/sci/ - Science & Math

Oops. I mean please explain why photons traveling at light speed are a theoretical limit to matter on a terminal velocity... etc

>>7618727
The rule F = ma that you know from Newtonian physics is an approximation. In reality, the rule is that, for mass objects with bigger velocities compared to mass objects with smaller velocities, you need a larger force to achieve the same acceleration. As the velocity nears the speed of light, the amount of force needed skyrockets towards infinity. So, you would need a so-called "infinite" amount of force to accelerate a mass object to light speed, a finite speed.

The cool part about relativity is that this is true for every observer, no matter their current velocity. In the above example, we might have an object at 90% of the speed of light, and it takes a much larger amount of force, i.e. energy, to accelerate the object from 90% c to 95% c. However, from the perspective of an observer already moving at 90% (quote unquote), our target object is at rest, and it takes the normal amount of energy to accelerate it from 0% c to 5% c.

Relativity is weird. You need to throw out a lot of your intuitive understanding of how the world works.

Speed is relative and has no actual limit.

>>7618733
are you a scientist or are you just copy-pasting shit from wikipedia ?

>>7618745
I am not a practicing scientist by the conventional narrow definition. I am a scientist in the broad definition in that I endorse and use scientific principles in my life.

I wrote that from scratch. No copy-paste.

>>7618733
>Relativity is weird. You need to throw out a lot of your intuitive understanding of how the world works.
Hey Tom, please stop spreading your bullshit.

>>7618751
??
Who is Tom?

>>7618753
What you wrote is word for word the lecture of this man http://www.physics.csbsju.edu/105/p105_12.html

>>7618755
Ok. I have no idea who that person is. I have no way to demonstrate that I'm not that person, nor do I have a way to demonstrate I'm not copying from that person. So, meh.

>>7618757
I'm on to you slut.

Regardless of where the anwers came from, thank you for adding to this discussion and linking to relevant material. Much appreciated. I am out of science now and into a humanities PhD... but science questions pop into my head from time to time.

> use Einstein's theory of special relativity to explain light speed as a possible and theoretical limit
You have it backward. Relativity comes about because we observe through experiment that the speed of light is a constant. Photons always move at the speed of light. Relativity follows as a direct consequence of this fact, combined with the observed laws of electromagnetism.

You might like to read about the Michaelson-Morley experiment, or even better, check out the chapters on relativity at http://www.feynmanlectures.info/

>>7618726
>certain particles could move faster than light in some instances
This is sort of true in some sense that depends on the way you calculate the path of a beam of light (quantum electrodynamics), but it applies only over very short distances, and the average speed of any particle over the course of an entire process can never exceed that of light. That is, if you shoot a photon from A to B, then it might move a bit faster part of the way, and slower the rest of the way... but the total time it takes is always exactly the distance divided by the speed of light.

>>7618735
> Speed is relative and has no actual limit.
No, you are flat-out wrong.

>>7618726
Others have kinda of explained the light speed limit, you'd need infinite energy to get beyond it, but I'm curious what you mean by your book saying some things can travel faster than light in certain circumstances?

I'm guessing they were talking about certain quantum mechanical effects that seem to happen instantly. Its important to note that the jury is still out on what exactly is happening in these cases but even if there is some truly instantaneous action happening it still cannot be used for any FTL communication as far as we can tell since the results of these experiments seem to be fundamentally random (with 2 entangled particles for example we cannot influence which one will have an up spin and which one will be down we just know they will be opposite).

>>7618726
First of all,
>the relationship of photons to the speed of light

"The speed of light" is actually slightly but importantly distinct from the relativistic maximum velocity, [math] c[/math]. All massless particles, due to the way the dynamics of relativistic motion work, would travel at c at all times.

Light simply happens to be carried by a massless particle, and so therefore travels at c. It's also the most convenient thing we know of which travels at c, and the fact that the universe had an invariant speed was first discovered by measuring light's speed as the planet traveled in different speeds and directions along its yearly orbit.

As for where [math] c [/math] as a maximum speed limit comes from? That's a little more difficult to explain, because it comes from the mathematical structure of relativity.

I'm going to have to think for a bit as to the best way to explain why, exactly, there 'has' to be a maximum speed. I could just give you the non-answer that energy increases exponentially as you near c, or I could go a little deeper as to why that is and tell you that it's because of the way mass, energy, and momentum all interact in special relativity, and give you the math and show how it came out of the math, but that's not really an explanation because it doesn't explain WHY its true and why the math is that way.

