Genady Posted December 8, 2023 Share Posted December 8, 2023 2 minutes ago, joigus said: As used by @studiot: 2 minutes ago, Luc Turpin said: As in pushing the envelope; meaning testing limits and trying out new, often radical ideas, which I will be doing in other parts of Science Forums. I know and understand meaning of the phrase "pushing the envelope", but I don't know what "to develop the envelope" means. Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 One needs pushing at times in order to extend the number of operations which can be performed without thinking 7 minutes ago, Genady said: I know and understand meaning of the phrase "pushing the envelope", but I don't know what "to develop the envelope" means. Both Myself and Joigus (i believe) were under the impression that it was envelope "pushing" that was mis-understood; which I have to say surprised me, because you are so knowledgeable ; as for "develop", I have an idea of what is meant, but will let Joigus respond, if he wishes to do so! At times, my English is so-so, because I am happier in French. 1 Link to comment Share on other sites More sharing options...

Genady Posted December 8, 2023 Share Posted December 8, 2023 19 minutes ago, Luc Turpin said: One needs pushing at times in order to extend the number of operations which can be performed without thinking Both Myself and Joigus (i believe) were under the impression that it was envelope "pushing" that was mis-understood; which I have to say surprised me, because you are so knowledgeable ; as for "develop", I have an idea of what is meant, but will let Joigus respond, if he wishes to do so! At times, my English is so-so, because I am happier in French. I think that @joigus has already explained that the latter was just a word play. I take it as "nothing more than that." Link to comment Share on other sites More sharing options...

joigus Posted December 8, 2023 Share Posted December 8, 2023 12 minutes ago, Genady said: I know and understand meaning of the phrase "pushing the envelope", but I don't know what "to develop the envelope" means. Sorry for being obscure. At this point I'm sure I've been. I think we all agree there is something about measurement in QM that isn't entirely satisfactory. We have this wave function that seems to interact with electric, magnetic fields and so on. So it seems physical enough. But on the other hand, every time we obtain information from it about the corpuscular properties of matter, we are forced to update it in a way that's blatantly incompatible with the evolution law (smooth updating law) of Schrödinger's equation. Some people have thought of wildly new ways of thinking about it. New dimensions? Maybe quantum evolution is non-linear, and instead of linear operators we have to think of non-linear functionals? (Nelson, Madelung, Weinberg at some point,...) who else? Maybe in some sense the universe splits, and the quantum state is only relative to these infinitely many splittings? Maybe the only thing that makes sense is coherent/decoherent histories? (Everett, Wheeler, De Witt, Gell-Mann, Griffiths, Omnés, etc) Maybe waves are coming from the future? (Cramer et al.) Maybe QM only tells us about collectivities of experiments? (Leslie Ballentine and other people I forget?) Or maybe we should just take the theory seriously, do like Einstein did, and try to be what Nima Arkani Hamed has called "a revolutionary conservative": Instead of pushing the envelope, try to develop the envelope. Meaning: Try to update the principles without giving up the principles. I suppose what I mean is that the next idea is not likely to be suggested by a flight of fancy. Rather, it's likely to be about taking the principles dead seriously and wholeheartedly trusting that the solution would come from a re-interpretation/re-examination of the old principles rather than the finding of new principles. It's always been that way. SR, GR, QM, QFT,... It's always been that way. The conservatives --while listening very intently to the revolutionaries-- always found a way out. A conservative revolution. No need to demolish any edifice. That's what I mean by developing the envelope. 50 minutes ago, Luc Turpin said: Both Myself and Joigus (i believe) were under the impression that it was envelope "pushing" that was mis-understood; which I have to say surprised me, because you are so knowledgeable ; as for "develop", I have an idea of what is meant, but will let Joigus respond, if he wishes to do so! At times, my English is so-so, because I am happier in French. Thank you. I hope I made clear what I meant now. I used to be quite fluent in French. But that was a long time ago, unfortunately. Link to comment Share on other sites More sharing options...

