Dear Lawrence,
interesting math, in particular the special thinks about the E_8 and G_2. I have to study the projective Fano plane, an interesting relation.
Yes, the appearance of a single particle was also a surprise for me. Maybe I have to understand more of your work.
Very interesting ideas, thanks a lot for your time.
Torsten
Hi Lawrence,
I read through your essay, but have not returned to it yet - to read for detail. But I've noted some of your comments, and wanted to add one or two of my own. First off; I saw your EJTP paper on "Counting States in Spacetime" which you posted on Rick Lockyer's essay site, and I note several points of overlap with the following paper by Frank Potter.
Second; as I understand it octonions can indeed be represented as a system of 7 quaternions, but then the quaternion variables must be resolved in a definite order or sequence, or handled in a consistent way, as the effect of each term is cumulative (as with procedural steps or process stages). I think Rick uses the term ensemble multiplication.
But this is not quite the same as saying that the 'octonions are really a system of quaternions.' Maybe O is more fundamental than H, as Rick asserts. But perhaps saying octonions can be treated as an ordered or nested system of quaternions would work, though.
Regards,
Jonathan
In a response to Jonathan Dickau I make greater mention of these matters. I also make a bit of a pitch for your essay.
Cheers LC
Hi Jonathan,
Thanks for the paper. In looking at it I see many things which are in my notes and which I have in other papers and the book "Sphere Packing, Lattices and Codes" by Conway and Sloane.
The graininess of spacetime is something which I think only comes about with the measurement of black hole states. As I indicated on Giovanni Amelino-Camelia's essay blog site there is an uncertainty principle,
ΔrΔt ~ (2Għ)/c^4 = L^2_{Planck}/c.
which is commensurate with equation 1 on Giovanni's paper . Spacetime appears grainy depending upon the type of measurement one performs. In the case of a quantum black hole a measurement involves spatial and temporal coordinates in a null congruency called an event horizon. If one makes another type of measurement spacetime is then as smooth as grease on an ice skating ring. The measurements of delay times for different wave lengths from very distant gamma ray burstars indicate that space is smooth down to a scale 10^{-50}cm --- far smaller than the Planck scale. This then ties in with some interesting work by Torsten Asselmeyer-Maluga on the role of exotic four dimensional space in quantum gravity. These are homeomorphic spaces that are not diffeomorphic. In 11 dimensions the 7-dimensional is dual to the 4-dimensional space. The exotic 7-spheres found by Milnor are simpler, with only 7-distinct non-diffeomorphic forms, rather than an infinite number.
The octonions are a system of 7 quaternions. The exotic system in 7-dimensions I think might be connected to the automorphism G_2 in E_8 or SO(O). This would then connect with a physical meaning of octonions and nonassociativity in physics. The Polyakov path integral
Z[A] = ∫δD[ψ]/diff(ψ) Ae^{-iS[ψ]}
"mods out" diffeomorphism or equivalently gauge changes on a moduli. Yet with exotic spaces this definition becomes strange. However, if there are 7 quaternions which are related to each other by nonassociative products (ab)c - a(bc) =! 0, then the measure can maybe be realized according to associators δD[ψ]/diff(ψ).
I discussed octonions a bit with Lockyer, but he seemed a bit put off. As I see it, and from some experience, presenting a gauge theory with nonassociative brackets and stuff falls pretty flat, I am not necessarily saying this is wrong, but doing that sort of work has a way of getting people to present their backside to you. I think the role of nonassociators is best advanced by other means so that in the future they may simply be too convincing to ignore.
Cheers LC
Lawrence,
Sorry you were offended by my calling you out for posting on my essay blog without the common courtesy of having read the essay first. I only meant to inform you that you might possibly find some perspective on your question about how Octonion Algebra relates to physical reality since it was the thesis of my essay. Thanks for reading it later. I am curious about your characterization that it is just a gauge theory using associators. The Lorentz gauge mention was simply to demonstrate a point of commonality between 4D and Octonion presentations of Electrodynamics, that's it. Hardly a cornerstone of the presentation. I never once mentioned the associator, and frankly have never used non-associative brackets in any mathematical description. Octonion Algebra does indeed present a non-zero associator because it is a non-associative algebra. It MUST be so in order to be a normed composition algebra, hence a division algebra. Without this non-associativity and the remainder of O structure, it would be impossible for the algebraic invariances to match up the math to what we can measure or detect, and algebraic variances to give us clues on the math for what is hidden from us but none the less in play.
