I should add this;

When I wrote about the Octonions with Ray Munroe, I soundly rejected the Sedenions as being a curiosity mainly of interest to number theorists. But it appears I may have been a bit hasty, as most folks are with the Octonions - feeling they are more bother than they are worth. Of course; you can make Cantorian telescoping kites, but unless you are trying to navigate through hyperspace there is not much use for such a structure (tongue in cheek).

I note that hypervolume is maximal for S4 - so if it is the macroscopic basespace (the hidden space), it is potentially quite macro indeed. It seemed a step too far for me too, Michael, adding extra spaces and jumping to S15 - but now not so far fetched (after Joy's clever elaboration). Perhaps the stone at first rejected will become the key stone.

Regards,

Jonathan

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  • Post #423

Tom,

Me again.

" physically, there is no measure zero, no absolute nonlocal origin where motion ceases."

I still don't see how to explain centrifugal force otherwise. If something is spinning in a complete void, does it mean it cannot be spinning if there is no outside reference, therefore no centifugal force is being exerted, yet if one pinpoint of light were to appear and quantify this spin, then would the centrifugal effect suddenly come into play? It seems to me centrifugal force is due to spin relative to inertia. What is inertia, other than the spatial measure zero?

"The void is a singularity."

Not only is a singularity not zero, being one/single, but it is dynamic. Zero, being nothing, not only can't be something, it can't be dynamic, since it doesn't exist. This seems a bit like the ancient Romans not having a number zero, because the idea of a term to signify nothing didn't make sense to them, yet the Arabs found it very useful. Not to restart our most recent conversation about existence vs. non-existence, but as I made the point then, me getting a cup of tea doesn't physically exist, yet the fact it did exist recently is crucial to the existence of the cup sitting on my desk. I know physics is about what is, yet what is not is also important, but overlooked.

Hi Michael, Fred, and Jonathan,

Thank you for all your positive comments. This is of course just a start. The pot seems to hold water. Let us see whether it does hold water. At my end, there is nothing much for me to do as far as my framework for QT is concerned. In S15 I have S1 x S7 as a base space of the bundle, and that is sufficient for all my calculations to go through. The real work is for Michael to do. He has to check whether everything hangs together from the perspective of GR and Standard Model.

Fred, thanks for your email yesterday. It probably played some kind of subconscious role in my "breakthrough."

Below I am again attaching the paper on S15 I had attached in the previous long thread. It was just a passing thought for me at the time, but now S15 makes much more sense. In fact now I think Michael's starting point, namely S10 = S3 x S7, is totally ad hoc from the point of view of division algebras. S15, on the other hand, is the key fundamental space behind the algebra of octonions (cf. the first two pages of the attached paper).

I also watched Niles Johnson's video lecture again before posting the above comments (cf. what he says around 17:20 onwards). Watch it again if you can, just for fun.

Best,

JoyAttachment #1: 1_1248.pdf

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  • Post #425

Thanks for the acknowledgement Joy,

The way I see it is that at the most fundamental level Nature doesn't give a rat's ass about our mathematical rules that we have formulated to try to understand Nature. Take the void with the only property that it has is that it is a stage. Put a massless point entity in it. What are the mathematical properties of such a configuration? There are none that we can surmise easily. Perhaps the entity will fly off at infinite speed. Or perhaps it will just sit there. But we don't even know what that means (nor the infinite speed one) since there is nothing to relate it to. Nor can we have any concept of what dimension means. Now, put a whole bunch of identical massless point entities in the void with the proposition that they somehow interact with each other. What happens? We notice that some of our mathematical rules do describe the behavior of what is created by the interactions.

The point here being is that Nature starts with the least amount of mathematical rules and then the rules of the normed division algebras become emergent for reasons that Joy and others have been saying for a proper description of physical behavior as we know it right now. What I have proposed above seems very simplistic but we would have to give the point entity some kind of property to produce hbar. I just don't know what that could be yet.

Best,

Fred

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  • Post #426

Fred,

How about tension? If you have a dichotomy, say between equilibrium(the state of a massless point ) and infinity, the logical relationship is tension, which is potential energy and potential precedes actual...

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  • Post #427

Rather than tension between a point and its opposite, it is between the point/equilibrium and field/infinity.

Hi Joy, Jonathan, Fred and all

I certainly wouldn't call my S1*S10 -> S1*S3*S7 ad hoc. It is uniquely the simplest scheme - as in what Occam would have chosen - that realises the (S0,S1,S3,S7) condition - the closed spaces in R,C,H,O - in an obviously physically causal way - as in Einstein's basis for choice. It comes from the observation - because I was looking after having just produced a proof that QT couldn't be fundamental - that a map from S7 (O) to S3 (H) has the character of the Higgs vacuum and breaks the equivalence of the 7 dimensions of S7 (O) to S3(H)*S3(H)*S1(C). It is then a homotopy group condition that if the spheres of this symmetry breaking that ends with S1 had been unified in a closed simply-connected space - e.g. a sphere SN - then chiral fermionic topological monopoles would be produced with the eigenvalues of the Standard Model particle table. Unifying S3 and S7 in S10 is the simplest option - a minimal unification of physics (MinUP) - where in GR a closed universe is necessarily cyclical in time, i.e. S1*S10. On the other hand, in a geometric or topological scheme S15 is the natural upper limit - a maximal unification of physics (MaxUP).

