iMechanica - quantum
https://imechanica.org/taxonomy/term/3403
enA preliminary document on my fresh new approach to QM
https://imechanica.org/node/23078
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/411">Mechanics in the quantum regime</a></div><div class="field-item even"><a href="/taxonomy/term/3403">quantum</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Hello, World</p>
<p>Here is a document that jots down, in a brief, point-wise manner, the elements of my new approach to understanding quantum mechanics.</p>
<p>Please note that the writing is very much at a preliminary stage. It is very much a work in progress. However, it does jot down many essential ideas.</p>
<p>I am uploading the document at iMechanica just to have an externally verifiable time-stamp to it. Further versions will also be posted at this thread.</p>
<p>Comments are welcome. However, I may not be able to respond all of them immediately, because (i) I wish to immediately switch over to my studies of Data Science (ii) discussions on QM, especially on its foundations, tend to get meandering very fast.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
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<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://imechanica.org/files/0.7.NewShorterOutlineElementsNewApproachQP.pdf" type="application/pdf; length=93845" title="0.7.NewShorterOutlineElementsNewApproachQP.pdf">Version 0.7: An Outline of the Elements of a New Approach to Understanding Quantum Physics.</a></span></td><td>91.65 KB</td> </tr>
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</div></div></div>Mon, 11 Feb 2019 15:50:15 +0000Ajit R. Jadhav23078 at https://imechanica.orghttps://imechanica.org/node/23078#commentshttps://imechanica.org/crss/node/23078An interesting arXiv paper: "Precession optomechanics"
https://imechanica.org/node/10166
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/283">Mechanics of Photonic Devices</a></div><div class="field-item odd"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/3403">quantum</a></div><div class="field-item odd"><a href="/taxonomy/term/6207">photon</a></div><div class="field-item even"><a href="/taxonomy/term/6208">photon mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
</p>
<p>Just thought that the following paper archived at the arXiv yesterday could be of general interest to any mechanician:</p>
<p>
Xingyu Zhang, Matthew Tomes, Tal Carmon (2011) "Precession optomechanics," arXiv:1104.4839 [<a href="http://arxiv.org/abs/1104.4839" target="_blank">^</a>]
</p>
<p>
The fig. 1 in it makes the matter conceptually so simple that the paper can be recommended to any mechanician for his general reading, and not only to a specialist in the field.
</p>
<p>
<br />
--Ajit
</p>
<p>
[E&OE]
</p>
</div></div></div>Wed, 27 Apr 2011 07:26:09 +0000Ajit R. Jadhav10166 at https://imechanica.orghttps://imechanica.org/node/10166#commentshttps://imechanica.org/crss/node/10166FEM Is Not a Local Method (and It Isn't Global Either)
https://imechanica.org/node/4752
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/846">FEM</a></div><div class="field-item odd"><a href="/taxonomy/term/1010">FDM</a></div><div class="field-item even"><a href="/taxonomy/term/2608">BEM</a></div><div class="field-item odd"><a href="/taxonomy/term/3398">local theory</a></div><div class="field-item even"><a href="/taxonomy/term/3399">global theory</a></div><div class="field-item odd"><a href="/taxonomy/term/3400">sub-global theory</a></div><div class="field-item even"><a href="/taxonomy/term/3401">Fourier</a></div><div class="field-item odd"><a href="/taxonomy/term/3402">integral equations</a></div><div class="field-item even"><a href="/taxonomy/term/3403">quantum</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In the literature, FEM has sometimes been characterized as a local approach, but IMO this needs to be corrected.</p>
<p>The piecewise continuous trial-functions of FEM can be looked at from two different viewpoints:</p>
<p>(i) If FEM is seen as an expansion method making use of basis functions, then naturally the comparison is with the Fourier-theoretic approaches (and all the derived, consequent or similar ones). The basis functions for the latter are global in the sense they have supports all over the domain. This, indeed, is unlike the limited (piecewise) support of the FEM trial-functions.</p>
<p>(ii) Yet, on the other hand, if FEM is seen an integral approach, i.e. an approach which is based either on functionals or on domain integrals of the residuals, then notice that both such expressions enjoy support over a finite region—not infinitesimal. Consequently, FEM cannot really be said to be a local approach. Compare it, for instance, with FDM. Or, with the ideas of the differential calculus per say.</p>
<p>I therefore object to characterizations of FEM as a local approach. Also for its characterization as a global approach. I believe that FEM is “midway,” really speaking.</p>
<p>As a relevant aside, also consider here that, in structural FEM for instance, the potential energy (and its stationarity) *is* globally defined, and yet, the displacements are defined only in a piecewise manner—i.e. over only sub-intervals of the overall domain.</p>
<p>I, therefore, suggest that a term like “sub-global” (or "supra-local") might be used to characterize FEM. And also, other methods like FEM.</p>
<p>In between the two candidates considered here, the first (”sub-global”) appears a more complete description as compared to the second (”supra-local”.) The first also sounds more honest and less pseudo-intellectual. (A third candidate, viz. “ultra-local,” seems to imply exactly the opposite of the intended meaning: it seems to doubly emphasize the local nature. Hence, it is unsuitable.)</p>
<p>I, thus, vote for the “sub-global” term.</p>
<p>Other methods where this term becomes relevant and applicable include, for example, BEM. Also MD, wherein, despite the use of point-particles, the potential itself is not a point-phenomenon (just the way it also does not have infinite support due to the cut-off). As such, MD, too, too should be characterized as a “sub-global” method.</p>
<p>BTW, this issue is neither obscurely academic nor pedantic. … Here, ask yourself why quantum entanglement is at all considered to be so “counter-intuitive” or “dramatic” (or gets so hotly debated/discussed).</p>
<p>-----</p>
<p>Well thought-out corrections to my position would be welcome, as also any really relevant complementary observation(s).</p>
<p>Thanks in advance.</p>
</div></div></div>Thu, 05 Feb 2009 07:46:22 +0000Ajit R. Jadhav4752 at https://imechanica.orghttps://imechanica.org/node/4752#commentshttps://imechanica.org/crss/node/4752