So hang on while I think of how to type the next post.

>>7618988
Part of the problem with trying to explain Why, Really, Is The Speed Of Light The Limit is that "the speed of light is constant" is one of the fundamental postulates of special relativity, and once you assume that you're like 50% of the way to getting [math]c[/math] as an invariant maximum velocity. Einstein assumed this because it was pretty much the only way to explain a bunch of odd experimental results and theoretical arguments, and I don't really feel I understand those well enough to explain them.

And while I could also derive why this is true by assuming other postulates, then without knowing the evidence for why the speed of light ought to be constant, those other postulates would also seem really arbitrary - like, "Assume we live in Minkowski space."

I'm being too perfectionist here, trying to give the Best answer instead of merely a correct answer, but aargh.

>>7618726
in 2015, it is because of the poincaré group

>>/sci/thread/7556169#p7556231

>>7618726

Photons are traditionally said to be massless. In my opinion, one of the best explanations is here http://pastebin.com/eWJz9nPY

It's a bit long, but it is meant for a layman and quite interesting.

>>7618726
>>7619031
I think I can explain it in a sort of acceptable manner. I'll try and chuck in historical context as I go along.

Back in Ye Olde Days there were a few theories going around about the nature of the universe, Classical Mechanics and Electromagnetism being amongst the principal ones and what we are concerned with.

Now, Classical Mechanics pre-dated Electromagnetism by many years. And about the same time as its inception, one of the guiding assumptions in Physics was made i.e. 'The laws of physics are the same in all inertial frames'.

What this means is that if you are moving at some constant velocity [math] u [/math] and someone else is moving at a constant velocity [math] v [/math] then nothing you do will reveal a difference in the laws of physics from your respective viewpoints.

This seems perfectly reasonable. After all, we want our laws to hold for everyone no matter what speeds they're going at, or where they are. Otherwise they wouldn't really be laws, they'd just be local patterns.

Fast forward about two centuries later to the emergence of electromagnetism. James Clerk Maxwell appears as the culmination of decades of work in bringing the once separate fields of electricity and magnetism together and formulates his four equations, one of which is[eqn]\nabla\,X\mathbb{B}=\mu_0\epsilon_0\frac{\delta\mathbb{E}}{\delta\mathbb{t}}+\mu_0\frac{\mathbb{J}}[/eqn] where [math]\mu_0[/math] and [math]\epsilon_0[/math] are constants. Out of these equations popped out these terms [eqn]\nabla^{2}E_x=\mu_0\epsilon_0\frac{\delta^{2}E_x}{\delta^{2}t}[/eqn] which happens to be very similar to the form of a wave equation [eqn]\nabla^{2}f=\frac{1}{v^{2}}\frac{\delta^{2}f}{\delta^{2}t}[/eqn].

In other words, [math]\mu_0\epsilon_0[/math] term represents that [math]frac{1}{v^{2}}[/math] term in an electromagnetic wave equation.

Cont:

Let the Latex Gods be kind today.

>>7619330
>Fucking up this hard

Dude, there's a "Preview TeX" button in the vanilla 4chan extension now. It's at the top-left of the quick reply window.

>>7619330
Damn.

I think I can explain it in a sort of acceptable manner. I'll try and chuck in historical context as I go along.

Back in Ye Olde Days there were a few theories going around about the nature of the universe, Classical Mechanics and Electromagnetism being amongst the principal ones and what we are concerned with.

Now, Classical Mechanics pre-dated Electromagnetism by many years. And about the same time as its inception, one of the guiding assumptions in Physics was made i.e. 'The laws of physics are the same in all inertial frames'.

What this means is that if you are moving at some constant velocity [math] u [/math] and someone else is moving at a constant velocity [math] v [/math] then nothing you do will reveal a difference in the laws of physics from your respective viewpoints.

This seems perfectly reasonable. After all, we want our laws to hold for everyone no matter what speeds they're going at, or where they are. Otherwise they wouldn't really be laws, they'd just be local patterns.

