A most excellent read. Regarding the preferential counter-clockwise rotation ... That can be explained if both the classical wave equation and Shrodinger are being satisfied. That requires counter-clockwise rotation. Hamilton's work with quaternions combines with Euler's Equation to make some nice vectors.
Good Luck,
Gary Simpson
Houston, Tx
Dr. Klingman,
Great work! Taking into consideration all of your essay contests' entries, I am glad you are here. I think that theoretical physics, even if mostly correct within its current self-limited domain (my opinion), remains at too low a level of understanding of the nature of the full universe to yet be acceptable as the real foundational science. I have confidence that you are an important contributor to helping theoretical physics advance toward fullfilling in its expected role. I wish that I knew enough to travel that road myself.
Jame
Dear James Putnam,
Thanks for your kind remarks. I have read your essay and will followup with a post on your thread. Congratulations on the number of posts that you have attracted. I don't always remark upon your comments, but it is my observation that the level of your comments has much improved over the last year, and you truly do contribute a valuable perspective to this forum. For example, you played the part of an honest broker in Joy's threads, and that was very worthwhile. It is clear that the FQXi experience is one of learning and growth, for which we are all thankful.
Edwin Eugene Klingman
Dr. Klingman,
I too have found your essays fascinating, although my understanding of differential equations is way too rusty.
In the Extent of the Wave Function section, do the cylinders illustrate the bow wave, the trailing vortex (if there is one) or both?
Also, are the lengthening wavelengths as you get further from the particle discrete or continuous? If they are discrete, are the wavelengths harmonics?
Thanks in advance for your response.
Mark Olson
San Jose, CA
Dear Mark Olson,
Thanks, those are great questions. In geometric algebra the 'trivector' or volume form has both geometric and algebraic properties (as do all GA elements). In particular, it has volume and orientation (handedness) but it does NOT have a fixed shape. It's volume is normalized to unity.
I actually spent a good while trying to figure out how much of the circulation was in the 'bow' or leading wave and how much was trailing wave, and finally decided that it's the volume that is 'fixed', proportional to Planck's quantum of action, h. This follows from combining de Broglie's wavelength relation with the general relativity equation. The volume is the 'cylinder' defined by the circulation cross section times the length of one wavelength.
But whether it is actually a 'cylinder' (doubtful) or a 'teardrop' (perhaps) or something else, I don't know. I suspect it depends on velocity and probably local environmental factors. I find it useful to think of a vortex in terms of a tornado, whose shape changes but the entity endures. [Google 'tornado videos' for amazing examples.]
So I view the lengthening wave as continuous, but if it forms a closed orbit it must (for reasons of self-interference if nothing else) consist of an integral number of 'volumes' where each volume represents a quantum of action. The wavelength may vary slightly around the orbit as shown in on page 5. The relevant equation is (9).
Edwin Eugene Klingman
Dear Gary Simpson,
Thanks for the nice comment. I'll think about your remark. I tend to think of the handedness as originating in general relativity, and Schrodinger just has to live with it, but there may be other fruitful ways to conceive of it. I have now read your essay and left a comment there.
Edwin Eugene Klingman
Errata:
I have noticed that I used the term Fermi-Dirac twice in my paper. The first time, in reference to the partition function, is correct. The second use, on page 8, is in conjunction with the Hartree-Fock method, and here Fermi-Dirac should have been the Thomas-Fermi method.
Also, on page 4, I have used the lower case 'f' as a function of lambda twice. I probably should have used two different symbols, since one of the 'f's is a function of lambda, and the other of inverse lambda. Hopefully these oversights do not cause unnecessary confusion.
Edwin,
I've now had an opportunity to read your fascinating, well-written, well-organized essay carefully. While lacking sufficient expertise to comment intelligently on specific details of your argument, I certainly recognize the importance of the topic and the extent to which it is responsive (extremely) to the spirit of this competition.
Perhaps I'm hallucinating, but I have a strong and growing sense that we're on the verge of resolving some of the conundrums that have plagued physics for roughly the past century. The time to put some of these knotty problems behind us and move forward is long overdue.
Thank you for commenting on my essay. Fwiw, I've added a reply to your comment there which I hope will shed additional light on that topic.
Good luck in the competition!
jcns
Dear jcns,
Thank you for that very gracious comment.
I hope you are right about resolution of some century-old conceptual problems.
And thanks also for the response on your thread. I am in general agreement with you. I also feel that you are tackling a tougher problem than I am.
Edwin Eugene Klingman
Hi Edwin,
While reading about your C-field, the question occured to me: what is the difference between a field and an aether medium? I'm working on my own paper in which I argue that there is a medium; it's a medium made of waves. I don't like the word "field" beause a field can be turned off. I think there is a ubiqitous aether medium that is always present. But I get hammered for using the words aether medium. What is a field and how is it different from a medium?
