- #36
QuarkCharmer
- 1,051
- 3
Greg Bernhardt said:Right click on the equation to get a menu.
Ah, View MathML Source. Thanks
Greg Bernhardt said:Right click on the equation to get a menu.
I'm seeing some pretty serious problems in the post preview on Firefox 4: large chunks of the post text just don't show up. It doesn't seem to be a problem with the HTML or MathML markup, but rather with the way the browser's rendering engine interacts with it, because if I scroll down far enough to put the preview out of view and then back up, it'll look different. Plus, I can select sections of text to make them show up, but then other sections of the preview (and even of the page, outside of the preview) flicker in and out of view as I change the selection. A lot of the problem areas seem to start at instances of the / operator in the math, so perhaps the way that's being rendered is messing things up somehow. I suppose this could be a problem with MathJax itself, but I've been to several other sites that use it and never had this problem before (including the site where I originally posted the exact same thing I quoted), so there must be something specific to PF that is contributing to this problem somehow. (A sample screenshot attached - notice how part of the second matrix equation is cut off, as well as most of the lines above and below it. At other times multiple entire paragraphs would be missing.)However, you can _convert_ an amount of kinetic energy measured in one frame to another frame, if you know their relative velocity. If you're working at low speeds, the easy (approximate) way to do this is to just calculate the relative velocity, as you did. So if the train observer measures a kinetic energy [itex]K = \frac{1}{2}mv^2[/itex], the ground observer will measure a kinetic energy of [itex]\frac{1}{2}m(v + V)^2[/itex], or
[tex]K + \sqrt{2Km}V + \frac{1}{2}mV^2[/tex]
(in one dimension).
If you get up to higher speeds, or you want an exact expression, you'll have to use the relativistic definition of energy. In special relativity, the kinetic energy is given by the difference between the total energy and the "rest energy,"
[tex]K = E - mc^2[/tex]
One way to figure out the transformation rule is to use the fact that the total energy is part of a four-vector, along with the relativistic momentum,
[tex]\begin{pmatrix}E/c \\ p\end{pmatrix} = \begin{pmatrix}\gamma_v mc \\ \gamma_v mv\end{pmatrix}[/tex]
where [itex]\gamma_v = 1/\sqrt{1 - v^2/c^2}[/itex]. This four-vector transforms under the Lorentz transformation as you shift from one reference frame to another,
[tex]\begin{pmatrix}E/c \\ p\end{pmatrix}_\text{ground} = \begin{pmatrix}\gamma & \gamma\beta \\ \gamma\beta & \gamma\end{pmatrix}\begin{pmatrix}E/c \\ p\end{pmatrix}_\text{train}[/tex]
(where [itex]\beta = V/c[/itex] and [itex]\gamma = 1/\sqrt{1 - \beta^2}[/itex]), so the energy as observed from the ground would be given by
[tex]E_\text{ground} = \gamma(E_\text{train} + \beta c p_\text{train})[/tex]
The kinetic energy is obtained by subtracting [itex]mc^2[/itex] from the total energy, so you'd get
[tex]K_\text{ground} = \gamma(E_\text{train} + \beta c p_\text{train}) - mc^2[/tex]
which works out to
[tex]K_\text{ground} = \gamma K_\text{train} + (\gamma - 1) mc^2 + \gamma\beta c p_\text{train}[/tex]
where [itex]K[/itex] is the relativistic kinetic energy and [itex]p[/itex] is the relativistic momentum.
If you wanted it in terms of energy alone:
[tex]K_\text{ground} = \gamma K_\text{train} + (\gamma - 1) mc^2 + \gamma\beta\sqrt{K_\text{train}^2 + 2 mc^2 K_\text{train}}[/tex]
You might start to notice a similarity to the non-relativistic expression above ([itex]K + \sqrt{2Km}V + \frac{1}{2}mV^2[/itex]), and indeed, if you plug in some approximations that are valid at low speeds ([itex]\gamma \approx 1[/itex], [itex]\gamma - 1 \approx V^2/c^2[/itex], [itex]K_\text{train} \approx \frac{1}{2}mv^2 \ll mc^2[/itex]), you will recover exactly that expression.
diazona said:...I'm seeing some pretty serious problems in the post preview on Firefox 4...
jhae2.718 said:Greg, are we on MathJax 1.1? Edit: dumb question, you're linking to their CDN.
