My latest paper with Jonathan Dickau uses a minimum 10-D TOE to explain superluminal neutrinos, and has been published in
I would like to draw your attention to the last two sections: "Geometric Attributes of Higher Dimensions" and "Thermo-Geometric Instabilities of the Octonion 7-Sphere" on pages 1806-9.
We present a case for why the 7-sphere should not be stable. In my opinion, this complicates, and may even negate, any conclusions that Joy and Tom may have made regarding 7-sphere geometry.
Paul Reed replied on Nov. 14, 2011 @ 10:33 GMT
Ray
Why is it: "I think it is clear that we live in a quaternion Spacetime, and that we don't directly experience octonion physics"?
Where is the evidence for this, other than mathematical models addressing a particular problem as envisaged? The second part of the sentence having a cetain amount of 'convenience' about it. That is, the maths used proves x, we just cannot see (literally) it. [Note: I know this is Joy's statement].
Paul
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T H Ray replied on Nov. 14, 2011 @ 11:49 GMT
Ray,
Joy's framework does not exclude complex numbers. It excludes complex results.
Tom
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Ray Munroe replied on Nov. 14, 2011 @ 13:18 GMT
Hi Paul,
Here is the paper on octonions and quaternions that Jonathan and I wrote together a few months ago:
In Defense of Octonions I hope that this clarifies my position on these hypercomplex numbers.
When I said "I think it is clear that we live in a quaternion Spacetime, and that we don't directly experience octonion physics", I mean that the Minkowski metric of Spacetime is clearly quaternion in its form. Regarding octonion physics, if non-associativity is part of physics, then I have accidentally over-looked it.
Hi Tom,
I understand that if we stay on the surface of Joy's 7-sphere, then all relative phases may be treated as 'real'. In a true octonion 7-sphere, all hypersurface components are imaginary, but the relative phases are real. Any mixing of radial and hypersurface components does introduce complex results, and I'm not sure what happens when we overlay 'unit' spheres of different dimensionality.
Have Fun!
attachments:
1995821PB.pdf
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T H Ray replied on Nov. 14, 2011 @ 13:46 GMT
Hi Ray,
But all real measurements ARE over manifolds (all real functions are continuous). The feature of Joy's model that prevents introduction of radial components is the spacetime "twist" facilitated by the topology of S^7 for continuous measures over the manifold of S^3 (S^2 X S^2). This features preserves time reverse symmetry and avoids the singularity -- technically speaking, a "naked" singularity.
Tom
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Ray Munroe replied on Nov. 14, 2011 @ 15:08 GMT
Hi Tom,
Yes - You have said this before, and I appreciate your efforts to fill in some of Joy's gaps. I would agree that a 'real' experiment will measure 'real' values, but are we ignoring the imaginary values (which are practical for representing dissipative systems - i.e. entropy) that are required by the Kramers-Kronig relations?
If my latest paper is correct, and 7-sphere geometry permits FTL tachyons, then concepts such as 'locality' and 'causality' are dead. Everything is entangled!
Have Fun!
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Joy Christian replied on Nov. 14, 2011 @ 15:20 GMT
Ray,
The key word here is "if" (concerning FTL tachyons).
I also have problems with your stability analysis of the 7-sphere. I simply don't believe it. I will say more when I have more concrete thoughts.
Also, let me quote something Tom said and you have consistently missed: "Joy's framework does not exclude complex numbers. It excludes complex results."
On the positive side, I quite like your paper in general.
Joy
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Ray Munroe replied on Nov. 14, 2011 @ 15:42 GMT
Hi Joy,
Thank You! 'IF' is a critical part of the argument. It will be interesting to see 'IF' the OPERA results withstand the rigors of scrutiny and independent confirmation.
My argument against the 7-sphere involves physics (minimization of the Thermodynamic state variable, Gibbs energy) and math concepts. Within the realm of purely mathematical reasoning, the 7-sphere is apparently stable. Would your analysis work either way - in a unified 7-sphere or in a broken 7-sphere? Or are we going to get complex phases between broken 'hypersurface' components?
I understand the statement "Joy's framework does not exclude complex numbers. It excludes complex results". Of course, octonion 7-spheres are hypercomplex numbers. Your point is that measurements taken on the hypersurface should be 'real'. I think that this is true in a 'timeless' or time-reversible model, but I question its application to models of reality that include entropy.
This entire problem may be more complicated than either of us realizes.
I wish you the best in your research with octonion 7-spheres.
Have Fun!
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Joy Christian replied on Nov. 14, 2011 @ 17:11 GMT
Ray,
As I have said before, if you are right and we have a genuine casualty violation in OPERA, then my work becomes a futile exercise. For then we have a major revolution at hand. I am not sure what the status of local causality would then be within such a non-local paradigm of physics.
"Would your analysis work either way - in a unified 7-sphere or in a broken 7-sphere?"
I am not sure. I haven't investigated the question as yet. The answer may depend on how broken or metastable the sphere is. As Fred mentioned earlier, momentary stability may be sufficient to maintain locality. More likely mathematical parallelizability is all that may be needed for my analysis to go through. We shall see.
In any case, I agree that the entire problem may be more complicated than either of us realizes.
Cheers,
Joy
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Edwin Eugene Klingman replied on Nov. 14, 2011 @ 23:27 GMT
Joy,
It is unclear to me exactly why we have a 'causality violation' in OPERA, one that would make your work "a futile exercise".
If one accepts the idea of tachyons, as imaginary mass particles with speeds ranging from infinite down to c as energy increases, perhaps so. But if one simply thinks of the particles as neutrinos that have, for a reason yet to be explained, traveled 1.000025 c from point a to point b, why is causality violated? What am I missing here?
Ray,
I too enjoyed your paper and hope to comment later.
Edwin Eugene Klingman
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Joy Christian replied on Nov. 14, 2011 @ 23:55 GMT
Edwin,
I am not saying that we necessarily have a causality violation in OPERA, even if their results are confirmed. As you say, we can simply replace the speed of photons with the speed of neutrinos as the universal speed agreed by all moving observers, and then there is no causality violation. But Ray is talking about (and counting on) tachyons, and we have to see which of the many ideas put forward best fits the details of the OPERA data. I personally do not believe for a second that OPERA results will be confirmed, but I am willing to keep an open mind.
Joy
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Ray Munroe replied on Nov. 15, 2011 @ 00:16 GMT
Thank You, Edwin.
If the OPERA experiment violates causality, then this violation is only weakly-coupled to our reality because neutrinos interact weakly. So Joy's (or Bell's) description of local reality would still be 99.999...% correct. To Joy's point, my model might not be the only way to describe 'superluminal' neutrinos. I am biased towards my model because it also leads to Quantum Gravity and a TOE.
Have Fun!
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Jason Wolfe replied on Nov. 15, 2011 @ 00:30 GMT
Hi Edwin,
You said, "If one accepts the idea of tachyons, as imaginary mass particles with speeds ranging from infinite down to c as energy increases, perhaps so. "
In the case of the tachyon, is there an equation or a good reason that the kinetic energy should increase as the tachyon approaches c? Or is this conjecture? I assume it must be conjecture.
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Ray Munroe replied on Nov. 15, 2011 @ 01:27 GMT
Hi Jason,
If you play with imaginary masses in Einstein's Special Relativity, you will find that a 'relativistic' (large gamma factor) tachyon travels only slightly faster than c, whereas a 'low energy' tachyon travels at near infinity. Although this might sound backwards, it is perfectly consistent with the idea that all particles travel at the speed of light in the limit as mass approaches zero - it doesn't matter whether that mass approaches zero along the real or imaginary axis.
My paper explains this in more detail.
Have Fun!
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Jason Wolfe replied on Nov. 15, 2011 @ 02:33 GMT
Hi Dr. Ray,
It's good to hear from you!
Objects with mass interact with a Higgs field. Mass is itself a property that makes things "not fly off at the speed of light", but move at a lower speeds. It is accepted physics that mass is "trapped" energy (trapped as rest mass energy). I have this idea that the Higgs field traps energy as particles, and somehow stores the kinetic energy between two massive particles in motion.
But a tachyon, IMO, should be a quantity of energy trapped by some Hyper-Higgs field with a speed of light c'>c. At least that's my opinion. Of course, I've been arguing that space-time/quantum vacuum/Higgs field are all manifestations of something quasi-physical that traps light as rest mass energy, and transmits light at c.
I haven't gotten a very warm reception with this idea. But I do have a picture of what a patch of space(-time) really consists of (lots and lots of waves). I'm taking a closer look at AdS-CFT correspondence which includes QM and GR.
I also came across a paper that seems to imply a faster speed of light; something about brane tension and a fifth dimension. If you like, I'll find it for you.
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Ray Munroe replied on Nov. 15, 2011 @ 02:51 GMT
Hi Jason,
As you will recall, we spoke of tachyons a lot a couple of years ago. With the OPERA 'superluminal' neutrino result, I revisited those ideas, and realized that if the scalar lepton has zero electric charge, then it would have properties very similar to a tachyonic neutrino, and possibly explain the OPERA result and the PMNS matrix.
I have heard a lot of 'fifth' dimension arguments lately. Tachyons are stable on a 2-brane, and my model requires at least 7-D to properly explain 'scalar fermions'. Five dimensions are not enough - Kaluza-Klein is insufficient to describe everything that needs to be described.
These 'scalar fermions' do have Higgs-like properties, and could be the origin of fermionic mass, but you should read the entire paper to see all of the connections.
I think of tardyons as 'relatively localized energy' that provide 'cause', and I think of tachyons as 'relatively non-localized energy' that provide 'entanglement'.
Regarding AdS/CFT theory, I need a G2 algebra with a graphene-like lattice on a 2-brane to explain 3 tardyonic generations. This starts to resemble a holographic boundary.
Have Fun!
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Jason Wolfe replied on Nov. 15, 2011 @ 04:28 GMT
Hi Ray,
R:"I think of tardyons as 'relatively localized energy' that provide 'cause', and I think of tachyons as 'relatively non-localized energy' that provide 'entanglement'."
That's interesting. I was reading the other day about entanglement. The experiment involved rotating polarized light filters in such a way that the spins we're correlated. I surmised that the entangled photons would belong to the same quantum system, perhaps even the same quantum wave.
It's interesting that you are using tachyons to perform tasks performed by quantum waves. At least that's my initial reaction. Because information can't travel faster than c, I presumed that transmitting energy IS transmitting information. As a result, tachyons can't have energy. At least that's my initial thought. We can beat this can around and discuss it.
Yeah, I was wondering about that Holographic stuff. I'm still trying to get the hang of tensors.
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Paul Reed replied on Nov. 15, 2011 @ 18:32 GMT
Ray
Your post 14/11 13.18
Thanks for the ref. I have no doubt I will not understand the maths as such, but will have a good go at trying to discern the underlying logic.
Can I run a sentence in this response back: “I mean that the Minkowski metric of Spacetime is clearly quaternion in its form”. Is the rest (unstated) of this sentence effectively: ‘that is, it does not necessarily follow that this conforms with our reality’ (or words to that effect)? I did note at the time that Tom spoke of : “physical nature of spacetime in Joy's model”. Whereas Joy confirmed to me: “we know therefore, that our reality has 7 spatial dimensions”.
An observation: Re OPERA, do not forget that we only receive a representation of reality via light. In other words what we ‘see’ is not reality, it is light’s ‘take’ on it. ‘Light reality’ is not reality. So, stuff could travel faster than light, we just would not see it. Stuff could exist that light just does not capture and convey to us. We might not have the sensory capability to detect stuff. To some extent this can be overcome when anomalies occur. It’s like being in the pitch dark. Given a candle you see x. Given an arc light you see x y z. Etc. Other than as a function of the conflation of reality with a light based representation of it, the latter being what we actually receive, there is no logical reason why light is reality’s speed limit. (Have fun, as you say)
Can I just ask why later (there’s been a lot of posts in a few hours!) you specifically refer to SR?
