I'm not sure why they couldn't reproduce their results? I'm also not sure if the MIT team did that particular double-slit experiment with the oil drops. The interesting part, for me, was that Couder team's trajectories are not compatible with Bohmian trajectories since they cross the axis of symmetry of the 2 slits. Bohmian trajectories do not.Hernik said:The group behind this study has not been able to reproduce Couder's double slit interference pattern from 2006.
bohm2 said:I'm not sure why they couldn't reproduce their results? I'm also not sure if the MIT team did that particular double-slit experiment with the oil drops. The interesting part, for me, was that Couder team's trajectories are not compatible with Bohmian trajectories since they cross the axis of symmetry of the 2 slits. Bohmian trajectories do not.
Yes, Bohmian trajectories do not cross in all versions or else they would not be consistent with QM:atyy said:But there are many possible forms of Bohmian dynamics (discussed eg. in http://arxiv.org/abs/0706.2522). Do the trajectories not cross in all versions of Bohmian dynamics?
Quantum Dynamics with Bohmian TrajectoriesNow recall the physics of the Bohmian evolution, which as we stressed in the introduction prevents trajectories from crossing each other...A trajectory crossing during a numerical simulation means that the simulated time-evolution is not Bohmian anymore, and thus not quantum mechanical, and therefore physically false.
The wave-induced added mass of walking dropletsIt has recently been demonstrated that droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic realm. The walker, consisting of a droplet plus its guiding wavefield, is a spatially extended object. We here examine the dependence of the walker mass and momentum on its velocity. Doing so indicates that, when the walker’s time scale of acceleration is long relative to the wave decay time, its dynamics may be described in terms of the mechanics of a particle with a speed-dependent mass and a nonlinear drag force that drives it towards a fixed speed. Drawing an analogy with relativistic mechanics, we define a hydrodynamic boost factor for the walkers...Some have further proposed that the interaction of moving particles with this vacuum field could give rise to a speed-dependent inertial mass, a feature of relativistic mechanics. We here explore the relevance of this perspective to the dynamics of walking droplets by inferring their wave-induced added mass.
nonequilibrium said:I like the quote(s), but the pilot-wave obeys the Schrödinger equation, which can hardly be called chaotic? Or is the claim that the Schrödinger equation is merely an effective description of a more chaotic, underlying medium?
bohm2 said:Another paper by the Bush team at MIT using the "pilot-wave-like" oil droplet model exploring for the first time possible connections/analogues to relativistic mechanics:
The wave-induced added mass of walking droplets
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2014/08/Boost-JFM.pdf
On the analogy of quantum wave-particle duality with bouncing dropletsWhile Bohmian quantum mechanics exhibits nonlocal features , the evolution of the droplet and the surface waves is rooted in hydrodynamics which is manifestly a local theory, unless incompressibility is assumed.
In the de Broglie-Bohm interpretation, the specific trajectory of the quantum particle does not backact onto the evolution of the wavefunction, whereas the droplet creates new surface waves at the position where it bounces. Those surface waves do evolve, to a very good approximation, according to a linear theory, but a direct mapping to the Schrodinger equation is not obvious...More importantly, however, the probability of finding a droplet in the minima never reaches zero as it does for a particle in the quantum case.
Here we note a striking contrast between the trajectories in the bouncing droplet system and those resulting from Bohmian mechanics. One of the tenants of Bohmian trajectories is that the trajectories are forbidden to cross each other, and in the double-slit experiment the trajectories from each slit will not cross the center line, but it is obvious that the trajectories in Fig. 5(d) have no such reluctance to do so.
With increasing which path information the probability density becomes more dependent on a single slit. Consequently the observed interference pattern becomes less pronounced as it is the wave function arising from both slits that gives rise to the pattern. We can make an analogy in the bouncing droplet system with the memory parameter being analogous to the which path information...The visibility will increase with increasing memory but never reach one, in contrast to quantum particles with a which path information of zero.
In view of this, it is not obvious to what extent the present classical analogy of quantum wave-particle duality can be maintained in more complex situations involving, e.g., more than one droplet.
bohm2 said:A more critical paper came out yesterday hi-liting some of the differences between QM, Bohmian mechanics and bouncing droplet analogues:
On the analogy of quantum wave-particle duality with bouncing droplets
http://arxiv.org/pdf/1410.1373.pdf
Hi,
Your question is excellent. We call a walker the ensemble of the droplet and its associated wave. Since the work you refer to we have shown that the wave field contains a memory of the past trajectory that is at the origin of the quantum like effects we observe. You will find attached a recent work dealing with this effect.
