Bignose

The definition of work is very clear cut. You may think that with a force there HAS to be work, but that doesn't coincide with the definition that every single physics text uses. The colloquial use of the word is significantly different than the physics use of the word. The physics definition is very clear. And, if a force is perpendicular to the direction of motion, the dot product between 2 perpendicular vectors is zero, by definition. That doesn't mean that nothing is going on. It just means that no work, according to the physics definition is going on. And, as this is a science forum, the physics definition of work is the one that will be used.

You are looking for the "error function": http://en.wikipedia.org/wiki/Error_function

The use of simplified models to demonstrate a point and a process and then building up to more complex phenomena is a tried and true method. When you 1st took physics, did you jump right into ballistics involving rotation and air resistance and non-spherical shapes, solving the full set of 3-D vector equations? No, you started off with a simple 1-d problem of a falling object neglecting air resistance. Then built up to 2-D problems, then adding simplified drag, etc. The source is not meant to be a rigorous perfect scientific paper. It is meant to demonstrate the idea in a way that most people can understand. If someone want to pursue more deeply, that is beyond the scope of that graphic. (BTW, what is the source on that graphic? -- it is good practice to at least link back to where you took that graphic from).

Since the earth and the bodies rotating about it move as one, the rotational effects aren't needed. That is, both our satellites and the Earth are moving at the same speed in our orbit around the sun. No correction is necessary. If the receiver was on the sun, and the transmitter on the Earth, then accounting for the effect would be needed.

One last time -- if the mean pattern underneath the chaotic pattern is non-zero, it could very well be significant. Do you know that the mean pattern is zero? If not, you cannot just dismiss because you say you can.

So, if it your own theory, then you shouldn't be answering someone else's questions with your idea unless you have definitive proof. Just because a supernova is 100BK, doesn't mean that it causes matter to become whatever was before matter (still undefined). It is fine that you have these ideas, but unless there is proof for them, you really shouldn't answer someone else's threads with your answers. The reasons are two fold. 1) if we want to discuss your ideas, we should have a separate thread for that. and 2) If your ideas are lacking in evidence, they really don't answer the original question.

gf, I don't know enough about earthquakes and geophysics to have an opinion about whether or not magma flows and earthquakes and volcanoes are related. All I have said is that things that look "chaotic" at one time scale can look very deterministic and non-random at another. So, just calling magma flows "chaotic" because "all thermal processes are chaotic" isn't right. At the very least, you need to define over what time scale you are observing this. You mentioned millions of years. Over millions of years, no matter what the randomness in the system may be, it is definitely possible that the mean flow and mean processes have an effect. You cannot just dismiss them because they are "chaotic." And, if convection currents is magma isn't heat transfer, what is? Just because my example was water in a pot, and your situation has molten rock, that doesn't mean that they are different. The underlying physics are the same. And finally, in what system can you not define a velocity? And how does not defining a velocity make something chaotic? Or even random?

Just repeating it again, doesn't make it right. I turn on the stove to the high setting. I put a pot of water on that burner. Given the heat flux (from the stove setting), the size, shape and material of the pot, and the volume of water I put in there, I can predict the average temperature of that pot of water in time. What I cannot predict is which molecules will vaporize into steam and which will remain in water. On the molecular scale, the randomness is significant. On the scale of the whole pot, the randomness is insignificant -- the mean temperature of the whole pot can be known. So, AGAIN, whether something is random (or "chaotic") really depends on the scales of interest. Something can be both random and non-random, depending on the scale. In fact, most things in nature seem to be this way. And, AGAIN, on the scale of millions of years, the randomness gets blurred out and the MEAN effects can be seen.

How do you know this? How is that figure, 100BK, known? What is matter "what ever it was before matter"?

Whether a process is chaotic or not depends greatly upon the time and length scale it is observed on. This is best demonstrated by example -- the water that comes out of my hose is turbulent. The motion of one one molecule of water in the hose is indeed random (what I assume you mean by chaotic, which has a precise mathematical definition, not really applicable here). And, the velocity of water in the exact middle of the hose over time will also be random and fluctuate about. However, the AVERAGE velocity and the AVERAGE movement of the water is very steady. The water only exists the hose, for example. The velocity is not so random as to include forward and backward motion. The turbulence in the fluid only results in the instantaneous velocity to fluctuate about the mean velocity. It is very easy to predict the mean velocity. Randomness in the heating is similar. The exact amount on energy any individual molecule gets will be random. However, the average temperature profile is significantly easier. Over long time, the fluctuations lose meaning. So, while on any one day, there may be a slug of liquid rock that is acting "chatoically", that in no way whatsoever precludes there being an overall average heating or motion that is very steady. That is, while at any moment the exact velocity of a current may fluctuate, the long-term average of that current may be very regular and steady. Thus, the plates can move in a "uniform fashion" despite the "fluctuation". Just like the water comes out of the end of the hose, despite the randomness of the turbulence in the flow. "Millions of years" is plenty of time to use an ensemble average and determine the mean effects, and not get caught up in the random fluctuations.