Fast forward about two centuries later to the emergence of electromagnetism. James Clerk Maxwell appears as the culmination of decades of work in bringing the once separate fields of electricity and magnetism together and formulates his four equations, one of which is[eqn]\nabla\,X\mathbf{B}=\mu_0\epsilon_0\frac{\partial\mathbf{E}}{\partial\mathbf{t}}+\mu_0\frac{\mathbf{J}}[/eqn] where [math]\mu_0[/math] and [math]\epsilon_0[/math] are constants. Out of these equations popped out these terms [eqn]\nabla^{2}\,E_x=\mu_0\epsilon_0\frac{\partial^{2}E_x}{\partial^{2}t}[/eqn] which happens to be very similar to the form of a wave equation [eqn]\nabla^{2}\,f=\frac{1}{v^{2}}\frac{\partial^{2}f}{\partial^{2}t}[/eqn].

In other words, [math]\mu_0\epsilon_0[/math] term represents that [math]\frac{1}{v^{2}}[/math] term in an electromagnetic wave equation.

Cont:

One more time.

>>7619337
Just saw your post now. I'm going to get that and stop screwing this up.

>>7619353
DUDE. USE THE FUCKING LATEX PREVIEWER. IT'S NOT EVEN IN 4CHANX FOR FUCK'S SAKE, IT'S IN THE GODDAMN FUCKING VANILLA SITE.

I WISH I COULD SHIT OUT MY ENTIRE COCK RIGHT NOW JESUS DONGS

>>7619356
>get that
Are you browsing 4chan?
You've already got it!

The "vanilla extension" is the one Moot added last year that gives you stuff like quick replies and those nice blue reply backlinks.

>>7619353
>>7618726
>>7619031
I think I can explain it in a sort of acceptable manner. I'll try and chuck in historical context as I go along.

Back in Ye Olde Days there were a few theories going around about the nature of the universe, Classical Mechanics and Electromagnetism being amongst the principal ones and what we are concerned with.

Now, Classical Mechanics pre-dated Electromagnetism by many years. And about the same time as its inception, one of the guiding assumptions in Physics was made i.e. 'The laws of physics are the same in all inertial frames'.

What this means is that if you are moving at some constant velocity [math] u [/math] and someone else is moving at a constant velocity [math] v [/math] then nothing you do will reveal a difference in the laws of physics from your respective viewpoints.

This seems perfectly reasonable. After all, we want our laws to hold for everyone no matter what speeds they're going at, or where they are. Otherwise they wouldn't really be laws, they'd just be local patterns.

Fast forward about two centuries later to the emergence of electromagnetism. James Clerk Maxwell appears as the culmination of decades of work in bringing the once separate fields of electricity and magnetism together and formulates his four equations, one of which is [eqn]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0\frac{\delta\mathbf{E}}{\delta\mathbf{t}}+\mu_0\mathbf{J}[/eqn] where [math]\mu_0[/math] and [math]\epsilon_0[/math] are constants. Out of these equations popped out these terms [eqn]\nabla^{2}E_x=\mu_0\epsilon_0\frac{\delta^{2}E_x}{\delta^{2}t}[/eqn] which happens to be very similar to the form of a wave equation [eqn]\nabla^{2}f=\frac{1}{v^{2}}\frac{\delta^{2}f}{\delta^{2}t}[/eqn].

In other words, [math]\mu_0\epsilon_0[/math] term represents that [math]frac{1}{v^{2}}[/math] term in an electromagnetic wave equation.

Cont:

4Chan says it should work now.

>>7619368
I am so unbelievably mad right now. Why is this not working, the preview says its all good. Except for that fraction at the end. That's my fault.

>>7619369
owned

[eqn]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0\frac{\delta\mathbf{E}}{\delta\mathbf{t}}+\mu_0\mathbf{J}[/eqn]

Tetse-ing.

>>7619432
Welp, time to complain to Hiro to fix the board. My bet is that there was a fuckup in updating somewhere, so the evaluation and the rendering are using different versions of MathJax.

>>7619432
[eqn]\nabla^{2}f[/eqn] What equations aren't working though?
[math]\nabla^{2}f[/math]

>>7619432
[eqn]\mathbf{B}[/eqn]

>>7619432
[eqn]\nabla\,X\;\mathbf{B}=[/eqn]

>>7619506
[eqn]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0[/eqn]
[eqn]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0\frac{\delta\mathbf{E}}{\delta\mathbf{t}}[/eqn]

>>7619510
[eqn]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0[/eqn]

>>7619513
[eqn]\mu_0\epsilon_0[/eqn]

I think this is the problem.