sethoflagos Posted December 8, 2023 Share Posted December 8, 2023 6 minutes ago, joigus said: I suppose what I mean is that the next idea is not likely to be suggested by a flight of fancy. Rather, it's likely to be about taking the principles dead seriously and wholeheartedly trusting that the solution would come from a re-interpretation/re-examination of the old principles rather than the finding of new principles. Like deciding not to simply ignore the advance wave in the wave equation? 11 minutes ago, joigus said: Maybe waves are coming from the future? (Cramer et al.) No probs so long as there's no informative content? Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 15 minutes ago, joigus said: Sorry for being obscure. At this point I'm sure I've been. I think we all agree there is something about measurement in QM that isn't entirely satisfactory. We have this wave function that seems to interact with electric, magnetic fields and so on. So it seems physical enough. But on the other hand, every time we obtain information from it about the corpuscular properties of matter, we are forced to update it in a way that's blatantly incompatible with the evolution law (smooth updating law) of Schrödinger's equation. Some people have thought of wildly new ways of thinking about it. New dimensions? Maybe quantum evolution is non-linear, and instead of linear operators we have to think of non-linear functionals? (Nelson, Madelung, Weinberg at some point,...) who else? Maybe in some sense the universe splits, and the quantum state is only relative to these infinitely many splittings? Maybe the only thing that makes sense is coherent/decoherent histories? (Everett, Wheeler, De Witt, Gell-Mann, Griffiths, Omnés, etc) Maybe waves are coming from the future? (Cramer et al.) Maybe QM only tells us about collectivities of experiments? (Leslie Ballentine and other people I forget?) Or maybe we should just take the theory seriously, do like Einstein did, and try to be what Nima Arkani Hamed has called "a revolutionary conservative": Instead of pushing the envelope, try to develop the envelope. Meaning: Try to update the principles without giving up the principles. I suppose what I mean is that the next idea is not likely to be suggested by a flight of fancy. Rather, it's likely to be about taking the principles dead seriously and wholeheartedly trusting that the solution would come from a re-interpretation/re-examination of the old principles rather than the finding of new principles. It's always been that way. SR, GR, QM, QFT,... It's always been that way. The conservatives --while listening very intently to the revolutionaries-- always found a way out. A conservative revolution. No need to demolish any edifice. That's what I mean by developing the envelope. Thank you. I hope I made clear what I meant now. I used to be quite fluent in French. But that was a long time ago, unfortunately. Loud and clear; it was more than my original impression of what it meant. i may be going off on a tangent again, but to me we live in a non-linear world, and if it is such, should we not have non-linear theories trying to explain it? Link to comment Share on other sites More sharing options...

Bufofrog Posted December 8, 2023 Share Posted December 8, 2023 12 minutes ago, Luc Turpin said: i may be going off on a tangent again, but to me we live in a non-linear world, and if it is such, should we not have non-linear theories trying to explain it? I'm pretty sure that is what we have. Link to comment Share on other sites More sharing options...

sethoflagos Posted December 8, 2023 Share Posted December 8, 2023 6 minutes ago, Luc Turpin said: i may be going off on a tangent again, but to me we live in a non-linear world, and if it is such, should we not have non-linear theories trying to explain it? We already have them! They are explicitly represented in the systems of partial differential equations that describe most macroscopic physical processes eg Navier-Stokes equations, macroscopic form of Maxwell's equations, Heat equation, Fokker-Planck eqn etc. etc. Link to comment Share on other sites More sharing options...

joigus Posted December 8, 2023 Share Posted December 8, 2023 31 minutes ago, sethoflagos said: Like deciding not to simply ignore the advance wave in the wave equation? Yes. I must say I don't know a lot about the transactional interpretation. Now that I think of it, I wouldn't call the transactional interpretation a flight of fancy. It's taking known physics and putting it to good use, which is what I think is likely to be the answer to the questions most people would like to see answered. 31 minutes ago, sethoflagos said: No probs so long as there's no informative content? Yes. From what I remember in the Wheeler-Feynman theory of radiation, they devised a perfect absorber at spatial infinity that guaranteed that no causality-violating effect would take place. 13 minutes ago, Bufofrog said: I'm pretty sure that is what we have. One of the big misteries about quantum mechanics has been this one precisely. I'd phrase it like, where does non-linearity come into play in quantum mechanics? Non-linearity is ubiquitous in Nature. How come linearity seems to be a sine qua non of QM? It's very strange. 16 minutes ago, sethoflagos said: They are explicitly represented in the systems of partial differential equations that describe most macroscopic physical processes eg Navier-Stokes equations, macroscopic form of Maxwell's equations, Heat equation, Fokker-Planck eqn etc. etc. Exactly. You'd expect microscopicity to be the realm of non-linearity. Instead of that, the operational rules (the prescriptions to relate the maths to the measurables of the experiments) become considerably weird and unintuitive --but linear!!--, while the evolution law of the state becomes... linear too??!! Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 17 minutes ago, Bufofrog said: I'm pretty sure that is what we have. Yup! 15 minutes ago, sethoflagos said: We already have them! They are explicitly represented in the systems of partial differential equations that describe most macroscopic physical processes eg Navier-Stokes equations, macroscopic form of Maxwell's equations, Heat equation, Fokker-Planck eqn etc. etc. I am aware of such theories, but might be showing my lack of knowledge, again: are we not mostly still using linear theories to understand our world? And, maybe the most obvious answer to you, but still need to ask the question even if I look stupid! Qm equations are linear or non linear? Link to comment Share on other sites More sharing options...

