Re: [Vo]:Emergent Quantum Mechanics
Very interesting. Dave -Original Message- From: Harry Veeder hveeder...@gmail.com To: vortex-l vortex-l@eskimo.com Sent: Sat, Mar 30, 2013 12:07 am Subject: Re: [Vo]:Emergent Quantum Mechanics On Fri, Mar 29, 2013 at 11:46 PM, Harry Veeder hveeder...@gmail.com wrote: http://www.nonlinearstudies.at/quantummechanics.php Emergent Quantum Mechanics One is here reminded of Feynman’s famous discussion of the double slit, and his introductory remark: We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way and has in it the heart of quantum mechanics. In reality, it contains the only mystery. However, the above-mentioned recent classical physics experiments not only disprove Feynman’s statement w.r.t. the double slit, but prove that a whole set of “quantum” features can be shown to occur in completely classical ones, among them being the Heisenberg uncertainty principle, indeterministic behaviour of a particle despite a deterministic evolution of its statistical ensemble over many runs, nonlocal interaction, tunnelling, and, of course, a combination of all these. We are referring to the beautiful series of experiments performed by the group of Yves Couder using small liquid drops that can be kept bouncing on the surface of a bath of the same fluid for an unlimited time when the substrate oscillates vertically. These “bouncers” can become coupled to the surface waves they generate and thus become “walkers” moving at constant velocity on the liquid surface. A “walker” is defined by a lock-in phenomenon so that the drop falls systematically on the forward front of the wave generated by its previous bouncings. It is thus a “symbiotic” dynamical phenomenon consisting of the moving droplet dressed with the Faraday wave packet it emits. Couder and Fort report on single-particle diffraction and interference of walkers. They show “how this wavelike behaviour of particle trajectories can result from the feedback of a remote sensing of the surrounding world by the waves they emit”. Of course, the “walkers” of Couder’s group, despite showing so many features they have in common with quantum systems, cannot be employed one-to-one as a model for the latter, with the most obvious difference being that quantum systems are not restricted to two-dimensional surfaces. However, along with the understanding of how the Schrödinger equation can be derived via nonequilibrium thermodynamics, also the mutual relationship of particle and wave behaviour has become clearer. A video of the walkers http://www.youtube.com/watch?v=nmC0ygr08tE The pilot-wave dynamics of walking droplets Harry
Re: [Vo]:Emergent Quantum Mechanics
Harry, This fits nicely into place with my technique for analyzing electromagnetic systems. I start with something that is well understood and easy to measure such as a very low frequency electromagnetic wave and mentally increase its frequency. Zero frequency is valid so you can measure the electric field from the device as well as the magnetic field. Since these are both static in this case, it is not too difficult to determine how these fields behave. It is quite apparent that there is no particle like behavior in this case. So, I ask why should there be a difference in basic form as the frequency rises. The question arises as to when the other behavior starts and I can not determine a reason for a special cut off point to exist. I use this logic to keep increasing the frequency upwards. The double slit as well as all other similar experiments fall into place very well when I consider electromagnetic phenomena as composed of waves. The main experiment that I recall which causes me trouble is when a single photon of light passes through the double slit and can be detected at only one location that matches the underlying interference pattern. A continuous wave should not behave in this manner according to my understanding. To counter the above situation is the measurement of diffraction for atoms, electrons, and etc. These are understood to be point like objects which should pass through just one slit. The fact that these projectiles also generate interference patterns suggests that something unusual is occurring that is not restricted to waves alone. Perhaps the discussion that you have posted below can help to clarify the true situation. Dave -Original Message- From: Harry Veeder hveeder...@gmail.com To: vortex-l vortex-l@eskimo.com Sent: Fri, Mar 29, 2013 11:46 pm Subject: [Vo]:Emergent Quantum Mechanics Robin, Sorry I did some googling and I learned there are ways you can derive some quantum conditions from classical physics. What remains to be seen is if all features of quantum mechanics can be derived classically, but it appears from reading the essay below, that more and more features are coming to have a classical explanation. Harry http://www.nonlinearstudies.at/quantummechanics.php Emergent Quantum Mechanics An Approach via Sub-Quantum Thermodynamics Considering a theory as emergent if it “contains or reduces to another theory in a significant manner or if its laws are tied to those of another theory via mathematical connections” [Robert Carroll], we propose that quantum mechanics is such a theory. More precisely, we propose that quantum theory emerges from a deeper, more exact theory on a sub-quantum level. In our approach, one assumes that the latter can be described with the aid of nonequilibrium thermodynamics. We ask ourselves how quantum theory would have evolved, had the “tool” of modern nonequilibrium thermodynamics existed, say, a century ago. As has recently been shown, one can derive the exact Schrödinger equation with said tool, where the relation between energy and frequency, respectively, is used as the only empirical input [Grössing], with the additional option that even the appearance of Planck’s constant may have its origin in classical physics. For an extensive review of our respective papers, and for connections to similar work, and, in particular, to Fisher information techniques, see [Carroll 2010]. In a recent review for Entropy (2010), to be published shortly, we have summarized the results of our works relating to the derivation from purely classical physics of the following quantum mechanical features: Planck’s relation E=hbar.omega for the energy of a particle, the Schrödinger equation for conservative and non-conservative systems, the Heisenberg uncertainty relations, the quantum mechanical superposition principle, Born’s rule, and the quantum mechanical “decay of a Gaussian wave packet”. We have, a.o., also proven that free quantum motion exactly equals sub-quantum anomalous (i.e., “ballistic”) diffusion, and, via computer simulations with coupled map lattices, we have shown how to calculate averaged (Bohmian) trajectories purely from a real-valued classical model. This was illustrated with the cases of the dispersion of a Gaussian wave packet, both for free quantum motion and for motion in a linear (e.g., gravitational) potential. The results are shown to be in excellent agreement with analytical expressions as they are obtained both via our approach, and also via the Bohmian theory. However, in the context of the explanation of Gaussian wave packet dispersion, quantitative statements on the trajectories’ characteristic behavior are presented, which cannot be formulated in any other existing model for quantum systems. As is well known, the main features of quantum mechanics, like the Schrödinger equation, for example, have only been postulated,