Paul
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Ray Munroe replied on Nov. 15, 2011 @ 19:44 GMT
Hi Paul,
Admittedly, some of the math does get crazy beginning around page 802. If you can decipher Examples 1 and 2, they will help you understand my position.
Basically, I'm saying that Electromagnetism and Relativity pretty clearly have the 1 scalar + 3 vectors nature of quaternion math. Yes - we can reduce it down to vector algebra, and try to ignore the quaternion aspects of these equations, but then special applications, such as the Riemann-Sommerfeld Equation and the Minkowski Tensor, slap us in the face with the reality of quaternion math-physics.
My latest paper uses 10-D to explain 'superluminal neutrinos'. I seem to have a quaternion 3-sphere of Electro-Color (Table 1 with 3+1 ‘colors’), and octonion decay products (possibly another quaternion 3-sphere or a super-Euclidean 4-ball?) of Gravi-Weak (Table 2).
I suggested that Jason look at Special Relativity because tachyons are a simple extension of SR with imaginary mass.
IF neutrinos interact with tachyons that can travel FTL, that doesn't mean that we can send a signal FTL. EM phase velocity can exceed c, but we cannot send an EM signal faster than c. Also, any violations of Relativity are weakly-coupled (neutrinos are weakly-coupled to our reality). So Relativity is generally obeyed, and this violation may be evidence for new physics such as Quantum Gravity.
Have Fun!
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Steve Dufourny replied on Nov. 16, 2011 @ 00:01 GMT
Hi Ray,
Hi Jason the creative, you know I have thought about several of your ideas for the travel inside our universal sphere.I beleive really it is possible to decrease the space between two cosmological spheres. And also to decrease our internal clock. Apparently if the fermions can be accelerated, so we can have a very important velocity. So if these 3 parameters are checked , it is relevant for the future universal travels. But For that, we need also a kind of topology in 3D of this universal sphere. I beleive strongly that it exists a central sphere inside this universal sphere. So this topology can help.
Ray,Hope you are well, I have had several neurological problems. So my parano is a result of these epilepsy and asperger syndrom perhaps I don't know. But I take my meds :) and I work on me, I try to relativate. I am sorry Ray if I was parano against you. I am going to be more cool, you shall see, you are my friend Ray.
Dr Cosmic Ray, I have thought about your tachyons in your model. Witht the news of the LHC,I think that it is not possible for a boson because it is under the laws of the special relativity. But the fermion(turning in the other main sense in my theory)is not a boson. So we can in logic, perhaps if there are not statistical errors, go above this c for fermions so for the mass. What do you think Ray ?
Regards
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Jason Wolfe replied on Nov. 16, 2011 @ 00:57 GMT
Steve,
I did run into sphere topology recently. I think the holographic principle uses spheres.
Ray,
I do know about the idea that FTL velocities cause gamma to become imaginary. But I think that this breaks gamma; gamma wasn't intended to be used this way. Don't get me wrong, I still think there exists a way to make information and energy travel faster than c. But to do this, you have to find a superluminal space-time where c' (c'>c) is the new "speed of light". This changes gamma to,
This is also a way to avoid causality issues.
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Ray Munroe replied on Nov. 16, 2011 @ 02:17 GMT
Dear Steve,
I am sorry for your difficulties, but you sound better now.
My tachyons are 'scalar leptons'. These scalar leptons mix eigenstates with the three known neutrino flavors via the PMNS matrix. I know that this sounds like an oxymoron because scalars are bosons, and leptons are fermions (not bosons). These tachyons arise out of a minimum 7-D geometry (possibly related to Joy's metastable octonion 7-sphere - see Tables 1 and 2 of my latest paper), and are stable on a 2-D membrane (maybe the G2 holographic boundary with 7-fold symmetries - but that leap of reasoning is unnecessary) where they obey Anyonic statistics. A TOE must deal with the differences between fermions and bosons, and treating a 'unified fermi-boson' (or 'scalar lepton') like an generic Anyon seems like a legitimate approach.
Dear Jason,
Why do you worry about imaginary gamma factors? Did you read the paper on Octonions and Quaternions that Jonathan and I wrote in Prespacetime 2 (6)? Complex numbers are used in physics modeling a lot. That paper also emphasizes the obvious hyper-complex quaternion nature of the Riemann-Sommerfeld equation and the Dirac equation. And yet you worry about imaginary gamma factors? I think that the important point is that we observe the real components of complex and hypercomplex numbers. We do not DIRECTLY observe the tachyon. It mixes eigenstates with the mu neutrino, and oscillates back and forth between unobserved scalar leptons and observed mu neutrinos.
I gotta go. My daughter needs help on her science fair project.
Have Fun!
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Jason Wolfe replied on Nov. 16, 2011 @ 02:21 GMT
Math editor got me. Try this again.
If there exists such a superluminal space-time, then you could travel at v = 100c; if c' = 10000c, then there would be very little time dilation.
The math editor is being fussy. Just replace c with c'. This allows you to avoid using tachyons.
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Jason Wolfe replied on Nov. 16, 2011 @ 02:32 GMT
Ray,
Like I said before, I like superluminal drive topics. Here are two articles that I'm looking at.
http://xxx.lanl.gov/abs/gr-qc/0107097
http://lanl.arxiv.or
g/abs/gr-qc/0202021
Imaginary numbers should really be reserved for phasors. The problem with accepting an imaginary number for gamma is that gamma is the time dilation between two observers.
If the time between two observers is imaginary, then it's unreal. I don't know how that would work.
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Ray Munroe replied on Nov. 16, 2011 @ 03:51 GMT
Hi Jason,
OK - You just subverted the entire discussion into one of scales. c vs. c' represent two different scales. That is not what I'm talking about. OPERA's result was only 25 ppm faster than c, it wasn't 100 c. Relativistic 'scalar leptons' travel slightly faster than c, which is slightly faster than relativistic neutrinos. They are just barely on opposite sides of the light cone. Now allow these eigenstates to mix: a scalar lepton, and three neutrino flavors of spin, into a quaternion-like 4x4 generalized PMNS matrix. We do not directly observe the imaginary scalar component of the quaternion. We directly observe the real spin components of the quaternion, and infer the existence of the imaginary scalar quaternion component by virtue of its FTL properties.
Have Fun!
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Jason Wolfe replied on Nov. 16, 2011 @ 04:22 GMT
Ray,
There was a rumor that the tachyonic nuetrino was caused by a delay in the GPS satellite system. Do you know if this was checked and ruled out?
Anyway, I didn't mean to subvert the conversation into one of scales.
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Paul Reed replied on Nov. 16, 2011 @ 07:49 GMT
Ray
Your post 15/11 19.44
Thanks for responding. I’ll try my best to understand it.
Blimey, not sure I want to be slapped in the face by the Riemann-Sommerfeld Equation and the Minkowski Tensor!! Don’t bother to answer it, but my original question here was really, which is reality and which is not necessarily so (ie a mathematical model).
I asked about SR, ie as opposed to GR. My view being that there is only one theory. SR represents a particular circumstance (ie special-the clue is in the title!) where the variables and their relationships are played out (eg involves only uniform rectilinear and non-rotary motion, and no gravitation force).
On the subject of c, I am just fascinated to understand how the speed of a particular particle has so much influence, apparently, in reality. It is a particle, and it travels. So what? Functionally, by virtue of evolution, it has become the means whereby we receive sight based information about reality, but that does not make it a key determinant of reality. It just means that the reality we see is what light determines it as being.
Paul
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Paul Reed replied on Nov. 16, 2011 @ 08:04 GMT
Jason
You post 16/11 00.57
Yes you could do that. But why not try the simple approach first, and disassociate light, as in its reality as an entity, from light, as in its evolutionary functional role of enabling us to see? But then I just talk philosophy don’t I, rather than simple common sense (according to some)!! Try simple first. See my response to Ray above and my other post (15/11 18.32).
Paul
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Jason Wolfe replied on Nov. 16, 2011 @ 11:45 GMT
Dear Paul,
I guess the "simple approach" depends upon who you ask. Scaling the speed of light has lots of interesting effects. It also resolves any causality problems.
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Ray Munroe replied on Nov. 16, 2011 @ 13:07 GMT
Hi Paul,
I like the acronym "KISS" - Keep It Simple Stupid! By the way, I'm not calling you 'stupid', I'm just saying that more people will understand 'simple'. Please read the paper!
OK - I'll get even more basic than the Riemann-Sommerfeld equation. Spacetime consists of three spatial vectors and one time scalar. This is a quaternion symmetry (3 vectors + 1 scalar) - it is definitely not an octonion symmetry (7 vectors + 1 scalar) - although such an octonion symmetry *MIGHT* exist in hyperspace (Garrett Lisi's E8 TOE could arise from close-packing of an octonion hyperspace, though Lisi refuses to accept such a possible reality). We directly experience the non-commutative property of quaternions in vector cross-products where A x B = -B x A (also called axial vectors or pseudo-vectors). To my knowledge, we do not directly experience the non-associative property of octonions.
Dear Jason,
I did not reference the paper that claimed OPERA had made a GPS/ Relativistic correction error. I have heard a lot of criticism against that paper - especially on Philip Gibbs' viXra blog. We need to give OPERA time to doublecheck their calculations and rerun the experiment with shorter duration neutrino bursts. Within the next couple of years, Fermilab's NOvA experiment will be up and running. Hopefully they can explore this FTL phenomenon - if it exists - and see if the FTL phenomenon depends on neutrino flavor and energy.
Have Fun!
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Paul Reed replied on Nov. 16, 2011 @ 15:01 GMT
Jason
Perhaps "scaling" has a precise meaning(?), my point was, in crude terms, forget light. It's just photons 'travelling', and they happen to enable us to see (literally). Now what are you left with, of which, obviously, photons is a part. But, once you have nullified their acquired functionality, how in reality, does this particular elementary particle have the influence on reality ascribed to it?
Ray
Will do, but granddad duties come first. Now you've used a similar phrase again, ie "we do not directly experience the non-associative property of octonions". Before it was "Regarding octonion physics, if non-associativity is part of physics, then I have accidentally over-looked it". In simple terms this means....?
Paul
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Ray Munroe replied on Nov. 16, 2011 @ 15:57 GMT
Hi Paul,
I wrote a detailed response to your questions, and then it crashed!
I stand by my statement that spacetime is quaternion. Joy is only looking at the 3-D hypersurface components of a 4-D 3-sphere. He is not looking at the radial component. Please read the first few pages of my "In Defense of Octonions" paper.
If reality is an 8-D 7-sphere, then we have 7 perpendicular spatial dimensions, and I need to patent a 7-D TV.
The associative property is A*(B*C) = (A*B)*C. This property may be violated in octonion algebra.
Have Fun!
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Paul Reed replied on Nov. 17, 2011 @ 11:30 GMT
Ray
Ha, shame. Unless it is a very simple response, I do it in Word then copy it across. But then being all philosophical what else would one expect from me???????? I will now try your paper.
Paul
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Joy Christian replied on Nov. 17, 2011 @ 11:48 GMT
Ray,
You wrote: "Joy is only looking at the 3-D hypersurface components of a 4-D 3-sphere."
This is wrong. I am saying that the 3-D hypersurface *is* a 3-sphere---i.e., our three-dimensional space has the topology of a parallelized 3-sphere. More generally, I am saying that the spatial component of the spacetime is seven-dimensional, namely a parallelized 7-sphere, and quantum correlations are the evidence that we live in such a parallelized 7-sphere. I think you have misunderstood my model in more than one way, and that may explain some of the things you have been saying about it.
Joy
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T H Ray replied on Nov. 17, 2011 @ 12:29 GMT
Ray,
I think this is a very important point that Joy makes -- at least, it is to me, because it was the first connection I made to something that I understand; I had explored those consequences of S^3 in general terms in my ICCS 2006 paper (esp. 3.2, 5.6.1 and 5.9). The more I studied Joy's research, the more deeply I understood that the constraints imposed by physical results on the equator of S^3 are consistent with the constraints imposed by the topology of S^7.
