# I What equation is this one?

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1. Feb 7, 2017

### DelfinDelfin

I have a t-shirt with a next print:

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. Feb 7, 2017

### Mapes

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
3. Feb 7, 2017

### Staff: Mentor

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
4. Feb 7, 2017

### Orodruin

Staff Emeritus
The Christoffel symbols usually have two subscripts and one superscript, which the equation has.

5. Feb 7, 2017

### Staff: Mentor

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.

6. Feb 7, 2017

### Orodruin

Staff Emeritus
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.

7. Feb 7, 2017

### Staff: Mentor

Wait, I got confused. Yes, one up, two down. Ignore my previous post.

8. Feb 7, 2017

### Khashishi

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.

9. Feb 7, 2017

### DrGreg

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.

10. Feb 7, 2017

### Staff: Mentor

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.