iMechanica - Comments for "What would you choose as the Top 5 Equations? Top 10?"
https://imechanica.org/node/10188
Comments for "What would you choose as the Top 5 Equations? Top 10?"enIsnt that a trivial result of a clever defenition
https://imechanica.org/comment/16820#comment-16820
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<p><em>In reply to <a href="https://imechanica.org/comment/16685#comment-16685">Here are two equations that might make my top 10 equations</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>midhun<br />
student<br />
iitm</p>
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</ul>Mon, 30 May 2011 13:52:59 +0000midhun1987comment 16820 at https://imechanica.orgReplies re. Top 5/10 Equations
https://imechanica.org/comment/16733#comment-16733
<a id="comment-16733"></a>
<p><em>In reply to <a href="https://imechanica.org/node/10188">What would you choose as the Top 5 Equations? Top 10?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hi all,
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0. Thanks for all your suggestions. (I lost my first draft while typing---accidentally closed the reply window. Will try to recapture as much thought as possible.) Detailed comments below.
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<strong>1. </strong><strong>Zhigang</strong>, I completely missed out on these two equations! Thanks for introducing a principle as fundamental and as general as the second law of thermodynamics, in this discussion!!
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Out of those two equations, however, methinks, dS = dU/T would always compete better than S = k ln W to make it in the shortest of the short lists. And there go I---I now have to face the wrath of so many physicists!! But still...
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The application of certain basic conceptual ideas concerning the nature of the physical universe (which, I, in my notes on "The Universe: Finite or Infinite" (still under preparation) call the principle of composition), together with the more basic continuum definition of entropy, could lead to the Boltzmann equation. However, theoretically tracing the converse would be difficult, IMHO. That's the general idea why I would pick out dS = dU/T over S = k ln W.
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<strong>2. Noureddine</strong>, I don't really expect the so called unifying equation to be here any time soon, or, for that matter, ever. The nature of physics is just not like that. Still, if it is possible to have such an equation, then every other equation would be encompassed by it. Surely, also e = mc^2, which, in any case, is only an implication of the classical EM theory together with Lorentz transformation.
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Now, the energy-mass conversion was a profound insight, theoretically, and of a lot of consequence, practically (think atomic energy and atom bombs). Yet, while compiling the shortest of the short list of equations of all times, I am not sure if it merits to be mentioned indpendently, regardless of what hippies, music- and "culture"-people in general have made of it.
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Similarly, the Gauss equation is already a part of the Maxwell equations. So, it need not be mentioned separately.
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But then, you still have one (or six) open slots anyway! What would you fill them with?
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<strong>3. "sasaborg"</strong>, I think the Euler identity can be said to have been already well-absobed in the Fourier transform equation (the way we know it, in its modern form---i.e. including the cosines as well as the sines.)
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I am curious what you would have to say for the remaining 4 (or 9) slots which are, like, totally like, still open to you!
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<strong>4. Siva</strong>, a couple of points:
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4.1 I think that you can perhaps collapse the two momenta conservation principles into one. If you do that, then, with Newton's second law (defining the force and the torque) as an additional given, the energy conservation principle already comes out as an entailment---it need not be stated separately.
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However, though personally I am not too sure of it, the mainstream physicists' view seems to be that the converse is not necessarily true. They say that the momentum conservation always holds---whether in the relativistic regime or the quantum mechanical one. But not the energy conservation.
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4.2 Which brings me to the second point. Not all of physics lies within those four laws; you have to specify some additional equations/ideas to take you to the relativistic and quantum mechanical regimes.
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Anyway, you still have one (or six) more slots open for you to think of!!
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<strong>5. Finally, how about a few more equations</strong> that we could perhaps be talking about?
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How about Hiesenberg's relation (Dp Dx = \hbar/2)? Here, again, many physicist suggest that the parallel relation concerning energy and time (De Dt =\hbar/2) is not on the same footing. (That was one consideration behind my point 4.1 here.)