Once I grasped that point, it was easy to verify that Joy's model is time symmetric and fully relativistic. Therefore, a true counterexample to Bell-Aspect and consistent with EPR.
Tom
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Steve Dufourny replied on Nov. 17, 2011 @ 16:03 GMT
Hi all,
It is intresting but I must insist on the importance of the 3D realism. The only reality is this 3D. If you parallelize the systems in an evolutive point of vue. Of course so the superimposings must respect the distribution of reals. The realism is so a pure 3D. The computing permits to characterize the algorytms. The recursivities are essential and important. The operators of this realism must be inserted witht the biggest possible determinism. You can not have an other reality than this 3D at its present and locality.
The convergences can be compute respecting the correct distribution. So the evolution and the increasing of mass are essential also. If the volumers are not inserted in the mathematial superimposings, never the correct convergences can be reached. The properties of these superimposings are not violated, they just permit to class the evolution like with the SR.The associativity seems always a good partner ...
What do you think dear thinkers ?
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Rick Lockyer replied on Nov. 17, 2011 @ 16:07 GMT
Say hey Ray,
Read your “Defense of Octonions”. Could you explain what you mean be an algebraic basis element like i oscillating between two values? Are you conflating basis element and coefficient? The basis elements are immutable. They are hangers for the distinct coefficients of an algebraic element and are distinctly and singularly defined by the operation of multiplication.
On your complaint about non-associativity, where is the beef? There are Octonion double product terms that are associative, and those that are anti-associative. First, you should come up with a rational for something physical absolutely needing to be represented by associative math, then see if within an Octonion representation it indeed is not. Remember when you praise quaternions for their associativity yet accept non-commutivity, that Octonions admit seven quaternion sub-algebras.
The commutation and associative positions of these algebras are road signs for the observant. The order of operations is significant to full understanding of the application of these algebras to physical reality. That is why I label the details “product histories” and make a big deal about saying you can’t look at the product terms in a final result and know all you need to about what is represented. When you come to understand there are 30 aliases for fitting seven basis elements suitably in seven triplets (part of quaternion sub-algebras) and any one starts the definition of Octonion algebra, there are 480/30=16 algebraically significant different Octonion multiplication tables. None are superior to any other, so physical representations should not care which one is used. If you take the time to look at my work, I have shown all physically meaningful forms are indeed what I call “algebraic invariants”. You get the same result for all 16 algebras.
Joy,
Are you excluding the possibility of a seven dimensional manifold that admits an infinity of possible parallelizable spheres, a manifold on which a suitable tangent space forms a basis for a calculus on the manifold? Are you implying a singular sphere?
Having fun with Octonions,
Rick
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Ray Munroe replied on Nov. 17, 2011 @ 16:32 GMT
Dear Joy, Tom and Paul,
OK - It looks like our respective definitions are some of the sticking points that we have here, so I will state my interpretation of these concepts.
S^3 Euclidean space consists of 3 real spatial dimensions.
The 3-sphere is the 3-D real spatial hypersurface of a 4-D ball, but excludes the inner hypervolume of said ball.
The spacetime quaternion...
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Dear Joy, Tom and Paul,
OK - It looks like our respective definitions are some of the sticking points that we have here, so I will state my interpretation of these concepts.
S^3 Euclidean space consists of 3 real spatial dimensions.
The 3-sphere is the 3-D real spatial hypersurface of a 4-D ball, but excludes the inner hypervolume of said ball.
The spacetime quaternion consists of 3 real spatial dimensions and 1 imaginary time dimension with that relative phase of 'ict'.
Applying these concepts to a quaternion 3-sphere, the 4-D quaternion 3-sphere represents 3 real spatial dimensions with an infinitesimally thin radial shell that corresponds with the present time. Time exists as the 4th dimension of that 3-sphere only for the 'present'. We can model ever-changing time as an ever-expanding (the radial component is equal to 'ict' and is always increasing) 3-sphere. For those people who doubt the reality of time as a 4th dimension, this model allows time to exist as a 4th dimension for 'now', but then yesterday disappears into a fog of memories and tomorrow hasn't yet been written. Our 'time-vision' is extremely 'near-sighted' (Can LASIK surgery correct that type of 'myopia'?).
Close-packing of 3-spheres leads to a 4-D 24-cell lattice with 5-fold symmetric pentachoron basis vectors (this symmetry is important to Table 2 of my latest paper), that may be represented by the F4 Lie Algebra.
Similar ideas may be applied to an octonion 7-sphere. Now the hypersurface consists of 7 real spatial dimensions (where is the remote control for my 7-D TV?), and the implied radius may be modelled as an ever-expanding time 'ict'.
Close-packing of 7-spheres leads to a 8-D Gosset lattice that may be represented by the E8 Lie Algebra. If the 7-sphere is stable, then this E8 lattice and algebra may help reinforce the fundamental usefulness of Garrett Lisi's E8 TOE (but recall that E8 does not contain complex representations, and cannot represent CP violation, so it can only be part of a TOE).
Then Joy sets the quaternion 3-sphere and the octonion 7-sphere equal to unit radius. This is equivalent to setting the different hyper-spheres to equal time (because radius equals 'ict'). I think that this may be true for one given moment in time, but I'm not sure that this is true for every given moment in time (or more specifically, 'history' represents the collection of 'present' times in proper sequence, and this equality needs to hold for each and every value of the 'present' time).
As such, I think that Joy's model represents 'frozen time' or 'reversible time', but does not contain entropy as a fundamental property. Because his model lacks certain thermodynamic properties, he does not yet realize that maximum hypervolume and minimum Enthalpy for the 5-ball combined with maximum hypersurface area and maximum Entropy for the 6-sphere causes a fundamental Thermo-geometric instability of this 7-sphere that we all love so much.
That is the way I see it. If it helps any of you, then that is good. If you disagree with these points, then we will probably always disagree.
Have Fun!
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Ray Munroe replied on Nov. 17, 2011 @ 17:00 GMT
Hi Rick,
Jonathan wrote that sentence. I thought he was talking about 'i' representing oscillatory systems, but we might have to ask him personally.
Anti-commutativity arises in the vector cross-products of Electromagnetism.
Do you have a good physical example for anti-associativity? I'm not opposed to octonions (that paper was "In Defense of Octonions") - I just think that quaternions may be more stable, and may more-closely represent reality.
Hi Steve,
I know that you are more comfortable with an S^3 Euclidean space (no spacetime quaternion 3-sphere, no octonion 7-sphere,...), but you model 'change in time' as rotating 3-D 3-balls (I know you call them 'spheres', but mathematicians are talking about the n-D hypersurface shell surrounding an (n+1)-D solid ball when they use the term 'n-sphere'). Does your model include entropy?
Have Fun!
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T H Ray replied on Nov. 17, 2011 @ 17:26 GMT
Hi Ray,
I don't find Joy's model that complicated. In fact, I think Lawrence's criticism that the framework suffers from the "combining of (mathematical methods)" is a strength rather than a liability, and it also helps obviate your more serious concerns:
You wrote, " ... Joy sets the quaternion 3-sphere and the octonion 7-sphere equal to unit radius. This is equivalent to setting the different hyper-spheres to equal time (because radius equals 'ict'). I think that this may be true for one given moment in time, but I'm not sure that this is true for every given moment in time (or more specifically, 'history' represents the collection of 'present' times in proper sequence, and this equality needs to hold for each and every value of the 'present' time)."
Joy has no need to even mention time (and doesn't IIRC) because the whole dynamic system is fully relativistic. This means that classical time-reverse symmetry is the only property of time required, and that is already built into the structure, because every point is a 3-sphere (I discuss this in my ICCS 2006 paper, as well as the significance of the hypersphere metric you mention above).
In a 2-dimension analog, my "Ferryman diagram," that (M) can occupy any point of n-space means that observed states become time-dependent by mere choice of initial condition within the parallelized S^3 topology, and one need not again refer to time, only to observed states and the statistical inferences -- which are determined, not probabilistic -- that one can make from those observations.
You wrote, "As such, I think that Joy's model represents 'frozen time' or 'reversible time', but does not contain entropy as a fundamental property. Because his model lacks certain thermodynamic properties, he does not yet realize that maximum hypervolume and minimum Enthalpy for the 5-ball combined with maximum hypersurface area and maximum Entropy for the 6-sphere causes a fundamental Thermo-geometric instability of this 7-sphere that we all love so much."
Entropy may be formulated for open, as well as closed systems. Because Joy's model has implications for the cosmological initial condition (one of the first and most exciting potential results that I noticed from it), current evidence for a universe expanding on the border between open and closed strongly supports Joy's model, which also has the potential to solve the cosmological horizon problem without ad hoc assumptions.
I don't want to overstate the case -- I just want to note that Joy's mathematical completeness makes obvious that those concerns are considered and disposed of. At least, formalistically.
Tom
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Steve Dufourny replied on Nov. 17, 2011 @ 18:56 GMT
Hi Ray, you know what I think about this entropy.I have explained that it was the entire energy of our universe. We could nourrish our planet with 1 water drop during a long long time. It exists the maximum entropy in all. The fields and the time are correlated. The evolution of mass and its increasing become eseentials. Ray, I have explained also what are the uniquness and what are my rotating spheres and what are my 3 equations .The rotating 3D spheres answer to all, you know it. The changement of words shall not change several evidences. When I have knew Fqxi of course noboby spoke about spheres or balls(don't forget that I have explained also what are the entangled spheres and what are their proportions and what are their finite serie with the correlated wvolumes, I have also explained what is an incompressible sphere like a liquid.I have explained also what is the finite serie and the decreasing of volumes correlated with the cosmological number....).
I am not against the fact that people spoke about my works, but you must understand that these 3 equations and the gauge of rotating spheres, balls if you prefer and the universal 3D sphere are from my theory.
What do you think about these 3 equations Ray?
E=(c³o³s³)m
F=S s1s2/r²
mcosV=Constant for all physical 3D spheres, quant. or cosmological.
You shall understand that the finite serie for the number of uniqueness is very important. So the realism and the determinism must be inserted with the biggest rationality. That's why a model must be realistic and purely objective respecting the proportions with the rotating spheres or balls if you prefer, in all case the sphere is like an incompressible liquid, coded . What I find fascinating is the fact that the central sphere is the biggest volume. Like for our cosmological fractal and its serie of uniqueness. The rotating spining spheres are universal in fact. Their rotations are proportional with mass..., and m and hv are differenciated by a different sense of rotation. That explains the polarization fermions/bosons.
What do you think about these equations ?
Best Regards
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Ray Munroe replied on Nov. 17, 2011 @ 19:07 GMT
Hi Tom,
You said "Joy has no need to even mention time (and doesn't IIRC) because the whole dynamic system is fully relativistic".
The 3-sphere occupies 4-dimensions. How does Joy define his 4th dimension? Omission is not a definition. Of course, a 4-D quaternion spacetime is fully relativistic because it contains the Minkowski metric (-1,+1,+1,+1), but it also has a time-like dimension (with that radical 'ict' phase) that you and Joy keep side-stepping in your (lack of complete) definitions.
You also said "This means that classical time-reverse symmetry is the only property of time required". I guess you didn't like the way I stated this as "As such, I think that Joy's model represents 'frozen time' or 'reversible time', but does not contain entropy as a fundamental property" because I emphasized the point that Joy's model is unrealistic in the fact that it does not consider the Second Law of Thermodynamics.
I think that the crux of our disagreement boils down to properties of time - whether those properties are of a Relativistic and/or Thermodynamic nature.
