duration definition: It is the period of change and transformation that movement allows and men limit.

        Then the so called "time" is movement .When we think we are measuring "time" we are not conscious, that in fact we are measuring movement, as we always did, we do and we are going to keep doing it. Knowing this does not change any physic law. We have to remember that classic physics, relativity and quantum mechanics were created, developed and physicist keep working with them with out the need to know of "The nature of time", but knowing that "time" it is not a mysterious thing, but movement, a quality or property of everything with physical existence, we know that we can related it to anything of physical existence.

        Not only is needed to quantized general relativity to the goal of the "the theory of everything" but we also can understand conclusions of general relativity like "that velocity and gravity slows time" in GPS (imagine an analogical clock) the satellite one slows respect it's similar on land why? because the satellite clock inertia, because it's speed slows clock parts movement, slowing it's functioning respect the one on land, what slows it is not "time", but it's functioning

        Gravity slows the clock in the valley respect it's similar on top of the mountain, because the first one is affected for more gravity than the other, gravity slows clock parts functioning it is not the "time" than slows.

        Since Heraclito to Einstein passing through Newton men always ask themselves, What it is time? to reach reality, they should ask themselves What we are measuring? And quite easily they would find out that was movement. All the other things that can be made knowing this it would make this to long.

        Time probably is a remnant word which represented a very important concept for men that mankind forgot it's meaning as Einstein pre-scientific concepts. "Time dilation" as in GPS is what everybody thought was the satellite clock time slowing respect to it's similar on land, We can prove now that what really happen is that the satellite clock is functioning slower (not time) because its inertia at 27.000 Km.h, respect to it's similar on land. "Time dilation" can happen because of gravity action on clock parts making the clock in the valley slower respect to the one on top of the mountain . What becomes slower is not "time" but movement clock movements.

        Héctor Daniel Gianni

        E-mail: hectorgianni38@hotmail.com

          • [deleted]

          Hector

          As you say, time is not the timing devices, these just 'tell' the time. The reference is actually a conceptual constant rate of change. In other words, within the realms of practicality, all timing devices are synchronised to this (the same point applies to distance). The purpose of timing being to calibrate rates of change. Alteration is what is occurring physically, which apart from substance (ie what altered), and order (ie in what sequence it did so), happens at a rate.

          Einstein (or more precisely Poincaré) did not understand this, which gave him the 'ability' to argue for a timing differential in physical existence, having conflated physical existence with the photon based representation of it which we receive. There, obviously, being a time delay between these two actual physical occurrences. So, he shifted a timing differential which occurs at the end of the physical process to the start. The light he refers to is not observational light, it is a time and distance measuring device, which as a reference, must be constant. This is why, in attempting to explain the core idea of relativity he always uses examples in which there is lightening, or a ray of light, etc, because this disgiuses the fact hat there is no light for observers to see with.

          All this is immediately obvious in 1905 section 1, part 1

          Paul

          • [deleted]

          Paul:

          Thank you for your answer, my language is Spanish, but I will try to be as clear as possible. What I am saying in my article is much, much radical than you thought; in fact I am replacing "time" by movement.

          Gravity, inertia, rationality tell us that always existed we just put them a name. Time did not, time was a man creation is not something with physical existence is just a word, as I called a "remnant word", that probably represented an important concept for man and mankind forgot it's meaning, Einstein to space and time call them pre-scientific concepts.

          Our senses tell us about gravity and inertia continuously since we born. Scientists talk about time, because they have not other way to refer to it. When Einstein was asked about time, "Time," he said, "is what clocks measure and nothing more." Of course he was right, because is the only thing we knew about it, that's why has not definition, or empiric meaning it is not sensed by any of our senses, nobody can describe or recognize it. is not a scientific fact. If Einstein continue his thought to, what are we measuring? He would realize that with a "constant" movement (the clock) we are measuring "fractions" as the hour, of the "constant" earth rotation movement. We are measuring movement with movement, and not that with the clock movement we thought were measuring "time".

          "Time" is movement. With this what we are changing will run out a mysterious word "time" and we replaced it by movement, a quality or property of every thing with physical existence, what this really mean? that it can be related to every physical force or event. (I read 1905) movement is different in every point in space because not only would be affected by gravity, also by inertia and this forces will depend on which part of space we considered movement. I understand that Einstein or any other physicist understood why velocity and gravity slow "time" , if they knew that "time" is movement, easily could be understood that inertia because clock velocity and gravity can affect movement.

          If we know that "time" is movement "time dilation" is "movement extension", much better is "movement slowing". With my best whishes

          Héctor Gianni

          • [deleted]

          Hector

          I have not read your article, and have not got time today, but will do. Presumably it is referenced above? So I will just respond to your post now.

          It is not movement, that is just a specific form of change. The physical occurrence is alteration, or change, (ie from one physically existent state to the next), irrespective of what that involves, ie why the state altered and how. Time is the duration unit of the measuring system timing, which calibrates rates of change against a conceptual constant rate of change.