If you get the boat rocking in just the right manner, perhaps. But, I think that nm is envisioning this thing being able to zip along at whatever speed he wants. And, since testing in space isn't easy, testing on water is a significantly cheaper and viable alternative. The rail with the slug of mass is all supposed to be internal, there isn't supposed to be any interaction with the water. If he built this thing, and the boat was rocking, it would be easy to see on a video that rocking would invalidate the results. If he had a calm body of water and a calm boat (no rocking allowed), and just his slug of mass spinning around, AND the boat was moving solely because of the spinning mass (no wind, or current, etc.), then he's got something. You and I both know that it won't work the way he wants it to work. However, I am tired of him coming here and writing things like "so you cant just say something will not work and expect people to believe you , just as you cant just say something will work and expect people to believe you. " It is obvious words aren't going to change his mind, so I was trying to get him to go out and actually build what he wants to build and try it out for himself. Hopefully he will be able to convince himself when it fails that the idea isn't going to work and maybe he will then actually study what the laws of physics do and don't say. As I wrote, it is obvious that the forum members give it their best shot; there really isn't any more point to arguing is there? So, nm, go and do this for yourself. Be fair about it -- no cheating in any of various ways -- and report back. If you being back objective, indisputable, iron-clad evidence, then we'll all admit we were wrong and that our understanding of physical law needs to be amended. Please don't expect me to hold my breath, however.

No, address swansont's point about translation. As in the other thread, I agree that it will not translate by the laws of physics we know today. I also suggested that your build a model of your device and take it out on a boat on a calm body of water. If your idea works as you say it will, it should also be able to propel a boat across water. Again, going back to YOUR point about not just taking someone's word for it, why don't you go out and do it? Show us all wrong. Until that time, however, again citing the laws of physics that have been validated billions of times is all the justification that us skeptics need.

You can subtract v2 from v1. That's Δv. But, you also need Δt. You can either use the graph, or divide by t1 subtracted from t2. But, you definitely cannot just ignore Δt.

OK, I'll bite. You can't just say that your idea will work and epect me to believe you. Show how you intend to break the laws of physics as we understand them today, and show why the billions of validations of those laws have been wrong to date. Thanks.

It may be "biased" by i_a's choice of major, but it is nonetheless a rather true statement. Chemical engineers learn a little bit of everything these days -- a jack-of-all-trades to a certain degree. They learn mechanics engineering subjects, like fluid mechanics and heat transfer. They learn bioengineering subjects, like biology. They often take at least one circuits class, so they have a little electrical engineering under their belt. In addition, they usually have to take at least 1 controls class, so they have some practical programming experience and controller experience. They learn chemical reactions, both from a chemistry side and an engineering side. They may not get deeply in-depth in any of these subject, but in most modern ChE curricula, the students learn a little bit about a lot of different things. And, the wide variety of industries ChE majors go into reflects this. Up to 30 years ago, 90% of ChE graduates ended up in Houston at an oil refinery or at a large chemical manufacturer like Dow. Today, ChE's go into those, but they also go into food processing, agribusiness, pharmaceuticals, bioengineering, etc. etc. I have actually met more people with ChE degrees not working in the chemical industry than ChE degreed people who are working int he chemical industry.

And I think that it is fair to say that this isn't quite "right". As above, it is not impossible for someone to be able to contribute meaningfully without a PhD, though unlikely. Any group of people that share a significant accomplishment are similar. Runners treat people who run marathons differently than people who just jog for 2o mins after work. Bicyclists who have completed "a century" are treated differently that people who just zip around town and campus. Mountain climbers are always asked "how high have you been?" Golfers who have scratch handicaps are treated differently than weekend duffers. (all I can think of are sports analogies at the moment...) etc. etc. Completing a PhD is similar. Everyone else who has done it understands -- they went through the same process. They have made the same sacrifices -- in time and potential income for love of a subject. I think one important difference is that very often completion of a PhD includes publications of at least one paper to a peer-reviewed scientific journal. The peer-reviewed part is really important, because you have other anonymous reviewers who judge the work and when the paper is accepted, you know that the community considers it a worthwhile contribution. Being able to claim that is "joining the club".