You also said "Because Joy's model has implications for the cosmological initial condition (one of the first and most exciting potential results that I noticed from it), current evidence for a universe expanding on the border between open and closed strongly supports Joy's model, which also has the potential to solve the cosmological horizon problem without ad hoc assumptions." I see similar potential in this model IF WE RECOGNIZE THAT TIME (technically the imaginary phase 'ict') AND RADIUS ARE EQUIVALENT.
Have Fun!
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Joy Christian replied on Nov. 17, 2011 @ 21:23 GMT
Rick,
You asked: "Are you excluding the possibility of a seven dimensional manifold that admits an infinity of possible parallelizable spheres, a manifold on which a suitable tangent space forms a basis for a calculus on the manifold? Are you implying a singular sphere?"
Yes, I am implying a singular 7-sphere (taken as a space-like hypersurface). I am not sure whether my analysis can go through for a seven dimensional manifold that admits infinitely many parallelizable spheres. The crucial property I need to respect Bell's locality condition is the property of closedness under multiplication. Only the four parallelized spheres have this property. S^0 and S^1 are no good, because they lack torsion, and hence are incapable of reproducing the strong quantum correlations. That leaves S^3 and S^7. But S^3 is good enough only for simple quantum systems, like two-level systems. I am thus left with a singular S^7. It has all the properties I need to reproduce any quantum correlation while respecting local causality.
Joy
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T H Ray replied on Nov. 18, 2011 @ 00:11 GMT
Hello Ray,
No time right now to be detailed, but we're not sidestepping anything. Geometric algebra (spacetime algebra) translates smoothly to Minkowski tensor metric analysis. It must, for Joy's framework to be fully relativistic.
Tom
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Ray Munroe replied on Nov. 18, 2011 @ 01:17 GMT
Hi Tom,
You said "Geometric algebra (spacetime algebra) translates smoothly to Minkowski tensor metric analysis. It must, for Joy's framework to be fully relativistic."
Yes - Quaternion 3-sphere Geometric Algebra DOES translate to the Minkowski metric algebra IF the fourth dimension (of the 4-D 3-sphere) is equated with 'ict' time.
Do you purposely choose not to talk about the imaginary phase of time-like dimensions? Do you purposely choose not to define all relevant concepts?
Inconsistencies in the treatment of time are the easiest way to introduce complex phases here. In fact, the Kramers-Kronig relation basically says that dispersion of energy (the property of entropy) may be mathematically treated with imaginary phases.
Have Fun!
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Rick Lockyer replied on Nov. 18, 2011 @ 08:11 GMT
Ray,
You asked:
Do you have a good physical example for anti-associativity?
The Octonion 8-current is an algebraic invariant derived from the sum of four dual products, two full Octonion differential operator multiplications on the Octonion potential function. All four have both associative and anti-associative components if you were to modify the order of application.
The requirement is to craft algebraic expressions from full Octonion forms. This places all multiplication rules in play. These rules and the product histories determine algebraic invariant and variant partitioning of the results. This is what is important. Commutation and associativity characteristics just happen in the process. Along with conjugation, they can be useful tools in writing full Octonion expressions that reduce to desired results.
If one were to look at the final summed invariant 8-current result, the product terms in each of the four dual products that would change sign for the alternate application order have all been removed in the sum. The desired result is an algebraic invariant, and these terms would be algebraic variants.
So although there is no demand here for non-associativity, there is no difficulty presented and hence no issue using a non-associative algebra. There is no reason to seek a justification for using Octonion Algebra by finding a physical need for non-associativity.
Rick
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Paul Reed replied on Nov. 18, 2011 @ 11:13 GMT
Ray
Your post 17/11 16.32
Now I have not had time to read your paper (school play, buying Barry Manilow tickets-just don’t say a word!), but I know I will not understand the maths, per se.
However, maybe the key to this is in time, given what you are saying in that post?
There are two important concepts in respect of time: a) what it is, b) how that relates to the...
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Ray
Your post 17/11 16.32
Now I have not had time to read your paper (school play, buying Barry Manilow tickets-just don’t say a word!), but I know I will not understand the maths, per se.
However, maybe the key to this is in time, given what you are saying in that post?
There are two important concepts in respect of time: a) what it is, b) how that relates to the fundamental form of our reality and how we are aware of that. Before addressing this in a few paragraphs, I would ask that people accept it is not philosophy.
What is referred to as time is a conceptualisation of an inherent quality of reality, which is change, and the frequency thereof. It is not time, but change, that we are experiencing. Reality (a spatial construct) is changing. Change does not necessitate ‘space or value’, in the sense that only one existent state, in any given change sequence in respect of any given entity, can exist at a time.
Change involves:
- sequence, which is a number of discrete states in a specific order
- frequency, the speed at which any given state replaces its predecessor
From the elementary particle perspective, entities are changing at every point in time. But that level of detail, ie reality is ultimately ‘elementary particles moving’, does not aid in the understanding of most change processes. So, any given sequence of change is decomposed to an appropriate level; an accurate, but conceptualised perspective of reality. At that level of definition, the frequency of change varies, and the same entity may be considered in terms of a number of different attributes (ie change sequences).
Every change sequence has an intrinsic frequency of change, a duration between the existence of each successive state, which could vary in any permutation. So, there is a duration for each state in a sequence of change, and therefore, by definition, there is a duration for the entire sequence to occur (ie the sum of the individual durations).
We have created a change duration measuring system, known as time. It enables the quantification of rates of change, or comparison of disparate sequences of change, in terms of a common denominator, which is, of itself, irrelevant. Logically, the best unit for this system would be the quickest, non-variable, example of change in reality.
In sum, had time been understood at the outset, the concept would not have been invented, and consideration would revolve around change sequences in terms of change units. It is timing, not time. We are comparing, and identifying differences, in the frequency of change, in any given change sequence for any given entity.
This then needs to be overlaid onto the fundamental constitution of reality, which is: 1) existent state, 2) existent representation of (1) which organisms can sense, 3) receipt of (2) by organism, 4) processing of that received information. The point being that there are different existent time-lines for any given existent state (apart from the fact that what we receive is an independently existent representation). Timing can be effected within each of these continua, or across them.
Because there is a disconnect between actuality and what we receive as being a representation of it. In the context of timing, it is not only important to recognise this differentiation, in itself, but also to recognise the capability of the medium involved in gathering and conveying this information. So, in terms of experience, both the maximum number of states and the fastest rate of change potentially experienceable, is a function of the maximum frequency with which the medium conveying the information to us is able to differentiate them. This could differ from what actually exists, but should be inferable.
Furthermore, if the medium transmitting the experienceable state has a constancy of movement, (which as a minimum means that it takes a very similar duration to travel on each occasion, at least during the occurrence of the sequence being experienced), then any sequence of change will inevitably be perceived as one directional, and in the sequence in which it actually occurred. Whilst the apparent frequency of change experienced, will depend on the relative spatial position (caused by relative movement) of the entities and observers involved.
Paul
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T H Ray replied on Nov. 18, 2011 @ 12:06 GMT
Hi Ray,
I think you are assigning unnecessary properties to time. Remember, Joy's framework is coordinate free.
You ask, "Do you purposely choose not to talk about the imaginary phase of time-like dimensions? Do you purposely choose not to define all relevant concepts?"
In a time-dependent, relativistic, continuous function model, spacetime is implicitly defined in relation to events. In other words, field properties are fully integrated with particle properties (cf Higgs field)such that time symmetry guarantees chirality between events without singularity and without assuming nonlocality -- the built-in torsion "twist" structure is independent of scale, so that choice of initial condition guarantees quantum correlations to infinity (and resolves the conflict between Bose and Fermi statistics). All of this actually follows from Einstein's description of spacetime geometry; the critical elimination of singularity plus more sophisticated technigues in vector analysis and topology complete Einstein's program (developments that Einstein himself predicted).
You wrote, "Inconsistencies in the treatment of time are the easiest way to introduce complex phases here. In fact, the Kramers-Kronig relation basically says that dispersion of energy (the property of entropy) may be mathematically treated with imaginary phases."
Again, the properties you assign to time are not relevant to a time-dependent scale-invariant dynamic system in a simply connected space. If you examine it closely, you will find that the space of every quantum-mechanical description of entropy (and every description in fact, must be quantum mechanical, following from statistical mechanics) is multiply connected (i.e., begs probabilistic statistics). No such discontinuity applies to Joy's framework, where hidden variables are local and continuous variations in the trajectories of correlated events. As I said or implied earlier, entropy does not prevent a problem for a time dependent, time symmetric, scale invariant model.
Ray, thank you for asking the important questions!
Tom
(PS to the adminstrators -- and thank you for taking steps to combat the spam bot vandalism of this site!)
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Joy Christian replied on Nov. 18, 2011 @ 12:50 GMT
Hi Ray,
I am afraid you have got my picture all wrong. In my picture the parallelized 7-sphere represents a real spacelike hypersurface. Unlike you, I am not identifying the scalar component of my quaternion (or octonion) with time. I do set the radii of the quaternion 3-sphere (or octonion 7-sphere) equal to unity, but that has nothing whatsoever to do with time. Moreover, as I have explained before, I am not concerned about signalling or relativistic non-locality but only about no-signalling or quantum non-locality. As Bell explains in his last paper (which I have linked in the introduction of this blog), the latter non-locality can be analyzed by considering spacelike separated regions at equal times. Unlike in the case of possible relativistic non-locality, the concerns of Bell and mine have nothing to do with time or duration per se, because the correlations we are trying to analyze are correlations between objects at a given fixed time. The only difference between Bell's analysis and mine (for the simple case of EPR-Bohm correlation) is that he implicitly uses a non-compact 3-space in his analysis, whereas I use a compact 3-space (namely, a parallelized 3-sphere) in my analysis. All the other concerns you raise (such as entropy, enthalpy, thermodynamic stability, etc. etc.), are at best conceptually tangential to my main concerns, and at worse mathematically irrelevant to my proposed picture. I think you are trying to compare your apples with my oranges simply because they both happen to be delicious fruits.
Joy
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Ray Munroe replied on Nov. 18, 2011 @ 15:27 GMT
Hi Joy,
Apples and Oranges? OK - Let me get back to your model. The 3-sphere is the infinitesimally thin outer shell of a 4-ball. I realize that the 3-sphere hypersurface itself only contains 3 dimensions, but it definitely implies a 4th radial dimension. In quaternion spacetime, this 4th dimension is time with an imaginary phase 'ict'. Your model is concerned with 'local' vs. 'non-local'...
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Hi Joy,
Apples and Oranges? OK - Let me get back to your model. The 3-sphere is the infinitesimally thin outer shell of a 4-ball. I realize that the 3-sphere hypersurface itself only contains 3 dimensions, but it definitely implies a 4th radial dimension. In quaternion spacetime, this 4th dimension is time with an imaginary phase 'ict'. Your model is concerned with 'local' vs. 'non-local' reality. Perhaps it is legitimate for you to set both the 3-sphere and 7-sphere radii equal to the same value (I'm not certain about unity, but that is another detail) because it sets equal time and helps define 'here and now' so that we may define 'local' vs. 'non-local' reality.
I really don't know why you and Tom refuse to address the 4th dimension. This could be an important insight into understanding time.
You commented on how octonion 7-spheres provide a torsional twist that your model requires. This is very interesting, because my latest TOE model requires a minimum of 7-D to define 'scalar leptons' that have this weird higher-dimensional 'twist'(Equation 6 in my latest paper). My 'twist' unifies fermionic and bosonic properties.
Hi Tom,
You talked about unifying fermions and bosons, and I think that this is one level of requirement for a TOE. However, the generalized union of Fermi and Bose statistics seems to lead to Anyonic statistics. And this seems to introduce tachyons. And tachyons are the most non-local entity that I can imagine. I think that tardyons are relatively localized energy that provide 'cause', and tachyons are relatively non-localized energy that provide 'entanglement'.