joigus Posted December 8, 2023 Share Posted December 8, 2023 3 minutes ago, Luc Turpin said: Qm equations are linear or non linear? They are linear in at least two different senses I know of: 1) Evolution is linear [quantum state](at time t'>t) = [Linear operator][quantum state](at time t) and, 2) probabilities of observing property Q with particular value q: amplitude(Q=q, at time t) = [linear operator on q][quantum state](t) The probability being the square of the absolute value of this probability. So linearity plays a big role in QM to say the least. So, mathematically, what it's telling you is "dynamical states are vectors" and "observable attributes are special matrices acting on those vectors". Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 1 minute ago, joigus said: They are linear in at least two different senses I know of: 1) Evolution is linear [quantum state](at time t'>t) = [Linear operator][quantum state](at time t) and, 2) probabilities of observing property Q with particular value q: amplitude(Q=q, at time t) = [linear operator on q][quantum state](t) The probability being the square of the absolute value of this probability. So linearity plays a big role in QM to say the least. So, mathematically, what it's telling you is "dynamical states are vectors" and "observable attributes are special matrices acting on those vectors". Thanks Jogus; I gotten that from your post preceeding the one above. Non-linearity is what makes the world really go "round and round". Joigus that is: you gals-guys know much; I pale in comparison to all of you! Link to comment Share on other sites More sharing options...

sethoflagos Posted December 8, 2023 Share Posted December 8, 2023 (edited) 1 hour ago, Luc Turpin said: I am aware of such theories, but might be showing my lack of knowledge, again: are we not mostly still using linear theories to understand our world? Not in the general case. Navier-Stokes for example are parabolic Quote The Navier–Stokes equations (/nævˈjeɪ stoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances... ... The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are a parabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g. they are never completely integrable). I think a key point to understand is that while Newton's Laws of Motion and Newton's Law of Viscosity (and the underlying quantum laws that give rise to them) are both linear in themselves, when they are employed in combination (as in Navier-Stokes), the nett result is non-linear. In general, the more interactions you add (linear or otherwise) to the analysis, the more non-linear the end product. This is can be understood as the basis of complexity in the macroscopic world. Edited December 8, 2023 by sethoflagos 1 Link to comment Share on other sites More sharing options...

studiot Posted December 8, 2023 Share Posted December 8, 2023 2 hours ago, Luc Turpin said: I am aware of such theories, but might be showing my lack of knowledge, again: are we not mostly still using linear theories to understand our world? And, maybe the most obvious answer to you, but still need to ask the question even if I look stupid! Qm equations are linear or non linear? Good question, especially if you actually know what linear means ? 2 hours ago, joigus said: They are linear in at least two different senses I know of: 1) Evolution is linear [quantum state](at time t'>t) = [Linear operator][quantum state](at time t) and, 2) probabilities of observing property Q with particular value q: amplitude(Q=q, at time t) = [linear operator on q][quantum state](t) The probability being the square of the absolute value of this probability. So linearity plays a big role in QM to say the least. So, mathematically, what it's telling you is "dynamical states are vectors" and "observable attributes are special matrices acting on those vectors". Vector spaces are the backbone of linear mathematics. I already mentioned a while back that with the Schrodinger equation (which is linear) we are working in the vector space of square integrable functions of class C∞ However the relativistic version of Schrodinger is non linear ( Dirac equation, Klein Gordon equation etc) https://en.wikipedia.org/wiki/Nonlinear_Dirac_equation This bears out Seth's comment that combining linear operators may result in a non linear equation. +1 It should also be remembered that of the famous Four Laws (of Thermodynamcs) , only the First Law is linear and even has q and w as incomplete differentials. Back to Luc, Heisenberg's Uncertainty Principle is not even an equation - It is an inequality like the Second Law of Thermodynamics. Pauli Matrices are linear. Link to comment Share on other sites More sharing options...