          There is no such phenomenon as 'time dilation', because time is physically non-existent. It is a reference system to establish when, and/or for what duration, something physically occurred. There is no such phenomenon as space, as in 'a spatial position where nothing exists'. Or perhaps to be more precise, we have not proved it so, and as we can only detect something which is different from something else, not nothing, we could not track this nothing as a reference anyway. It may be that when a differential in force incurred causes a change in momentum, it also causes a change in dimension (this being their original thought-particularly Lorentz), but that will not make any difference to the misconception of time which is the crux of the problem. The timing differential is between physical occurrence and receipt of light.

          In simple language. The physical existence we are able to investigate (we can dream up all sorts of possibilities, but that is not science) exists in one definitive physically existent state, at a time. We know there is something, and that it alters, which means it is existential sequence. Physical existence is only spatial. Change is a feature of the difference between one physical existence and another, not of any such physical state.

          Paul

          17 days later
          • [deleted]

          Since one of the principles of GR is the equivalence of acceleration and Gravity, I wonder if the experiment can be constructed to operated inside a centrifuge. The outer slit (high gee part) would be the slow clock and the slit near the center of rotation would be the " normal" clock. Instead of light use a 300 MHz rf beam generated with a traveling-wave tube amplifier where the slits can be 1 meter apart

          Cheers Bert Murray

          www.lhdev.com

            • [deleted]

            Bert - that is indeed sensible and we had similar ideas.

            Caslav

            • [deleted]

            Attached is a paper where double slit was performed using microwaves in the 10 Ghz range (3 cm wavelength). Is 3 cm enough of a separation adequate to detect time dilation?

            http://arxiv.org/pdf/1105.1137v2.pdf

            Cheers, Bert

            17 days later
            • [deleted]

            Dr Brukner,

            Is your analysis related in some way to the one by Paul Dirac in his Lectures on Quantum Mechanics? A quick example is this partial quote from page 66 of the currently paperback version: "... it doesn't seem possible to fulfill the conditions which are necessary for building up a relativistic quantum field theory on curved surfaces." His arguments are based on a use of Hamiltonian methods that I strongly suspect are equivalent to the assuming the existence of a flat space, thus leading to the overall incompatibility. Are Dirac's arguments related to yours, or am I misunderstanding the intent of your analysis?

            Cheers,

            Terry Bollinger

            a month later
            • [deleted]

            Fundamental time which is a numerical order of change has only a mathematical existence. Emergent time which is aduration of change enters existence when measurement by the observer.

            http://dx.doi.org/10.4006/0836-1398-26.1.113

            5 months later

            Einsteinians Will Measure Gravitational Time Dilation Again

            "The World's Most Precise Clock Could Prove Einstein Wrong (...) Einstein also predicted that clocks in different gravitational fields would tick at different speeds. For example, a clock in Boulder, Colo., which is a mile above sea level, would feel a slightly weaker gravitational pull than a clock at sea level in Washington, D.C. As a result, it would tick just a bit faster and after 200,000 years it would be a full second ahead. That's not much of an effect, but it's big enough for most atomic clocks to measure. And Ludlow's clock can register the change in gravity across a single inch of elevation. That kind of sensitivity will allow scientists to test Einstein's theories with greater precision in the real world."

            "Gravitational time dilation", devised by Einstein in 1911, is one of the greatest hoaxes in today's science. Consider light falling (or climbing up) in a gravitational field:

            Dr. Cristian Bahrim: "If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies."

            Robert W. Brehme: "Light falls in a gravitational field just as do material objects."

            University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light."

            "The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."

            Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

            The picture is more than clear - in a gravitational field, the speed of light varies like the speed of any material body, just as predicted by Newton's emission theory of light, and this variation has been confirmed by the Pound-Rebka experiment. Yet some Einsteinians find it safe to ignore all this and teach the blatant lie that the speed of light remains constant in a gravitational field:

            Brian Cox, Jeff Forshaw, p. 236: "If the light falls in strict accord with the principle of equivalence, then, as it falls, its energy should increase by exactly the same fraction that it increases for any other thing we could imagine dropping. We need to know what happens to the light as it gains energy. In other words, what can Pound and Rebka expect to see at the bottom of their laboratory when the dropped light arrives? There is only one way for the light to increase its energy. We know that it cannot speed up, because it is already traveling at the universal speed limit, but it can increase its frequency."

            Richard Epp: "One may imagine the photon losing energy as it climbs against the Earth's gravitational field much like a rock thrown upward loses kinetic energy as it slows down, the main difference being that the photon does not slow down; it always moves at the speed of light."

            Stephen Hawking, A Brief History of Time, Chapter 6: "A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a photon, however, must continue upward at a constant speed..."

            Where does the courage of Brian Cox, Jeff Forshaw, Richard Epp and Stephen Hawking come from? The blatant lie (the speed of light is constant in a gravitational field) can be taught relatively safely if the teacher has assumed that a clock on the ground runs slower than a clock at the top of a tower ("gravitational time dilation"). With this assumption, light emitted by the top will be measured to have a higher frequency on the ground not because its speed has increased, as predicted by the emission theory, but because the unit of time on the ground is dilated and encompasses more wavecrests, Divine Einstein, yes we all believe in relativity, relativity, relativity.