Hi Rick,
I know that we can write any of these equations in quaternion or octonion formalism. My question is whether such formalism leads to noticeable simplifications that would expose the 'fundamental' need for such formalism. One example is the Riemann-Sommerfeld equation. This one quaternion equation contains two of Maxwell's equations (Gauss' Law for electricity and Ampere's Law), and justifies its utility as a more generalized, more compact formalism.
Joy needs a torsional twist from octonions. Perhaps this requires an octonion physics effect that we do not yet understand.
Hi Paul,
Barry Manilow tickets? Did your wife/ girlfriend corner you, or did you lose a bet? I went to a Larry the Cable Guy concert last month because my wife bought the tickets, and it was easier to go to the concert than to argue about it. I really think that Larry's old TV stand-up routines are funnier than his new stuff, but we have to keep the ladies in our lives happy!
Regarding 'change' - Newton invented Calculus so that he could properly define 'change'. It just so happens that acceleration is the second derivative of position with respect to time, and concepts of time pre-existed Newton. If you are trying to define a new concept, it is only natural to define it in terms of familiar concepts.
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T H Ray replied on Nov. 18, 2011 @ 17:19 GMT
Hi Ray,
You wrote, "I really don't know why you and Tom refuse to address the 4th dimension. This could be an important insight into understanding time."
It just isn't necessary, Ray. Let me try something else -- you being a fellow Southerner, perhaps you play a string instrument. You know, then, that there are guitars and basses that unlike conventional instruments are not equipped with frets; they have a plain fretboard like a violin, upright bass or Hawaiian guitar. Suppose we called frets by the name "coordinates." Then it would have meaning to speak of the fourth fret or the twelfth fret to identify a location, just as it has meaning in coordinate geometry to speak of a time coordinate, or time as the "fourth" dimension, in a system of spacetime coordinates.
In a coordinate free system, however, we can play the same notes and chords without any such reference (indeed, we can like Leo Kottke, make beautiful music without ever pressing the strings to the fretboard at all). In fact, a little reflection will inform one that absence of coordinate geometry is an absolute requirement for local realism. The problem of getting across his ideas in an unfamiliar mathematical language has dogged Joy's efforts from the beginning -- however, the mathematics lives in a completely self-consistent classical logic.
You said, "You (Tom) talked about unifying fermions and bosons, and I think that this is one level of requirement for a TOE. However, the generalized union of Fermi and Bose statistics seems to lead to Anyonic statistics. And this seems to introduce tachyons. And tachyons are the most non-local entity that I can imagine. I think that tardyons are relatively localized energy that provide 'cause', and tachyons are relatively non-localized energy that provide 'entanglement'."
Tachyons aren't physical. They are a necessary symmetry in relativistic particle physics, a theory artifact, just like time-reverse symmetry in classical physics. The unification of Bose-Einstein and Fermi-Dirac statistics that I was talking about is a field unity, as in quantum field theory and topological quantum field theory.
Tom
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Joy Christian replied on Nov. 18, 2011 @ 17:32 GMT
Hi Ray,
Forget apples and oranges. Be happy. OPERA collaboration has confirmed their results. You are a step closer to being right.
I nevertheless continue to disagree with you about your interpretation of my picture. I am happy with the 4th (or 8th) dimension representing time. But I am not happy with that dimension being radial to my spheres. Because that would lead to spheres growing in time and consequently quantum correlations changing with time. This is contrary to what is observed in experiments (at least in cases like the EPR correlation). So, I prefer to keep the radii fixed and time represented non-radially. The 3-sphere and 7-sphere of my picture need not have either unit radii or the same radii, but whatever they are they better not change with time.
Concerning the torsional twist, have you read
this paper of mine? It explicitly shows that quantum correlations are nothing but manifestations of the torsion within the 7-sphere.
Joy
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Paul Reed replied on Nov. 18, 2011 @ 18:03 GMT
Ray
Your post 18/11 15.27
One has to respect other people’s musical tastes-on occasions!
You say: “I really don't know why you and Tom refuse to address the 4th dimension. This could be an important insight into understanding time”. Watching these exchanges I thought so too. Hence my post of 18/11 11.13.
Now I could be wrong, but in all the times I have said that, nobody has come back at me and indicated that they really understood what was being said, and then a comment based on that understanding as to whether it was right or wrong.
I am saying time does not exist. Frequency of change in anything and everything does. That means, what is misconceived as time is change, and that only proceeds in one direction, and has a definitive grounding (ie it is not a ‘dimension’), it is a real effect in any given entity. We can compare change, or quantify the frequency thereof, via our measuring system (known as time), but this is timing. In doing that we are just comparing frequencies of change and identifying differences.
Paul
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John Merryman replied on Nov. 18, 2011 @ 18:10 GMT
The time radii expanding, relative to the spatial dimensions? Maybe the space is shrinking relative to the present time, events falling into the past... Or they exist in some larger cycle of actual physical processes where these two mathematical constructs represent opposite sides of the dynamic process?
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Rick Lockyer replied on Nov. 18, 2011 @ 18:30 GMT
Ray,
"Simplification" does not imply a reduction in dimension. Electrodynamics is only part of the issue. There is gravity. Sticking to 4D, which was an increase in dimensional expectations last century, forced the complexity of needing to tensorize the E-B fields, and go someplace else to explain gravity.
With an Octonion approach to Electrodynamics, you have the simplification of flat rank approach, and gain gravity back to a potential theory approach fully coexistent with the EM fields. This happens because you now have sufficient dimensions in your approach to span the space.
The magnetic and gravitational field sit inside the same quaternion sub-algebra of the Octonions. The three electric field components do not exist inside a quaternion sub-algebra. This allows the electric field to have its noticeable characteristics that are distinct from the other central force.
More dimensions - simpler.
Rick
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Ray Munroe replied on Nov. 18, 2011 @ 19:01 GMT
Dear Friends,
It seems that I stirred up some conversation about time and music.
Joy - In relativity, time has that imaginary phase relative to space that would make it 'perpendicular' - at least in the Argand plane. I think you can justify equal radii by saying that 'local' measurements are made at simultaneous times.
Tom - I liked your analogy to stringed instruments. Yes, I play a little bit of guitar, but made a choice years ago to spend more time on my physics than my music. I understand that the 3-sphere doesn't NEED the 4th dimension to be defined. I just think it helps to put a reasonable physical analogy with every part of the model.
Paul - Ooops! Sorry if I insulted your choice of music. I would go to a Barry Manilow concert if my wife made me go, or if he was performing a free concert in my back yard, but probably not otherwise.
In my interpretation of this quaternion 3-sphere model, time exists as the 4th dimension only for 'now'. The analogy is that the 3-sphere is the 3-D infinitesimally thin spherical shell of the 4-D 4-ball. This infinitesimally thin radius corresponds to 'now'. We have natural change intervals when we progress from this 'now' to that 'now'.
John - The range of possible radii is from zero to positive infinity. We could start at zero and count up, or we could start at infinity and count down. Based on our assumptions of the Big Bang and an expanding Universe, I think it makes more sense to count up. If we knew that our Universe was contracting and didn't have an idea of the age of the Universe, it might make sense to count down (to the Big Crunch).
Have Fun!
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Ray Munroe replied on Nov. 18, 2011 @ 19:20 GMT
Hi Rick,
I was composing my responses to the others while you were writing me.
I realize that any union of EM and Gravity must involve more than one 4-D quaternion. My latest paper proposes a minimum 10-D TOE. All I'm saying is that Cayley-Dickson construction allows us to write 8-D as octonions OR as a complex pair of quaternions. If we have a clear physical need for the anti-associative property, then we should use octonions. Otherwise, the question of whether Nature is naturally quaternion pairs vs. octonions remains open. In my TOE model, I might have a quaternion of Electro-Color combining (weakly) with a quaternion of Gravi-Weak into an octonion of Electro-Color-Gravi-Weak that then combines with a G2 of Generations.
Hi Joy - I'm sorry. I forgot to comment on that 23 page paper. I'm not sure that my brain can handle it. Maybe I'll start bleeding at the ears before my brain actually explodes. Equation 99 uses SO(8), SO(7) and G2. I have used SO(8) and G2 a lot in my models. I have doubts about the usefulness of SO(7) or Spin(7).
Have Fun!
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John Merryman replied on Nov. 19, 2011 @ 03:04 GMT
Ray,
I realize I'm working with a limited data set here, but since you do take the effort to reply forthrightly, I would like to lay out the situation as I see it.
According to both theory and observation, space is flat. Gravitational contraction and spatial expansion are inversely proportional. While there are any number of theories and partial observations which tend to emphasize expansion, the simple fact is that they are as closely balanced as we can measure.
So space is collapsing in those gravitational fields, according to Einstein. And it is expanding between the gravity fields.
Einstein felt it necessary to describe a stable universe, so he added the cosmological constant, which was dismissed, but now that the rate of expansion doesn't match an even decline from the most distant sources, but appears to have a natural expansion, it has been revived.
Now just suppose, for a few moments, that photons are not always point particles, but expand to fill space and contract when contacting mass. This might also explain the two slit experiment, as the light ripples through the slits, but collapses to a point on contact with the surface of the detector. This way, the light would be the medium and the waves, as well as the particle manifestations, would be the disturbances to this expanding field. Since the only way we can measure or otherwise experience light is to disturb it, it is the wave and particle manifestations we can measure, thus partially or completely collapsing this energy into structure/information/mass.
In this way, expansion is as much a function of radiation, as gravity is a function of mass.
So energy is always expanding out, while mass and its quantifiable features are always contracting in.
Thus that Einsteinian three dimensional space/measurable events is contracting in, as the fourth dimension of present energy/light expands out.
On the other hand, the current model requires some enormous patches, from inflation to dark energy.
Okay, you can push the reset button now and go back to the standard model, but I just wanted to explain how I'm seeing this relationship of energy expanding out, constantly creating and growing new structures, as these structures first expand energetically, but eventually lose more energy than they gain, becoming rigid structures before completely collapsing into the final malstrom and radiating away all remaining energy. So that relativistic balance between collapse and expansion, as structure goes future to past, while energy goes past to future.
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Paul Reed replied on Nov. 19, 2011 @ 07:43 GMT
Ray
Your post 18/11 19.01
Your assumption about another liking Barry Manilow was correct, he looked to me like someone who had escaped from the morgue last time I saw him on TV!
“In relativity, time has that imaginary phase relative to space that would make it 'perpendicular'”. At the risk of stirring up another hornet’s nest, is this true? Or, is it true that what is really driving the Theory of Relativity is a presumed change in length dimension (ie only one-dimensional effect) which occurs when a force (eg gravity) is applied which also changes momentum (velocity and direction)? Time, as in timing, is just a consequence. That is, in this somewhat elastic/amorphous world, stuff is not quite where you would expect it to be (which includes light which is equally affected), and hence timing will be out unless the effect of dimension alteration is factored in to the calculations. But the ‘dimension alteration’ effect (which was deemed to be real) was somewhat forgotten about in the explanation of the theory, and time (which was really just timing) reified. In effect, the latter became a surrogate for the former.
“In my interpretation of this quaternion 3-sphere model, time exists as the 4th dimension only for 'now'”. Ok, but for now anyway, all I can do is reiterate that the representation of ‘time’ must be in terms of change to an n spatial dimension world. Because ‘time’ is purely a measuring system, a human conception. What is actually happening, and therefore must be represented in any model, is change (which has a frequency) in any entity in respect of any given attribute (eg movement, texture, brightness, etc). Though at the elementary particle level it is fundamentally about movement.
I am speaking out of turn (in that I do not, and probably never will, understand the maths, per se), but even “infinitesimally thin” worries me. Because it is still ‘there’. Whereas, in reality, it is not there at all. What exists are entities (be they electrons or elephants) which are changing, one existent state, at a time, at varying frequencies. There is no 'hiding' behind some concepualisation of time, any model can only have a representation of entities (with spatial dimension) changing.
