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Message Subject BUBBLEGATE - Proof of Successful Sonoluminescence (Acoustic Intertial Confinment Fusion) Experiments COVER-UP
Poster Handle Anonymous Coward
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V. CONCLUSION.
When James Clerk Maxwell[4] wrote the second
edition of his Treatise on Electricity and Magnetism
he included a quaternion representation of his electromagnetic equations, but he did not include both
left-hand and right-hand derivatives, and the differential
operator nabla was restricted to the 3-dimensional space
form lacking a time component, and so his work is
fundamentally different from that presented here. ()
Indeed, in the calculus of quaternions the differential
operator almost always appears on the left acting
towards the variable on the right, ignoring the other alternative. And even though, Charles Jasper Joly[5] notes
the distinction in his book A Manual of Quaternions,
the importance of the idea goes unnoticed, unexplored,
and unused. As a consequence of this, an important
field component went missing in Maxwell's Equations,
and all of modern physics has developed from there
perpetuating one of the consequences of this oversight,
namely, that the electromagnetic field possesses six
components, whereas, as we have shown, there should
be seven.
float
 Quoting: Le Comte de Saint Germain


Oh dear. I got all excited about this very thing when I was working on my undergrad physics degree. I taught my sell quaternion algebra and learned to do the field equations the way Maxwell intended. There is nothing missing from the modern treatment. The version that is taught at the undergrad level using vector calculus, and time-invariant solutions is only scratching the surface of E-M theory. If you use the four-vector transform (tensor), all the information you speak of is preserved. You can do the math for your self, but I think its over most peoples heads.

I suggest forgetting about the physics for a little while and just concentrate on the math, study the theory of vector calculus and why it works, and then study quaternions and how they work and carefully compare the two. You will find that that there are differences in how operations preserve and manipulate information.

Then go back to the physics and apply each mathematical approach to the same problems and it will be come obvious why Maxwell used the quaternions and why the vector calc approach is what they teach.
 Quoting: Anonymous Coward 25276568


if the operations, v, and, v, are considered representative of the forms nabla to-the-right, and, nabla to-the-left, respectively, then these expressions with the square root of nabla, acting from both sides simultaneously, could be considered the forms of nabla that act to-the-center. The modern vector analysis of Heaviside-Gibbs can then be seen as utilizing those nabla to-the-center operation ideas, extracted from the complicated quaternion calculus, and written symbolically, x v and . v, as though they were some kind of nabla to-the-right operations, whereas in fact the new forms are really algebraically 'central' operations, and neither proper left nor proper right handed expressions at all, despite appearances when written.

Of course, given that the vertical wedge, , is indeed symmetrical about the vertical, with no left hand nor any right hand suggestion being implicated in the symbol's shape, and considering that this is entirely consistent with its modern use effectively as a nabla to-the-center operator, one could argue that this was the real reason why the handed form, , was finally turned up to the vertical. This idea would have alot of merit, if only for the fact that nothing remotely suggesting this has ever appeared in the public scientific literature anywhere before.

It may seem that the new vector algebra was simply a shorthand way of writing these left-right quaternion expressions. But, the effect of the changes went deeper than this. One cannot really just combine left and right actions from Hamilton's system to make it equivalent to the new vector algebra, because the structures are so different. What we see here, when using the left-right combinations to exhibit the form of the operations in quaternions, is partly the impact of that "first" thing lost when mathematicians depreciated the value of the symbol, , by turning it around 90o, thus returning the important "polarity" to the realm of obscurity
 Quoting: Le Comte de Saint Germain


No modern physicist uses the 3-d vector calc approach, this is taught as a way of familiarizing students with various mathematical techniques. The four-vector tensor transform is a good place to start, but this is also at least 50 years old.
 Quoting: Anonymous Coward 25276568


first they laughed at me. Then they said that it can be done, but first I'd have to learn to cube the sphere. The problem just went from 2D to 3D. Then they said that in order to do that (cube a sphere) I'd have to move it up another dimension, to 4D. But, in order to solve that I'd have to go to another dimension higher, to 5D, and so on to infinity. They said that once I solved it for infinity then all I'd have to do is unfold it back down the other side to the square. Simple. Then they laughed some more.

Then it got really heavy. They asked me if I'd met the "5 ancient numbers". I said no, who are they and they said that the answer to the problem is within the 5 ancient numbers and those are:
e, i, phi, pi and zero

herethere
 
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