            Pentcho Valev

              8 days later

              Glorious Confirmations of General Relativity

              According to Jean Eisenstaedt, in 1960 general relativity was confirmed for the first time by an experiment done on earth:

              Jean Eisenstaedt: "Le renouveau n'est pourtant pas loin et on peut le dater asssez précisément. C'est sans doute, en 1960, le succès de l'expérience de Robert Pound et Glen Rebka qui le marque scientifiquement. Pour la première fois, une expérience terrestre confirme la relativité générale, en vérifiant avec précision que les fréquences d'émission des atomes sont modifiées par le champ de gravitation de la terre."

              In fact, the Pound-Rebka 1960 experiment confirmed Newton's emission theory of light:

              Albert Einstein Institute: "...you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

              Needless to say, all previous (cosmic) confirmations of general relativity were also fraudulent:

              Jay Holberg: "In January 1924 Arthur Eddington wrote to Walter S. Adams at the Mt. Wilson Observatory suggesting a measurement of the "Einstein shift" in Sirius B and providing an estimate of its magnitude. Adams' 1925 published results agreed remarkably well with Eddington's estimate. Initially this achievement was hailed as the third empirical test of General Relativity (after Mercury's anomalous perihelion advance and the 1919 measurement of the deflection of starlight). IT HAS BEEN KNOWN FOR SOME TIME THAT BOTH EDDINGTON'S ESTIMATE AND ADAMS' MEASUREMENT UNDERESTIMATED THE TRUE SIRIUS B GRAVITATIONAL REDSHIFT BY A FACTOR OF FOUR."

              Jean-Marc Bonnet-Bidaud: "C'est ce qu'aurait dû trouver Adams sur ses plaques s'il n'avait pas été "influencé" par le calcul erroné d'Eddington. L'écart est tellement flagrant que la suspicion de fraude a bien été envisagée."

              "...Eddington asked Adams to attempt the measurement. (...) ...Adams reported an average differential redshift of nineteen kilometers per second, very nearly the predicted gravitational redshift. Eddington was delighted with the result... (...) In 1928 Joseph Moore at the Lick Observatory measured differences between the redshifts of Sirius and Sirius B... (...) ...the average was nineteen kilometers per second, precisely what Adams had reported. (...) More seriously damaging to the reputation of Adams and Moore is the measurement in the 1960s at Mount Wilson by Jesse Greenstein, J.Oke, and H.Shipman. They found a differential redshift for Sirius B of roughly eighty kilometers per second."

              [link:alasource.blogs.nouvelobs.com/archive/2009/01/index.html]"D'abord il [Einstein] fait une hypothèse fausse (facile à dire aujourd'hui !) dans son équation de départ qui décrit les relations étroites entre géométrie de l'espace et contenu de matière de cet espace. Avec cette hypothèse il tente de calculer l'avance du périhélie de Mercure. Cette petite anomalie (à l'époque) du mouvement de la planète était un mystère. Einstein et Besso aboutissent finalement sur un nombre aberrant et s'aperçoivent qu'en fait le résultat est cent fois trop grand à cause d'une erreur dans la masse du soleil... Mais, même corrigé, le résultat reste loin des observations. Pourtant le physicien ne rejeta pas son idée. "Nous voyons là que si les critères de Popper étaient toujours respectés, la théorie aurait dû être abandonnée", constate, ironique, Etienne Klein. Un coup de main d'un autre ami, Grossmann, sortira Einstein de la difficulté et sa nouvelle équation s'avéra bonne. En quelques jours, il trouve la bonne réponse pour l'avance du périhélie de Mercure..."[/link]

              "The eclipse experiment finally happened in 1919 (youre looking at it on this very page). Eminent British physicist Arthur Eddington declared general relativity a success, catapulting Einstein into fame and onto coffee mugs. In retrospect, it seems that Eddington fudged the results, throwing out photos that showed the wrong outcome. No wonder nobody noticed: At the time of Einsteins death in 1955, scientists still had almost no evidence of general relativity in action."

              New Scientist: "Enter another piece of luck for Einstein. We now know that the light-bending effect was actually too small for Eddington to have discerned at that time. Had Eddington not been so receptive to Einstein's theory, he might not have reached such strong conclusions so soon, and the world would have had to wait for more accurate eclipse measurements to confirm general relativity."

              Stephen Hawking: "...it was not until 1919 that a British expedition, observing an eclipse from West Africa, showed that light was indeed deflected by the sun, just as predicted by the theory. This proof of a German theory by British scientists was hailed as a great act of reconciliation between the two countries after the war. It is ionic, therefore, that later examination of the photographs taken on that expedition showed the errors were as great as the effect they were trying to measure. Their measurement had been sheer luck, or a case of knowing the result they wanted to get, not an uncommon occurrence in science."

              Pentcho Valev