youngone

Okay, so I got the answer for the second question which is 9!-(3P2*8!)+(3P3*7!)=151200. But when I tried to get the answer for the next question I keep on getting it wrong. Can you please correct my working? My working is 9!-(4P2*8!)+(4P3*7!)-(4P4*6!).

Recently, I was looking through my sister's Maths Textbooks and I saw a very interesting topic I could learn. So for the next few days I learnt the basics of permutations and their applications. All was well until I stumbled upon a question that I was unable to solve. With no one else to turn to (my sister has not yet been taught permutations yet), I decided to post my question on the boards. The question goes like this: There are 9 books arranged on a shelf. 2 of them are labelled A, 3 of them are labelled B and 4 of them are labelled C. How many permutations of the books are there if: a)none of the books labelled A were next to each other. b)none of the books labelled B were next to each other. c)none of the books labelled C were next to each other. I managed to answer question a) but not questions b) and c). I answered question a) like this: Since we want to find the number of permutations with none of books A next to each other, we just need to find number of permutations with books A next to each other and subtract it from the number of permutations without restrictions. So the number of permutations without restrictions is 9!=362880. Next we group the 2 books labelled A and consider it as one block. So, the number of permutations within books is 2!=2 while the number of permutations with the remaining books and the block of books A is 8!=40320. Therefore the number of permutations with books A next to each other is 2!*8!=80640. Finally we just subtract the number of permutations with books A next to each other from the number of permutations without restrictions which is 9!-(2!*8!)=282240 and it matches the answer at the back of the textbook. I tried to use the same method for the remaining questions but it did not work. You cannot group up three or four of the books together and try and find the number of permutations because you would not take into account the fact that even only 2 books can be next to each other. I also tried grouping up only 2 of the books and using the nPr notation (3P2 or 4P2) but I still got the wrong answer. So, can anyone here help me to solve this problem?

Ha ha ha!! Everyone makes mistakes so you are pardoned. Living in Brunei is actually very difficult, generally because of its slow education system. There are no proper Physics lessons unless you are a Form 4 (which I will be next year!) because all Science subjects such as Biology and Chemistry are taught as General Science. I am also guessing that the only university in my country does not offer any Advanced Physics Courses. So apparently, the only way I'll ever become a physicist is to go overseas. I am considering going to Cambridge in the UK but I a might feel a bit alienated because I am Chinese and I don't think there are many Chinese in UK. I feel that you're right about me being too young to fully grasp everything about relativity. I understand the concept of time dilation and length contraction but maybe not for relative dissynchronicity and simultaneity. Maybe when I grow up and learn additional mathematics I should be able to understand the complex equations behind relativity. Looks like I have to be going now. I sincerely thank you for all your help and patience in helping me sort through some of my problems.

Heh heh, no reason to say Happy Thanksgiving. I live in Brunei, a place nobody has ever heard of and we don't celebrate Thanksgiving. Anyway I hope you had a Happy Thanksgiving. Okay, I still don't get much about the dissynchronized clocks in the same frame of reference. So I will tell you what I know about the whole situation again and then you correct me, Ok? The astronaut twin travels from point A (space buoy) to point B (Earth) 0.866 lightyears apart at a speed of 0.866c whereas the earth twin stays on Earth. When the astronaut twin passes both twins will start their watches and later measure their times when they meet up at B. To prevent any confusion we ignore any Doppler shift effects. To the earth twin, he starts his watch as soon he computes the astronaut twin passes point A. The earth twin measures 1 year for the journey and reckons the astronaut twin took only 6 months in the astronaut twin's time. To the astronaut twin the journey takes 6 months and reckons the earth twin recorded the journey as taking only 3 months. But actually the astronaut twin saw the earth twin start his watch 9 months before he passed the sun so they end up agreeing that the astronaut twin had elapsed less time. This part I now understand. Now, you suggested a clock placed at the space buoy that was in sync with the earth's time. But when the astronaut twin passed it, it read time that was 9 months earlier than the earth's time. What I want to know is if the clock on the space buoy would still read 9 months earlier than the earth's clock as the astronaut passed by it or would it read 9 months later because the astronaut twin was closer to the earth's clock? Can you also tell me everything else that you know about this?

Ok, let me just get this straight: Two clocks separated by a distance that are in sync in one frame of reference will be computed (not seen) as being out of sync to an observer travelling at a certain velocity relative to the clocks' frame of reference, right? So that means that the astronaut twin will see the clock on the space buoy have an earlier time than the clock on the earth even after factoring and taking into account the Doppler Shift and distance between those two clocks?

Ok, so if the astronaut twin was already in relative motion when he passed the space buoy, he would conclude that the earth twin started his watch 9 months in his own time before he passed the buoy, right? But he would still compute the clock on the space buoy would read 9 months earlier than on the earth even though according to the earth's frame of reference, both clocks are in sync. Now what is the cause for the clocks going out of sync? One more thing (We can do this after we handle the above situation). Instead of considering the astronaut twin moving before he reaches the buoy, let us say he starts on the space buoy and accelerates to 0.866c in a certain amount of time and reaches the earth twin. What is the difference between the other situation and what happens in this scenario?

