Large Hardon Collider

[Eliseos]

Is "v/c= 1-10E6" supposed to be "v/c = 1*10E-6"? If so, you can ignore relativistic effects there. If not, the problem doesn't make sense since v is so much greater than c.

[BerenTebogo]

No it's 1 - 10E-6 as in v = .99999c

[Kaylia]

Okay so I just started my Applied Modern Physics class and I'm feeling a bit overwhelmed by the first homework set. Usually takes me a bit to adjust to the professor / teaching style / new formulas and all but I'm feeling stupider than normal here. I've taken (what I think to be) every approach to this problem that makes sense but I'm not getting an answer that matches the textbook and even just doing crazy stuff looking for numbers that would be similar isn't yielding any positive results. HALP PLZ

"A supernova at a distance of 175,000 light years from Earth emits particles that travel in a straight line to Earth. If these particles travel with a speed v such that v/c= 1-10E6
how long will the trip last, as measured by an observer traveling with the particle? "

What I assumed to be the correct-ish track was to take the length contraction formula and the dt = dt'/sqrt(1-v^2/c^2) formula try to relate them using v = distance over time. Yadda yadda. Also tried solving into the length contraction formula but nothing is really coming up that makes any sense whatsoever.

Physics is all about feeling stupid.

You spend 1 week of your life feeling stupid because you can't understand the problem, but as soon you understand, you will start feeling stupid because it was so simple and obvious it makes no sense to have spent that much time.

[edit]
Big mistake

[BerenTebogo]

So for the time I just take the evaluated gamma function and put it into t' = gamma(t - vx/c^2) ?

Still not used to using ANY of these equations

Edit: Wait, nevermind...I think the time in light years divided by the gamma function gives the time in Earth years that I was looking for. How does it get from LY to EY though? I didn't really carry my units through, bahaha.

[Kaylia]

Dont listen to what I said, big mistake, I will write a better answer in a few minutes lol

[BerenTebogo]

lol

[Woozie]

I should have worded my thought differently. What I was saying is that I don't believe it is wrong for a physicist to look into string theory if his intuition tell him to do so. Right now, it doesnt really work, but it's not impossible that someone someday will eventually manage to find a better interpretation that clean up the current mess. I personally don't think that's where the best solution is because "hidden variables/dimensions" feel like a cheap way to avoid the problems instead of answering it, but I can't turn down their attempt either on that basis that "it can't works".

I'm not exactly sure what you mean by "the way physicists do their math". It's true that sometime, physicist will cut corner, but it's usually an educated approximation that we need to find a non-numerical solution. It's not part of the theory, but an approximated result derivated from it.



Pressing "esc" do that, and it fucking sucks.

Physicists have a very strong tendency to do things that just aren't rigorous. You're right that the vast majority of the time they do this, it's for an approximation and isn't a vital part of the theory, but sometimes new theories do end up with parts that aren't mathematically sound. This is especially prevalent in theoretical physics, where scientist often have to use brand new math that even mathematicians are just now starting to touch, or create brand new math because mathematicians haven't developed anything they can use yet. When a physicists creates new math, he often doesn't bother making it as rigorous as a mathematician would when they make new math. A physicists gets it to the point where it "makes sense" and is "probably" true and they consider their work done.

Non-rigorous stuff does end up being a part of scientific theories. It's not really that uncommon for mathematicians to be unhappy with physics theories due to lack of rigor. We even have a branch of physics dedicated solely to proving "proven" theories just because newer theories often aren't on a rigorous-enough setting (some branches of mathematical physics do nothing but give a rigorous framework to existing theories). Most of the popular theories today were not on a rigorous foundation at first. Newton's calculus was terrible by today's standards, and so was his mechanics based on it. Things didn't become rigorous until Cauchy, Laplace, Euler, and a few others came along. Quantum mechanics had its share of issues too until some mathematicians put it on a more rigorous footing later on (as well as Dirac, but even his foundations weren't completely rigorous). Quantum Field Theory had the well-known renormalization problems, which I'm sure you're already familiar with.

I've had this discussion before with a professor I worked with, and he gave really good reasons why physics is better off the way it is as opposed to approaching it like mathematicians. As solid as his arguments were, they mostly depended on the fact that "proof" in physics is experimental, not deductive. For things beyond the standard model, where experiment is likely at least a few decades away, I wouldn't completely agree with his arguments. And that obviously goes for string theory too, where experiments may not ever come.

[Kaylia]

Okay, back.


Basically, yeah. Evaluate gamma and plug it in T' equations. You already have every other parameters in the question (delta T and deltaX).

[Woozie]

http://chzmemebase.files.wordpress.c...h-a-downer.jpg

Awesome

[Kaylia]

Non-rigorous stuff does end up being a part of scientific theories. It's not really that uncommon for mathematicians to be unhappy with physics theories due to lack of rigor. We even have a branch of physics dedicated solely to proving "proven" theories just because newer theories often aren't on a rigorous-enough setting (some branches of mathematical physics do nothing but give a rigorous framework to existing theories). Most of the popular theories today were not on a rigorous foundation at first. Newton's calculus was terrible by today's standards, and so was his mechanics based on it. Things didn't become rigorous until Cauchy, Laplace, Euler, and a few others came along. Quantum mechanics had its share of issues too until some mathematicians put it on a more rigorous footing later on (as well as Dirac, but even his foundations weren't completely rigorous). Quantum Field Theory had the well-known renormalization problems, which I'm sure you're already familiar with.

Where sciences would be without Newton, Dirac and a few others? It's not like their "lack of rigor" was harmful and slowed us down, it's their works that triggered new field of research in both mathematics and physics.

