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To: r9etb; dalight
Now he may or may not be correct about this.. for ultimately this might lead to some sense of predestination.

The Feynman Path Integral, by the way, explains why predestination seems to be an ingredient of QM (in fact, the Principle of Least Action, which the FPI is an extension of, says the same thing in classical mechanics.) You can describe physics as the result of a Lagrangian in which the past and future are connected by functionals acting under some constraint. In this view, the end points appear to determine all the paths between them, which indeed they do: under the action of the constraint -- The Principle of Least Action -- this results in a single trajectory through phase space (in classical physics) or a set of trajectories in QM.

Completely equivalent to this is the Hamiltonian formulation of mechanics. In the Hamiltonian perspective, starting points are arrived at by application of the time-evolution operator. As you may know -- but for the benefit of passersby -- it is a first year grad-students' exercise to prove these two formulations are mathematically equivalent (after you struggle through Goldstien.)

So something that seems entirely predestined (Lagrangian mechanics) can arise from something where states move through time purely from one infinitesimal starting point to the next under the influence of the Hamiltonian, and vice versa. The reason two so fundamentally different ways of looking at time evolution appear the same is that the underlying physical principle -- The Principle of Least Action -- governs both.

62 posted on 08/18/2009 2:18:42 PM PDT by FredZarguna (It looks just like a Telefunken U-47. In leather.)
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To: FredZarguna
The Feynman Path Integral, by the way, explains why predestination seems to be an ingredient of QM (in fact, the Principle of Least Action, which the FPI is an extension of, says the same thing in classical mechanics.) You can describe physics as the result of a Lagrangian in which the past and future are connected by functionals acting under some constraint. In this view, the end points appear to determine all the paths between them, which indeed they do: under the action of the constraint -- The Principle of Least Action -- this results in a single trajectory through phase space (in classical physics) or a set of trajectories in QM.

While this understanding is deep and internally pleasing, it is limited as many models in physics in requiring that a boundary of consideration exists where specific boundary conditions can be stated and maintained. F=Ma only exists after all of the confounding and interfering terms are removed. This allows for a purity of exposition of the underlying principle when the messy chaotic details would just get in the way.

However, this is not the real world. The real world and more specifically physical reality is the all of the interactions all of the time including the simple ones governed by simple physical or chemical interaction but also including those that are modified by the force of choice and intent that are driven by analysis, subjectivity and even whim.

One admits that human intention limited as it is modifies the great events of time and space very little, but that they can at all is a question that begs to be answered in the presence of the proposition that an INVARIANT set of quantum possibilities may exist. Normal physics does not concern itself with attempting to predict the intentions of the experimenter or scientist or boy at the corner drug store, but this theory posits that all of this is preordained if the Set is truly fixed. Worse, it is the very function of the collapse of possibilities into the reduced set that represents the remaining possibilities that provides the arrow of time making it irreversible. However, I am reading way to much into this. I have to actually dig at the original discussion to make any more or less of it.

66 posted on 08/18/2009 2:47:10 PM PDT by dalight
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