For instance: are all eigenfunctions favoured, or are all non-eigenfunctions supressed?
All physical laws are laws of prevention and at the same time of cause. Could you give an example of a physical law which you believe not a such one?
Thank you sincerely Ekaterina. I like your answer.
I would say that information content of quantum wave packets, prior to measurement, is neither caused nor prevented. Likewise the value outcome of any one measurement. Also, I would say, that probability in quantum measurement is caused: possibly while all other probabilities are prevented. There is also the question of chaotic indeterminacy, of which I know nothing.
sir can you please elaborate more on the question? seems very interesting but can't really picture it.
Thank you Rajat.
If I give an example. When an apple falls DOWN from a tree, is that motion caused, or are all other motions prevented? Do these two amount to the same, or Is there an excluded middle of possibilities that are neither caused nor prevented, where not-caused is not identical to prevented?
Eigenfunction of what? For each system, there is a set of observables that don't commute, that is, have not a common set of eigenfunctions.
Perhaps conservation laws are laws of prevention.
The term "prevention" is very antropologic - and sounds like some kind of law language (criminal prevention, etc...). However, we see sometimes more the prevention than the cause in some physical laws or their application. Examples: Inertia Law in Mechanics, Heron's Principle of minimal effort (with a special application in optic), Archimede's Principle, Principle of minimal potential energy, defining minimal surfaces (eg, why are the planets round), etc. I observe that we psychologically interpret Physical laws as being laws of prevention, if they speak about the apparition of some force of reaction to some different action. If the Big Bang would have been only a local phenomenon (and so should be written big bang and not Big Bang), its apparition can be interpreted as the reaction to some pre-existent condition - like density or entropy in a very big volume of space being to small. "Horror Vacui" in a very proper sense... So another presumptive law of prevention.
This question seems to arise from a misunderstanding of quantum mechanics. As a matter of fact, Schrödinger has titled his pioneering papers as "Quantization as an eigenvalue problem". At once, he himself (!) has realized, that the mathematics of eigenvalue problems belongs to *classical* problems (strings, organ pipes etc.).
If quantization is understood as a selection problem (in agreement with Einstein's 1907 paper on the specific heat of solids) rather than as an eigenvalue problem, both, Schrödinger's requirement can be fulfilled (see my 2005 paper with Dieter Suisky and my 2006 book with Springer publ.), and your question can be answered. the latter in full Agreement with Schrödinger 1926, 4th Commun., § 7.
Looking forward,
Peter
Steve,
I wonder if we compare linear systems with dynamical systems there may be route into your problem.
With simple linear systems (ignoring for the moment, the philosophical problem associated with the concept of' 'cause' vs 'correlation'), it might be argued that the identification of a 'positive' and limited cause seems unambiguous. However, in dynamical systems the identification of a simple cause is much more problematic.
It seems to me that, given the fact that ALL components of a dynamical system play a role in determining the system's evolution, it is in the dynamical domain that the possibility exists for an ambiguity between cause and prevention such as you describe.
Chris Davia
The point I am getting at in this question is the following idea. In classical theory, everything that happens is caused, while everything that does not happen is prevented. But in quantum wave packets, indeterminate 'happenings' might regarded as a "domain of freedom" that is not prevented, but is not caused either.
Steve,
the basic quantum equations (Schrödinger, Dirac etc.) are as deterministic as the basic classical ones (Newton, Lagrange etc.).
I think in the example of apple falling down, clearly all other forces are prevented from being acted upon the object except gravity which prevails. Now when the conditions are ideal and only gravity is acting the the two things can be same. But imagine hard wind blowing and now when the apple falls, it goes downward as well as in the direction of wind. You can also imagine a leaf from tree. Eventually both will come to rest on the ground but other forces which cause leaf or apple to change the direction. Basically gravity is the force that prevents the apple from going in any other direction but downwards whereas external forces such as wind cause the motion of apple away from ideal position that would be right below the point it was detached from tree. I feel it would be safe to say that in ideal cases prevention takes place and in non ideal mix. And since nothing is ideal, we see a mixture of cause and prevention taking place. I hope i made my thought clear here.
This question needs a clearcut contextualization before being answered.
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