In the double slit experiment, while the droplet passes through one slit the associated wave passes through both so that one could say that the walker passes through both.
Our system is similar to a pilot wave system and this is what we are working on recently. These models are usually called de Broglie - Bohm models, a term that is very misleading because the two approaches are different from one another.
Bohm gets a dynamical equation from Shrödinger equation so that it concerns the dynamics of a maximum of probability. What de Broglie had in mind was a the dynamics of an individual particle associated with a wave.
Our system appears to be closer to de Broglie.
Best regards
Yves Couder
Yes, I know. But if trajectories cross, then you won't get QM predictions.liquidspacetime said:Which is completely missing the point. Walking droplets have nothing to do with Bohmian mechanics. de Broglie-Bohm theory is incorrectly named as de Broglie disagreed with it.
See post 94.Now recall the physics of the Bohmian evolution, which as we stressed in the introduction prevents trajectories from crossing each other...A trajectory crossing during a numerical simulation means that the simulated time-evolution is not Bohmian anymore, and thus not quantum mechanical, and therefore physically false.
bohm2 said:Yes, I know. But if trajectories cross, then you won't get QM predictions.
See post 94.
I'm not trying to refute anything. I'm interested in understanding how close of a quantum analogue, the walking droplet model is. I was under the impression (maybe wrongly) that if trajectories cross-over, then that model isn't a good quantum analogue.liquidspacetime said:You keep on insisting on referring to Bohmian mechanics, which has nothing to do with walking droplets, in order to refute walking droplets. Why is that?.
Why is Bohmian mechanics fundamentally flawed?liquidspacetime said:Bohmian mechanics is fundamentally flawed. Bohmian mechanics does not correctly represent physical reality. Bohmian mechanics has nothing to do with physical reality.
bohm2 said:I'm not trying to refute anything. I'm interested in understanding how close of a quantum analogue, the walking droplet model is. I was under the impression (maybe wrongly) that if trajectories cross-over, then that model isn't a good quantum analogue.
Why is Bohmian mechanics fundamentally flawed?
vanhees71 said:The only thing that's save to say is that there is nothing like wave-particle duality in modern quantum theory. Ironically with "modern" we label a theory which was completed nearly 90 years ago. The only problem is that didactics is behind by 100 years, unfortunately particularly high-school didactics (at least here in Germany). They still teach "old quantum mechanics", including Einstein's outdated photon picture and the Bohr-Sommerfeld model of the hydrogen atom. The result are wrong (and even qualitatively wrong) pictures about weird things as "wave-particle duality" or photons as if they were little minature billard balls. The abuse of the word "photon" is the worst of all of this didactical sins, as you can see in this forum. Most of what's called "photon" in the public media and in high-school physics (and unfortunately sometimes even at university) is in fact well described by the semiclassical approximation, where the electromagnetic field is described as classical background field, interacting with quantized matter particles. This is particularly true for Einstein's famous formula on the photoelectric effect. It's somwhat ironic that Einstein got his Nobel prize for the only piece of his great work that's totally outdated today and not for that part that must be counted to the most important achievements in physics for centuries, namely general relativity and statistical physics.
Bohm mechanics is just one more of many metaphysical interpretations of the quantum-theoretical formalism. It does not predict more than minimally interpreted quantum theory but is liked by some people who think it would be nice to have the idea of particle trajectories from classical mechanics translated into the quantum world. Unfortunately they are forced to complicated non-local dynamics which confuses the subject more than it helps to understand it, and this, as stressed above, without any additional merit in the sense of the physical core of the theory, which is the quantum-theoretical formalism with Born's probabilistic interpretation of the quantum state, not more and not less.
On a fundamental level our contemporary understanding of matter and its interactions (except gravity, which is not yet understood in terms of quantum theory) is a quantized relativistic-field picture anyway. One should say, however, that also this is with quite some probability only an effective theory and not the last word, as is general relativity for the description of the gravitational field, which is purely classical.
Whether there will ever be a better more comprehensive theory, future will perhaps tell. Thinking to have the final answer to all physics questions was always wrong in the past. It's a quite well-known story about Planck's try to figure out, what to do after finishing high school. He asked a renowned physics professor about physics, and this guy told him, it would be a waste of such a brillant mind as Planck to study this subject, because everything is in principle known, and the only task is to measure things to ever higher accuracy to confirm the known laws. The "little clouds" on the horizon of theoretical physics (mostly in statistical physics at the time) will be solved simply by measuring things more accurate. So the professor adviced Planck to better study ancient Latin and Greek rather than physics. Fortunately Planck hasn't followed this advice and later opened the window to the quantum world, leading to the resolution of all the "little clouds" on the horizon of theoretical physics.