Rick
Thanks Lawrence,
That nicely spells out where you are coming from. Glad you enjoyed the Potter paper, also. I've not looked at Giovanni's essay yet, but a quick read through of Torsten's paper has made it a 'must read' for the insights he shares. I am certainly not put off by your comments or Rick's and have found a lot of fascinating insights on the forum - even in the points of dispute.
I am glad the back and forth has kept everybody thinking. More fun lies ahead!
all the best,
Jonathan
Jonathan,
First off I have not gotten around to reding your paper yet. It is taking me some time to get to them all.
Torsten's work is pretty hard stuff. The differential geometry of exotic spheres runs pretty deep. I studied this for my masters in mathematics. It has been a while since I have thought much about that. It did occur to me that exotic spherse might have something to do with quantum gravity.
I try to get as many people with their theoretical ideas and results together, because it is not likely that any of us b ourselves will come to the "big picture."
Cheers LC
In indicated to Giovanni Amelino-Camelia there should be some connection between the theory κ-Minkowski spacetimes and the boost system he advances with twistor theory. The connection to twistor theory is I think not hard to see. The boost operator P_μ that acts on [x_i, x_0] = ilx_i such that
P_μ > [x_i, x_0] = il P_μ > x_i
The coordinates (x_j, x_0) we write in spinor form
x_j = σ_j^{aa'}ω_{aa'}
x_0 = σ_0^{aa'}ω_{aa'},
where ω_{aa'} = ξ_a ω_{a'} ξ_{a'}ω_a. This commutator has the form
[x_i, x_0] = σ_j^{aa'}σ_0^{bb'}[ω_{aa'}, ω_{bb'}]
= iC^{cc'}_{aa'bb'} σ_j^{aa'} σ_0^{bb'} ω_{aa'}
= i|C| σ_j^{aa'}ω_{aa'}
where the magnitude of the structure matrix is |C| = l. In general this may be written for
x_j = σ_j^{aa'}ω_{aa'}
x_0 = σ_0^{aa'}ω_{aa'} iq_{aa'}π^{aa'},
where the commutator [ω_{aa'}, π^{bb'}] = iδ_a^bδ_{a'}^{b'} and the general form of the commutator is then
[x_i, x_0] = i|C| σ_j^{aa'}ω_{aa'} iσ_j^{aa'}q_{bb'}[ω_{aa'}, π^{bb''}
[x_i, x_0] = ilσ_j^{aa'}ω_{aa'} - σ_j^{aa'}q_{aa'}.
The boost operation B = 1 a^l_jP^j on the commutator [x_i, x_0] is then equivalent to the commutation between spinors [ω_a, ω'_b] for ω'_b = ω_b iq_{bb'}π^{b'},
[ω_a, ω'_b] = [ω_a, ω_b] iq_{bb'}[ω_a , π^{b'}]
= C^c_{ab} ω_c iq_{ab}.
This could be explored more deeply. Ed Witten demonstrated the "twistor revolution" in string theory. If twistors are connected to κ-Minkowski spacetime there might then be a link between string theory and LQG and other "edgelink" type of quantum gravity theories. This would be potentially interesting, for this might serve to correct the difficulties with each of these.
Cheers LC
Lawrence,
You wrote: "Einstein changed Newton's laws by adjusting the first and third laws, motivated by the locality of electromagnetic fields predicted by Maxwell's equations."
Einstein did not adjust anything - he just introduced two postulates the second of which was false. In 1887 the Michelson-Morley experiment had refuted the light postulate and had confirmed the variable speed of light predicted by Newton's emission theory of light. It is time for you, Lawrence, to stop claiming that Banesh Hoffmann, John Norton and John Stachel are wrong:
http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
"Relativity and Its Roots" By Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."
http://www.aip.org/history/einstein/essay-einstein-relativity.htm
John Stachel: "An emission theory is perfectly compatible with the relativity principle. Thus, the M-M experiment presented no problem; nor is stellar abberration difficult to explain on this basis."
http://www.philoscience.unibe.ch/documents/kursarchiv/SS07/Norton.pdf
John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."
http://philsci-archive.pitt.edu/1743/2/Norton.pdf
John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."
Pentcho Valev pvalev@yahoo.com
I am not sure why you decided to make your life's work to discredit relativity. You keep posting the same thing over and over, with the same references.
The invariance of the interval, equivalently the constancy of the speed of light, means in addition to the three rotations of space there are three Lorentz boosts. The physics of this has been tested literally thousands of times in many different ways. The empirical support for relativity is simply overwhelming. You are not going to find many people here who are well grounded in physics who agree with you.