Re: [Vo]:Emergent Quantum Mechanics
In reply to Harry Veeder's message of Fri, 29 Mar 2013 23:46:30 -0400: Hi, [snip] As has recently been shown, one can derive the exact Schrödinger equation with said tool, where the relation between energy and frequency, respectively, is used as the only empirical input [Grössing], with the additional option that even the appearance of Plancks constant may have its origin in classical physics. Note that Plancks constant has the dimension of energy x time, so when they introduce the relation between energy and frequency, respectively, is used as the only empirical input they are in fact introducing Plancks constant. Regards, Robin van Spaandonk http://rvanspaa.freehostia.com/project.html
Re: [Vo]:Emergent Quantum Mechanics
On Fri, Mar 29, 2013 at 11:46 PM, Harry Veeder hveeder...@gmail.com wrote: http://www.nonlinearstudies.at/quantummechanics.php Emergent Quantum Mechanics One is here reminded of Feynman’s famous discussion of the double slit, and his introductory remark: We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way and has in it the heart of quantum mechanics. In reality, it contains the only mystery. *However, the above-mentioned recent classical physics experiments not only disprove Feynman’s statement w.r.t. the double slit, but prove that a whole set of “quantum” features can be shown to occur in completely classical ones, among them being the Heisenberg uncertainty principle, indeterministic behaviour of a particle despite a deterministic evolution of its statistical ensemble over many runs, nonlocal interaction, tunnelling, and, of course, a combination of all these. *We are referring to the beautiful series of experiments performed by the group of Yves Couder using small liquid drops that can be kept bouncing on the surface of a bath of the same fluid for an unlimited time when the substrate oscillates vertically. These “bouncers” can become coupled to the surface waves they generate and thus become “walkers” moving at constant velocity on the liquid surface. A “walker” is defined by a lock-in phenomenon so that the drop falls systematically on the forward front of the wave generated by its previous bouncings. It is thus a “symbiotic” dynamical phenomenon consisting of the moving droplet dressed with the Faraday wave packet it emits. Couder and Fort report on single-particle diffraction and interference of walkers. *They show “how this wavelike behaviour of particle trajectories can result from the feedback of a remote sensing of the surrounding world by the waves they emit”.* Of course, the “walkers” of Couder’s group, despite showing so many features they have in common with quantum systems, cannot be employed one-to-one as a model for the latter, with the most obvious difference being that quantum systems are not restricted to two-dimensional surfaces. However, along with the understanding of how the Schrödinger equation can be derived via nonequilibrium thermodynamics, also the mutual relationship of particle and wave behaviour has become clearer. A video of the walkers http://www.youtube.com/watch?v=nmC0ygr08tE The pilot-wave dynamics of walking droplets Harry
Re: [Vo]:Emergent Quantum Mechanics
More great walking droplet videos. Two walking droplets colliding and attracting http://www.youtube.com/watch?NR=1v=Xm_6Gi4Jqbg This video begins with a bunch of bouncing droplets in a regular array. Watch the collisions closely. Sometimes the droplets merge, sometimes they don't. http://www.youtube.com/watch?v=yCWpGfuyAjU Harry On Sat, Mar 30, 2013 at 12:07 AM, Harry Veeder hveeder...@gmail.com wrote: On Fri, Mar 29, 2013 at 11:46 PM, Harry Veeder hveeder...@gmail.comwrote: http://www.nonlinearstudies.at/quantummechanics.php Emergent Quantum Mechanics One is here reminded of Feynman’s famous discussion of the double slit, and his introductory remark: We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way and has in it the heart of quantum mechanics. In reality, it contains the only mystery. *However, the above-mentioned recent classical physics experiments not only disprove Feynman’s statement w.r.t. the double slit, but prove that a whole set of “quantum” features can be shown to occur in completely classical ones, among them being the Heisenberg uncertainty principle, indeterministic behaviour of a particle despite a deterministic evolution of its statistical ensemble over many runs, nonlocal interaction, tunnelling, and, of course, a combination of all these. *We are referring to the beautiful series of experiments performed by the group of Yves Couder using small liquid drops that can be kept bouncing on the surface of a bath of the same fluid for an unlimited time when the substrate oscillates vertically. These “bouncers” can become coupled to the surface waves they generate and thus become “walkers” moving at constant velocity on the liquid surface. A “walker” is defined by a lock-in phenomenon so that the drop falls systematically on the forward front of the wave generated by its previous bouncings. It is thus a “symbiotic” dynamical phenomenon consisting of the moving droplet dressed with the Faraday wave packet it emits. Couder and Fort report on single-particle diffraction and interference of walkers. *They show “how this wavelike behaviour of particle trajectories can result from the feedback of a remote sensing of the surrounding world by the waves they emit”.* Of course, the “walkers” of Couder’s group, despite showing so many features they have in common with quantum systems, cannot be employed one-to-one as a model for the latter, with the most obvious difference being that quantum systems are not restricted to two-dimensional surfaces. However, along with the understanding of how the Schrödinger equation can be derived via nonequilibrium thermodynamics, also the mutual relationship of particle and wave behaviour has become clearer. A video of the walkers http://www.youtube.com/watch?v=nmC0ygr08tE The pilot-wave dynamics of walking droplets Harry