Paul
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Ray Munroe replied on Nov. 19, 2011 @ 16:01 GMT
Dear John,
I really don't have a problem with most of Einstein's ideas. A 100+ years of data have mostly seemed to confirm his ideas.
A couple of points with which I do have problems:
1) the Cosmological Constant is a 'fudge factor', IMHO. In my book, I used Variable Coupling Theory to describe 'Dark Energy' in terms of force strengths that have varied - in conjunction - over the history of our Universe. IF the Cosmological Constant really does exist, its incredibly small size of 10^(-123) might imply 'cross talk' from a larger scale, AND its repulsive nature might imply a fifth force that is related to gravity.
2) OPERA's recent result implied FTL travel. This is not allowed within the framework of Relativity but, if anything were to trump Relativity, it would be something like Quantum Gravity.
By the way, I studied the Standard Model in detail as a grad student and think it is too ugly to be the 'truth'. Not every Physics PhD drinks the 'Kool-Aid' - some (most?) of us question the 'system' our entire lives. Please read my latest paper. My description of 'superluminal' neutrinos also includes a TOE that contains the Standard Model as a sub-component, but also explains other symmetries that haven't been well-explained in my opinion (such as why are there three generations?).
Dear Paul,
I know that in Newton's Classical physics, time is introduced as change (dt), and your observations could be a correct interpretation of that part of theory. But then Einstein's Relativity introduces concepts such as time dilation that - IMO - pretty much imply that time is a fourth dimension.
I'm slightly far-sighted (I use cheapo reading glasses when working at the computer, but not when I drive), and can see spatial distances very well. But our 'time vision' is very near-sighted. We 'see' and experience now. We do not 'see' tomorrow (hopefully, it hasn't yet been written), and we do not 'see' yesterday (although we may have memories of it).
I have always been one of those who considered time as the fourth dimension. This concept works very well with Quaternion math-physics. But time is clearly different from space. Perhaps the difference is that it only exists momentarily? I think that this interpretation is fully-consistent with the quaternion 3-sphere that is part of Joy's framework.
Have Fun!
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Paul Reed replied on Nov. 19, 2011 @ 17:04 GMT
Ray
I effectively referred to 'time-dilation' above, see 'hornet's nest' para. What I will do is start another thread on that, so that this one does not go 'off-topic'. And perhaps another one on 'seeing' and past/present/future, though I did post some stuff at the end of ths Topic in response to Frank.
She who likes B Manilow, has been otherwise engaged, so I've had some time to look at the maths. Obviously I cannot comment on it as such, which has never been my point in respect of Joy's framework/model, but here are some thoughts.As they are general they are not directed at your particular view, you just happen to be the addressee.
Maths
My overriding thought is that this maths is seen as being a proper representation of reality, and hence outcomes occur in reality. As opposed to, this maths works to solve a particular problem, as defined. Now, whether one can achieve the latter whilst not fulfilling the former is another issue.
1 There is an assumption along the lines that, since this maths is ‘pure’ ( eg commutativity and associativity are removed), then reality must have developed/ be constituted in accord with these rules. The reaction to that being, unless independently proven otherwise, that cannot be presumed. And a more pragmatic reaction would be, why should reality be so ‘pure’ in its form. It is ‘something’, and hence could be ‘not pure’.
2 The maths is able to model oscillatory systems. But waves are irrelevant, in the following sense. Whether ‘it’ (whatever ‘it’ is) moves, of itself, in some wave-like manner, or ‘it’ is effectively transferred by a chain reaction across something else, in a wave-like manner, that involves movement, ie more than one occurrence. In other words, there has been elapsed time, ie more than one existent state-something has changed.
In any measuring system, the base unit should be that which is indivisible, given the attribute as it occurs in the given reality being considered. By definition then, a unit of time, must be that within which no change whatsoever occurs. So existence must be that which is occurring at any given point in time. In respect of any given sequence of change for any given entity, any existent state of that sequence can only exist one at a time.
3 The above is a specific circumstance of the more general point already made. We only have entities which have n spatial dimensions. These entities change. At a frequency. In respect of a variety of attributes. We can measure this frequency of change in respect of one attribute, or a number of, for one entity. Or compare different frequencies manifest in different entities in respect of the same attribute, or compare different attributes in different entities. Timing is about the comparison of frequencies of change. Timing (aka time) must not be modelled as anything else, particularly in any way reified as a ‘dimension’.
Paul
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John Merryman replied on Nov. 19, 2011 @ 17:16 GMT
Ray,
Yes, the cosmological constant is a fudge factor, with the very specific purpose of balancing the effect of gravity on a universal scale, in order to maintain a stable universe. Consider that when Eddington verified relativity, he did so by measuring the degree stars appeared to move, as their light was bent by the sun. Did those stars actually move? Of course not! When we measure the light from distant galaxies as being redshifted, does it really mean those galaxies are actually moving away from us, or is it an optical effect, similar to the bending of that starlight?
Consider that we appear to be at the exact center of this expansion. In order to explain it in terms of an expanding universe, there are two choices; Either we are at the virtual center of the entire universe, or space is expanding in such a way as that every point appears as the center. I do feel this possibility is enormously complicated by the fact that we still assume a stable speed of light. Such that were the universe to double in size, two galaxies x lightyears apart would presumably be 2x lightyears apart. How can it be argued that the very fabric of space is expanding, when this most fundamental measure of intergalactic distances is presumed to remain stable?
On the other hand, if this redshift is due to optical effects, then it makes a lot of sense that redshift is proportional to distance and there are not commensurate lateral motions.
So why is it that we insist redshift can only be a function of the actual recession of other galaxies, when the resulting theory requires so many fantastical patches, from inflation to dark energy?
Because we treat light as a physical particle and the only other way to explain how it could be redshifted is if its passage were otherwise interfered with, ie, tired light. The reason we know it is a particle is because it interacts with our measuring devices as a particle and the only other measure we have suggests a wave, but there is no medium to transmit this wave.
If you don't like my idea of light as the medium, while the particle and wave characteristics are effects of interference, consider this idea for explaining redshift. It actually works on the same underlaying principle, that the quanta of light mass absorbs is a sampling of the entire spectrum, not just a bunch of single spectrum photons:
http://www.fqxi.org/data/forum-attachments/2008CChri
stov_WaveMotion_45_154_EvolutionWavePackets.pdf
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Ray Munroe replied on Nov. 19, 2011 @ 18:26 GMT
Dear Paul,
We use math to model reality. My goal is to model a TOE. In this goal, I started with Electro-Weak Theory, and progressed to the Standard Model, Georgi-Glashow SU(5), Georgi SO(10)/ Spin(10), and Supersymmetric extensions of those models. The only one of those models that even comes close to explaining 3 generations of matter is SO(10)/ Spin(10), and that may just be coincidence....
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Dear Paul,
We use math to model reality. My goal is to model a TOE. In this goal, I started with Electro-Weak Theory, and progressed to the Standard Model, Georgi-Glashow SU(5), Georgi SO(10)/ Spin(10), and Supersymmetric extensions of those models. The only one of those models that even comes close to explaining 3 generations of matter is SO(10)/ Spin(10), and that may just be coincidence. In my book, I explored ideas such as SU(7) and SU(11)~SO(16). In fact, I still keep going back to variants of SU(11) as you may see in Equation 11 of my latest paper.
The math seems to be an unwanted necessity, and mathematical constructs such as the 7-sphere may or may not represent anything real. But I keep looking for that mathematical structure that might be able to house all of these ideas and symmetries. Simultaneously, I think it is appropriate to understand the phenomenology that might tag along with that math.
In the case of Joy Christian's 7-spheres, 3-spheres and 1-spheres (the 0-sphere is kind of weird and I won't discuss it - I think it is simply the set of all points), these are seemingly STABLE geometrical forms (they are parallelizable and thus stable against cyclonic perturbations such as are implied by the Hairy Ball theorem) that also correspond directly with relevant Lie Algebras: E8, F4, and G2, respectively; AND correspond directly with hypercomplex algebras: the octonion, the quaternion, and complex numbers, respectively.
The largest exceptional algebra is E8. The largest Normed Divisor Algebra is the octonion. These structures - the 7-sphere, the E8 Gosset lattice, and the octonion - ALL deserve attention.
The 7-sphere has 7 perpendicular spatial components on its hypersurface, but it occupies 8 dimensions. Similarly, the 3-sphere has 3 perpendicular spatial components on its hypersurface, but it occupies 4 dimensions. In both cases, a dimension is being 'overlooked'. This extra dimension is the scalar component of the respective octonion and quaternion, and corresponds directly to 'ict' in the quaternion Minkowski metric of Relativity.
As far as I'm concerned, you may build whatever model that you think is reasonable and necessary, but you should follow through and develop all of that model's implications.
I'm sorry to hear about your concert plans...
Dear John,
I used to teach Physics and Astronomy. I am sure you are aware of the Doppler effect for sound. If a siren is approaching, its pitch sound higher. If a siren is receding, its pitch sounds lower.
We can also measure the distance to the nearest stars with parallax. The idea is that the Earth moves from one side of our Sun to the other (a difference of 2 AU) over the course of a half year. The nearest stars will seemingly change their position with respect to the more distant stars (that represent a 'fixed' background) by small angular shifts. These angles (usually seconds of degrees) are then converted into distances using simple trigonometry. This method of determining stellar distances led to the definition of a 'parsec'. We can consider this our 'standard' for stellar distance measurement - analogous to power being rated in 'horse power', or luminosity being rated in 'candle power'.
Spectral analysis led to other breakthoughs in determining stellar distances. First, by studying those nearby stars, we determined that blue stars are brighter than yellow are brighter than red, and that the color of a star determines its luminosity. Now we can use the inverse-square law to determine distance to a star based on the brightness that we measure on Earth vs. the brightness that we expect from its color.
Second, Edwin Hubble used shifts in spectral lines to determine the red or blue shift of stars based on the Relativistic Doppler effect (that is obtained via Relativistic theory) to determine whether those stars were moving away or towards us (just like the siren example above). When he graphed his data, he discovered that more distant stars also seemed to be receding faster as a linear dependance - Hubble's Law.
For nearby to intermediate stars, we have at least a couple of different ways to measure stellar distance. As long as we have an experimental double-check, I think it is OK to take this data as being 'true'.
For more distant stars and galaxies, we really only have Hubble's Law. Weird stuff happens for distant galaxies. This is where we get results that imply 'Dark Energy'. Either Dark Energy does rule our Universe, or a simple linear form for Hubble's Law breaks down, or (as I proposed in my book) the coupling constants for gravity and electromagnetism varied in the early Universe.
Paul and John - I have to get to work on my 'honey-do' list. Can we reel this discussion back closer to Joy's ideas?
Have Fun!
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Steve Dufourny replied on Nov. 19, 2011 @ 23:31 GMT
Hi,
The center of our Universe can be considered like correlated with the hypothetical BB. Like I explained before, we can imagine a main central sphere possessing the biggest volume. I magine at this moment an expansion due to a multiplication of the uniqueness, the serie is specific with volulmes decreasing from this center. So the expanison is spherical, so we can have indeed an expansion with accelerations and decelerations towards a maximum volume of the universal sphere. So we can correlate the density like a cause of the begining of the contraction. So this contraction begins at this maximum volume. The system is purely in 3D for all thermodynamical correlations. This expansion contraction possesses a specific oscillation, so the mass is essential. If now you inseert the number of uniqueness for the quantum spheers and for the cosmological spheres inside this universal sphere. So we have a perfect universal sphere in 3D with a specific dynamic of evolution. The rotations spinal and orbital of quantum spheres and cosmological spheres show us the road of the optimization of thus uniersal 3D sphere and its central sphere. I am very intrigued by this central sphere Ray in the quantum world and for the center of our universe. It is so intriguing this central sphere where all turns around
Central sphere...fractalization giving the uniqueness.....multiplication of this system......spherical expansion...acceleration deceleration ...maximum volume of the unievrsal sphere...thermo correaltions(mass, density, critic point,volumes, pression...)so the contraction or the equilibrium can appear at this maximum. We can have a contraction towards the perfect balance between cosmological spheres after this maximum. This central sphere is important like the topology , so we must know where we are at this moment? and how we turn around the central sphere.
