I'm interested to know, does your theory of gravity explain the various "problems of mass" at all these scales, or have you worked out the calculations that far yet? I'm also interested in knowing what the ultra-high energy behavior of this theory is. From what I gather, there is a problem with embedding quantum fields in curved space-time when energy levels get too high.
I have not solved any of the 4 problems listed in the talk. I have very specific proposals for each. The Higgs may be resolved because the hypercomplex terms can break gauge symmetry will not altering the gauge symmetry need by EM. The other 3 might be solved with a new classical term I call the relativistic rocket effect. I have not been able to apply that to real world data.
Your question concerns quantization, which should be easy since the proposal is linear, unlike GR. Hard math.
I'm currently planning on going into theoretical physics, but right now I'm just an undergrad, and I know more about GR than QFT.
Could you explain to me what is meant about the problems encountered at higher energies (like Planck masses, etc.) when one tries to embed quantum fields in a curved metric? I think I read it has to due with the fact that QFT is background dependent and GR is background independent. Thanks for your time.
I read "Godel, Escher, Bach", not the new book. I am staying closer to numbers than Hofstadter. The graph theory in this video suggests how one can set up the accounting system for self-reference: only through the use of real numbers. Real numbers map to time while imaginary numbers map to space.
You state that there are enormous deep philosophical implications concerning the the loop formed by the relationship of the vertex and loop edge for the reals.
This I think is reflected in the fact that the reals have montonicity or a counting principle, which is not the case for complex numbers or generalizations, without taking extra steps on the graph (modulo a phase) to get back to 1.
A different way to say the same thing is that the real numbers are a totally ordered set, while complex numbers are not.
The _philosophical_ angle has to do with what it means to be independent. If I am part of a loop, I can return to myself. The loop might involve 70 trillion cells, but we do hang together through spacetime, looping through the time part to get older together. I suspect a similar thing happens to you wherever you are.
So the temporal portion of a quaternion being a "self-referring loop" (the connection to the Reals) is what holds the spatial parts together? This makes sense because although we are 3-D in space, to talk of "being' in one spatial dimension independently of the other two is absurd. Quaternions therefore force space (i,j,k) to be path-dependent in terms of time. This should be the math of modern physics.
I am reading the technical paper with that title now (by Gull, Lasenby, and Doran). pfft! The title says "spacetime" - as in space and time are joined in bed together and may not be separated - yet they avoid contact by treating space as a vector and having the real scalar time. Part of their approach is to be able to work in arbitrary dimensions. pfft! For 400+ years, we have only taken data in spacetime, it is all we need.
scalar time? 5.1-2 on page 15 uses four vectors... dunno, like i said, it's mostly over my head or rather out of my time as i barely got into classical mechanics, some QM and electrodynamics... so relativity and QFT is mostly just a folk tale for me. perhaps read their paper III [27]. "our approach again clarifies the role of antisymmetrical terms"...
The standard model is for EM, the weak, and the strong forces. It says nothing about gravity. This is one reason why gravity does not get along with the rest of physics.
For complex numbers and quaternions, i.i = j.j = k.k = -1. For hypercomplex numbers, i.i = j.j = k.k = +1. To make them a division algebra, the Eigenvalues of the matrix representation need to be excluded (a technical point, but surprising if you are/become familiar with the jargon).
Sorry to give a banal answer, but self-study from credible sources can work with much work. There are so many roads in mathematics, physics, and mathematical physics. The best thing about working creatively with quaternions has been that I do those three at the same time. Working out the two limit definition of a quaternion derivative on a quaternions manifold led to a reason for the difference between classical and quantum mechanics.
I'm interested to know, does your theory of gravity explain the various "problems of mass" at all these scales, or have you worked out the calculations that far yet? I'm also interested in knowing what the ultra-high energy behavior of this theory is. From what I gather, there is a problem with embedding quantum fields in curved space-time when energy levels get too high.
MadScientistsPrimer 2 years ago
I have not solved any of the 4 problems listed in the talk. I have very specific proposals for each. The Higgs may be resolved because the hypercomplex terms can break gauge symmetry will not altering the gauge symmetry need by EM. The other 3 might be solved with a new classical term I call the relativistic rocket effect. I have not been able to apply that to real world data.