Cheers LC
Hello Lawrence and Mr.Danoyan,
You know Lawrence.When I am not parano, I see the convergences with strings and the 3D.
So I am discussing,:) The light permits to compse all the colors.The angles indeed are relevant.I saw this idea from Mr Dicarlo on the hread of Mr Barbour.
If the angles and the volumes are inserted with the correct quantum finite number, it becomes very relevant for our correct 3D architecture, the sphere and its spheres. The combinations are very numerous (rotations spinal,rotations orbital,volumes, serie finite !!!,linear velocity, sense of rotation differenciating m and hv.It permits to unify the gravitation with the 3 other foundamental forces.).
Lawrence I am persuaded that we can create a 3D holographic Sphere and its spheres, cosmologic and quantic. If we consider that the space and the mass and the light are the same at a kind of zero absolute.So if the quantum number is finite and precise.So it implies a real relevance when we insert the rotations and motions more the volumes and the angles. The puzzle is simple and complex. It is relevant to consider that the cosmological number is the same. This serie is so universal. The fractalization in a pure road of primes number seems very relevant with the main central sphere, the most important volume, the 1.
The QCD can be optimized in fact Lawrence. Perhaps that the volumes are still very relevant considering the main light from the main central sphere.
I think that the oscillations can be correlated with rotations and the QM. I see the light turning at the maximum but in the opposite sense than this gravitation in evolution. If the space is also an quantum entanglement.So it is interesting to see its velocities of rotations.and the sense also.In the logic the lattices between spheres disappear in the perfect contact.And if the main central sphere is the most important volume.So it is interesting to see how this space can be checked.In my line of reasoning, the space between sphere can imply so a contraction of this space, like witha vaccuum, but of course two points are necessary, an arrival and a departure of course.It is relevant because we can decrease the space between cosmological spheres.If the arrival point has an other solution ,it is relevant. The second relevance of this line of reasoning is that the mass can be changed in light, so we move at c.The third relevance is that we can decrease with my model,the internal clocks, so the rotations of sphers, so the duration. Now if we check these 3 quantum systems.So we can 1 decrease the space between two spheres.2 we can go at c.(we reencode the mass at the arrival point) and 3 we can decrease our internal duration, so we utilize less of time during the travel. It is the principle of future teleportation. It is there that the volumes of spheres are essential for the stability of informations during the reencoding.
It is very relevant at my humble opinion.
Best Regards
Lawrence,
Roger Schlafly wrote in his site:
"Pentcho, you are right that the emission theory was the only known explanation [of the null result of the Michelson-Morley experiment] in 1887..."
Is Roger right? Also, Lawrence, you used to claim that John Norton is wrong when he says that:
http://philsci-archive.pitt.edu/1743/2/Norton.pdf
John Norton: "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."
Do you still believe Norton is wrong, Lawrence?
Pentcho Valev
I have not yet read Schlafly's essay or read the posts on his blog. I am not particularly interested in revisiting old stuff like this. Whether one can interpret the M-M experiment in different ways is of little interest to me. Lorentz interpreted the result as due to a length contraction that nullified the effect of the putative aether. Einstein was apparently not aware of the M-M experiment at all. Which ever is the case with interpreting the M-M experiment it is not relevant. Special relativity has been tested by many dozens of other types of experiments repeated many thousands of times. I am not sure why anybody would want to take up the cause of trying to overturn relativity this way. There were people up to the early 19th century who wanted to overturn Newton as well.
Cheers LC
The fact is that, in 1887, Newton's emission theory stating that the speed of light varies in accordance with the equation c'=c+v (v is the speed of the light source relative to the observer) was the ONLY existing theory capable of explaining the null result of the Michelson-Morley experiment.
You find this fact unimportant and accordingly occupy the top of the community rating list. I find this fact extremely important and am at the bottom. Simple isn't it?
Pentcho Valev
As for the rankings, there are two possible reasons for this. The first is that relativity is all wrong and has been propped up for over a century by an international scientific conspiracy. Those involved with the conspiracy or who believe its falsehood are wrongly voting your paper down. The other possibility is that you are simply wrong in your thesis that relativity is wrong based on an interpretation of an experiment performed over 130 years ago. You are not alone in such conspiracy claims. Some people who advance local hidden variables cry how the physics world has gone astray, and more recently a certain politically motivated "alt-science" community claims there is a big conspiracy to demolish the economy with global warming concerns by climatologists.
