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  1. sweetser

    Gauge symmetry in EM by inspection

    Hello: I was under the impression that gauge symmetry was a property of the Lagrange density. Here is the Lagrangian for EM written out in its components: \begin{align*} \mathcal{L}_{EM} &= J\cdot A +\frac{1}{2}\left(B^2-E^2\right) \quad eq.~1\\ &=\rho \phi - Jx Ax - Jy Ay - Jz Az \\...
  2. sweetser

    Einstein's Field equations & quaternions / octonions

    Solid technical reason to skip quaternions: representing the Lorentz group The Lorentz group is vital to modern physics. Minkowski figured out that the Lorentz boost was like a rotation in spacetime. Since quaternions do space rotations, it should be a simple step to do spacetime rotations...
  3. sweetser

    Einstein's Field equations & quaternions / octonions

    Maxwell field equations Hello: I am glad my book is being put to use, that was the goal. This is an ongoing research project. I wish I could keep the book up-to-date, but there is only so much time in a day (I have a full time job, wife, and 2 year old). Here is the right way to derive the...
  4. sweetser

    In search for a holistic perspective on the physical reality

    The energy density of a gravitational system is NOT negative. Sure lots, hell, most people get this one wrong. This story was written up really well here, http://mathpages.com/home/kmath613/kmath613.htm" [Broken]. I recommend this page highly because it shows an honest struggle Maxwell faced...
  5. sweetser

    Exact Gauge Symmetry of the Standard Model

    Agreed. My question is how is that shown in math notation. If one takes an element of math symmetry U(1) and multiplies by an element of SU(2), the result belongs in the group SU(2). In the physics context, the electroweak symmetry U(1)xSU(2) is a different gauge symmetry than weak symmetry of...
  6. sweetser

    Exact Gauge Symmetry of the Standard Model

    Hello: The gauge symmetry of the standard model is written in authoritative places like wikipedia :-) as U(1)xSU(2)xSU(3). This would have 12 elements in its Lie algebra corresponding to one photon, W+, W- and W0 or Z, and the 8 gluons. I recall reading discussions that such a...
  7. sweetser

    Unifying Gravity and EM

    Creatively seeing sine Hello: On occasion I pitch my quaternion animations to people who have written something on quaternion. The usual reply is no reply. Sometime we exchange a few emails, then go our separate ways. This time I found out the fellow was visually impared. My animations...
  8. sweetser

    Unifying Gravity and EM

    Quaternions are not only Cl(0, 2) Hello: Clifford algebra = Geometric Algebra. David Hestenes has promoted GA as a label over Clifford algebra because Clifford was one guy who worked on some aspects of this approach, while Geometric Algebra suggests what the math does. I only figured...
  9. sweetser

    Unifying Gravity and EM

    Mathematical fields Hello Max: We share a common suspicion about the focus of efforts in the most prestigious centers of study on the planet. Lee Smolin and Peter Woit are the biggest voices in the professional community. My focus is on constructing a viable alternative, so I like to stick...
  10. sweetser

    Unifying Gravity and EM

    Quaternions in Lagrangians Hello: Preparing the talk for Midwest Relativity Meeting was quite productive. It forced an interesting shift: I actually need to use quaternions for the action, tensors will not suffice. It is ironic that it has taken so long for me to insist on using quaternion...
  11. sweetser

    Unifying Gravity and EM

    Talk last weekend and this weekend Hello: Last weekend, I went to the Fall APS/AAPT meeting at the University of Massachusetts, Boston. They have a lovely campus, right next to the JFK library on the water. It was a sunny and warm day thanks to global warming. The first speaker was also...
  12. sweetser

    Unifying Gravity and EM

    Gravity versus EM Hello Max: I do have a word description about these two forces that is based on looking at the equations and solutions for quite some time. Here goes... Stuff in Nature is pretty well isolated from each other after a separation lasting 13 billion years. In an ideal...
  13. sweetser

    Unifying Gravity and EM

    Three definitions of a 4-force Hello Lut: I have used 3 definitions for force. One is the derivative of the 4-momentum with respect to the interval tau. I saw that in a discussion of the Lorentz force of EM in Jackson, the end of chapter 11. This is the dP/dt and dE/dx one. The second...
  14. sweetser

    Unifying Gravity and EM

    Bicycle wheels and disc galaxies Hello: In this post we will think about momentum for a disk bicycle wheel and a disk galaxy. The similarities between the two systems may give support to the relativistic rocket effect discussed here. A disk has all of its mass in a plane. Both of the...
  15. sweetser