Your question concerns quantization, which should be easy since the proposal is linear, unlike GR. Hard math.
dougsweetser 2 years ago
So, at the moment, it's a bit incomplete?
I'm currently planning on going into theoretical physics, but right now I'm just an undergrad, and I know more about GR than QFT.
Could you explain to me what is meant about the problems encountered at higher energies (like Planck masses, etc.) when one tries to embed quantum fields in a curved metric? I think I read it has to due with the fact that QFT is background dependent and GR is background independent. Thanks for your time.
MadScientistsPrimer 2 years ago
Anyone read Douglas Hofsadter's new book, I Am A Strange Loop (2007)?
wresing 2 years ago
I read "Godel, Escher, Bach", not the new book. I am staying closer to numbers than Hofstadter. The graph theory in this video suggests how one can set up the accounting system for self-reference: only through the use of real numbers. Real numbers map to time while imaginary numbers map to space.
sweetser 2 years ago
You state that there are enormous deep philosophical implications concerning the the loop formed by the relationship of the vertex and loop edge for the reals.
This I think is reflected in the fact that the reals have montonicity or a counting principle, which is not the case for complex numbers or generalizations, without taking extra steps on the graph (modulo a phase) to get back to 1.
69erthx1138 2 years ago
A different way to say the same thing is that the real numbers are a totally ordered set, while complex numbers are not.
The _philosophical_ angle has to do with what it means to be independent. If I am part of a loop, I can return to myself. The loop might involve 70 trillion cells, but we do hang together through spacetime, looping through the time part to get older together. I suspect a similar thing happens to you wherever you are.
I can also be part of a different loops.
sweetser 2 years ago
So the temporal portion of a quaternion being a "self-referring loop" (the connection to the Reals) is what holds the spatial parts together? This makes sense because although we are 3-D in space, to talk of "being' in one spatial dimension independently of the other two is absurd. Quaternions therefore force space (i,j,k) to be path-dependent in terms of time. This should be the math of modern physics.
69erthx1138 2 years ago
"imaginary numbers are not real"
jogayot 2 years ago
they are if you talk about phase
DavidAKZ 2 years ago
pfft ;)
google the full phrase with "".
"i" can be even interpreted as volume of space...
anyway, way over my head, and i quit my studies all too son, but this stuff interested me once.
jogayot 2 years ago
I am reading the technical paper with that title now (by Gull, Lasenby, and Doran). pfft! The title says "spacetime" - as in space and time are joined in bed together and may not be separated - yet they avoid contact by treating space as a vector and having the real scalar time. Part of their approach is to be able to work in arbitrary dimensions. pfft! For 400+ years, we have only taken data in spacetime, it is all we need.
sweetser 2 years ago
so, like, your saying geometric algebra is pfft?
scalar time? 5.1-2 on page 15 uses four vectors... dunno, like i said, it's mostly over my head or rather out of my time as i barely got into classical mechanics, some QM and electrodynamics... so relativity and QFT is mostly just a folk tale for me. perhaps read their paper III [27]. "our approach again clarifies the role of antisymmetrical terms"...
jogayot 2 years ago
Re gravity, what does the standard model say about its existence ? I thought i . i = -1
DavidAKZ 2 years ago
The standard model is for EM, the weak, and the strong forces. It says nothing about gravity. This is one reason why gravity does not get along with the rest of physics.
For complex numbers and quaternions, i.i = j.j = k.k = -1. For hypercomplex numbers, i.i = j.j = k.k = +1. To make them a division algebra, the Eigenvalues of the matrix representation need to be excluded (a technical point, but surprising if you are/become familiar with the jargon).
sweetser 2 years ago
Thanks. Can you point to a suitable reference to help a person with a physics background but half baked notions of relevant mathematics ?
DavidAKZ 2 years ago
Hello David:
Sorry to give a banal answer, but self-study from credible sources can work with much work. There are so many roads in mathematics, physics, and mathematical physics. The best thing about working creatively with quaternions has been that I do those three at the same time. Working out the two limit definition of a quaternion derivative on a quaternions manifold led to a reason for the difference between classical and quantum mechanics.
Good luck working the dough.
sweetser 2 years ago
Thanks Doug. Do you have any recommendations as to what mathematical modeling software to use ?
DavidAKZ 2 years ago
Thanks for making this video. Interesting as always.
BrandonFurtwangler 2 years ago