Steve
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Ray Munroe replied on Nov. 20, 2011 @ 00:39 GMT
Dear John and Steve,
I thought that Relativity makes it impossible to define a special frame of reference, and thus we cannot specify the 'center' of the Universe. Furthermore, reconstructing our (2+1)-D data for galactic locations probably would not be very accurate, and wouldn't include the sizable effects of 'Dark Energy'.
Have Fun!
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John Merryman replied on Nov. 20, 2011 @ 01:55 GMT
Ray!
That's why they had to come up with the idea that space is something that expands!!!
Originally this wasn't taken into consideration, because space was just being treated as a measurement, so if everything was flying away from each other, then the measurement and thus space was expanding. But since the redshift was proportional to distance and there was no lateral motion, it did appear that we were at the center of this bubble.
Can you explain why the speed of light is stable, when space is supposed to be expanding?????
If someone could explain some of this in halfway coherent terms and not just "you don't understand the math," maybe I could accept there is some sense in there and it just isn't another episode of mass delusion. I'm sure that a thousand years ago, very learned scholars were convinced of giant cosmic gear wheels, just as today, they are convinced of block time, inflation and dark energy.
Maybe the math adds up, but it added up for epicycles too. It's the physics that seems like junk out.
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Ray Munroe replied on Nov. 20, 2011 @ 02:34 GMT
Dear John,
You said "Can you explain why the speed of light is stable, when space is supposed to be expanding?????"
I agree that this is a relevant question. In my book, I discussed the possibility of Variable Coupling Theory - that coupling constants would have varied up until about 5 billion years ago, this variation would have explained 'Dark Energy', and these coupling constants finally found a 'thermal equilibrium' at their current values. Here is a free partial preview of
my book. Just click the 'preview' link under the picture of the book cover. It might take a couple of minutes to load. Particularly relevant are equation 15 and figure 2.
Perhaps the speed of light *DID* vary in the distant past, but there is no reason to think that it has recently.
Regarding lateral motion, please recall that we can only measure angular stellar changes for nearby stars - say within our galaxy, not for distant stars. Now, we might be able to measure the rotation of a distant galaxy by comparing relative shifts on opposite sides of the galaxy. This is why I call this a (2+1)-D problem. The relativistic Doppler effect allows us to measure motion towards or away from us easier than laterally.
Hubble invented Hubble's Law because it 'worked' for the set of stars that he was using. I'm not as certain that it works for galaxies that are 10 billion light years away.
I guess you don't understand the math... Just kidding!
Have Fun!
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Anonymous replied on Nov. 20, 2011 @ 02:50 GMT
Hi John ....lol because the earth rotates, hope that my past posts are still there...
Happy to see you again John, I am here again and of course for always now.
Well let's rebin since the begining. We are going to dance and rock a little.
Hi Ray, The Dark energy like I repeated several x here on Fqxi is just hypothetical, so of course the center of our universe is more rational than the dark energy. This center is an evidence, of course we have a subjective interpretation due to our limits and constraints due to our young technology.But this central 3D sphere is important, like for our quantum world and its coded uniqueness!
Second I d like to go more far with maths with you Ray here on FqxI.The geometrical algebras when they want to describe our realism, objective and deterministic, must respect several foundamentals. You like the Noether Theoren Ray ? I like it personally. I like several of your ideas with you and Joy and Tom, that said I see several irrationalities due to several errors of superimposings. So the properties loose their coherences, that's why you have bizare hidden variables.You know Ray, the universal recursivity is not a simple play, but precise calculations of ultim series.
You know if you insert my real 3D rotating spheres balls, of course the rationalities can appear. But you, tom, Joy rests with these strings. The mass must be quantized at my humble opinion ? I really don't understand why you insist with the lie algebras ? There are many kinds of algebras Ray and the beauty is when these algebras converge respecting the realism. A tachyonic boson is not possible for example. But why so, people insists in saying that the symmetry exists giving a tachyonic boson ???a boson must respect the SR!
It is an example between many examples.Let's take an other example important, the irreversibility of time, why so many people says that we can reverse this time. I see only a possibility on computing but in the reality it is an irreversible constant, so why people says that this time can be reversed ???
Ray why do you say that the LHC says that it implies the FTL...never these datas says this. Furthermore it is probably a statistical error or it is a fermion , accelerated, it is totally different than the tachyonic boson correlated with FTL. The Time I am repeating is irreversible. CPT: CP yes T no :)It is so evident.
You see ray I am speaking more quiet now lol,I just discuss quietly and surely.
Friendly , let's have fun and let's rock around physics....and our clocks, irreversible of course....:)
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John Merryman replied on Nov. 20, 2011 @ 03:55 GMT
Ray,
I will look at your book soon, but it's bedtime now and I have to go to Jersey tomorrow(daughter at a horse show..)
The lateral reference was shorthand for pointing out that we don't appear to be in a normal expansion of points, but much more of a lensing effect, such that there is a direct correlation between distance and redshift and the greater the distance, the greater the magnification of redshift. As if the effect is being compounded by more distance being covered. Originally it was simply assumed the furtherest sources were simply traveling that much faster, since they were closest in time to the singularity event and have been slowing since. In fact, the need for dark energy wasn't because the expansion is speeding up, but that it wasn't slowing fast enough, that there was some additional force maintaining the rate of expansion. It has become an increasingly complex theoretical contraption to explain what lensing would explain very simply.
Maybe lightspeed was different at other times, but that doesn't address the problem. The idea that the universe is expanding is based on observed redshift. The assumption is that this is due to a doppler effect, but the doppler effect only works with changes of distance in stable space. When the train is moving away, it isn't stretching the tracks, or the space, but is simply putting what was in front of it, behind it. What was a mile away, is now two miles away. That doesn't stretch the units of measurement, only adds units of measurement. If we are going to argue that space is expanding, then the units of measurement should expand as well. We would stretch that ruler, so the foot is longer, if that makes any sense. If we simply have two feet, instead of a longer foot, it's back to square one and there is no way to explain why we would appear to be at the center of the universe, other than we really are at the center of the universe, or it's all a lensing effect. The. math. does. not. add. up.
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John Merryman replied on Nov. 20, 2011 @ 03:58 GMT
Paul Reed replied on Nov. 20, 2011 @ 08:54 GMT
Ray
Your post 19/11 16.01
This post addresses para 2. A post addressing para 1 has been posted as a new thread at the end of this Topic.
For physics there are three seperate existent continua, with their own time-lines, to consider. Confusing these leads to the muddling of future, present, past, or timing. There is 1) actuality, 2) representation of that, 3) receipt of latter by observer(s).
So timing can either be effected a) within the time-line of any of these, or b) across them.
For example. A sequence comprises 10 existent states.
When in a) the existence of each state is timed. So state 1 at zero, state 2 at 3n (n being time units), 3 at 5n, 4 at 10n, etc, etc. (The frequency of change from one existent state to the next could be any permutation).
When in b) at a point in time, in (1) it could be (say) state 7 which exists at that point in time, 8-10 are still to come into being, whilst states 1-6 have been in existence (only one existent state can exist at a time). States 4-6 are still in existence as representations (2) at certain spatial positions (ie light, noise, heat, etc, representing existent states, which have now ceased to exist). Whilst in respect of (3) representations of states 1-3 have been received (eg hit eyeball, ears, etc) and ceased to exist).
For a different, say nearer, observer, then at the same point in time as chosen above, only 6 is still in existence as light/noise/etc, 1-5 having by received by that observer.
Time does not exist. It is timing, the measurement of frequencies of change in entities. Moreover, that timing must not confuse reality, and representations of that which we receive. Both are existent phenomena, and are independent of us, but they are different from one another. And we sense (see, hear, etc) the latter, not the former.
Paul
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Paul Reed replied on Nov. 20, 2011 @ 09:45 GMT
John
Your post 19/11 17.16
When it comes to expansion of the whole of reality, apart from the limitations as to what part of it we can ever perceive, if everything is expanding, then the effect is omnipresent, ie it cannot be detected from the current perspective. The only effect that can be detected is if in the past, that rate of expansion was different, which results in information reaching us from that period(s) which does not tally with what is to be expected, ie it demonstrates a difference in expansion rate from that which must be occurring at the present. Moreover, we only know of this information on the basis of what light represents to us, the actuality might be different, ie light is unable to convey it.
Paul
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Paul Reed replied on Nov. 20, 2011 @ 10:13 GMT
Ray/John
I drafted and posted those two responses (one here, the other as a new thread (My post 20/11 08.57) deliberately without reading the intervening ones, So I would just add:
1 Ray, you will get a TOE if you obey the rules of reality!!
2 Ray,I am taking all three granddaughters to the Albert Hall this afternoon, clssical music finishing with Tchaikovsky's 1812 to cannons, rifles and fireworks. Hope this is more to your approval!!
2 Doppler has been raised. Ignoring any possible dimension alteration effect (addressed in that new 20/11 08.57 post), then the effect of an apparent change in the frequency of something during a change in movement, is easily explained as an optical illusion, as follows:
Light is the information medium in an experience based on sight. As light travels, there is a delay between the existence of a state and its perception. That delay will vary as a function of the individual spaces involved (which depends on relative movement), and the speed with which the light travelled in each perceptual experience. Whilst the perceived order of sequence will never vary, assuming that light has a reasonable degree of constancy of movement (ie is not fundamentally erratic).
The perceived frequency of change of a sequence will remain the same, so long as the on-going relative spatial position remains constant amongst everything involved. Because, while the value of the delay is different depending on each individual space, it remains constant. However, when relative individual space is altering (because relative velocity is altering), then the perceived rate of change alters, because the delay is ever increasing (or decreasing) at a rate which depends on the rate at which individual spaces are altering. It is a perceptual illusion. The intrinsic frequency of change in the sequence being experienced does not alter, either in order to create this effect, or as a consequence of this effect being realised. [NB: This explanation takes no account of the possible influence of length alteration].
Paul
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Ray Munroe replied on Nov. 20, 2011 @ 15:49 GMT
Dear Friends,
Lots of comments require lots of responses. Let me briefly attack these...
Hi Steve,
You said "The Dark energy like I repeated several x here on Fqxi is just hypothetical, so of course the center of our universe is more rational than the dark energy. This center is an evidence, of course we have a subjective interpretation due to our limits and constraints due to...
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Dear Friends,
Lots of comments require lots of responses. Let me briefly attack these...
Hi Steve,
You said "The Dark energy like I repeated several x here on Fqxi is just hypothetical, so of course the center of our universe is more rational than the dark energy. This center is an evidence, of course we have a subjective interpretation due to our limits and constraints due to our young technology.But this central 3D sphere is important, like for our quantum world and its coded uniqueness!"
My Variable Coupling Theory can explain so-called 'Dark Energy'. There is no need for 'Dark Energy' - it is a misinterpretation of the data. I would agree that a center of the Universe probably did exist at the Big Bang, but I do not think that Relativity will ever allow us to identify that 'magical' reference frame.
You also said "The mass must be quantized at my humble opinion ? I really don't understand why you insist with the lie algebras ? There are many kinds of algebras Ray and the beauty is when these algebras converge respecting the realism. A tachyonic boson is not possible for example. But why so, people insists in saying that the symmetry exists giving a tachyonic boson ???a boson must respect the SR!"
I agree that the mass must be quantized. That is exactly what I did in Table 2 of my latest paper when I defined Gravi-Weak.
