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January 21, 2018

ARTICLE: Searching for the Impossible [back to article]
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Anonymous wrote on Jan. 17, 2015 @ 19:28 GMT
It is interesting the existence of the class of undecidable problem; I am thinking that a chaotic system, and the corresponding quantum system, have different evolution with different initial condition; so that the machine precision change the solution, so that the solution depends on the machine, so that each solution is not a true solution.

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Anonymous wrote on Jan. 19, 2015 @ 06:10 GMT
Can this give some hints for experimental observation??

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Robert H McEachern wrote on Jan. 19, 2015 @ 15:42 GMT
Assuming "something" should be described as a "superposition", is, in the limit, equivalent to assuming that the "something" has a property that is "undecidable". The limit is the uncertainty principle, which has to do with resolution, not accuracy.

In other words, the undecidability, is inherent in the assumption, that superposition is the best way to mathematically describe every "something", not the "something" being observed. The property that is undecidable, is "How many spectral components exist within a superposition, with the smallest possible time-bandwidth product?"

A system, like an FM radio receiver, that knows the answer to that question, a priori, does not need to "decide" that issue, based on measurements. But that does not mean the issue is undecidable. It simply means that a priori information is required to make the decision.

The paradox of undecidability only arises, when physicists make the bad assumption, that nothing in the cosmos, is capable of exploiting such a priori information.

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Jonathan J. Dickau replied on Jan. 20, 2015 @ 15:27 GMT
Good call Rob..

To call it a superposition may indeed obscure its true nature, by assuming a level or type of quantum-ness that is not realized in physical systems. The discrete bands noted by Stern and Gerlach reflect that the system measured offers a range of unique possibilities, but the optical fiber problem seems to be a question of whether the measurement at the terminus is assumed to be Classical or not.

The defect may lie in thinking of the degraded coherent state as maximally entangled with the background (i.e. as a superposition with all nature), rather than assuming that a physical system can regard this as a kind of local ground state. This 'settled' condition is providing a kind of a priori knowledge which the 'superposed' Eigenstate view lacks.

All the Best,


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John R. Cox replied on Jan. 20, 2015 @ 16:54 GMT
Rob and Jonathon,

P-p-please, sirs. I want some more. (Pip)

Your remarks are very informative for me of the physical nature that quantum theory addresses. Do continue, thanks. jrc

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Robert H McEachern replied on Jan. 20, 2015 @ 18:25 GMT

You can find some more info, in my 2012 FQXI essay, about the nature of Fourier superpositions.

The most important point is this; as it is usually measured, a Gaussian function has the minimum time-bandwidth product. Consider two scenarios, both involving multiplying noisy sinusoids, with a Gaussian "window" function:

Case 1) A single noisy sinusoid, is multiplied by the...

view entire post

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John R. Cox wrote on Jan. 22, 2015 @ 05:57 GMT

Okay, textbook. Graphically the exponential function describes a parabola, so the usage of 'e' apparently 'smooths' out the transform of probability distributions from Fourier into Gaussian. I had been thinking Gaussian terms, as in electrostatic or electromagnetic units, so had also misunderstood 'Gaussian window' as a range of intensity rather than probability.

Gettin' there. jrc

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Jonathan J. Dickau wrote on Jan. 22, 2015 @ 17:22 GMT
Hi Folks,

I've been trying to read the above comments, and encountering a weird truncation of the content on the bottom, when I expand the comments. But I noticed I could read a bit more after John left the comment above, so I'm hoping I can get things to expand out further by increasing the lower page boundary - simply by adding more content to the default page representation. I apologize if this rambling comment annoys anyone, but I am trying to use plenty of lengthy words in the hopes that a voluminous block of text can solve the display problem, without having to get the techies involved.

We will have to see, if the addition of a comment or two on the bottom lets people see the entire block of comments above. I imagine it must be my browser version, OS, or something machine-specific, and I hope this page displays correctly for most everyone else. But I wanted to explore the possibility the issue might be self-correcting.

All the Best,


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Jonathan J. Dickau wrote on Jan. 22, 2015 @ 17:34 GMT
A little better..

In fact; I can read almost all of the above block now.

So I will write a few more lines.

I see that all the extra space I am creating on the bottom is allowing me to see almost all of the comments above. So I am adding just a bit more content.

This additional verbiage, added for no purpose of communication whatsoever, will help me to see Rob's response to John in the block above.

Thanks for your patience folks!

Have Fun!


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Jonathan J. Dickau replied on Jan. 22, 2015 @ 17:38 GMT

It worked!

I can read the whole block of comments above now, and collapse them when I'm done. So I can get to see all of the content.

All the Best,


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John R. Cox replied on Jan. 22, 2015 @ 18:47 GMT

I started having the same problems on 1/19/15 when Microsoft tricked me into an update of windows 8.1. Now I can get control of my own idiot box. Same old bait and switch. jrc

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John R. Cox replied on Jan. 22, 2015 @ 20:44 GMT

What worked for me after choosing 'show all replies', was to click the maximize icon upper right corner (Windows) which resulted in a half screen, then click again and I get full screen and no bottom of page truncation. jrc

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Christopher Inman wrote on Jan. 25, 2015 @ 19:03 GMT
I thought it had been decided that the relationship between was set at the generation of the entangled particles and so one particle did not, in itself, change when the other was read. Is there a difference between determining a state and discovering a state?

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jay wrote on Feb. 28, 2015 @ 19:57 GMT
is this not Entscheidungsproblem?


I don't know if I can decide

calculus, Church–Turing thesis, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem

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