studiot

yet in the post immediately following my note that it is sometimes defined you post this How is this to be taken by someone trying to learn? I do wish folks would stop being so categoric (and wrong) because it is preventing the OP moving on to understanding what can be evaluated (without calculus at his level).

Hello morgsboi, You don't need calculus to understand when you can arrive at a proper value for zero/zero/ or infinity / infinity. Take a look at the expressions I showed in your other thread about this. Can you see that in the one case the top and bottom of the fraction gets smaller and smaller the more terms you add and in the other (which is called an infinite product) the top and bottom gets larger and larger?

Yes I saw that and I think the threads could profitably be combined. However you have avoided my point that in certain circumstances the ratios zero/zero and infinity/infinity can be evaluated. Further there was no stated requirement to remain within either the reals or the complex numbers. Both the limits in the series ratios I displayed exist and are zero or infinity.

Since I don't agree with a blanket statement that division by zero is unavailable I showed how to do it in certain circumstances. So I invite all the naysayers to disprove this. morgsboi has point even if only a partial one.

Time travel is change of temporal coordinates. I see no reason to limit (Pun intended) this to large changes. Waiting is no more a statement of time travel than the statement that Africa extends from 10 degrees to forty degrees longitude at the equator is a statement that Africa is travelling round the equator 30 degrees. No one has evidence of the validity of this statement.

TransformerRobot, Your responses seem to me a good way to discourage those prepared to have a real scientific discussion with you about your question. Perhaps if you responded to their comments rather than just throwing out more wishful thinking your might progress your cause.

Maybe but what about [math]\frac{{1 - \frac{1}{2} - \frac{1}{4} - \frac{1}{8}. - ....}}{{10 - 9 - 0.9 - 0.09 - ....}}[/math] or [math]\frac{{3*4*5*6*.....}}{{2*3*4*5*6*7.....}}[/math]

I don't follow the relevance to this thread.

According to current theory it is impossible for material objects to travel at the speed of light. What has not been proved is that such bodies cannot travel faster than light, since we do not have adequate theory for this situation.

Yes indeed your quote is excellent. It hints at further deductions that may be made about the common misconception of "time travel" in general. An object has an extent (duration) along the time axis, just as along the space axis. So why all the talk of time travel as moving one point of that extent when the same proponents would never dream of moving an isolated section in space.

I wonder if questions of this type arise frequently because of the scant treatment paid to infinite sequences, series and products these days in early maths and also if this is why questioners shy away when it is pointed out that the ratios 0/0 and infinity /infinity can result in a definite value.

I directly addressed the title of your thread' I asked three questions about your statements to establish a basis for discussion You did not answer one of them. Yet you complain when your own questions are not answered. A discussion is two way and based on what can be agreed, not what is in doubt. So if you wish a real discussion let us start again.

Perhaps you didn't fully appreciate what I said about indicator diagrams? In dimensional analysis (Buckingham's theorem) you take energy and divide it by temperature you obtain a definite quantity. The scientific community has chosen to award this quantity the name entropy. Do you deny this?

Hello Austin, Access to the globe has opened up greatly in the last twenty years. This has coincided with significant progress in the earth record, both paleontological and other rock sciences. This has brought great opportunity. However the work requires funding and the current world recession has brought belt tightening measures along with the financial examination of projects with a move towards those showing financial rewards. So, if you can establish post somewhere there is much to be done. But be prepared to find mineral exploration in the fore. go well

Indeed so. The original macroscopic derivation of entropy does not rely on system granularity. It took the world one hundred and fifty years to establish the mechanical equivalence of heat and move towards a proper theory of energy. Caloric was dispensed with at that time. It took a further fifty years to establish the connection between the statistical mechanics of granular systems and the mechanics of continuous systems we call thermodynamics. Which connection are you arguing with?

Well here is one view of what we mean by a scientific law and how we come by it. 1)When we observe the the world around us we divide things into individual compartments we call systems. 2)When we look within individual systems we distinguish patterns in the objects or characteristics that make up those systems. 3)Sometimes we note that we can see the same pattern in more than one system. 4)We do this by matching participating elements (putting them into one to one correspondence). 5)If this pattern is repeated over many systems we call it a law and use the list of systems involved to specifiy the scope of the law (ie the conditions under which it is valid). 6)Both the last two ( 4 & 5) statements can then be used to examine new or further systems to make predictions about them and potentially extend or refine the law. All too often problems arise when people ignore the conditions of applicability part of the process. go well

Both [math]\frac{0}{0}[/math] and [math]\frac{\infty }{\infty }[/math] can sometimes be evaulated. Some techniques are included in elementary calculus and even pre-calculus. This does not mean I endorse the original post.

seconded. pmb But surely in your opening post you showed that Goldstein played the good guy by acknowledging that there are different interpretations of the phrase 'classical mechanics' and defining precisely what definition he was going to employ? I repeat my comment one more time that there are yet more sorts of mechanics than quantum v classical. I even offered the example of a type which is sensitive to scale (colouring of cellular automata) which is neither quantised nor does it follow normal rules. go well

ajb is the differential geometry guru hereabouts, perhaps you could persuade him to contribute. For a curve in 3 D the curvature can be in two directions at once and different at every point. Curvature is a point function. play with this Wolfram demonstation http://demonstrations.wolfram.com/FrenetFrame/

Now you are getting somewhere. Curvature is only defined at a point, as the limit you describe. It makes no sense to talk of the curvature at more than one point at a time since it may differe from point to point. However in order for curvature to exist you need at least one extra dimension for it to exist in. Is this what you are trying to describe?

Well you don't seem to have attracted much action so far here with this paper. I can assure you that entropy is just as much a physical quantity as say surface tension. Have you ever heard of indicator diagrams? There are many pairs of quantities that when multiplied together have the dimensions or units of energy. Entropy and temperature are one such pair and entropy was introduced to pair with the already established quantity, temperature, so that when plotted on a T - S indicator diagram a useful statement about energy could be made. Surface tension and area are another such pair. In my view, this way provides a more natural introduction to entropy, without the magical connotations so often ascribed.

What about curvature and extent (duration) in timelike axes as well as spacelike ones?

But what about mechanics that is neither quantum nor the other?

As already noted there are other forms of mechanics besides relativity, quantum and Newtonan/Hamiltonian/Lagrangian.

So what's wrong with absorbing relativity into 'classical'? Where would you place relativity and quantum mechanics? My distinction would be between the mechanics of continua (which includes relativity) and the mechanics of discrete systems (which includes quantum mechanics ) and also scale dependent mechanics.