A serious theory will need rigorous mathematics sooner or later, I will give you that. However, I don't believe new theory can be built on solid mathematics right away, because the formalism needed rarely exists at the time. What you need instead is a strong natural principle that agree with experimentals data (energy is conserved for example).

If you're able to observe a pattern, describe it, and predict results , you're on the right track. A more rigorous mathematical approach will let you clean the model, and deduce more informations out of it, but essentially, if it can be observed, you should be able to described it mathematically.



[edit]
I'm not saying that lack of rigor is always excusable. You can't overlook an infinity, a discontinuity, or a divergent series easily, but if your model can predict something, it's just a matter of time before someone reword it with better mathematics.

[Woozie]

You're right that their methods didn't slow us down and in fact were pretty good at pushing us forward, which is one of the things my professor pointed out. Like I said, I agree with it being done in most physics for reasons you and my professor pointed out (even though it still bothers me a lot when I see it), but for theoretical physics, where experiment isn't even an option for a while, I feel like more emphasis should be placed on being rigorous since you can't really depend on experiments helping you weed bad theories out from the good ones any time soon.

[Woozie]

Okay, so after thinking about it, I realize that listing those examples work against my argument since each of those theories became huge successes despite not being completely rigorous by mathematician's standards. I guess what I'm saying is that even though I know physics is better off this way, it still bothers me anyways but I'm willing to accept it due mainly to our ability to experiment (something mathematicians can't do). That's why it's harder for me to accept it in string theory and other things beyond the standard model, as these theories often can't be experimented on any time soon.

[Kaylia]

There isn't many physicists or mathematicians that are okay with paradox, divergence or other irregularities. Ultimately, everyone is trying to solve the issues, they are just doing it differently (or at least, it's the impression I have).

A physicist will move forward despite uncomfirmed assumptions to see the whole picture as soon as possible, a mathematician will take his time to make sure everything is right and that what was done is understood properly. This is not to say that phycisist can't be rigorous, and that mathematician can't follow their intuition, but it's usually the difference between both. I'm tempted to say quality versus quantity, but it would make us look bad, and I strongly believe that both are needed to progress at a decent pace (physics intuition to get a rough sketch, and rigorous mathematics to complete the picture)

I agree with you when you say that mathematical rigor can be used to weed out bad ideas, but at the same time, it force you into a very specific model. This isnt always a good thing when you're not exactly sure where you want to go, and want to keep as many road open as you can.

[Max™]

Course, sometimes following the math to any length puts you on a....

[Kaylia]

Okay, so after thinking about it, I realize that listing those examples work against my argument since each of those theories became huge successes despite not being completely rigorous by mathematician's standards. I guess what I'm saying is that even though I know physics is better off this way, it still bothers me anyways but I'm willing to accept it due mainly to our ability to experiment (something mathematicians can't do). That's why it's harder for me to accept it in string theory and other things beyond the standard model, as these theories often can't be experimented on any time soon.

I kinda agree with you on this because I usually feel that way about rigor in physics (especially in applied physics where I work), but at the same time, I have to give theoreticians the benefit of the doubt as long they are actively trying to design experiments and improve the formalism and rigor.

[Woozie]

How did I miss this one?

http://www.latenightwithjimmyfallon....-8210/1242077/

Not nearly as good as the original though.

♫"Enough with the name callin
The Webb sees in infrared, that s*** is ballin' "

lol, NASA engineers spittin them lyrics.

Edit: Are the women at NASA really that hot?

♫"I'm feelin like Cleveland...and y'all LeBron"

♫"Replacin Hubble aint funny
It's not like Hubble Terrence Howard askin for more money"

[Kaylia]

For some reason, we ended up talking about rigor in my Advanced QM class today. I wish you were attending it Woozie because what my teacher was saying is pretty close to what you said, and his methods (reformulation of mechanics/QM) are extremely clean mathematically. It's pretty fun everytime (except that it last around 8 hours instead of the usual 3h30).


There was also a nice jab at String Theory (or holographics principle) at some point that I'm scared to translate since I wouldnt be able to put it quite as nicely as he did. It was about mapping higher dimension with lower dimension element (surface with lines, lines will dot) ...they are basically "Zeno's paradoxing" themselves with their mathematics.

[Woozie]

Clearly your professor reads these forums to decide what he thinks he should teach that day. Admit it, Eliseos. We know you're Kaylia's professor. No point in trying to hide it any longer.

Next week's lecture is about why ESP isn't real.

[Eliseos]

Since Woozie can clearly read my thoughts about my lecture topics, next week's lecture will be about something else!

[Max™]

Make sure you set up counterthought spoofs so when you're busy thinking about what you're trying to not think about, you don't accidentally think about a guy touching your dick.
http://www.dethklok.org/wp-content/u...1/Capture2.JPG

Bonus:
http://www.sciencedaily.com/releases...0202133321.htm

ScienceDaily (Feb. 2, 2011) — NASA's Kepler mission has discovered its first Earth-size planet candidates and its first candidates in the habitable zone, a region where liquid water could exist on a planet's surface. Five of the potential planets are near Earth-size and orbit in the habitable zone of smaller, cooler stars than our sun.
http://www.sciencedaily.com/images/2...0202133321.jpg


Candidates require follow-up observations to verify they are actual planets. Kepler also found six confirmed planets orbiting a sun-like star, Kepler-11. This is the largest group of transiting planets orbiting a single star yet discovered outside our solar system.

http://www.sciencedaily.com/releases...0202134725.htm

ScienceDaily (Feb. 2, 2011) — Scientists using NASA's Kepler, a space telescope, recently discovered six planets made of a mix of rock and gases orbiting a single sun-like star, known as Kepler-11, which is located approximately 2,000 light years from Earth.
http://www.sciencedaily.com/images/2...0202134725.jpg