A bit of Googling suggests that there exist rendering problems with FF 4.*.
Hm... the site I took my example from also uses MathJax 1.1:jhae2.718 said:Greg, are we on MathJax 1.1? Edit: dumb question, you're linking to their CDN.
A bit of Googling suggests that there exist rendering problems with FF 4.*.
but there are no rendering errors.MathJax v1.1
using local STIX fonts
TeX Input Jax v1.1
HTML-CSS Output Jax v1.1
mml Element Jax v1.1
tex2jax Extension v1.1
MathZoom Extension v1.1
MathMenu Extension v1.1
TeX/noErrors Extension v1.0.1
TeX/noUndefined Extension v1.0.1
Firefox v4.0
Mark44 said:Pages with any appreciable amount of LaTeX take a lot longer to load, it seems. For example, this page took about 15 - 20 sec. to load.
Borek said:I don't remember why there are \textrm here, that's just copy/pasted from somewhere else. Where does the red come from?
cepheid said:Sorry if this is known already, but this LaTeX output doesn't work on the mobile version of the site. At least, that's true when running the Safari app in iOS 4. All I see is the LaTeX source code instead.
Sorry, I meant to include that info but forgot. I'm using IE 8.Greg Bernhardt said:What browser are you using? I would think in a current version of FF or Chrome that the JS processing would be slightly faster than downloading images.
Mark44 said:...I'm using IE 8...
flyingpig said:Please don't fix what's not broken!
You guys should search the feedback forum for threads with the word "latex" in the title. The LaTeX feature is definitely broken, and the change isn't at all sudden. LaTeX previews haven't worked properly for more than a year. I think there are at least 30 threads about it. The move to MathJax has been discussed in public at least since February. The admins probably started talking about it long before that.Nebuchadnezza said:Why the sudden change?
Give the admins some time to work things out. If it still looks ugly when they say that they're done, then you can start whining about it.flyingpig said:Sorry to say I really hate the new look. The images are smaller, and arew just ugly compared to the old font. Please bring back imgtex =)
It's still completely messed up for me. I assume we're talking about #38. It looks fine until I put my mouse pointer over a math expression, and then stuff disappears, including plain text below the quote box.jhae2.718 said:Not having any problems with Diazona's post anymore.
jhae2.718 said:I see LaTeX fine on iOS 4.3. Posted from my iPad.
\phi(x)=\left\langle\frac{z}{\|z\|^2},x\right\rangle
Fredrik said:I'm using Firefox 4.0.1 on Windows 7 SP1.
This is a post I wrote some time ago that contains a lot of math. I'm having similar problems with that. Another weird thing is that that link should automatically scroll to post #13, but for some reason that doesn't quite work.
cepheid said:Hmm, yes, but are you looking at the full or the mobile version of the site? I'm looking at the mobile version. I think my iOS version is 4.2.1, and I'm running it on an iPhone 3G.
Fredrik said:I'm using Firefox 4.0.1 on Windows 7 SP1.
Fredrik said:[tex]\phi(x)=\left \langle \frac{z}{\|z\|^2}, x \right \rangle[/tex] (jhae2.718: I've modified the TeX markup to the left)
Code:\phi(x)=\left\langle\frac{z}{\|z\|^2},x\right\rangle
micromass said:I'm having similar problems in Frederik's posts. I'm also using firefox, by the way...
jhae2.718 said:Try installing the STIX fonts locally. I'll bet that both Greg and I have those, which is why we don't have problems.