joigus Posted December 8, 2023 Share Posted December 8, 2023 2 hours ago, Luc Turpin said: Thanks Jogus; I gotten that from your post preceeding the one above. Non-linearity is what makes the world really go "round and round". Joigus that is: you gals-guys know much; I pale in comparison to all of you! I'm just an old geezer with an inclination for the philosophically spicy aspects of science, but thank you. 20 minutes ago, studiot said: However the relativistic version of Schrodinger is non linear ( Dirac equation, Klein Gordon equation etc) https://en.wikipedia.org/wiki/Nonlinear_Dirac_equation I disagree. The relativistic version is: https://en.wikipedia.org/wiki/Dirac_equation which is linear. It's the one that's used in the standard model, for example. Klein Gordon is also linear: https://en.wikipedia.org/wiki/Klein–Gordon_equation You can also play with it and introduce a non-linear self-interaction term. You also have sine-Gordon, which was extensively studied by Sidney Coleman, for example: https://en.wikipedia.org/wiki/Sine-Gordon_equation which has beautiful, beautiful solutions called "breathers"... There is a non-linear model of the Schrödinger non-relativistic equation which is cubic in the quantum amplitude: https://en.wikipedia.org/wiki/Nonlinear_Schrödinger_equation Etc. The subject is extraordinarily rich and full of forks in the way. Non-linearisation of evolution has been tried. One example is this modified non-relativistic Schrödinger equation with a self-interacting term \( \psi \left| \psi \right|^{2} \). Another one is the NL Dirac equation, which is relativistic, but non-linear in evolution. Another more drastic attempt to refurbish the whole thing is non-linear quantum mechanics, in which the whole suite of postulates is re-defined in terms of non-linear functionals instead of linear operators. If anyone is interested and has an alternative life to study it, I think here's a "reports" kind of article (that I haven't read): https://arxiv.org/pdf/1901.05088.pdf And so on, and so on. 1 Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 3 hours ago, joigus said: One of the big misteries about quantum mechanics has been this one precisely. I'd phrase it like, where does non-linearity come into play in quantum mechanics? Non-linearity is ubiquitous in Nature. How come linearity seems to be a sine qua non of QM? It's very strange. Strange indeed! 2 hours ago, sethoflagos said: Not in the general case. Navier-Stokes for example are parabolic This is can be understood as the basis of complexity in the macroscopic world. Can you substantiate on both? 32 minutes ago, studiot said: Good question, especially if you actually know what linear means ? Vector spaces are the backbone of linear mathematics. I already mentioned a while back that with the Schrodinger equation (which is linear) we are working in the vector space of square integrable functions of class C∞ However the relativistic version of Schrodinger is non linear ( Dirac equation, Klein Gordon equation etc) https://en.wikipedia.org/wiki/Nonlinear_Dirac_equation This bears out Seth's comment that combining linear operators may result in a non linear equation. +1 It should also be remembered that of the famous Four Laws (of Thermodynamcs) , only the First Law is linear and even has q and w as incomplete differentials. Back to Luc, Heisenberg's Uncertainty Principle is not even an equation - It is an inequality like the Second Law of Thermodynamics. Pauli Matrices are linear. I think that i know what linear means, but for most of your response to my post, i admit in struggling to understand. As for the Heisenberg uncertainty principle, i know too that it is a principle, not an equation. Maybe i didi not use the right terms in formulating my question. Equations are frequently mentioned to “justify” (probably not the right word) qm and “apply” qm Link to comment Share on other sites More sharing options...

studiot Posted December 8, 2023 Share Posted December 8, 2023 17 minutes ago, joigus said: I disagree................ Yes you are right. +1 Thanks for all the extra detail. But please remember tha many of these equations are 'linearised' (approximated linearly) in order to be able to solve them. Even special relativity employs a linearised quadratic for this. 12 minutes ago, Luc Turpin said: i know too that it is a principle, not an equation. It's an inequality. Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 3 minutes ago, studiot said: It's an inequality. Thank you for the correction I will llok up inequality right away Link to comment Share on other sites More sharing options...

joigus Posted December 8, 2023 Share Posted December 8, 2023 2 minutes ago, studiot said: But please remember tha many of these equations are 'linearised' (approximated linearly) in order to be able to solve them. Oh, absolutely. Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 I am contemplating leaving this thread, because i am extracting a lot out of it, but not contributing much.due to my limited knowledge of the subject matter Link to comment Share on other sites More sharing options...

sethoflagos Posted December 8, 2023 Share Posted December 8, 2023 56 minutes ago, Luc Turpin said: Can you substantiate on both? Bien sur. Voila: https://fr.wikipedia.org/wiki/Équations_de_Navier-Stokes https://fr.wikipedia.org/wiki/Complexité Link to comment Share on other sites More sharing options...

Luc Turpin Posted December 8, 2023 Author Share Posted December 8, 2023 16 minutes ago, sethoflagos said: Bien sur. Voila: https://fr.wikipedia.org/wiki/Équations_de_Navier-Stokes https://fr.wikipedia.org/wiki/Complexité Merci, french text was very useful in understanding first link second link: complexity as in chaos-cmplexity theory? e.g. inherent repetition, patterns, self-organisation, interconnectedness, self-similarity, and constant feedback loops. Link to comment Share on other sites More sharing options...

