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I What equation is this one?

  1. Feb 7, 2017 #1
    I have a t-shirt with a next print:

    sin-tc3adtulo.jpg

    But I am not sure what equation is. I only know that is something related with light. But I haven't found it. I am not sure if it is one from quantum electrodynamics or some advanced course in physics. I would appreciate that somebody could tell me which one is
     
  2. jcsd
  3. Feb 7, 2017 #2

    Mapes

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    I don't have much of a guess, but since nobody else has responded, I'll tell you that to a mechanical engineer, the general form looks similar to d'Alembert's[/PLAIN] [Broken] principle (see equation 1 in that link) in mechanics in that you seem to have an infinitesimal displacement on the far right and an acceleration on the left-hand side. But more broadly, d'Alembert's principle is a variational approach (see, e.g., Fermat's[/PLAIN] [Broken] principle, which is an example of variational methods applied to light propagation). Not much, but it might help your search.
     
    Last edited by a moderator: May 8, 2017
  4. Feb 7, 2017 #3

    mfb

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    The ##\Gamma## looks like a Christoffel symbol (although it should have two indices as superscripts and one as subscript), and the equation seems to be about general relativity.
     
    Last edited: Feb 7, 2017
  5. Feb 7, 2017 #4

    Orodruin

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    The Christoffel symbols usually have two subscripts and one superscript, which the equation has.
     
  6. Feb 7, 2017 #5

    mfb

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    All examples I found had it the opposite way. Maybe both ways are common. Well, just a matter of convention of course.

    Edit: I got confused, ignore this post.
     
  7. Feb 7, 2017 #6

    Orodruin

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    The Wikipedia page you link to has it the "normal" way. Two down and one up. I have never seen two up and one down.
     
  8. Feb 7, 2017 #7

    mfb

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    Wait, I got confused. Yes, one up, two down. Ignore my previous post.
     
  9. Feb 7, 2017 #8
    Something looks funny about that equation. It looks like there are dot products ##x^R \cdot \gamma##. Which means that ##x## and ##\gamma## are tensors. But if that's the case, then what rank is ##\gamma##? The rank of the LHS and RHS ought to be the same, but it doesn't seem possible. The second term in the curly brace seems to have a dot between the two derivatives, but this might just be a multiplication. All the dots might be simply multiplications. It's too bad that mathematical notation can be so ambiguous.
     
  10. Feb 7, 2017 #9

    DrGreg

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    First, I think the ##R## really should be a ##k## and has been transcribed incorrectly.

    I would guess this is supposed to be what, in more conventional tensor notation, would be written:

    And God said:$$
    \frac{D^2\gamma^k}{dt^2} = \frac{d^2\gamma^k}{dt^2} + \Gamma^k{}_{ij} \frac{d\gamma^i}{dt} \frac{d\gamma^j}{dt}
    $$... and there was the Universe...*

    It expresses acceleration along a curve ##\vec{\gamma}(t)## in non-Cartesian coordinates, where ##\vec{x}^k## is the ##k##th coordinate dual basis covector and so ##\gamma^k = \vec{x}^k \cdot \vec{\gamma}##. But they seem to have messed it up and I can't work out why there's an extra ##(\gamma(t))## in the middle of it all. Presumably the ##\delta_k## is the basis vector too.

    *Translation assisted by Google Translate
     
  11. Feb 7, 2017 #10

    jedishrfu

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    I think its an artificially contrived equation designed to look cool similar to Japanese t-shirt logos with nonsense English.

    But Dr Greg's explanation is quite plausible too.
     
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