    Unifying Gravity and EM

    Dark energy and the relativistic rocket effect Hello: All forces must have a cause and an effect. For a disk galaxy, there is the Newtonian force, Fij Rr Cos(\theta), whose effect is the centripital motion. At the current time, this is all that is used to calculate the momentum profiles of...
  16. sweetser

    Unifying Gravity and EM

    Symmetry and torque forces Hello: Symmetry is useful to think about because it can pinpoint what can be ignored. Feynman emphasized looking for things that add up, knowing we can ignore things that cancel. This is what I drew on my board this morning: The two Fv's point in opposite...
  17. sweetser

    Unifying Gravity and EM

    Disk galaxy momentum profile - the drawing Hello: To use Newton's law of gravity, masses and distances must be known. For a disk, one cannot treat it as an effective point mass. Instead, the galaxy needs to be chopped up into little bits, and add up each contribution. My plan is to do...
  18. sweetser

    Unifying Gravity and EM

    SUSY and dark matter Hello Vanick: Supersymmetric (SUSY) proposals have been with us for over 30 years. During that time, every time a new more powerful collider has come on line, part of the justification was the search for the SUSY particles. The same is claimed for the Large Hadron...
  19. sweetser

    Unifying Gravity and EM

    The plan Hello: Here is a picture of the plan I have for calculating the rotation profile of a galaxy: I had included a higher resolution image in the previous post, but apparently it was too large to be accepted here (600x450 pixels, 57k works). Doug
  20. sweetser

    Unifying Gravity and EM

    Disk galaxy momentum profile - the plan Hello: Personal stuff: I spent the month of July drifting. I was bummed that neither the trip to Brazil nor the MIT GR course created lasting dialogs with the participants. Although I am familiar with not connecting, both events involved...
  21. sweetser

    Unifying Gravity and EM

    Hello Ghost_of_PL: > most likely this is my last post on this subject This discussion is becoming repetitive, so that is good news for general readers of this thread. Your weakest statement is this assertion: > Your matrix representation can fare no better since it also admits stand...
  22. sweetser

    Unifying Gravity and EM

    Square of a quaternion Hello Ghost_of_PL: There are only 4 slots in a quaternion, something that is obvious from the 4x4 real matrix representation used in the Mathematica notebook. Looking back, I not only used a variation on a common definition (which would normally have i, j, k for e_1...
  23. sweetser

    Unifying Gravity and EM

    Basis vectors and quaternions Hello Ghost_of_PL: Good old fashioned algebra rocks! The only way I really learn something is with paper and pencil (so I can erase a lot). I did not understand what your issue was, but now I have a better grasp of it. I did define what I meant by a...
  24. sweetser

    Unifying Gravity and EM

    Inverse of curved quaternions Hello Ghost_of_PL: Great question! I had not looked at all the details, and your post got me to think about them. There is hope that the algebra represented in equations 11-15 will be a division algebra since as M approaches zero, the algebra approaches the...
  25. sweetser

    Unifying Gravity and EM

    Force Hello: I am taking the General Relativity course 8.06s at MIT's Professional Institute. It is great fun that I get to think and chat about physics for four days. It has been work the 4 vacation days and $2k for the class. At lunch, one fellow said his biggest concern was with...
  26. sweetser

    Unifying Gravity and EM

    Cosmology Hello Joe: I have not been able to download the 2.8G torrent yet, so I will present some of my thoughts about cosmology independent of that video. Cosmology has major problems, and they know it. I try and be careful in discussing these issues, to call it by the problem with the...
  27. sweetser

    Unifying Gravity and EM

    Picturing quantum field theory Hello: There are two groups that understand the odd ways of relativistic quantum field theory. The first group are the elite people who hang around the physics departments of major research universities. They don't bother to teach quantum field theory to...
  28. sweetser

    Unifying Gravity and EM

    Screws and Quaternions Hello: How would you described the motion of a screw? It is a combination of linear and angular motion, with the angular motion perpendicular to the linear. At the meeting in Brazil, I learned the way most people handle this problem: they use dual quaternions. I had...
  29. sweetser

    Unifying Gravity and EM

    Hello Lut: I was projecting to the minds of three dead men, Hamilton, Grassmann, and Clifford, whose lives where lived within the 1800's, well before the insights of 1905. Doug
  30. sweetser

    Unifying Gravity and EM

    The geometric product Hello: Today I will discuss the geometric product, a tool used extensively for people applying Clifford algebras to problems in physics and robotics. Here is the definition: ab = a.b ~+~ a \wedge b \quad eq~1 There are a number of great features to this...
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