KJW Posted December 8, 2023 Share Posted December 8, 2023 Talking about linear vs non-linear physics, below is a connection between linear quantum mechanics and non-linear classical mechanics: Klein-Gordon equation: \[\frac{1}{c^2}\frac{\partial^2\psi}{\partial t^2} - \frac{\partial^2\psi}{\partial x^2} - \frac{\partial^2\psi}{\partial y^2} - \frac{\partial^2\psi}{\partial z^2} = -\frac{m^2c^2}{\hbar^2}\psi \] \[\psi = \psi_0 exp(\frac{i}{\hbar} S(t,x,y,z))\] where [math]S(t,x,y,z)[/math] is the action. \[\frac{\partial^2\psi}{\partial t^2} = \frac{\partial}{\partial t}(\frac{\partial}{\partial t} \psi_0 exp(\frac{i}{\hbar} S)) = \frac{\partial}{\partial t}(\frac{i}{\hbar} \psi_0 exp(\frac{i}{\hbar} S) \frac{\partial S}{\partial t}) = \frac{i}{\hbar} \psi_0 exp(\frac{i}{\hbar} S) \frac{\partial^2 S}{\partial t^2} - \frac{1}{\hbar^2} \psi_0 exp(\frac{i}{\hbar} S) (\frac{\partial S}{\partial t})^2 = \frac{i}{\hbar} \psi \frac{\partial^2 S}{\partial t^2} - \frac{1}{\hbar^2} \psi (\frac{\partial S}{\partial t})^2\] Similarly: \[\frac{\partial^2\psi}{\partial x^2} = \frac{i}{\hbar} \psi \frac{\partial^2 S}{\partial x^2} - \frac{1}{\hbar^2} \psi (\frac{\partial S}{\partial x})^2 \;\;;\;\; \frac{\partial^2\psi}{\partial y^2} = \frac{i}{\hbar} \psi \frac{\partial^2 S}{\partial y^2} - \frac{1}{\hbar^2} \psi (\frac{\partial S}{\partial y})^2 \;\;;\;\; \frac{\partial^2\psi}{\partial z^2} = \frac{i}{\hbar} \psi \frac{\partial^2 S}{\partial z^2} - \frac{1}{\hbar^2} \psi (\frac{\partial S}{\partial z})^2\] Thus: \[-i\hbar (\frac{1}{c^2}\frac{\partial^2 S}{\partial t^2} - \frac{\partial^2 S}{\partial x^2} - \frac{\partial^2 S}{\partial y^2} - \frac{\partial^2 S}{\partial z^2}) + (\frac{1}{c^2}(\frac{\partial S}{\partial t})^2 - (\frac{\partial S}{\partial x})^2 - (\frac{\partial S}{\partial y})^2 - (\frac{\partial S}{\partial z})^2) = m^2c^2\] In the classical limit of [math]\hbar = 0[/math], the linear second-order Klein-Gordon equation becomes the non-linear first-order Hamilton-Jacobi equation: \[\frac{1}{c^2}(\frac{\partial S}{\partial t})^2 - (\frac{\partial S}{\partial x})^2 - (\frac{\partial S}{\partial y})^2 - (\frac{\partial S}{\partial z})^2 = m^2c^2\] Link to comment Share on other sites More sharing options...

sethoflagos Posted December 8, 2023 Share Posted December 8, 2023 (edited) 1 hour ago, Luc Turpin said: second link: complexity as in chaos-cmplexity theory? e.g. inherent repetition, patterns, self-organisation, interconnectedness, self-similarity, and constant feedback loops. Yes. However, I find the word 'chaos' more misleading than helpful. Lorentz (or deterministic) chaos has the particular sense of Quote Chaos: When the present determines the future, but the approximate present does not approximately determine the future. ...which may appeal to mathematicians but not to me. I much prefer to think in terms of systems that spontaneously trend towards high diversity. This correlates in simple proportion to both maximal entropy and quantum entanglement. As an engineer, this helps give an inituitive feel for how, for example, the system's thermodynamic and chemical equilibria are likely to evolve. Edited December 8, 2023 by sethoflagos small clarification Link to comment Share on other sites More sharing options...

Genady Posted December 8, 2023 Share Posted December 8, 2023 6 hours ago, Luc Turpin said: we live in a non-linear world I struggle to see how linearity or non-linearity can be applied to a world. Link to comment Share on other sites More sharing options...

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