Rob McEachern

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About Rob McEachern

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  1. Feeling the need to eat and feeling hungry are two very different things, for those dealing with frequent low blood glucose levels. It is not low blood sugar that makes you feel hungry. For example, a type-1 diabetic may feel absolutely bloated and stuffed after finishing a large meal, but still have a dangerously low (and still plummeting) blood glucose level, as the result of a fast-acting insulin injection, which may enter the system, before almost any of the previously consumed food has. Pure glucose gels and tablets, when eaten, enter the blood stream much faster than other carbohydrates, like pasta, and more than an order of magnitude faster than fat and protein. So the answer to your question is all about the timing. When your body really needs glucose, it needs it now - not an hour from now, much less a day from now. It is rather like needing air; it does not matter if you can be supplied with all the air in the world, a few minutes after your heart and/or brain have been permanently damaged due to an earlier short-term lack. A type-1 diabetic can lose consciousness in a matter of minutes, once their blood sugar starts to plummet, even when their stomach is full. The problem is, it is full of food, including most types of carbohydrates, that are absorbed more slowly than a fast-acting insulin. Consequently, it is not just the quantities of carbohydrates and insulin that matter, in this type of situation, but their respective absorption rates. That is why a very rapidly absorbed carbohydrate, like pure glucose, may need to be consumed, in spite of a full stomach. Once a diabetic has become unconscious, and thus unable to consume anything, the situation may be quickly reversed by either injecting glucose directly into their bloodstream, or as is usually preferred, by giving them an injection of the hormone glucagon, which causes the liver to rapidly (in a matter of minutes) release glucose into the bloodstream. An over-weight person is likely to have type-2 diabetes. They too will have problematic swings in their blood-glucose levels, just not as extreme as those likely to be encountered by the rarer type-1. But in either case, hunger and low blood glucose levels are not the same thing; one may feel the need to "eat something", in response to symptoms other than hunger, that tend to become familiar to diabetics, that have to deal with these other symptoms, on a fairly regular basis.
  2. It should be even more obvious, that if you change V, V will no longer be constant, as stipulated in the text book quotes, as the defining property of a free particle.
  3. Yes it is. E= (Kinetic energy + Potential energy) = (K+V). So (E - V) = K+V-V = K; the potential exactly cancels out in the special case, where V is a constant, regardless of what the value of the constant is. Note also that, given the expression for p, p2/2m = (E-V) = K = mv2/2, just as one would expect, for a free particle with only kinetic energy. The momentum cannot change if the particle is free.
  4. Of course - because the potential has no effect, thus, the particle is free. Here is a quote from Merzbacher, "Quantum Mechanics", second edition, pages 80-81: .
  5. It is not possible. The solution that you gave and claimed; "Which I think is more useful as you can plug numbers into it." Is not a solution to Schrödinger's equation, if the energy changes. You will find the same thing in any other text book on the subject. The author of the text cited, was David Bohm - a rather highly regarded figure, in quantum theory.
  6. In the book, there is a two-step process to evaluate a square potential: (1) solve the equation when the potential is constant everywhere (Swansont's question), which is done in the first paragraph, and then (2) evaluate what happens when a second level is introduced. But, if there is no second level (as in the question that was asked), then all the rest of the book, after the first paragraph is irrelevant: There is no second level that is less than the first. Potential wells exist when there is a relative change in potential. The partial derivative of kx with respect to x, depends upon both the derivative of k and the derivative of x, with respect to x. The derivation of your solution assumed the derivative of k with respect to x is identically zero - there is no dependency on position. It also assumed that the derivative with respect to time is also identically zero - there is no dependency on time. Hence, k is being assumed to be a constant, right from the start; it depends on neither of the two variables (position and time) in the equation. I fail to see why you find that to be an interesting result; all it says is that a static sine-wave exists. How does that revelation enlighten your knowledge of reality?
  7. There can be no well, if the potential is constant everywhere; wells require more than one level of potential. Where there is a well, there can be no free particle. Nothing can change in the solution you gave, because, in the derivation of that solution, "k" was unwittingly assumed to be independent of both time and position.
  8. It does not change in your solution. That solution was derived by assuming the potential is zero, and E is a constant. You can find a simple derivation of that solution, in the last answer given on this page: https://physics.stackexchange.com/questions/347996/when-solving-the-schrodinger-equation-how-do-we-know-what-functions-to-use-exp Just set the potential V0 = 0 and solve for "k". But note that now, you have left out the "x" in the solution. It should also be pointed out, that the very first step in this "derivation", assumed that the derivative of "k" with respect to x is zero. Think about the consequences of that assumption. Everything. Because it demonstrates that Schrödinger's equation is just the expression for the Fourier transform of a wave function, transformed into a differential equation. Consequently, all the properties associated with wave functions (such as the uncertainty principle, superposition, entanglement, vacuum fluctuations, the Born rule etc.), turn out to be purely mathematical properties of Fourier transforms and have nothing to do with physics per se. In other words, these properties are properties of the mathematical language being used to describe physical phenomenon - not properties of the phenomenon being described. Consequently, attempting to interpret any of these properties as a physical phenomenon, rather than as mere side-effects of a specific mathematical technique (Fourier transforms) being employed, is a pitfall, that has confused the physics community for 90 years. See: https://books.google.com/books?id=hEHCAgAAQBAJ&pg=PA232&lpg=PA232&dq="In+any+region+where+V+is+constant,+the+solution+of+the+wave+equation+is"&source=bl&ots=n0Kf89ulEE&sig=b-_mFvKHojT3NTPKOew-0CugX-g&hl=en&sa=X&ved=0ahUKEwiG2cTrvdnaAhWjrVkKHTgiCDoQ6AEIKjAA#v=onepage&q="In any region where V is constant%2C the solution of the wave equation is"&f=false
  9. You stated you were only concerned with solutions "for a single particle translating freely in space": a potential, that has any effect whatsoever on a particle, implies that the particle is not free. is not even a function of time, so it does not represent anything "translating" anywhere.
  10. Equation (2) is the general solution!
  11. You have reversed both cause-and-effect and history. Schrödinger derived his equation, for a free particle, from the a priori known Fourier Transform of the wave-packet that he (following de Broglie) "associated" with a particle, as a sort of tracking mechanism. The derivation of the Schrödinger equation for a free particle, consists of little more than computing the first partial derivative of the Fourier transform with respect to time, then the second partial derivative with respect to position, and then equating the two.
  12. Exactly my point. Superpositions only exist as a mathematical abstraction, and abstractions do not collapse. So was the entire physics community. Schrodinger set out to develop a physical model of the trajectory of a particle, by using Fourier transform based superpositions, to describe a wavepacket, that "accompanies" a particle as it moves. But he eventually realized that while his equation provided a good computational model, for producing results, it resulted in an absurd physical model. Thus, he introduced his cat, in an attempt to convince people that one should never attempt to "interpret" a wavefunction as anything other than a useful computational device, which has no known relevance to a physical model, such as an actual propagating wave. In the case of the coin, as in the case for spin and polarization, the state being observed, is not a property of the entity being observed. It is a property of how the observer decides to observe it - the observer will obtain different results, if the entity is observed from different "directions". In other words, "calling" an entity "spin up" or "heads" is not a statement about the state of the entity. It is merely a statement about what the observer happens to "measure" when observing the entity from a particular direction.
  13. Yes. A coin is in a superposition of being both "heads" and "tails". Always. Even after you "call it" one or the other.
  14. The Logical solution to the Twin Paradox Explained comprehensively