Hi Edwin,
I quoted your paper from page 8: "Basically, 3-space physical waves are real, 3N-space probability waves abstract."
In the paper I hope to submit, I asserted the existence of aether medium waves. I modelled them after wave-functions and the electromagnetic frequency spectrum. When I read your sentence, I interpreted you to be saying that there does exist, as a physical phenomena of nature, a 3-space physical wave. Is that what you meant?
Hi Jason,
If you believe that the "aether medium" is always present, you should probably use those words. I'm not sure I can provide a simple 'one size fits all' definition that exactly matches your needs. I assume you looked on Wikipedia. There are vector fields and, supposedly, scalar fields, also supposedly Dirac fields, boson fields, axion fields, etc, etc and of course the real physical electromagnetic and gravitomagnetic fields. Mathematically everything can be 'turned off and on', but it sounds like you really want an always present 'background' medium. As for the word 'ether', even Nobelist Frank Wilczek uses it although he updates it with a sexy name. He defines it as "a space-filling material" and considers it the 'primary reality'. (see 'Lightness of Being') By the way, he defines field as 'a space-filling entity'. Take your choice.
And yes, 3-space means waves in three dimensions (plus time) as opposed to (or in addition to) the mathematical waves in higher dimensions, such as Schrodinger's 3N configuration space. But I caution you that your idea of 'wave functions' and my idea of wave functions have been very different in the past, so be careful how much of my essay you try to apply to your ideas. It's probably better just to explain as well as you can what kind of waves you mean.
I look forward to reading your paper when you finish it.
Edwin Eugene Klingman
It's funny; what I call aether medium waves are always present in the sense that the EM spectrum is always available, permitivity and permeability are also always available. In another sense, they can vanish. For example, the Double slit diffraction experiment inspired my idea of aether medium waves. There is one wave-function for each slit. In my interpretation, the wavefunctions act like a pathway that the particle can take; these wave-functions are what interfere with one another, not the particle(s). But when you close one of the slits, and there is only one slit, then there is only one wave-function; the other wave function goes away, and there is no interference pattern. I'm not sure how to reconcile this.
Hi Edwin,
I was thinking about your C-field. The C-field is the particle's connection to gravity, is that right? In your essay, you said, "The C-field circulation induced by momentum (or mass current) provides a solution to the general relativistic field equation and also solves the quantum mechanical wave equation:"
The Einstein equations include a Cosmological term, "Eistein's greatest mistake - or not". The cosmological term refers to the intrinsic energy of the vacuum. So the extrinsic energy must be things like matter, photons, mass, kinetic energy, momentum, the stress energy tensor.
Then, the intrinsic energy of the vacuum would be able to expand or contract the vacuum (which is a fancy way of saying that it induces gravitational acceleration).
I think your C-field should be in the intrinsic energy "column", and the momentum that induces the C-field should be in the extrinsic energy column.
Is it reasonable to interpret the C-field this way?
Jason,
First I'd like to ask a favor. In order to help others (and me) make sense out of these comments, could we keep our discussion to one thread, instead of opening up a new thread every time a new thought arises? Just use the "Reply to this thread" link after the last comment between us. It's easy. Otherwise reading through all the comments becomes much more scatter-brained. Thanks.
Second, you shoot from the hip, and you are amazingly creative in your thinking, but I try not to write any words that I cannot backup in some way. So when you say "The C-field is the particle's connection to gravity, is that right?" I'm not sure how to answer this. Not if you're thinking about the gravito-electric field, which is the acceleration that most people identify as 'gravity'. But the equations also describe a gravito-magnetic field, just as the electro-magnetic equations describe an electric field and a magnetic field. That's why I made the analogy of the (del cross C = p) with the (del cross B = j) where B is the magnetic field and j is the charge current j~qv while C is the gravito-magnetic field and p is the mass current p~mv which is also the momentum (density). But the magnetic field interacts with charge only, and since it is uncharged, it does not interact with itself, while the C-field interacts with mass (in motion) and since the field has energy it can interact with its own mass-energy. The net result is that you need to think of the magnetic field, but with the proviso that it is potentially self-interactive. It's generally safe to analogize with magnetism, but not always.
At the moment I don't make use of the intrinsic-extrinsic categorization that you ask about, so I'm unsure how to answer you. I don't see a great deal of utility in that schema, but of course I may be missing something. You ask if it's reasonable to say "I think your C-field should be in the intrinsic energy "column", and the momentum that induces the C-field should be in the extrinsic energy column." It may be reasonable. In previous essays I've discussed the particle physics implications of the C-field and the cosmological implications of the C-field, but in this essay I'm going to restrict consideration to the quantum mechanical implications of the C-field. That's complex enough for one essay.
As my last essay paragraph indicates, there's a lot packed into this essay, and it will almost certainly require more than one reading if you really want to understand the theory. I would have to read it many times myself, if I were starting from scratch. This could mean that I tried to put too much into it, but the problem is complicated and has confused people for a century, so the answer is important, and I did not feel that leaving out crucial aspects would serve any purpose.
