Bignose

No, there's a reason for dx to be there. It is the infintesimal change of position. So, rather than be cryptic, and not answer the question I've asked twice. How about I ask it is a slightly different way: please post an example where your definition is needed and the old definition fails. That is, post one of your 'new successes'. While you're at it, also post explicitly how your formula reduces to the tried in true in all the situations where there are past successes (there are a lot of them).

And this doesn't answer my question. [math]v = \frac{dx}{dt}[/math] has been supremely successful. Why does it need a replacement?

A small nit, but the above isn't right. 3.141592654 is not equal to pi, but is a close approximation 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 is the approximation to 100 digits, but it is not equal. Nit picking? Yes. Correct and important to realize that the above are both just approximations? I say also, yes.

why do we need a replacement for [math]v = \frac{dx}{dt}[/math] ?

AH HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA HA. That's a good one. So, all joking aside, basically you're saying here that you have zero interest in doing any science, then. If so -- and it would be nice if you would go ahead and confirm this for me -- I'll just go ahead and big you adieu and ask that you not participate on a science forum any more. Since, like, ya know, we like to discuss science here.

You are talking about an arithmetic series. Lots of properties of these series have been looked at. http://mathworld.wolfram.com/ArithmeticSeries.html is as good a start as any.

This happens all the time when taking experimental data. It requires careful analysis of the data to know how to handle it properly. Sometimes, it is appropriate to just take the curve that fits all the data best. Sometimes it is best to just throw out that point and figure out if you need to take another sample. Sometimes, the data will tell you that the model you picked is wrong. It really depends a lot on the errors expected from your measuring device, and just the random errors that always exist in real data. As you can image, talking about this field is far more lengthy than just a single forum post can handle.

It is only 'logical' if it makes predictions that agree with the observations. So far, 100s of posts in this thread later -- there is completely non-pithy evidence at its most generous. When those simplifications you cite above were discovered -- guess what, all the evidence fit really, really nicely into the observations -- something that your idea has to date failed to do. And, I really wish you'd drop this religious persecution vein in your replies. I'm not persecuting you. Just trying to get to you answer questions. Lastly, speaking of which, you didn't really answer my question. Considering the non-pithy evidence you've presented, and furthermore your admittance of your lack of knowledge about the current model and the properties of the particles in question -- how can you be so confident that your idea is the right idea? How can you be so sure that your model is superior?

Maybe, just maybe, that is why the standard model is what it is today? I mean, don't you think that of the thousands of people who worked on this, they if there was a great gross simplification that could have been made, that it might have already been found? Don't you think that maybe it is just possible that the standard model is complicated so that it can make some correct complicated predictions? You readily admit that you don't understand the current model. And now you readily admit that there is a bunch more that you (and by association your model) cannot explain -- tell me again why you are so sure that your model is superior?

An inequality (I am assuming you meant y = x^2, without an equals sign, you haven't stated any equations). Since the LHS and RHS sides won't be equal, you know that (1,20) isn't a valid solution to the equation. That is what an equation does -- it maps out valid solutions. It really doesn't say diddly about points that aren't solutions except that they aren't solutions.

Consider a system with just two particles, 1 and 2. The position vector of these two particles can be represented by r1 and r2. To fully describe the state of the system, you can use a single vector with six dimensions. r = <r1x, r1y, r1z, r2x, r2y, r2z>. If you know the probability density of how likely each particle can be in each point in space, you can integrate over the 6 dimensions to calculate the properties of the system. Note that this is exactly how the mathematics of gases are done -- though usually with more than just 2 particles. Not enough dimensions for you? Let each particle not just be described by its position, but also its velocity. Now you have a 12 dimensional system. Need to also add acceleration? 18 dimensional. How about not just assuming that the particles are spherical, but at asymmetrical -- you can introduce an orientation vector to describe how each particle is orientated. Now we're up to 24 dimensions. Now, let's allow that asymmetrical particle to have a rotational velocity and acceleration. That gets us up to 36 dimensions. I could continue, but I think my point is made. So, since it is relatively simple to get up to 36 dimensions, tell me again why a 4th is so special?

higher than 3-D, they tend to just apply the prefix 'hyper-' in front of the analogs. E.g. 'Hyper-volume', 'hyper-surface', 'hyper-sphere'.

Three point-like bodies observed inside a proton due to scattering is rather compelling. How much more direct do you want? We'll never be able to build a microscope powerful enough to actually 'see' them if that is what you're waiting for. Like newts, why don't you review the literature for all the evidence? Without a great deal of compelling evidence, the idea of them wouldn't have survived the last 40+ years of particle physics scrutiny.

