studiot

Hello Michel. Where did you get these ideas from? You seem rather mixed up about dimensions and embedding. You embed an n dimensional object in a space that has at least n+1 dimensions. An n dimensional object is part of an n dimensional spce, it is not embedded. A n dimensional object will not fit into a space of less than n dimensions. However it is possible to map an n dimensional object into a space of lower dimension. This is called a projection, which is the subject of projective geometry.

If you look over this thread, you will note that your issue (underlined) is off the topic of this thread. I guess that the moderators have allowed you (and me) to continue, as with a previous poster's off topic stuff, because the original question was well discussed some months ago. My responses to your issue have each time acknowledged where you were right or had a good point to make. Including this one. You clearly haven't read posts given by myself and others properly or you would has seen the answer to this question. Furthermore Newtonian gravity is not the only mechanical property to be affected by the distribution of mass as well as the absolute value. Knowing this is key to understanding the difference between moment of inertia and product of inertia for instance. Unfortunately your intransigent rudeness in replying is getting in the way of your own understanding and proper expansion of the explanation, perhaps even leading to such ridiculous claims as 'something multiplied by zero tends to infinity'

Never mind Bells. Determinancy is mathematically untenable as follows. Consider an assembly of exactly 1,000,000 atoms of a radioactive substance with a half life of exactly 1 year. At t = exactly one year count the number of atoms. How many will there be (exactly)? If physics is determinate then this question should have an exact answer. Experimentally we do not observe this. We observe a statistical spread of answers. But mathematically there is worse. Suppose instead of a million atoms we stared out with 1,000,001. Now what will the one year count reveal, since you can't cut an atom in half?

So discuss physics in general and quantum physics in particular. And stop claiming that relativity and quantum physics cannot be combined. You have google the same as I do, Item 3 on my google search is this lecture from Berkeley University: There are plenty of others to choose from http://hitoshi.berkeley.edu/221B-S02/Dirac.pdf.

Isn't that the answer you require, or do hospital patients spin where you come from?

Either you are trolling or you really don't understand even high school mathematics. My graph is sound and quite understandable using only high school mathematics.

What is 'the sample' in each case? What does each technique measure?

Like it +1

The OP for this thread Of course there are. Logic, or even rational thinking which is less restrictive does not address objectives or preferences and likes in any way. I like blue You like green There is no logic to either of these statements, but they constrain and direct our thinking, our view of the external world and even our actions. There is no logic to doing anything. That is logic alone provides no motivation, only a methodology I like sausages. I can go about obtaining sausages in a rational or irrational way, it makes no difference to the motivation. But equally the motivation makes no difference to rational of obtaining sausages over tuna. Without motivation logic would be (almost) totally useless.

I leave tuna, marlin and shark fishing to proper fishermen. It is a well respected activity. So if I wanted to know what was a good catch weight etc I would ask a proper fisherman. Because I really don't know. So please leave particle physics to particle physicists and ask. Incidentally, a more interesting question than can you have motion without time? is Can you have time without motion? For time can also measure the duration for which nothing happens.

So how does your calculations make Newton wrong? You didn't say, merely claimed him to be wrong. You have a good point, but Rather than sneering at others, if you acted like a true scientist and investigated you might find out something new and even learn something. All you have begun to show is that the gravitational attraction depends not only on the total mass but also on the distribution of that mass. Exactly as Newton's equation. Here is a plot of what happens as you vary the relative sizes of two masses held at constant distance apart with a constant total mass sum. You get a non linear curve with a maximum force when the two masses are equal, and zero force when one of the masses is zero. It is but that explanation is woefully inadequate. Firstly a push can also be exerted by non matter agents. Secondly just limiting the discussion to matter, are you aware of the difference between body forces, surface forces, direct and shear forces?

Re-read post#6 (+1 to phi) You might just as well argue that because having a hammer allows you to drive a nail hammers are the cause of nails. PS you might also like to comment on my post#10 and hey you are recorded as the starter of this thread.

You are absolutely right, I was too quick there. Well done for spotting that. +1

Indeed but rudeness does not validate your view either. I seem to recall noting before that the first person to develop a relativistic 'correction' to the Schrodinger equation was Paul Dirac, back in the 1930s. There have been other versions since but the thing with all relativistic corrections is that the participants have to possess sufficient relative velocity to make the corrections significant.

If I recall correctly, you have already been told that more advanced quantum theory includes relativistic effects.

If this sentence has meaning I cannot determine it.

Well it seems that the OP has lost inerest, and I'm not sure anyone else is interested either. If fact my posts were not taking the thread off topic but were introducing some necessary background to the observation Which fourth dimension? Don't forget that the local and global coordinate systems may contain different axes and may not match directly if they do. Moreover scalars such as temperature that I placed at position (x,y,z) don't take up any xyz space. But place a normal a tangent, a vector or a tensor at (x,y,z) then you need a set of local axes as well as the global ones. The mathematical name for the correspondence function is a chart. But of course the local axes at one point may not match the local axes at another so we also need the correspondence between these and the term here is a connection. Heavy stuff, but worse is to come. The above assumes isotropic or linear axes, but the axes themselves my not be linear. The comment about log graph paper was intended as a precursor to a gently introduction to this matter.

It can indeed be difficult to allocate where pushes and pulls occur in a system of forces for instance in order to pull the desk in your example you will need to push with your feet against the floor. However a body which can only contract can only exert a pull in its contraction. This is the case in biomechanics in muscles for instance. There are no muscles that can expand like a balloon to provide a push. So pretty well all the muscles in your body work in pairs, each pulling in opposite directions, to generate the desired motion of the body part. There is a very interesting book comparing the way nature achieves mechanical and other goals as compared to how artificial constructs achieve the same objectives. Cats Paws and Catapaults Steven Vogel

Why must I keep reinventing the wheel every time this question comes around? Motion is only one form of change. So whilst the OP has a point that because we observe motion we need a running variable to describe it, we also use this variable for other changes. A simple example of motionless change is radioactive decay.

To help you a little since you are at last acknowledging other points of view One very powerful technique for testing any theory or hypothesis is that of hindcasting. In other words take known previous conditions with known prior outcomes and apply the hypothesis to see if it successfully predicts the known outcome.

I was hoping that mathematic would expand on his (her?) statement. I don't want to steal someone else's thunder. Anyway I was going much further than that. The difficulty is which way to go next since developing (1),(2),(3) and (4) directly leads on to a very startling idea that we need more than one coordinate system and coordinate space and then onto explaining tensors. The other way is to introduce local and global coordinate systems. The two tie together in the end. There are also some (mathematical 'funnies' on the way such as the non existence of the y axis on log graph paper and the non existence of both axes on log-log graph paper)

Yes but a = 0 is the limiting situation for my case 1, with a=0, PX = PCsin(a) = PCsin(0) = 0. Does this calculation work for a = 180? (case 4)

Hello augurys and welcome. We call any form of submitted work homework. You should read this. http://www.scienceforums.net/topic/75772-read-this-before-posting-in-homework-help/ But don't be afreared, there are several expert Chemists here, who love to help those who help themselves as well.

The term you are looking for is selectivity (as opposed to sensitivity which is the minimum detectable amount). Here is a good start. http://www.restek.com/Technical-Resources/Technical-Library/Editorial/general_GNAR1743-UNV Is this homework?

You'll find some in your Monopoly box.