# Maxwell's Equations on a t-shirt: summing up light **URL:** \ **Category:** Factual Questions\ **Created:** [November 28, 2004, 4:03pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002 "2004-11-28T16:03:45Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![Ross](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@Ross](https://boards.straightdope.com/u/Ross)\ **Post date:** [November 28, 2004, 4:03pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/1 "2004-11-28T16:03:45Z")
In [this thread](http://boards.straightdope.com/sdmb/showthread.php?p=4706363), **quothz** describes a t-shirt: > [@quothz](#): > > My favorite, spotted at a UNM physics symposium: > > And God said: > [Long formula, presumably describing the emission of light from fusion within a star.] > And there was light. To which **Mathocist** replies > [@Mathochist](#): > > Those are undoubtedly Maxwell’s Equations, either in differential or integral form. They’re the fundamental equations of the electromagnetic field (light). Now, I’d very much like to get my hands on such a shirt, and I usually have to do this by making one myself. I wondered if someone could tell me just which is the equations on [this page](http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html) is actually the one that should be in the slogan. 'Cos there’s loads of different equations there and I’m a bit stumped, never having got past quadratic equations. Ta. ---
**Author:** ![TellMeI\_mNotCrazy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tellmei_mnotcrazy/32/3419_2.png) [@TellMeI\_mNotCrazy](https://boards.straightdope.com/u/TellMeI_mNotCrazy)\ **Post date:** [November 28, 2004, 4:08pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/2 "2004-11-28T16:08:30Z")
Maybe this pic will help? (A little hard to read, unfortunately). [http://www.oceanoptics.com/applications/tshirt.asp](http://www.oceanoptics.com/applications/tshirt.asp) ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 28, 2004, 4:35pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/3 "2004-11-28T16:35:45Z")
A little further down your google results gets you [this page](http://scienceworld.wolfram.com/physics/MaxwellEquations.html), which should be a little clearer. The first four equations are probably the most widely recognized. ---
**Author:** ![TellMeI\_mNotCrazy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tellmei_mnotcrazy/32/3419_2.png) [@TellMeI\_mNotCrazy](https://boards.straightdope.com/u/TellMeI_mNotCrazy)\ **Post date:** [November 28, 2004, 4:40pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/4 "2004-11-28T16:40:49Z")
Yeah I saw that one too, but I know next to nothing about Maxwell’s equations, or how to understand them, so I picked the one that most clearly was the formula the OP was looking for (assuming he wanted specifically the “and there was light” one) ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [November 28, 2004, 4:55pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/5 "2004-11-28T16:55:35Z")
> [@ultrafilter](#): > > A little further down your google results gets you [this page](http://scienceworld.wolfram.com/physics/MaxwellEquations.html), which should be a little clearer. The first four equations are probably the most widely recognized. I’d use the equations in MKS units (the second set of 4 equation in that link). CGS is becoming old-fashioned. ---
**Author:** ![Ross](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@Ross](https://boards.straightdope.com/u/Ross)\ **Post date:** [November 28, 2004, 6:53pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/6 "2004-11-28T18:53:25Z")
Thank you, that’s very cool. It looks like the only way for me to do this is to copy and paste the gifs of the equations onto a t-shirt design, then have that printed on as a picture. Presumably there’s no way of rendering the equations that would fit into the standard characters allowed in the text boxes on design-your-own-shirt sites? (I know it’s a stupid question, but if I didn’t ask it, I wouldn’t know FOR SURE) ---
**Author:** ![Ross](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@Ross](https://boards.straightdope.com/u/Ross)\ **Post date:** [November 28, 2004, 6:57pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/7 "2004-11-28T18:57:30Z")
Just found this as someone’s sig on another forum: > [@](#): > > God said, “div D = rho, div B = 0, curl E = - @B/@t, curl H = J + @D/@t,” and there was light. Does that make sense to you guys? Or would I have people coming up and telling me I should have Maxwell’s Equations there instead? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 28, 2004, 7:17pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/8 "2004-11-28T19:17:29Z")
