# What is the hardest equation you have come across in your Physics career?

1. Jul 1, 2011

### TJRichards160

Hi! I want to test my Physics teachers knowledge with a really complex question. Possibly something like the tie break question in the TBBT episode 'The Bat Jat Conjecture' even though it is not correct, but something similar which is hard! So, what is the hardest question you have come across in your career?

2. Jul 1, 2011

Ask your teacher to find a general solution to the Navier-Stokes equation.

3. Jul 1, 2011

### TJRichards160

I need answers and correct workings as well, so I can check his answer and correct him if he is wrong.

4. Jul 1, 2011

### FroChro

You don't really know how science works, do you? Large part of it is about asking good questions, questions that are both interesting and simple enough to be answerable. There's no shortage of questions which your teacher (or anyone else) wouldn't be able to solve. Regardless of that, why do you want to do it? If he is good teacher/good physicist there is no reason to do it. If he is good teacher/bad physicist you can find your question yourself, unless your intellectual abilities are as high as your morale standards. If he's bad teacher, focus on that.

5. Jul 1, 2011

### rcgldr

One interesting but initally simple looking problem that was solved here at physics forums a while back involved calculating the time it took for two 1 kg point masses starting at zero velocity and 1 meter apart to collide into each other due to gravity (with no external forces involved). The tricky part was figuring out how to solve one of the integrals, so that one was more of a math problem than a physics problem.

6. Jul 1, 2011

### BobG

Do you mean you want to ask him to explain the equation? Why it works?

Best bet is to search for an equation that has a lot of people credited with discovering it. That usually means that nobody really understood what was discovered and let it fade into obscurity before being rediscovered by somebody else, only to fade into obscurity because no one really understood it, only to be rediscovered again, and so on.

The Hermann-Bernoulli-LaPlace-Hamilton-Gibbs-Runge-Lenz-Pauli vector would be an example (okay, it's really only known as the LaPlace-Runge-Lenz vector, but LaPlace was really the third person to figure this relationship out).

Of course, you'd really want an example that related to what you were talking about rather than some random question. And I'm not sure what you'd prove, anyway. But, at least it would probably be an interesting equation to discuss.

7. Jul 1, 2011

### Staff: Mentor

What is your intention in doing this? Are you hoping to make your instructor look foolish? Or does your instructor encourage the students to come up with challenges that s/he enjoys solving?

8. Jul 1, 2011

### nlsherrill

Are you serious?

Even if you did stump your professor, this wouldn't prove he/she wasn't intelligent. If you try this, more than likely your professor will embarrass you instead of the other way around.

I knew a kid who would do just this in my previous physics classes. More often than not he would have the answer to the question and the kid looked like the complete stuck up jerk that he is.

9. Jul 1, 2011

My suggestion doesn't have a known answer as of yet. It is one of the great remaining problems in science/mathematics.

10. Jul 1, 2011

### danR

I will assume the student and the teacher understand each other's personalities and suggest the 3-body problem(s).

11. Jul 1, 2011

### TJRichards160

He encourages us to give him challenging problems. He likes to test his knowledge and he also teaches us and then explains. He likes me and he wants me to advance in Physics. He sees my potential and thinks I can handle it. So, we have been working through some problems and I just wanted more of a challenge!

12. Jul 1, 2011

### danR

I sensed this. Try the 3-body problem. Though I think he will be ready. It's famous.

I remember being in a physics class discussion group in the general meeting room, and looking around, and wouldn't you know, there's a book sitting 5 feet from me: 'The Three-body Problem'. That shelf sits about 10 feet from one of the world's foremost experts on Quantum Gravity.

Edit: put it this way: 'I can see how someone would calculate the orbital motions of the Earth and moon, but how does it work with the sun added?

13. Jul 1, 2011

### Naty1

How will you know if the answer given here is correct??

Open Roger Penrose's THE ROAD TO REALITY and take an equation from almost any page past about page 100.....

14. Jul 3, 2011

### Acut

That is indeed an interesting problem, but there's a much simpler solution. Instead of using integrals, use Kepler's laws. Pretend that you have a very, very eccentric ellipse - so that the ellipse looks like a straight line. Then apply Kepler's laws and you'll find the answer without any really complicated math.

15. Jul 6, 2011

### FroChro

Then I apologize for my rather aggressive comment.

Actually, how can you do that? Kepler's law of dependence between ratios of periods and dimensions of similar trajectories (or just mechanical similarity) doesn't allow you to compute periods of motions, only ratios. Conservation of angular momentum itself (kepler's 2nd law) does neither. It implies only that "area of elipse"=("angular momentum"/2*(reduced)mass)*period . You need to know complete solution of "kepler's problem" (more than just kepler's laws) to actually know dependence of area of elipse on angular momentum and energy, and therefore being able to compute (half)period, don't you?

16. Jul 6, 2011

### Superstring

Would you mind posting the solution to that problem?

All I could come up with was the differential equation:

$$G +r''(t)r(t)^2 = 0$$

The solution to which I have no idea.

17. Jul 7, 2011

### FroChro

$$r''(t)r(t)^2$$ must be not dependent on time, as you can see from your equation. What about trying function of type $$k\cdot t^{\alpha}$$ ,where k,alpha are constants? Once you determine alpha (this can be also derived from one of kepler's laws, as someone suggested), try to find more general solution, and/or use time inversion invariance property of the problem we are trying to solve.

Edit:
Oh, sorry. I was wrong. Folowing my advice you''l get just one very special solution not directly applicable to our problem. (Plus you can't use kepler's laws as straightforwardly as I thought this time.)

I would try following way: (let's set G=1/m,m=2) We have v^2-1/r=energy, therefore $$v=\frac{1}{\sqrt{R}}\sqrt{\frac{1-\frac{r}{R}}{\frac{r}{R}}}$$ where R is r(0). (We also have D(r)(0)=0) Now dt=dr/v, therefore (after substituing r/R=x) $$T=R^{\frac{3}{2}}\int\limits_0^1 \sqrt{\frac{x}{1-x}}dx$$ Value of integral is pi/2. Here, kepler law, or mechanical similarity, is directly applicable.

Last edited: Jul 7, 2011