I tend to avoid these things, along with claims the 9/11 attack was an inside job, grassy knolls with Kennedy's assassination, Princess Diana's death was an inside job, and so forth. It is not possible to absolutely prove these things false, but seriously entertaining them is probably about as productive as masturbation is with impregnating your wife.
Cheers LC
That "relativity is all wrong" is a fact often hinted at by high-ranking Einsteinians:
http://www.perimeterinstitute.ca/pdf/files/975547d7-2d00-433a-b7e3-4a09145525ca.pdf
Albert Einstein (1954): "I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics."
http://www.fqxi.org/community/articles/display/148
"Many physicists argue that time is an illusion. Lee Smolin begs to differ. (...) Smolin wishes to hold on to the reality of time. But to do so, he must overcome a major hurdle: General and special relativity seem to imply the opposite. In the classical Newtonian view, physics operated according to the ticking of an invisible universal clock. But Einstein threw out that master clock when, in his theory of special relativity, he argued that no two events are truly simultaneous unless they are causally related. If simultaneity - the notion of "now" - is relative, the universal clock must be a fiction, and time itself a proxy for the movement and change of objects in the universe. Time is literally written out of the equation. Although he has spent much of his career exploring the facets of a "timeless" universe, Smolin has become convinced that this is "deeply wrong," he says."
http://www.newscientist.com/article/mg20026831.500-what-makes-the-universe-tick.html
"Newton and Leibniz debated this very point. Newton portrayed space and time as existing independently, while Rovelli and Brown share Leibniz's view that time and space exist only as properties of things and the relationships between them. It is still not clear who is right, says John Norton, a philosopher based at the University of Pittsburgh, Pennsylvania. Norton is hesitant to express it, but his instinct - and the consensus in physics - seems to be that space and time exist on their own. The trouble with this idea, though, is that it doesn't sit well with relativity, which describes space-time as a malleable fabric whose geometry can be changed by the gravity of stars, planets and matter. If the central property of space-time is the result of the existence of matter, how can we be sure that space and time exist on their own and are not convenient illusions? "Hence my hesitation," Norton says. While Norton hesitates, Smolin is intent on rescuing time. He believes time has to be real and that it is a fundamental property of the universe."
http://www.amazon.com/Faster-Than-Speed-Light-Speculation/dp/0738205257
Joao Magueijo, Faster Than the Speed of Light: The Story of a Scientific Speculation, p. 250: "Lee [Smolin] and I discussed these paradoxes at great length for many months, starting in January 2001. We would meet in cafés in South Kensington or Holland Park to mull over the problem. THE ROOT OF ALL THE EVIL WAS CLEARLY SPECIAL RELATIVITY. All these paradoxes resulted from well known effects such as length contraction, time dilation, or E=mc^2, all basic predictions of special relativity. And all denied the possibility of establishing a well-defined border, common to all observers, capable of containing new quantum gravitational effects."
https://webspace.utexas.edu/aam829/1/m/Relativity.html
Alberto Martinez: "Does the speed of light depend on the speed of its source? Before formulating his theory of special relativity, Albert Einstein spent a few years trying to formulate a theory in which the speed of light depends on its source, just like all material projectiles. Likewise, Walter Ritz outlined such a theory, where none of the peculiar effects of Einstein's relativity would hold. By 1913 most physicists abandoned such efforts, accepting the postulate of the constancy of the speed of light. Yet five decades later all the evidence that had been said to prove that the speed of light is independent of its source had been found to be defective."
Pentcho Valev
Science and physics are not about certitude. We can never be certain that our understanding about the world is complete, any more than science can't prove that Cthulhu will not arise from his sleep and destroy everything. We can though say that within the domain of applicability that relativity, and more specifically special relativity, operates well. With respect to the issues raised by Smolin these pertain to questions with a possible quantum underpinning of general relativity.
Cheers LC
Lawrence
Your information about 8 gluons known from theory.
My point of view notion "color" proposed for saving Pauli's principle.
But Pauli principle not valid in 2D space
http://fqxi.org/community/forum/topic/1444
Color not need in 2d space
As well as in 2d no gravitation,no Gn
See my essay http://fqxi.org/community/forum/topic/1413
I will try to get to your paper in the near future.
Cheers LC
My quote from Wittgenstein is I think closer to the actual German.
The emergence of unitarity means that it is the simplest of modular functions which occurs when there is no nonlocal physics with the singularity. In some of my comments on this blog I discuss this in some greter detail.
Cheers LC