>>7619510
[math]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0[/math]

>>7619517
[eqn]\nabla\,X\;\mathbf{B}=\frac{\delta\mathbf{E}}{\delta\mathbf{t}}[/eqn]

>>7619516
...Or not. What the fuck?

Okay, so

[eqn]\nabla\,X\;\mathbf{B}=\mu_0\epsilon_0[/eqn] doesn't work, but

[eqn]\mu_0\epsilon_0[/eqn] does, and
[eqn]\nabla\,X\;\mathbf{B}=[/eqn] does too.

What about

[eqn]\nabla\,X\;\mathbf{B}=\mu_0[/eqn]

>>7619516
>>7619518
[eqn]\nabla\,X\;\mathbf{B}=[/eqn]

I'm not sure if it is.

>>7619513
[eqn] \nabla \times \mathbf{B} = \mu_{0} \epsilon_{0} [/eqn]

>>7619520
Got it.

[eqn]\nabla\,X\;\mathbf{B}=\mu_0[/eqn]
[eqn]\nabla\,X\;\mathbf{B} = \mu_0[/eqn]
[eqn]\nabla\,X\;\mathbf{B} = {\mu_0}[/eqn]
[eqn]\nabla\,X\;\mathbf{B} \neq \mu_0[/eqn]

>>7619530
>>7619530
Alright! So that's the problem.

4chan's LaTeX rendering does NOT like the digraph =\. Throw a space in there (= \) and it works.

>>7619520
[eqn]\nabla\,X\;\mathbf{B}=\epsilon_0[/eqn]
[eqn]\nabla\,X\;\mathbf{B}=\epsilon_0\frac{\delta\mathbf{E}}{\delta\mathbf{t}}[/eqn]
[math]\nabla\,X\;\mathbf{B}=\epsilon_0[/math]
[math]\nabla\,X\;\mathbf{B}=\epsilon_0\frac{\delta\mathbf{E}}{\delta\mathbf{t}}[/math]

>>7619532
>[eqn] \nabla\,X\;\mathbf{B} = \mu_0 \epsilon_0 \frac{ \delta \mathbf{E} }{ \delta \mathbf{t} } + \mu_0 \mathbf{J} [/eqn]

Testing my hypothesis.

>>7619532
Huh. Weird. Should we report this? I'm going with probably.

>>7619535
Alright! Not only does that work, apparently you can greenTeXt.

>>7619539
You're full of discoveries tonight, aren't you anon?

>>7619535
[eqn]\nabla \times \mathbf{B} = \mu_0\epsilon_0\frac{\delta\mathbf{E}}{\delta\mathbf{t}}+\mu_0\mathbf{J}[/eqn]

X is really not the right character to use for the cross product.

>>7619542
I couldn't fine the right character so I just went with it. If you know the LaTeX for it, I'm all ears

>>7619542
Oh, OK, looks like it's not just =\ but probably also +\ too. When I got it working the first time I just threw whitespace everywhere it looked like it might be a problem, but I only spaced =\ here.

Trying again with the throw-whitespace-everywhere theory: [eqn] \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{ \delta \mathbf{E} } { \delta \mathbf{t} } + \mu_0 \mathbf{J} [/eqn]

>>7619542
*find.

>>7619546
\times

>>7618726

SR does not explain it.
It is simply an observable fact of the universe that light (and indeed all massless particles) has a finite speed, which is the same in all frames of reference.
Knowing this, and the fact that the laws of nature are all the same in any given inertial frame of reference, one may deduce SR.
There is no more explanation for the value of c than there is for the mass of the electron.

>>7619547

>
[eqn]\nabla^{2}f = \frac{1}{v^{2}}\frac{\delta^{2}f}{\delta^{2}t} + \mu_0\mathbf{J} [/eqn].

I just read your LaTeX. Now I know what the cross product is.

>>7619547
minimal test cases:
[eqn]\alpha+\beta[/eqn]
[eqn]\alpha=\beta[/eqn]
[eqn]\frac{1}{2}\alpha[/eqn]

>>7619558
>[eqn] \nabla^{ 2 } f = \frac{ 1 } { v^{ 2 } } \frac{ \delta^{ 2 } f }{ \delta^{ 2 } t } + \mu_0 \mathbf{ J } [/eqn]

[eqn]\nabla^{2}f= \frac{1}{v^{2}}\frac{\delta^{2}f}{\delta^{2}t}[/eqn].