I hope this helps a little.
Edwin Eugene Klingman
Edwin
I would agree with your bottom line. Though I of course can only arrive there in generic terms. These concepts of superposition, etc, are contrary to the way in which physical reality occurs (or at least as far as we can establish, and once one crosses that line any speculative belief is a good-or bad-as any other). Physical existence is not uncertain. At any given point in time it has a definitive existent state, and only one at a time. We are just incapable of defining it, so can only do so via probability, etc. We should not be invoking strange characteristics in physical reality to rationalise our failure. Nothing can affect anything else, directly, unless they are adjacent (obviously anything can have an indirect effect on anything else, but this is a pointless statement). The notion of waves involves a sequence of different physically existent states. And anything that is deemed to exist, must have a physically existent presence to correspond with it.
Paul
Hi Steve! :)
Hi Edwin,
Intrinsic energy actually has to do with the expansion of the universe (positive intrinsic energy). Calling intrinsic energy a mere acceleration field is premature on my part.
You said, "Diagram (2) for pCrrr−=ﾃ--∇ simply shows a circle around momentumpr but from orbital dynamics, we know that the wave must extend over several wavelengths in order to support self-interference. De Broglie's ph=λ defines a wavelength and thus a minimum extent of the wave function, but maximum extent could range from one wavelength to infinity, since Schrﾃｶdinger's wave packet is conceptually built of monochromatic plane waves of infinite extent."
It's a great idea to think of wavelengths that extend for an infinite number of cycles in every direction. That is certainly what I had in mind when I thought of aether medium waves. Since nature offers a frequency spectrum to use, I decided to define the vacuum of space as the entire range of frequencies, from radio waves to gamma rays, as the necessary and sufficient foundation of the vacuum and fabric of space-time. Particles have momentum because waves of the EM spectrum have momentum of p = h/lamda; a particle with mass is just a group of AM waves.
Positive intrinsic energy would cause space to expand via the mechanism of causing each frequency in the spectrum to undergo a wavelength expansion of
[math]\lambda_{initial} --> \lambda_{final}[/math]
Curvature of space-time occurs when the stress energy tensor distorts the frequency spectrum across the entire range of wavelengths. You C-field is probably responsible for some kind of contraction of the wavelengths that surround the momentum.
I like your Eq 9 and how you address Kepler's law. I've puzzled over Kepler's law for many weeks now.
:) Jason
ps I like like always your pure creativity.
Don't stop please
Regards to both of you
Hi Steve, hope things are going well with you.
Dear Jason,
Although I say that "Schrödinger's wave packet is conceptually built of monochromatic plane waves of infinite extent", the point I develop is that this is a terrible idea, adopted by people who understand Fourier series but have no conception of physical reality. Schrodinger does it to mathematically create "wave packets", but since the waves don't stay in phase the packets ALWAYS disperse-- one of the problems of the Copenhagen interpretation. It's conceptually the same as when you say "particle with mass is just a group of AM waves". The problem is that the waves disperse. So how can you account for protons lasting forever? (Electrons last for a long time too.)
Also, a small point: it's not "my" C-field. The C-field equation was discovered by James Clerk Maxwell about 150 years ago, and also by Albert Einstein about 100 years ago. Not until 2006 was the field measured and a very large coherency factor discovered. As I note, the longest running NASA experiment measured the de-coherent C-field of a large thermal body (the Earth) and reported it in 2011. The last thing I want is the idea that it's 'my' C-field. It's not mine. It's been here since the beginning. It is an integral part of gravitational dynamics.
Edwin Eugene Klingman
Dear Edwin,
I like Fourier series. Aether medium waves are elegant, beautiful, and have all that SO(3) gluon, strong interaction particle building stuff built into the aether waves as ... I'm flexible, just hold my aether waves together. At the extreme temperatures during the big bang, quarks, baryons and other stuff formed. I'm OK with my aether waves producing particles and forces (strong/weak) during the big bang. Heck, I'm ok with aether waves having 11 dimensions and behaving string-ishly at high temperatures. But I need all particles to be made of aether waves, across a frequency spectrum, so that time can progress in the particles and in the vacuum. The frequency emitted by cesium is 9.1GHz I believe; Cesium makes for a good atomic clock. I think nature uses the whole frequency spectrum as time progressing clock. In other words, time exists (and waits for nobody) because of the frequency spectrum from radio waves to gamma ray frequencies. So I need these aether waves to permeate particles with mass, so that particles of mass can evolve in time.
I still like this C-field idea that you've adopted. I think it's compatible with my aether wave ideas. I think that the c-field is made out of a bandwidth of waves that obey c=lambda*f.
I invite you to punch a hole in my theory. I can account for the existence of time, and the existence of distance.