As Joy has repeatedly pointed out, the 7-sphere, 3-sphere, 1-sphere and 0-sphere are special geometrical representations because they are parallelizable, and thus stable against cyclonic perturbations (for example, if the Earth's surface was a 3-sphere rather than a 2-sphere, we would not have Hurricanes). Close-packing of the hyperspheres leads to the 8-D Gosset lattice and E8, the 4-D 24-cell lattice and F4, the 2-D hexagonal graphene lattice and G2, and the set of all points, respectively. When we also consider the relationship of these geometrical representations with octonions, quaternions, complex, and real numbers, we have an appreciation for the power of these mathematical tools. Close-packing of your 3-balls leads to the Face-Centered-Cubic lattice and the SO(8) Lie Algebra, and may be related to 3-vector algebra but isn't a complete quaternion.
Tachyons have imaginary mass. I see no restriction why a boson or a fermion cannot be a tachyon. The superluminal particle that I have used to explain the OPERA results is a 'scalar lepton'. I know that sounds like an oxy-moron, but I explained this oddball particle state in my paper.
You said "Ray why do you say that the LHC says that it implies the FTL...never these datas says this. Furthermore it is probably a statistical error or it is a fermion , accelerated, it is totally different than the tachyonic boson correlated with FTL"
The OPERA collaboration between LHC and the Gran Sasso laboratory apparently measured FTL neutrinos. My paper explains how this could happen with a quaternion-like generalized PMNS matrix mixing eigenstates between 3 flavors of neutrinos and a scalar lepton. I am hoping these results are not an error - OPERA has already released a paper saying that they double-checked themselves and continue to stand behind their results.
I have heard others talk about 'accelerated fermions'. Neutrinos are 'sterile' to color and electromagnetic charges, and are very lightweight. Are you saying that the Earth's weak gravitational pull could accelerate very lightweight neutrinos beyond c? First of all, SR prevents this, and secondly it doesn't sound very likely. Left-handed neutrinos participate in the Weak force (right-handed do not), and bremsstrahlung of left-handed neutrinos into electron-positron pairs would DEcelerate any left-handed neutrinos.
You said "The Time I am repeating is irreversible. CPT: CP yes T no :)It is so evident."
I agree! My latest TOE model contains the complex representations needed for CP violation. Joy's model represents reversible time, and thus excludes entropy and CP violation. But when comparing the 'here and now' his model might be sufficient (but I'm not defending his model).
Dear John,
You said "Originally it was simply assumed the furtherest sources were simply traveling that much faster, since they were closest in time to the singularity event and have been slowing since."
I don't agree with the use of the word 'assumed' here. Edwin Hubble graphed stellar distances (obtained by stellar color and the inverse square law) with redshift (obtained from spectral lines - a different concept from overall color) and got a cluster of data that fell near a straight line that we now call 'Hubble's Law'. The data - at least for stars of intermediate diatances - reinforces the 'assumption' to the point that it is now called a 'Law'.
You said "In fact, the need for dark energy wasn't because the expansion is speeding up, but that it wasn't slowing fast enough, that there was some additional force maintaining the rate of expansion"
Your statement is consistent with the current epoch, but some weird stuff happened 5-10 billion years ago. Go study the data.
You said "The idea that the universe is expanding is based on observed redshift. The assumption is that this is due to a doppler effect, but the doppler effect only works with changes of distance in stable space"
That is why we call it the Relativistic Doppler effect, and not just the Doppler effect. If we treat EM radiation as wavefronts, then we get a 'bunching' and 'spreading' of wavefronts for those stars moving towards vs. away from us. Light travels at c, so we must use SR to make relativistic corrections to the distance between wavefronts based on the realtive velocities of the source and the observer.
Dear Paul,
As I said earlier, I am one of those people who has always considered time to be the fourth dimension. If the quaternion 3-sphere is a reasonable model of reality, then this might imply that time exists as the 4th dimension only momentarily, and is thus quite different from the spatial dimensions that we accept as 'real'.
Have fun with your granddaughters. I'm 53 and have a 12-year-old daughter. I got started late enough in life that I wonder if I will ever get to see or know grandkids, but I'm not rushing that now - middle school is tough enough.
I used to listen to a lot of 'crazzy' music - punk, alternative,... Years later, I taught at a Baptist-sponsored University, and I would 'freak out' my students by talking about my grad school days when I slam-danced at the punk rock mosh pits. I grew up to be apparently 'normal', so they did not expect that of me.
I gotta get back to the 'honey-do' list.
Have Fun!
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Steve Dufourny replied on Nov. 20, 2011 @ 16:44 GMT
Hi Ray,
1 the fractal Ray is a decreasing of volumes from the main central sphere, so the FCC, foundamentals for the uniqueness is specific. So the lattices disappear in the maximum contact!
2 the mass is quantized with the proprotions of rotating spheres or balls if you prefer, but there also the fractal is a decreasing of volumes and an increasing in number. We begin from 1 towards x, finite groups.
3 Your model seems interesting
4 The neutrinos are fermions, so it is possible that we can accelerate them, but is is just a hypothesis. For the tachyonic bosons, it is not possible, because the bosons must respect c and the SR. We have , so , 2 solution or 3 even, 1 it is an error, 2 it is an accelerated fermion,3 it is a false publicity from the LHC to have funds.
5 you see why the model of joy is false , just due to this reversible time, furthermore the entropy is not respected. It is just a false subjective model for the computing. The realism is more than this. Your model is more rational, with some errors, but it is relevant. CP yes T no....
6 This central universal sphere is fascinating. This most important volume is fascinating.
7 revolution spherization :)
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Ray Munroe replied on Nov. 20, 2011 @ 17:28 GMT
Hi Steve,
You mentioned fractals, and I agree that fractals and scales are probably important. My last FQXi paper (reprinted in Prespacetime Journal 2 (6) with original references rather than 'popular' Wikipedia references) addressed this idea.
Fred Dither recently asked if I had considered the Apollonion Gasket - since it is a geometrical interface between the G2 hexagonal graphene lattice (that I used for dimensions 9 and 10) and fractals. You and I had similar discussions a couple of years ago.
You might want to look up Howard Georgi's 'unparticles'. The 'unparticle' is assumed to be massless, and thus scale-invariant. People have also studied neutrinos with regard to this symmetry because neutrinos are 'nearly massless' (at least relative to other mass scales).
I also think that some Ising model ideas (Zamolodchikov and Coldea et al.) may lead to scale invariance, and may provide a natural imaginary mass (just rotate Zamolodchikov's solutions through an angle of 72 degrees, and you change a ratio of 1.618 into -0.618 with a negative mass-squared).
Jason Wolfe is trying to use properties of scales to explain OPERA's 'superluminal' neutrinos, but scales might argue for a speed limit of, say, 100 c - not 1.000025 c. This is a more subtle effect, IMHO.
In the last two sections of our latest paper, Jonathan and I explained that hypervolume is maximized for the 5-ball, and hypersuface area is maximized for the 6-sphere, and gave thermodynamic reasons why the 7-sphere should be unstable. Because the 5-ball hass maximal unit volume, it implies that an 8-ball would have 5 spacious dimensions, and 3 compact dimensions. The evolution of these spaces may separate so much that they effectively become two different scales: a VERY spacious one, and a VERY compact one.
Have Fun!
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Joy Christian replied on Nov. 20, 2011 @ 18:16 GMT
Hi Ray,
Let me get back to apples and oranges. Both are fruits and both are round, but they are not the same fruits, and they are in fact not all that round. And therein lies the beef (i.e., non-associatively, closedness under multiplication, manifestation of torsion, etc., etc. versus thermodynamic instability, entropy, enthalpy, etc., etc.).
Let me elaborate:
You...
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Hi Ray,
Let me get back to apples and oranges. Both are fruits and both are round, but they are not the same fruits, and they are in fact not all that round. And therein lies the beef (i.e., non-associatively, closedness under multiplication, manifestation of torsion, etc., etc. versus thermodynamic instability, entropy, enthalpy, etc., etc.).
Let me elaborate:
You wrote:
"The 7-sphere has 7 perpendicular spatial components on its hypersurface, but it occupies 8 dimensions. Similarly, the 3-sphere has 3 perpendicular spatial components on its hypersurface, but it occupies 4 dimensions. In both cases, a dimension is being overlooked. This extra dimension is the scalar component of the respective octonion and quaternion, and corresponds directly to ict in the quaternion Minkowski metric of Relativity."
And you also wrote:
"In relativity, time has that imaginary phase relative to space that would make it 'perpendicular' - at least in the Argand plane. I think you can justify equal radii by saying that local measurements are made at simultaneous times."
I agree with the last sentence. However, as I mentioned before, for me what is important is to compare "one here and now" with "another here and the same now." In the language of relativity this amounts to comparing local events occurring on a spacelike hypersurface, which, I take to be a parallelized 7-sphere. Not just the non-scalar components of a 7-sphere, but the whole of 7-sphere. Of this 7-sphere what we actually "see" in our laboratories are of course events occurring within the same old three-dimensional Euclidean space. So there is no contradiction here with what we actually see in our laboratories and how I model the physical reality. This is shown explicitly in the examples of quantum correlations discussed in my papers.
Furthermore, it is vital to recognize that I take the whole of 7-sphere (or the whole of 3-sphere) and not just its non-scalar components as my hypersurface, because the crucial property of closedness under multiplication holds ONLY for the whole of 7-sphere (or the whole of 3-sphere) and not for any of its sections. If you separate out its scalar part as time, then the closedness under multiplication cannot be maintained for "here and now", and then Bell's locality condition is violated. In other words, we are then back to the magic of non-locality. So identifying the scalar component with time is simply not a viable option for me.
You also wrote:
"As Joy has repeatedly pointed out, the 7-sphere, 3-sphere, 1-sphere and 0-sphere are special geometrical representations because they are parallelizable, and thus stable against cyclonic perturbations (for example, if the Earth's surface was a 3-sphere rather than a 2-sphere, we would not have Hurricanes)."
I really like the hurricane analogy here. What a pity that we do not live on the surface of a 4-ball.
This brings me to the analysis of stability in your paper. What I find problematic is that you speak of volumes etc. of various spheres without mentioning the crucial difference in volumes of some of the spheres compared to those of their parallelized cousins. Specifically, it seems to me that you are thinking of all of the spheres as round spheres. But the parallelized spheres are anything but round in general. Their Riemann curvature tensors vanish identically, and as a result their torsions cannot be vanishing in general. This makes them geometrically very different from the non-parallelizable spheres. For example, the torsion of the 7-sphere is a variable function of its points. But I see no mention of this crucial difference in your analysis. How can you be sure that the volume of a round 7-sphere is the same as that of its parallelized cousin? After all, you do seem to have octonionic 7-sphere in mind. But octonionic 7-sphere is anything but round. How can you then compare it with a 5-sphere or 6-sphere, both of which are necessarily round?
Any thoughts?
Joy
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Ray Munroe replied on Nov. 20, 2011 @ 19:36 GMT
Hi Joy,
I think that my usage of the words spheres and balls is fully consistent with the definitions given on MathWorld. Wolfram is a math-physics genius. I don't think he would allow such an oversight on his website. Perhaps you are now talking about vector bundles? In general, I would expect a perfect hypersphere to be more stable than a deformed hypersphere, and vector bundles might represent the beginning of an instability, but I'm sure that there must be lots of computer simulations of deformed 2-spheres for hurricanes, golf balls and such.
We can treat
x^2 + y^2 + z^2 - (ct)^2 = 0 as the equation for a quaternion 3-sphere of radius 'ct', where the space-like dimensions, (x,y,z) are the quaternion vector, and the time-like dimension, 'ct' is the quaternion scalar.
Why isn't this a perfect sphere? What are we doing differently?
Have Fun!
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Joy Christian replied on Nov. 20, 2011 @ 20:08 GMT
Hi Ray,
x^2 + y^2 + z^2 - (ct)^2 = 0, with (x,y,z) as a quaternionic vector, is not a perfect (or round) sphe