>>7619560
[eqn]\alpha_\omega+\beta=\gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]

>>7619560
[eqn]\mu*\mu[/eqn]
[eqn]\mu* \mu[/eqn]

>>7619573
[eqn]\alpha_{\omega} + \beta = \gamma \frac{\mathbf{\mu^\pi}}{\delta }[/eqn]

>>7619569
>>7619573
It seems fine with multiplication, regardless of white-space.

>>7619577
>>7619573
>>7619569
>>7619560
>>7619558
>>7619535
>>7619532
There's a preview function now, niggers

>>7619582
>Didn't read the thread
>Calls other people niggers

>>7619532
>>7619535
>>7619547

>>7619573
[eqn] \alpha_\omega+\beta=\gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega}+\beta=\gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} +\beta=\gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta=\gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn
[eqn] \alpha_{\omega} + \beta =\gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{ \mu^\pi}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{ \mu^{\pi}}}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{ \mu^{\pi} }}{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{ \mu^{\pi} } }{\delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{ \mu^{\pi} } }{ \delta}[/eqn]
[eqn] \alpha_{\omega} + \beta = \gamma \frac{ \mathbf{ \mu^{\pi} } }{ \delta }[/eqn]

>>7619580

>>7619587
Do you need any help with testing things out, or are you good anon?

>>7619582
The whole reason this is happening is that some formulas which work in the preview don't work in the post. It appears to have something to do with whitespace.

For instance,
[eqn] \alpha_{ \omega } + \beta = \gamma \frac{ \mathbf{ \mu^{\pi} } }{ \delta } [/eqn] and [eqn]\alpha_{\omega}+\beta=\gamma\frac{\mathbf{\mu^{\pi}}}{\delta}[/eqn] both render identically in the preview function.

>>7619592
I'm just confused now.
It'd help if I could figure out a way to replicate it in a shorter formula. I can't find any pattern to it besides "throw whitespace everywhere and it helps eventually"

>>7619587
[eqn]\frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
[eqn] \frac{ \mathbf{\mu^\pi}}{\delta}[/eqn]

>>7619604
[eqn]\frac{\mathbf{\mu}}{\delta}[/eqn]
[eqn]\frac{\mathbf{\mu}}{2}[/eqn]
[eqn]\frac{\mathbf{1}}{2}[/eqn]

>>7619610
Alright, testing one last time:
[eqn]\frac{\mu}{\delta}[/eqn]
[eqn]\frac{\mu}{0}[/eqn]
[eqn]\frac{0}{\delta}[/eqn]
[eqn]\frac{0}{0}[/eqn]

>>7618735

>>7619613
Okay, so
[eqn]\frac{\mu}{\delta}[/eqn] works, but [eqn]\frac{\mathbf{\mu}}{\delta}[/eqn] does not, right?
So is it the mathbf operator specifically that's breaking it, or just nested brackets?

>>7619604
>[eqn] \frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
>[eqn]\frac{ \mathbf{\mu^\pi}}{\delta}[/eqn]
>[eqn]\frac{\mathbf{ \mu^\pi}}{\delta}[/eqn]
>[eqn]\frac{\mathbf{\mu^ \pi}}{\delta}[/eqn]
>[eqn]\frac{\mathbf{\mu^\pi}}{ \delta}[/eqn]

>[eqn] \frac{ \mathbf{\mu^\pi}}{\delta}[/eqn]
>[eqn] \frac{\mathbf{ \mu^\pi}}{\delta}[/eqn]
>[eqn] \frac{\mathbf{\mu^ \pi}}{\delta}[/eqn]
>[eqn] \frac{\mathbf{\mu^\pi}}{ \delta}[/eqn]
>[eqn]\frac{ \mathbf{ \mu^\pi}}{\delta}[/eqn]
>[eqn]\frac{ \mathbf{\mu^ \pi}}{\delta}[/eqn]
>[eqn]\frac{ \mathbf{\mu^\pi}}{ \delta}[/eqn]
>[eqn]\frac{\mathbf{ \mu^ \pi}}{\delta}[/eqn]
>[eqn]\frac{\mathbf{ \mu^\pi}}{ \delta}[/eqn]
>[eqn]\frac{\mathbf{\mu^\ pi}}{ \delta}[/eqn]

Let's see what works here.