Of the four Maxwell’s equations, the two which are relevant to light are Faraday’s law and Ampere’s law, the two which have a “del cross” in them (“del” is the name for the upside-down triangle symbol, and “cross” is the vector cross product, represented by an X symbol). In the text form you dug up from a sig, that would be the two equations which start with “curl” (another name for “del cross”). Since God was, at the time, working in a void, the form of the equations for vacuum is relevant, so you should have E and B instead of D and H (the latter being modified fields more convenient for working in the presence of materials). Also because it’s a vacuum, you can eliminate any term which contains J (the current). Finally, you have a choice of units (which makes the equations look slightly different), but for theoretical work, Gaussian units are usually preferred, in which electric and magnetic fields are measured in the same units. So what you’re left with is Del × E = -1/c dB/dt Del × B = 1/c dE/dt The "Del"s should be replaced by the upside-down triangle symbol, if possible, or possibly replace the “Del ×” by the word “curl”, and the "d"s in “dB/dt” and “dE/dt” are partial derivatives, so they should be curvy and look like a backwards “6” (the text form you found represents this symbol with the @ sign). The text form would be recognizable to anyone who’s familiar with Maxwell’s equations, but of course, being restricted to text, it doesn’t look as cool. And you should be warned that most t-shirts you can buy with the equations on them are incorrect, since they leave off the derivatives on the right hand sides of the equations. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [November 28, 2004, 8:07pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/9 "2004-11-28T20:07:27Z")
> [@Ross](#): > > Does that make sense to you guys? Or would I have people coming up and telling me I should have Maxwell’s Equations there instead? That _is_ the Maxwell equations. > [@](#): > > Presumably there’s no way of rendering the equations that would fit into the standard characters allowed in the text boxes on design-your-own-shirt sites? It wouldn’t look very legible that way. It would be simple to make a PDF file though, just use the equation editor in MS Word. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [November 29, 2004, 2:46am UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/10 "2004-11-29T02:46:02Z")
They used to sell Maxwell Equation sweatshirts at MIT, but without the “And God Said…” part to it – just the equations. And MKS units, at that. (This is irca 30 years ago. Idon’t know if they still do – I haven’t looked for them.) A company called **Inner Products** used to sell the “…and God Said…” version, along with a host of other techinical shirts, many of them hilarious. They catalog was The Journal of Academic T-Shirts, which had a cover that looked like that of Physical Review, of som other serious science journal. I don’t know if thy’re still at it. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [November 29, 2004, 2:50am UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/11 "2004-11-29T02:50:47Z")
Couldn’t fing Inner Products (defunct, or bought up, I suspect), but this site sells 'em: [http://www.gaftee.com/BeepBeepBeep/zMath.html](http://www.gaftee.com/BeepBeepBeep/zMath.html) ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [November 29, 2004, 5:29am UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/12 "2004-11-29T05:29:05Z")
The Tech (MIT) Coop still sells them, with the God Said part, [here](http://store.thecoop.com/coopstore/servlet/com.bst.servlets.EStoreWebControlServlet?object=EstoreGenTreeLib&method=ExpandMenu&categoryuno=398&parentuno=376) That’s one I never bought when I was at MIT. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [November 29, 2004, 2:01pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/13 "2004-11-29T14:01:17Z")
> [@Ross](#): > > Now, I’d very much like to get my hands on such a shirt, and I usually have to do this by making one myself. I wondered if someone could tell me just which is the equations on [this page](http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html) is actually the one that should be in the slogan. 'Cos there’s loads of different equations there and I’m a bit stumped, never having got past quadratic equations. If you can find such a shirt, see if you can get one of the ones that reads "And God said [Maxwell’s equations here] and _still_ there was no light. Even He forgot boundary conditions." Those are the best. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [November 29, 2004, 2:03pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/14 "2004-11-29T14:03:25Z")
> [@ultrafilter](#): > > A little further down your google results gets you [this page](http://scienceworld.wolfram.com/physics/MaxwellEquations.html), which should be a little clearer. The first four equations are probably the most widely recognized. ☹ No mention at _all_ of the differential forms formulation… ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [November 29, 2004, 5:46pm UTC](https://boards.straightdope.com/t/maxwells-equations-on-a-t-shirt-summing-up-light/277002/15 "2004-11-29T17:46:28Z")
Not the one the OP is thinking of, but it shocked me a bit when I first saw it, so I thought I’d share (wish I had a better picture). [Check out the shirt on the guy second from the left in the upper photo.](http://ridersinthesky.com/html/Fr1ridrs.htm)