Can you explain on this part some more? I realize that both clocks are out of sync but I want to know how is it in the very end both of their clocks agree that the earth twin has elapsed more time.

Ok, just a few more questions. I will use the same situation as previous but eliminate the turnaround and the first half of the journey. So, we say there are two points, A and B, 0.86 lightyears apart. On A is the earth twin while on B is the astronaut twin. The astronaut twin would then instantly accelerate (or consider him already moving) to 0.866c where gamma=2 (the time dilation factor, right?). The whole journey will take 1 year according to the earth twin and will see the other twin's time run at half speed (6 months) while the astronaut twin will take 6 months to complete the journey and see the earth twin's time run at half the speed (3 months). Now, what is the solution to the situation? Oh, and sorry for constantly pestering you like this. I would personally do the math but I don't know anything about the mathematics of relativity and if possible can you provide a website which teachs everything about the math in a simple manner?

Sorry for not posting in a while. I was travelling with my family recently. OK, I think I am starting to get it now. Apparently the math predicts that the twin who makes the return journey to the other twin ages more slowly. This is because the twin has to accelerate in the other direction resulting in a change of his/her frame of reference, am I right? This means that if the twin on earth was to jump into a spaceship and catch up with his/her twin, he/she would have aged less when compared to the twin, right? But what I still don't get is what each twin computes (not sees) throughout the whole event. OK, so at first, the one twin computes that time for the other twin runs slowly (let's say at half the speed) and vice versa. Now the earth twin will calculate that the first part of the journey takes 12 years in his/her own time. This means that the astronaut twin will take 6 years according to his/her own time and he/she will reckon that during the first part of the journey the earth twin will age only 3 years, right? Now what happens after this, when the astronaut twin makes the turnaround?

Sorry for not posting in a while. I was travelling with my family recently. OK, I think I am starting to get it now. Apparently the math predicts that the twin who makes the return journey to the other twin ages more slowly. This is because the twin has to accelerate in the other direction resulting in a change of his/her frame of reference, am I right? This means that if the twin on earth was to jump into a spaceship and catch up with his/her twin, he/she would have aged less when compared to the twin, right? But what I still don't get is what each twin computes (not sees) throughout the whole event. OK, so at first, the one twin computes that time for the other twin runs slowly (let's say at half the speed) and vice versa. Now the earth twin will calculate that the first part of the journey takes 12 years in his/her own time. This means that the astronaut twin will take 6 years according to his/her own time and he/she will reckon that during the first part of the journey the earth twin will age only 3 years, right? Now what happens after this, when the astronaut twin makes the turnaround?

Does this mean that when the second observer who is travelling changes his/her velocity and makes the return trip to the first observer who is at rest, the second observer will see the first observer's age increase dramatically when he/she starts to return back to the first observer? What are the reasons for this? Can you please explain it to me? PS Please be patient with me! I know I am very slow on this topic!

I'm a bit confused. Can you provide some more clarification and maybe an example?

But what if they were to compare their respective times later on? Since the first observer viewed the second observer's time slow down and the second observer viewed the first observer's time slow down, how can they tell who was the slower one?

Hey, thanks to all of you for your posts! Just one more thing: Same question as number 2 but involving time dilation. How would the second observer view the first observer if it is travelling at 0.9c relative to the first observer? The first observer would view time for the second observer to be moving slower. But how would the second observer view time for the first observer? Would it be faster or slower?

Hi, I'm only 15 years old and new to relativity and I'm finding it a little bit confusing. Here are some of my questions. 1) Consider two spaceships. Each spaceship moves away from each other at a speed of 0.9c. Now, would light from either spaceship reach the other? If possible, provide some reasons and maybe a few interesting bits along with your answer. 2) As we all know, if a first observer was to view another second observer travelling at 0.9c relative to him/her, he/she would view the second observer to be contracted according to the direction of travel. But how would the second observer view the first observer? Would the first observer appear contracted to the second observer? Again, if possible, provide anything interesting along with your post.

Same here too. At least you guys live in America, unlike me. I live in some place where nobody in the universe could possibly locate on a map (Brunei Darussalam). The education system over there STINKS! I am 15 years old and just finished Form 3; somewhere around Grade 9 in your country (I guess!). They teach maths very slowly in here. For example, this year, we were thought Pythagoras' Theorem. CAN YOU BELIEVE IT?! I knew this thing two years ago and I am bloody sure you guys knew it when you were in diapers! And do you know what the worst part is? Since the teaching of Maths and Science has been going slowly for the past few years, the next years will be way tougher than ever because we have to catch up with the world standard. I have been looking through my elder sister's maths and physics books in hopes of learning some more but it feels useless.