Jonathan, I think that you took that way the wrong way. It is very hard to read tone over a medium like a forum, and I did not get any of the implications that I think you read into it from ajb's posts. The simple truth is that it takes so much time to read and understand all the modern literature about a well-developed subject that most people don't have the time or inclination to do it, unless they are doing it for a living. That is, while one is receiving a stipend or grant or scholarship to go to school. Also, you have to be near a facility that has the literature or can get the literature you need to read with ease -- like a university literature. You will not find any modern journals of physics in the city library. So, it isn't so much that you have to have a PhD to contribute. But, you do have to have the background and understanding of someone who has done much of the same work as a PhD. You have to know the current theory because you have to make sure that what you are doing isn't just a repeat. You have to know the past theory, so that you don't repeat past mistakes. And, then you have to be able to add something new -- again, per previous threads, probably including some rather advanced mathematics. It is certainly possible for an amateur to have all that -- but you have to agree that it is rather unlikely. This is just a result of how mature science in general has become. 100 to 150 years ago, one could claim one's profession as "scientist" and be reasonably accurate. That is, 150 years ago, one could stay reasonably up to date with almost every major discovery in science and make contributions in a wide variety of fields. One could make contributions in mathematics, physics, chemistry, and biology. After that, one couldn't really keep up with a wide variety of sciences anymore, one had to become a "chemist" or "biologist" or "physicist". The amount of literature in each field was just too vast. Today, one cannot even call oneself a "physicist" anymore. One person cannot keep up with the entire field of physics. As ajb alluded to above, you have to specialize in the field -- string theorist, etc. And, many of the fields are like that today. One cannot just be a "chemist" anymore or a "biologist" or any of the other big fields -- each field has its own specialists in each little subject. In another thread a while back, I estimated that it would probably take a person an entire lifetime to read all of the scientific publications that are put out in any one month this year. The paper database that I use for search, Web of Science, catalogs over 10,000 journals. Most of those release an issue every single month (there are a few quarterlies, and a few that release 2 or 3 issue a month, but monthly is a good average). Each issue has between 5 and 15 articles. That would be around 100,000 scientific articles released per month right now. Now, that is all disciplines, but that is just to give you an idea of how much science is being published at this time. And why it literally takes people several years to catch up on the literature in their chosen specialty in their field before they even have an idea of what the history and the current state is, and what original contributions they may be able to make. So, again, it isn't that a PhD is required, but the way the vast majority of people have the opportunity to gain the requisite knowledge is in earning their doctorate.

Jonathan, I think that biggest problem here is that what you are suggesting isn't as simple as just getting enough people together and talking about it. It's not like a weekend hacker party where everyone brings their computer and everyone writes some code and at the end of the weekend you have a working program. It is something that literally would take years to get started. And, you'd have to have enough people with the requisite knowledge. As ajb wrote, this means several people with doctorates in theoretical physics. And doctorates alone are not enough (there are several members of this forum who have earned that degree, but they also have to have the knowledge in the specific areas, strings and quantum gravity loops. It takes years just to catch up and read the current literature before one can understand it all and learn how to add something that hasn't been done before. This isn't to say it isn't a worthy goal, it is just something that cannot be done over a forum and on a part-time basis. To do this write, you have to collect the right people together, and get grants written and given so that those people can work on it and get salaries for several years. It isn't something that can be done on a forum, or with a letter to a physics professor, or with a single meeting with a professor at a nearby university. And, as ajb said, unless you can offer something really profound (including the requisite mathematical description) or maybe several millions of dollars as a grant, it will be difficult to get someone to take you seriously. If you want to be part of this, it is going to take many, many years of the technical schooling and training, to become an expert in the area, publish papers in the areas and become known as an expert. It is not impossible for an outsider to bring up something new, but it is very difficult. Without a mathematical description, all you end up doing is telling a story. It may be a good story, but you can't use stories to make predictions about the physical universe. Mathematics is needed so as make very specific objective predictions. Such as "If I cause an electron and a proton to collide at velocity x, the collision will cause y to happen" where y may be emission of specific sub-particles, release of a specific amount of energy, etc. The prediction of exactly what y is comes from the mathematics. Without that kind of info, no one who is doing that kind of work (i.e. scientists) are going to be very interested. Because story telling is not science. Story telling may be in the first steps on the way to accomplishing science -- inspiration is a very funny thing -- but the first steps are not equal to the finished product. And, in this case, the finished product would take many years of hard work.