    I never said it was. I said "imply the existence of a force". Do you really wish to maintain the a gravitational potential does not imply the existence of a gravitational force, and that that in turn implies that objects at different heights from the center of gravity would experience different accelerations, if not preventing from falling by some other force?
  15. Is there any reason this Quantum Telegraph couldn’t work?

    However, interpretations do have a significant impact on where, or even if, one looks for answers. For example, last summer, I posted a link to a detailed demonstration, on this website, falsifying the supposed "loop-hole-free" verification experiments of Bell's inequality theorem. That was motivated by a different interpretation. I have noticed that the two of you, in particular (and many hundreds of others) have been noticeably silent about all the errors you have found in that demonstration (and before you ask, yes, the results have been replicated by others). Physicists like to disparage the "god of the gaps", all the while talking about wave-functions and super-positions, as if the "wave-function of the gaps" is more real than the "god of the gaps". But wave-functions and superpositions are no more necessary to explain observations than god is. And the continued belief in all such things has hampered scientific progress. That is the difference interpretations make; bad ones, based on unobserved gods, superpositions and wave-functions, induce dogma, which in turn stifles progress. So let me put this to you. Above I just told you why quantum theory is entirely probabilistic - not because reality is, but because quantum theory amounts to nothing more than a very complicated procedure for constructing histograms, in an attempt to describe that reality. That is not what was intended by its developers. But it is what they inadvertently developed, for better or worse. So why not take that new-found insight and try to develop a theory, that is not based on histogram-inducing, Fourier superpositions. Communications engineers (the inventors of information theory) did this a long time ago and it resulted in a revolution in communications technology. Maybe it is time the physics community gives it a try too, rather than "shutting up and calculating" the same old histograms over and over again and wondering why so little progress is being made, in fundamental physics.