Jeanway 0 Posted April 22, 2004 With so much speculation, why can't anyone find them? <_< Share this post Link to post Share on other sites
Angela 1 Posted April 22, 2004 you try catching some the that is reportedly faster than light according to Einstein! Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 Fine question, Jeanway. The spacetime continuum essentially extends into four dimensions (for simplicity, say four). The fourth dimension, in current paradigms can be represented with imaginary numbers ("imaginary" is just a very bad way of extending our number system. It's really not imaginary as we think of it). Well, in space and time, there are singularities when v=c. (Meaning that equations become undefined. Things approach infinity or negative infinity.) However, when v<c - the universe we live in, things are fine. We call this regime a "timelike continuum". And, when v>c, the equations are also defined well, but there is a factor of i (the square root of negative one), and when this is squared, we get negative values in the equations involving momenta. This is called a "spacelike" continuum. In this continuum v>c always. If you apply a force (impulse) to a particle, it's momentum will decrease along the direction or force - opposite what happens here. Now, here's the answer to your question. We can define a coordinate system in either reference frame and we can do transormations between coordinate systems in a continuum. Think of the question you asked about why coordinates are different in space and on the earth. We can fairly easily convert from one to the other becuase information can be transfered between these frames. (We use what are called Lorentz transformations to do this - essentially parametrized space coordinates on hyperbolic axes, i.e. x in one frame is a linear combination of hyperpolic functions of x and t in another). We say that they are causally connected. We cannot convert from a coordinate system in the spacelike continuum to one in the timelike continuum and vice versa. They are not causally connected. In a sentence: Light (information) does not go from a spacelike continuum to the next. Share this post Link to post Share on other sites
Jeanway 0 Posted April 22, 2004 Then shouldn't v=-c? <_< Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 Jeanway, here's a way of representing these continua. Get a piece of paper. Pretend for now that the universe has two dimensions, length (x) and time (t). Draw a coordinate system on the paper. X horisontal, time vertical. Any path drawn on that system is called the "world line" - where it is at time t. (Negative time is the past, positive the future.) What if you have a photon, which v=c? At time 0, say it's at x=0. At t=1s, it's at x=c*1, 2 seconds: x=2*c, etc. So we have coordinates (x,t) = (0,0), (c,1), (2c,2), (nc,n), and we can also have a photon going the other way, so that the x coordinates are negative as well. Draw these points and lines on the paper. This is called the light cone. Now, do this. (And I will not say anything else.) Draw points on the paper where you think an object with v<c is, and an object with v>c would be. Let me know what you get. This is how physicists think of space an time a lot. Here, I found a web site with good pictures: Light cone physics Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 Then shouldn't v=-c? <_< Another good question. Velocity is a "vector." It has direction. So negative velocity means it's just going the other way. Example: A car with v>0 is going away from me, and one with v<0 is coming towards me. This is tough stuff. In grad school, we pretty much proved that spacelike continua are non-causal in our continuum, forgot about it,and then went on to develop transformations for electromagnetic fields in free space, from charges, etc. My teacher, being rather sadistic, decided to make us derive the path of a relativistic electron near a magnetic monopole. (So it was OK to break Maxwell's equations, but we barely spent any time in the spacelike continuum.) Share this post Link to post Share on other sites
Jeanway 0 Posted April 22, 2004 Some teachers like to use torture under the guise of learning. I've had a few of those Sadististic um, can't say two bad words , so I know what you mean. <_< I'm so glad school is over :P Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 Yep. There's a text book that every grad student in my career has heard of and gone pale. It's called "Classical Electrodymics" by J.D. Jackson. It's a decent book, but incredibly hard. When I was grad school, after we passed that class, people made T-Shirts that said, "I survived Jackson '9x" I had a chance to meet the author one day, and he signed my copy for me. I've got a lot of respect for the man who could force me to stay up to the wee hours of the morning and push my sanity to the edge of the envelope and then haul it back in again and go back and do it the next day. Share this post Link to post Share on other sites
fenriz275 0 Posted April 22, 2004 Ok this may be a really stupid question but what is c? Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 Ok this may be a really stupid question but what is c? Not a stupid Q at all. Took humanity about 300 years to figure that out. c is the symbol conventionally used for the velocity of light in vacuo. It's a constant. 2.99*10^8 m/s. Pretty dang fast. Share this post Link to post Share on other sites
fenriz275 0 Posted April 22, 2004 So if c is a constant does that mean it has both a positive and negative value or is it like 0 and has neither? Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 Well, remember, c is just a number..... Velocity is a vector. It has both a magnitude (the number, in the case of velocity, sometimes called speed) and a direction (e.g., north). For example, I can say I'm driving 50mph north. I can also say I'm driving in the OPPOSITE direction (south, right?) For this, I can say I'm driving -50mph (or 50mph south). We can define coordinates such that a positive value is motion away, and a negative value is motion towards a reference point. That's all the negative means - two different direction. Share this post Link to post Share on other sites