>>7619617
[eqn]\mathbf{5}[/eqn]
[eqn]\mathbf{\mu}[/eqn]
[eqn]\frac{\mathbf{\mu}}{\delta}[/eqn]
[eqn]\frac{\mathbf{\mu}}{0}[/eqn]
[eqn]\sqrt{\mathbf{\mu}}[/eqn]
[eqn]\sqrt{\frac{\mu}{0}}[/eqn]

>>7619631
what the fuuuck.

>>7619625
>eqn] \frac{\mathbf{\mu^\pi}}{\delta}[/eqn]
>eqn]\frac{ \mathbf{\mu^\pi}}{\delta}[/eqn]
>eqn]\frac{\mathbf{ \mu^\pi}}{\delta}[/eqn]
>eqn]\frac{\mathbf{\mu^ \pi}}{\delta}[/eqn]
>eqn]\frac{\mathbf{\mu^\pi}}{ \delta}[/eqn]

>eqn] \frac{ \mathbf{\mu^\pi}}{\delta}[/eqn]
>eqn] \frac{\mathbf{ \mu^\pi}}{\delta}[/eqn]
>eqn] \frac{\mathbf{\mu^ \pi}}{\delta}[/eqn]
>eqn] \frac{\mathbf{\mu^\pi}}{ \delta}[/eqn]
>eqn]\frac{ \mathbf{ \mu^\pi}}{\delta}[/eqn]
>eqn]\frac{ \mathbf{\mu^ \pi}}{\delta}[/eqn]
>eqn]\frac{ \mathbf{\mu^\pi}}{ \delta}[/eqn]
>eqn]\frac{\mathbf{ \mu^ \pi}}{\delta}[/eqn]
>eqn]\frac{\mathbf{ \mu^\pi}}{ \delta}[/eqn]
>eqn]\frac{\mathbf{\mu^\ pi}}{ \delta}[/eqn]

This is what I did. It seems like all white space is fine except after a ^\ what about
[eqn]\frac{\mathbf{\mu^{\ pi}}}{ \delta}[/eqn]
which is
eqn]\frac{\mathbf{\mu^{\ pi}}}{ \delta}[/eqn]

>>7619650
Ah, alright, so it was just breaking up the character now let's try that properly:
[eqn]\frac{\mathbf{\mu^ \pi}}{ \delta}[/eqn]
which is:
eqn]\frac{\mathbf{\mu^ \pi}}{ \delta}[/eqn]

or

[eqn]\frac{\mathbf{\mu^ {\pi}}}{ \delta}[/eqn]
which is
eqn]\frac{\mathbf{\mu^ {\pi}}}{ \delta}[/eqn]

>>7619650
>\ pi
You just went full retard, man. \whatever is how LaTeX encodes control characters. So \pi is how you say "the Greek letter symbol for lowercase pi" Stick a space in there and you've just got "pi", "letter p followed by letter i"

Ok brainboyz, imagine this. A starship travels at almost lightspeed between two stars that are not in motion relative to each other. Because it's not a perfect vacuum there are like 1000 random particle collisions with the ship per lightsecond(totally made that up).

It's all good from star system's the point of view. The vessel is traveling at almost lightspeed so there are only max 1000 impacts per second, not heating the ship up much.

But from the ships view the distance to travel shortens to Amerifat walking range because of ay lmao relativistic length contraction. That would mean a lot more particle impacts per second and much more heating up of the ship, or? Is there something that also accelerates the cooling in return? Is my idea of heating up because stuff's in the way fucked?

>>7618747
Please kill yourself.

>>7619657
Yeah, I noticed that after I posted it. I'm new to LaTeX so it didn't click straight away.

>>7619631
>>7619643

It looks like there are a ton of ways you can get 4chan to render it right, but the whitespace just seems to be all over the space. So that looks like a dead end. The bes way forward seems to be to keep trying to see what inputs break it and what don't.

Also, someone should try getting ahold of An Hiro, or the mods and getting them to fix this. This would become sort of irritating if we kept on having to do this each time we want to LaTeX.


I've got work to do anon, so I'm afraid I can not offer you any more feeble aid. Good luck!

[eqn]F_{\mu\nu} = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}[/eqn]

[eqn]\partial_{\mu} F^{\mu \nu} = - J^{\nu} [/eqn]

>>7619689
Ship would be hot yo

>>7619689
No, you're correct and the ship would indeed heat up.

However, the heating is still tiny unless you're going implausibly close to lightspeed. There are pretty much no plausible technologies that could get a human-sized capsule up to even 0.99c.