Feynman lectures on physics: random walk

[YanaFFF]

TL;DR

Explain please

I do not understand the formulas (6.11) and (6.12) in volume 1 of the Feynman lectures on physics, the entire paragraph between equations (6.10) and (6.12) is generally not very clear. Please explain (preferably in simple language, I'm 13). Thanks!

 

[kuruman]

It would help if you provided links to those formulas for those of us a don’t have Feynman lectures on our shelves. It would also help if you were more specific about what exactly you don’t understand.

 

[Ibix]

As kuruman says, it's helpful to provide links to things you want to ask questions about. We're helping out just for fun, and you're more likely to get help if we only have to click on one link rather than hunt through search engines for references. It isn't always possible to provide links, of course, but the Feynman Lectures are all online on CalTech's website - this is chapter 6.

He's proposing a game: toss a coin and if you get heads take a step to the left, if you get tails take a step to the right. If you keep repeating this game, how far will you be from your starting point? The answer is the difference between the number of heads you've got so far and the number of tails you've got so far. This is $D$. He does algebra to get different expressions for $D$ in terms of the total number of tosses and the number of heads. This is useful because $N$ is not a random number and nor is 2, so the randomness of $D$ is dictated by the randomness of $N_H$, and he already did the maths for that.

6.11 is just a rearrangement of $D=2N_H-N$, stated in the paragraph above. 6.12 expects you to use 6.11 to see that the left hand side is the same as half the rms value of $D$ and then 6.10 to get the right hand side.

If that doesn't make sense, say which bits you don't follow and we'll see what we can do.

 

[YanaFFF]

As kuruman says, it's helpful to provide links to things you want to ask questions about. We're helping out just for fun, and you're more likely to get help if we only have to click on one link rather than hunt through search engines for references. It isn't always possible to provide links, of course, but the Feynman Lectures are all online on CalTech's website - this is chapter 6.

He's proposing a game: toss a coin and if you get heads take a step to the left, if you get tails take a step to the right. If you keep repeating this game, how far will you be from your starting point? The answer is the difference between the number of heads you've got so far and the number of tails you've got so far. This is $D$. He does algebra to get different expressions for $D$ in terms of the total number of tosses and the number of heads. This is useful because $N$ is not a random number and nor is 2, so the randomness of $D$ is dictated by the randomness of $N_H$, and he already did the maths for that.

6.11 is just a rearrangement of $D=2N_H-N$, stated in the paragraph above. 6.12 expects you to use 6.11 to see that the left hand side is the same as half the rms value of $D$ and then 6.10 to get the right hand side.

If that doesn't make sense, say which bits you don't follow and we'll see what we can do.

Thank you very much! That's exactly what I wanted to hear.

 

[kuruman]

We're helping out just for fun, and you're more likely to get help if we only have to click on one link rather than hunt through search engines for references.

Especially when one is using a smartphone to search.

 

[AlexisBlackwell]

Formulas (6.11) and (6.12) in Feynman's lectures on physics explain how the energy of a system changes if it is divided into two parts. This is called a change in the internal energy of the system. Formula (6.11) says that the change in internal energy depends on the change in the volume of the system and pressure. And formula (6.12) shows that the change in internal energy also depends on the heat received or lost by the system. Thus, these formulas help to understand how the energy of a system changes under different conditions.

 

[Doc Al]

Formulas (6.11) and (6.12) in Feynman's lectures on physics explain how the energy of a system changes if it is divided into two parts. This is called a change in the internal energy of the system. Formula (6.11) says that the change in internal energy depends on the change in the volume of the system and pressure. And formula (6.12) shows that the change in internal energy also depends on the heat received or lost by the system. Thus, these formulas help to understand how the energy of a system changes under different conditions.

Say what?