What does the probabilistic interpretation of QM claim?by A. Neumaier Tags: claim, interpretation, probabilistic 

#37
Mar1511, 11:25 AM

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PF Gold
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#38
Mar1511, 11:47 AM

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PF Gold
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But the parameters x and t in a quantum field have the definite meaning of position and time  not of a particle, but of the point where the field strength is measured. The rate of response of the detector at position x at time t is for a photon proportional to the intensity <E(x,t)^2>, where E(x,t) is the complex analytic signal of the electric field operator, and for an electron proportional to the intensity <Psi(x,t)^2>, where Psi(x,t) is the Dirac field operator. That one doesn't need the collapse is just a welcome byproduct of this view. 



#39
Mar1511, 12:51 PM

P: 1,744

Eugene. 



#40
Mar1511, 01:27 PM

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PF Gold
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#41
Mar1511, 02:08 PM

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In my understanding, quantum mechanics says that these kinds of events are not predictable as a matter of principle. Nature has an inherently random component, which cannot be explained. The best we can do is to calculate probabilities of these random events. That's what quantum mechanics is doing and it is doing it brilliantly. Once we agreed on the fundamental randomness of quantum events, there is no other way, but to accept the idea of collapse: The outcomes are not known to us before observations, they are described only as probability distributions. After the observation is made a single outcome emerges, so the probability distribution collapses. There is nothing there to understand about the collapse. Things that are fundamentally random cannot be explained or understood any better than simply saying that they are random. From my discussions with you I've understood that you have a different view on the origin of randomness. You basically believe that nature obeys deterministic fieldlike equations. The appearance of a mark on the photographic plate has a mechanistic explanation in which the impacting electron field interacts with the fields of atoms in the plate. This interaction leads to some physical migration of the field energy and charge density to one specific point, which appears to us as a blackened AgBr microcrystal. These migration processes involve huge number of atoms, so they are "stochastic" or "chaotic", and their outcomes cannot be predicted at our current level of knowledge. Nevertheless, you maintain that at the fundamental level there are knowable field equations as opposed to the pure chance. These are two different philosophies, two different world views, which could be completely equivalent as far as specific experimental observations are concerned. In general, I find it not fruitful to argue about ones philosophy, religion or political preferences. These kinds of convictions cannot be changed by logical arguments. So, perhaps we should agree to disagree. Eugene. 



#42
Mar1511, 02:58 PM

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PF Gold
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Collapse _always_ refers to the collapse of the state  that after the measurement, the state of the measured system is in an eigenstate of the measured observable!!! This is the only way to influence people's convictions. 



#43
Mar1511, 03:53 PM

P: 1,744

So, I agree that collapse = "the change of prior probabilities into posterior certainties". However, I disagree that the collapse ever happens in classical physica, because in classical physics everything is determined and predictable. If somebody has encountered a "probability" in classical physics, that's only because this somebody was too lazy or ignorant to specify exactly all necessary initial conditions. Somebody's ignorance and laziness cannot be accounted for in a rigorous theory. "Zillions of degrees of freedom" is also not a good excuse to introduce probabilities, because we are talking about principles here, not about practical realizations. Eugene. 



#44
Mar1511, 05:53 PM

P: 661

It should be pointed out that A Neumaier's suggestion that a deterministic chaotic dynamics may underly quantum randomness is not the standard view, and to even be consistent with modern experimental results requires some additional weird assumptions such as explicit nonlocality (Bohm) or information loss behind event horizons ('t Hooft).
http://www.nature.com/news/2007/0704...s0704169.html 



#45
Mar1611, 04:50 AM

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PF Gold
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This holds even more for unperformable measurements or preparations. 



#46
Mar1611, 04:56 AM

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PF Gold
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depend on how wee look = depend on the measurement apparatus (here our eye). Thus his statement confirms my hypothesis. 



#47
Mar1611, 11:17 AM

P: 661

I added that link to a mainstream science article to point out the mainstream view on quantum interpretation, just in case people think your "science advisor" tag adds credibility to your nonstandard view. But I'm not saying you're wrong, just that it's an an unusual model to be promoting. 



#48
Mar1611, 02:20 PM

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Eugene. 



#49
Mar1711, 03:43 AM

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field carrying charge)? To me these seem adequate to account for the experimental observations. 



#50
Mar1711, 10:57 AM

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PF Gold
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By the way, there are no nogo theorems against deterministic field theories underlying quantum mechanics. Indeed, local field theories have no difficulties violating Belltype inequalities. See http://www.mat.univie.ac.at/~neum/ms/lightslides.pdf , starting with slide 46. G. Ghirardi, Quantum dynamical reduction and reality: Replacing probability densities with densities in real space, Erkenntnis 45 (1996), 349365. http://www.jstor.org/stable/20012735 My only new point compared to them is that one doesn't need the dynamic reduction once one has the field density ontology. 



#51
Mar1711, 11:10 AM

P: 661

@A. Neumaier, I don't understand you, make it simple for me, is deterministic chaotic dynamics the fundamental mathematical description of reality in your model?




#52
Mar1711, 12:28 PM

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PF Gold
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In my thermal interpretation of quantum physics, the directly observable (and hence obviously ''real'') features of a macroscopic system are the expectation values of the most important fields Phi(x,t) at position x and time t, as they are described by statistical thermodynamics. If it were not so, thermodynamics would not provide the good macroscopic description it does. However, the expectation values have only a limited accuracy; as discovered by Heisenberg, quantum mechanics predicts its own uncertainty. This means that <Phi(x)> is objectively real only to an accuracy of order 1/sqrt(V) where V is the volume occupied by the mesoscopic cell containing x, assumed to be homogeneous and in local equilibrium. This is the standard assumption for deriving from first principles hydrodynamical equations and the like. It means that the interpretation of a field gets more fuzzy as one decreases the size of the coarse graining  until at some point the local equilibrium hypothesis is no longer valid. This defines the surface ontology of the thermal interpretation. There is also a deeper ontology concerning the reality of inferred entities  the thermal interpretation declares as real but not directly observable any expectation <A(x,t)> of operators with a spacetime dependence that satisfy Poincare invariance and causal commutation relations. These are distributions that produce exact numbers when integrated over sufficiently smooth localized test functions. Approximating a multiparticle system in a semiclassical way (mean field theory or a little beyond) gives an approximate deterministic system governing the dynamics of these expectations. This system is highly chaotic at high resolution. This chaoticity seems enough to enforce the probabilistic nature of the measurement apparatus. Neither an underlying exact deterministic dynamics nor an explicit dynamical collapse needs to be postulated. 



#53
Mar1711, 12:37 PM

P: 661

Sorry, but chaotic dynamics is an exact mathematical model, that's the whole point of it, you can't say it's "emergent". Sensitive dependence at infinitesimally small changes in the the dynamical parameters is part of the definition of chaotic dynamics. If you have a stochastic dynamics then you have stochastic dynamics, if you have deterministic dynamics then you have deterministic dynamics, there's no inbetween "emergent" type system.




#54
Mar1711, 12:56 PM

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PF Gold
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The same system can be studied at different levels of resolution. When we model a dynamical system classically at high enough resolution, it must be modeled stochastically since the quantum uncertainties must be taken into account. But at a lower resolution, one can often neglect the stochastic part and the system becomes deterministic. If it were not so, we could not use any deterministic model at all in physics but we often do, with excellent success. This also holds when the resulting deterministic system is chaotic. Indeed, all deterministic chaotic systems studied in practice are approximate only, because of quantum mechanics. If it were not so, we could not use any chaotic model at all in physics but we often do, with excellent success. 


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