fenriz275 0 Posted April 22, 2004 So c is being used as a reference point to define v? Am I even a little close? Share this post Link to post Share on other sites
nik 0 Posted April 22, 2004 umm....... yes, in a way. V is just velocity.... how fast something is going. In physics, we sometimes just like to say v is some multiple of c. So if I say v=0.7c, I mean that the velocity is equal to the speed of light times 0.7 - or 70% the speed of light. Share this post Link to post Share on other sites
WEAREBORG4102 0 Posted April 22, 2004 well we really can't even detect interdimensional rifts so tachyons are not going to happen soon... Nik, where do you work?? At Stanford or fermilab??? Share this post Link to post Share on other sites
nik 0 Posted April 23, 2004 Nik, where do you work?? At Stanford or fermilab??? Nope. Fine guess, though. Share this post Link to post Share on other sites
WEAREBORG4102 0 Posted April 23, 2004 WHERE??? I must know!!! Share this post Link to post Share on other sites
nik 0 Posted April 23, 2004 WHERE???I must know!!! Anonimity is a nice thing about these boards, it allows one to be themselves without worryin what others think. If I tell you, I would be giving away a huge amount of information about myself. There is a very good chance that you could infer who I am. Let me think on't, and maybe I'll PM you. Share this post Link to post Share on other sites
WEAREBORG4102 0 Posted April 23, 2004 I'm just curious... what can a 13 year old kid do to you?? if you doubt my age, PM -Harrykim- He goes to my school.... I just want to find out about particle physics as it is sooooo very cool!!! Share this post Link to post Share on other sites
Angela 1 Posted April 23, 2004 I am grateful you are here, you have taught me a lot. I am now curious as to who you are myself. You are an incredible mind on these topics and you have a lot of my respect. I was never good at the math side but the concepts and ideas, they have always fascinated me. Which is prolly the reason I read your posts in this forum. Feel free to reveal identity to me, I promise I will tell no one. It really isn't worth hurting others. Oh and you couldn't PM me your thoughts on Artificial Intelligence could you? Share this post Link to post Share on other sites
nik 0 Posted April 23, 2004 Aw, why not? With compliments like that, who can resist? You've got the PM. Share this post Link to post Share on other sites
nik 0 Posted April 24, 2004 what can a 13 year old kid do to you?? I could say something creative here, but I'll let it go. I like your persistence, Borg. Persistence....... it's a cardinal attribute of many great scientists. Share this post Link to post Share on other sites
Jeanway 0 Posted April 24, 2004 Yep. There's a text book that every grad student in my career has heard of and gone pale. It's called "Classical Electrodymics" by J.D. Jackson. It's a decent book, but incredibly hard. When I was grad school, after we passed that class, people made T-Shirts that said, "I survived Jackson '9x" I had a chance to meet the author one day, and he signed my copy for me. I've got a lot of respect for the man who could force me to stay up to the wee hours of the morning and push my sanity to the edge of the envelope and then haul it back in again and go back and do it the next day. OK, nik, try this one, The Origins of Intellect, Piaget's Theory, by John L. Phillips, Jr. I guarantee it'll give you a severe case of the bends Share this post Link to post Share on other sites
nik 0 Posted April 24, 2004 OK, nik, try this one, The Origins of Intellect, Piaget's Theory, by John L. Phillips, Jr. I guarantee it'll give you a severe case of the bends You know, I've heard of that book, but have never read it. I assume you've read it? Did you like it? I understand it's tough stuff. Share this post Link to post Share on other sites
Jeanway 0 Posted April 24, 2004 OK, nik, try this one, The Origins of Intellect, Piaget's Theory, by John L. Phillips, Jr. I guarantee it'll give you a severe case of the bends You know, I've heard of that book, but have never read it. I assume you've read it? Did you like it? I understand it's tough stuff. For one semester I had the bends almost every night. Share this post Link to post Share on other sites
Angela 1 Posted April 24, 2004 Piaget is required reading in degree courses in the UK. Debating the pros and cons on it is fun, especially when he makes generalisation based on children from geneva and on 30 at that. His theories we largely unfounded in societies outside of continental Europe and the idea that each stage of a childs development was a concrete stage to do with AGE is almost laughable. (I have personal experience on this one) Share this post Link to post Share on other sites
nik 0 Posted April 24, 2004 Piaget is required reading in degree courses in the UK. Debating the pros and cons on it is fun, especially when he makes generalisation based on children from geneva and on 30 at that. His theories we largely unfounded in societies outside of continental Europe and the idea that each stage of a childs development was a concrete stage to do with AGE is almost laughable. (I have personal experience on this one) Fascinating concepts! I must admit to really not reading too much Piaget, only bits and pieces. You must have given this much thought. I must find this book! Share this post Link to post Share on other sites
WEAREBORG4102 0 Posted April 24, 2004 what can a 13 year old kid do to you?? I could say something creative here, but I'll let it go. I like your persistence, Borg. Persistence....... it's a cardinal attribute of many great scientists. thanks for the complement!!!! :P Share this post Link to post Share on other sites
scaleman 0 Posted April 24, 2004 Umm, ok, i have to admit this page is beyond my comprehension :blink: . Share this post Link to post Share on other sites
Jeanway 0 Posted April 25, 2004 HEY, HE'S MINE!!! I FOUND HIM FIRST YOU GUYS :: Pushes UA and Wearborg out the door:: B) Tell them nik :blink: Share this post Link to post Share on other sites