Go back in the thread -- I cited the specific paper with the experimental evidence for them several times in this thread. Despite the thread going on for quite some time, it saddens me that newts hasn't bothered to find himself a copy of that paper and read it. He's never really given any kind of reason his model should show the three-point like bodies that the original paper reported. And, of course, since that paper in the 1960s, there have been quite a wealth of further evidence. Again, I think he should know the baby he's trying to throw out with the bathwater.

Aaaaaaand we're back to admitting that you know next to nothing about what you are trying to tear down. Really and truly -- why so reluctant to actually learn about the wealth of evidence that supports the current model, rather than just dismissing it because you don't particularly care for it? As I've written several times now, plenty of opportunity to improve on the current model, plenty of room for alternative models, too, but shouldn't you at least know a little something about the baby you throw out with the bath water?

Not a straightforward problem. You'd need to calculate the drag on the wheel, and how much resistance the wheel would feel, and hence at what speed the drag from the fluid accelerates the wheel is balanced by the friction deceleration... then you can calculate the possible power. There may be 'rules of thumb' out there is some old design manuals or similar, but again it isn't a straightforward problem. Lots of details to hash out. In reality, I would consider just building the thing and taking measurements rather than making and justifying all the assumptions that would be needed for a reasonable calculation.

Clearly some analytic solution exists for a non-trivial [math]\xi(t)[/math] Take [math]\xi[/math] = a constant (which is clearly smooth). Because that can be turned into one of the forms in the "Integrals With Roots" section: http://integral-table.com/integral-table.html#SECTION00004000000000000000

It generalizes the concept of the integral. Typically, the integral is introduced as the area under a given curve. Area is just a single specific example of a 'measure' -- there are many others. Take the following nasty function: f(x) = 1 if x is irrational, = 0 if x is rational. This function's integral isn't defined if you limit yourself to integral = area under the curve. But, with an appropriate measure, the integral can take on meaningful values. Searching for 'Lebesgue measure' should be a good start. There are plenty of good texts, depending in your current level of mathematical understanding. I bought a book at a library sale years ago called Volume and Integral by Rogosinski for like $1. Anything with a title like Measure and Integral or similar should fit the bill.

I wonder if the 'trick' here is to approach z = 0 from a different direction. Since z is complex, you get an infinite number of ways to approach z = 0.

I cannot agree more. This can be downright dangerous. It is all too easy in an engineering calculation to end up accidentally dividing by zero. If that gets set to zero, it is was too easy to miss a potentially costly or critical error.

And it is clearly going to be dependent upon the 'calculating device'. i.e if you program the formula using single precision real numbers, you'll get a different number than if you used double or quad precision reals. I think that this is awfully unsatisfactory for defining a value for [math]\cot 0[/math] for example. Depending on if you used your calculator or Excel, you'll get a different answer. I also am not so sure why it is so hard for people to accept that the answer is undefined.

But, Bell's Theorem has been verified experimentally several times: http://en.wikipedia.org/wiki/Bell_test_experiments We also 'only' have a theory of gravity... should we also give credence to speculative ideas that violate the theory of gravity too? It doesn't mean that we shouldn't keep testinbg Bell's Theorem, and for that matter we certainly don't know everything about gravity yet either. But, to date, many experiments validating Bell's Theorem have been found. Based on what has been posted, TEW would violate Bell's Theorem, ergo TEW cannot replicate or explain the experiments that have been done.

seriously? ok, whatever, here is my question in a 'numbered format': 1) provide some objective evidence that your pictures with all its whirls and swirls are a better idea than anyone else's pretty pictures with different whirls and swirls. Major emphasis on objective. when can I expect a direct answer to this question? Or an admittance that without objective evidence, that all you have is a story and not science?

it seems to me, that you haven't even considered many of the replies to you in this thread. I will gladly consider your idea is you can demonstrate some objective way that it fits with what we have observed to date.

here's the problem, then. How can you know it IS the 'basics of the concept' without quantification? How can you be so sure that what you have it right without checking it? What kind of hubris is that? How do we know that someone else who comes along with a different story, and even prettier pictures with more swirls and whirls in them isn't right? What seems right in your head is not enough to be accepted as a science. We've moved past just believing whoever is in a position of power, whoever can weave the best tale, whoever can seem the most 'logical', and whoever can shout the loudest to believing the person who shows their idea matches the observations the closest. That is a really important piece of progress there -- because how well ideas match observations is objective. There is no voting about it, no aesthetics, and no interpretations needed. It is just as simple as: idea A is right more often than idea B, ergo idea A is preferred. That certainly doesn't mean that we stop looking for ideas C, D, E, and Z to be even more right than both A and B. But, it does mean that we don't consider ideas that cannot objectively show themselves how correct or incorrect they are. So, I'll repeat the same things that others have been asking, albeit in a slightly different way: is there any way you can demonstrate objectively that your idea is better than anyone else's?