I think that you are possibly confusing everyday arguing with scientific arguing. Scientifically (and I hope ajb will fix anything I get wrong), both ideas are really still in some preliminary stages. That is, there has been very few experiments that directly support or negate the ideas. So, at this time, both ideas can only be explored mathematically and attempt to discover if the logical consequences of either end up making predictions that are against experiments that have been done. That is, it takes a lot of time and money and creativity to be able to make experiments that test the theories directly, and they just haven't been done yet. So, all that can be done is to make sure that the theories don't predict things that we know are wrong today. Scientifically, no one is saying that they can't be joined together, but if not many people are experts in both of the areas, there just may not enough interest to attempt that. Mathematically, exploring the implications of one or the other are complicated enough and certainly aren't easy to get to. I can easily see how people probably aren't satisfied that either one is explored enough yet that attempting to combine them may only complicate things needlessly and unhelpfully. By analogy, if you don't know to solve algebraic equations, attempting to throw some trigonometry into a problem and mix them together would really only muddle things up. You want to master algebra, and then master trigonometry, and then do problems involving both. Right now, they are trying to get each one nailed down separately, and then they will see if they may be common in some area. There may be some arguing from people not in the scientific community, that is almost wholly based on opinions and popularizations of the science. It is hard to argue about it unless you know the mathematics behind the idea. And, I am sure that there are disagreements about somethings in the scientific community. I have no idea if it is true or not, but at one time there seemed to be 5 different flavors of string theory that all seemed possible (i.e. not conflicting with current state knowledge). I am sure that people working on the problem each have their own preferences or intuition about which is right. But, in the end, experimentation will determine which flavor of the idea is most correct, not arguments. And that is the great thing about science. The scientists may have their individual opinions, but they all are waiting to see what the experiments say.

Because in an isolated system (and a spacecraft away from anything else in deep space is isolated), the total amount of energy will remain constant. If the ship expends some energy to accelerate a slug of mass on a track, at the very, very best, that slug of mass can return only the exact same amount of energy to the ship (via rail, etc.) And, since you included friction, it will actually deliver significantly less than originally used to accelerate it. And, if no mass leaves the ship, the entire system can do whatever it wants inside the ship, but it won't change the outside of the system. I suggest you build a prototype of your device, if you are so sure it will work. Go out on a lake, and have a boat with a circular rail. So long as the rail and slug of mass running on it doesn't interact with the water, it will be just like being in space. I predict that you can spin that mass however you want, but you won't move that boat (be sure to neglect any wind or current effects!). But, go do that experiment yourself and prove us all wrong. If you bring back objective indisputable proof, I guarantee that I will publicly admit I was wrong and you are right. And, I actually am not a very prolific poster at all, compared to many others here. That title was given to me by the site administrated, just as swansont's was. Sure, I fully admit it doesn't "mean" anything -- nor did I or anyone ever claim that it did in the first place. Physical law doesn't give a hoot if the person citing them is titled with "Maths Expert", or "Physics Expert", or "Kindergarten Expert" or "Banana Expert". Physical law just is. And, your claim on being able to propel a spacecraft just by spinning a slug of mass inside of it goes against physical law as we understand it today. So, again, go make your device and prove us wrong. Quit wasting your time here.

give me a break. He offered a "viable" reason your analysis is incorrect. It violates conservation of energy. Do you realize, that in EVERY SINGLE situation EVER observed, conservation of energy has been followed? NEVER has there been a situation found where conversation of energy has been violated. Many times it has been thought to have been broken, but in every instance, the error was found and in the end, conservation of energy held every time. It may very well be THE most tested physical law ever, and it has NEVER been broken yet. This of course does not mean that it is bullet proof and perfect. But, an awful lot of extraordinary evidence will have to be found to show a case when it has been broken. If you can provide this evidence, then let's see it. Otherwise, calling an analysis that violates the conservation of energy incorrect is perfectly justified, because no situation has ever been found that yet violates it. So, what else can you present to change minds instead of petty name calling and and whining about the "big bad naysayers"?

Yeah, that's why I asked, because if someone needs vector calculus and tensors, then they should start with the vector calculus. Because a lot of the tensor stuff is just an extension of the vector stuff (not all, but a lot of it).

just tensors or all vector calculus? if the later, I cannot recommend Shey's Div, Grad, Curl and all that more.

As another answer, temperature is also a scalar. One can easily imagine a temperature difference from one side of an object to another.

I have never heard of the names being specifically mentioned with an 11th order method. The common ones are 2nd order and 4th order. Usually when a 5th or 6th order are mentioned, there is another name associated with it, like "6th order Runga-Kutta-Nystrom". That said, there should be formulas wherein you can derive any order method. They are based on Taylor series and the like, just determine how many terms you keep before truncating the series. 11th order seems very high, what application are you trying to do where a 4th or even 6th order isn't sufficient?