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How about the Fokker-Planck equation? the d'Alembertian form of wave equation? the Dirac equation?
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Any others?
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<strong>6.</strong> I have been talking about this business of <strong>collapsing or subsuming</strong> <strong>equations into more abstract equations.</strong> A word is in order.
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It is sometimes said that you can take all conservation principles as nothing but mere applications of Noether's principle. Thus, if you cast Noether's principle into symbolic form, i.e. in the form of an equation, then all conservation equations can be said to be automatically deducible.
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However, to me, this line of thought seems uncalled for. Noether's principle seems to be rather a formal rearrangement of the already known physics rather than any *new* physical observation/discovery standing on its own ground. That's why I would be in favor of a more detailed listing of the equations---they seem to capture the physics of it better.
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Further, physics is an empirical science. If, tomorrow, some new physical phenomenon gets discovered, it is possible that the integration then required would be such that the more abstract schemes such as Noether's theorem might have to be jettisoned, but *some* of the more detailed equations might continue to hold. For instance, it is difficult to see how the second law might at all get violated!
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This point, together with a constrain as artificial as having to have only five/ten/fifteen equations, is what makes the compilation of such lists so very interesting.
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A long reply, once again! But, yes, I do look forward to more short-lists!! It's interesting, isn't it? (Thanks in advance.)
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--Ajit<br />
- - - - - <br />
[E&OE]
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</ul>Mon, 09 May 2011 13:18:37 +0000Ajit R. Jadhavcomment 16733 at https://imechanica.orgI prefere the following:
1.
https://imechanica.org/comment/16731#comment-16731
<a id="comment-16731"></a>
<p><em>In reply to <a href="https://imechanica.org/node/10188">What would you choose as the Top 5 Equations? Top 10?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>I prefere the following:</p>
<p>1. Newton's Second law</p>
<p>2. Conservation of Energy</p>
<p>3. Conservation of linear momentum</p>
<p>4. Conservation of angular momentum</p>
<p> All physics lies with in those laws and to derive every equation we begin from the above laws/equations... </p>
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</ul>Mon, 09 May 2011 08:59:51 +0000SivaSrinivasKolukulacomment 16731 at https://imechanica.orge^(i*Pi)+1=0
absolutely
https://imechanica.org/comment/16729#comment-16729
<a id="comment-16729"></a>
<p><em>In reply to <a href="https://imechanica.org/node/10188">What would you choose as the Top 5 Equations? Top 10?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
e^(i*Pi)+1=0
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absolutely totally :)
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</ul>Sun, 08 May 2011 23:40:32 +0000sasaborgcomment 16729 at https://imechanica.orgtop 5 equations
https://imechanica.org/comment/16707#comment-16707
<a id="comment-16707"></a>
<p><em>In reply to <a href="https://imechanica.org/node/10188">What would you choose as the Top 5 Equations? Top 10?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
ZAOUI Noureddine<br />
Electromechnical Engineer
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<strong>(1) Gauss equations</strong>
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<strong>(2) Maxwell equations</strong>
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<strong>(3) The equation defining the Fourier transform</strong>
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<strong>(4) E = mc^2</strong>
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<strong>(5) not yet unification equation,,, </strong>
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</ul>Tue, 03 May 2011 11:16:09 +0000Nzaouicomment 16707 at https://imechanica.orgHere are two equations that might make my top 10 equations
https://imechanica.org/comment/16685#comment-16685
<a id="comment-16685"></a>
<p><em>In reply to <a href="https://imechanica.org/node/10188">What would you choose as the Top 5 Equations? Top 10?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Here are two equations that might make my choice of top 10 equations:
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<ul><li>S=logW</li>
<li>dU=TdS</li>
</ul><p>It is hard to search for greatness in the equations themselves. Like any other great equations, they symbolize deep and far-reaching ideas. </p>
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</ul>Sat, 30 Apr 2011 21:55:00 +0000Zhigang Suocomment 16685 at https://imechanica.org