For S10, inserting a hole into a sphere gives a generic "torus", which for N>2 has a chrial twist giving it the right character for the Higgs vacuum. This gives us our first condition to test against S15 as the physical twist of the S3*S7 Higgs vacuum can vaguely be thought of as a half twist, whereas a fibre-bundle has a full twist. My S7 corresponds to the S7 fibre of S15 which has the full twist of a fibre-bundle with respect to the S8 base pace, but this isn't directly what matters. Joy then has the S8 splitting into S1 and S7, where the S3 fibre of this S7 is my S3 of physical space. If the split S8 -> S1*S7 has Z2 options, then the Higgs vacuum map S7 to S3 could be of the correct form, i.e. not the fibre-bundle twist. It all depends upon the character of the split S8->S1*S7, which is essentially required to be the spacetime split (of spacetime algebra) in disguise.

It should be noted that the spacetime split is easily disguised in H and O by switching from norm to square, as in both cases the real component squares positively whereas the remaining 3 or 7-vector is pure imaginary and squares negatively. Rick makes this shift in the D-Alembertian on page 7 of his essay, where after having made this change you technically no longer have a normed division algebra. For my S1*S3*S7 universe, I have to have the same change from norm to square (the spacetime split) on both H and O at the same time, i.e. the real parts of H and O coincide so that (1+3)+(1+7) is reduced to the required 1+3+7. The S8 split to S1*S7 would have to be of the same character, but where the starting space is S8, not just O.

Further progress on either route (S1*S10 or S15) seems to require answering the somewhat non-trivial question: just what the hell is time?

Best,

Michael

Hi Michael,

A quick thought on S8 splitting into S1 and S7. Such a splitting was of course my thinking in terms of the non-relativistic GHZ model discussed in my book (e.g., in Chapter 6). In the light of your comments above it seems more appropriate to keep S8 intact and think of it in terms of Lorentz or relativistic invariance. So, presumably, a relativistic GHZ-type state would not require me to split S8 into S1 and S7 while modelling the state within my framework. Geometrically this would then fit in more naturally into the fibration

S7 ---> S15 ---> S8.

Best,

Joy

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  • Post #430

Michael,

Have you considered that while we perceive the effect of time as past to future sequence, the underlaying dynamic is the changing configuration of what is, that turns future into past. To wit, that the earth doesn't travel the fourth dimension from yesterday to tomorrow, but that tomorrow becomes yesterday because the earth rotates. This makes time a quite logical and basic effect of action, similar to temperature. What it does to theory and the perceptions of reality on which theory is based, is a whole other matter. Time is not a real vector, because duration doesn't transcend the present, but is the state of the present between the occurrence of events. Information is not only transitory, but the destruction of information is also information. "Can't have your cake and eat it too." Particles cannot be isolated from their actions, because there is no such thing as a dimensionless point in time, without freezing the action creating it. Which would equate to a temperature of absolute zero.

Of course it solves the issue of multiworlds, as potential collapses into actual, rather then projecting from determined past into potential future, it is the actual, physical occurrence of events which determines the fate of the cat.

We induce principles from the occurrence of events, future becoming past, then use them to deduce what will occur, projecting past onto future.

Hi Joy,

I don't see how S8 can be interpreted in a relativistic way, as the crux of Relativity is the metric signature for the time dimension being of the opposite sign to the spatial dimensions, and any extra dimensions, which in S8 it isn't. I can't see how to interpret S8 either, as although it is 8D within the space - O? - as a sphere it is embedded in a 9D space -??. It would seem that to get relativistic physics here, you start with the normed division algebras and then have to switch from a proper norm to a square, which splits off the real parts of H and O from the imaginary parts - the spacetime split, where space here is in the most generic (non-time) sense. For my 1+3+7 scenario, this splitting off of the real parts from H and O can be assumed from the outset - which is as acceptable as starting with metric signature (-,+,...) in GR. However, the S15 scenario starts with an equivalence between all the dimensions and that makes such an assumption rather harder to make without explicitly supplying some sort of convincing justification.

Best,

Michael

John,

Consider it, yes, found a way to formulate it in a meaningful way, no. The difficulty with trying to formulate such a view is that it tends to end up being tautological. Reasoning about causation similarly tends to tautology as if there wasn't any causation you wouldn't be in a position to reason about it. That's not to say that it is necessarily impossible to base a physical theory on a well-formulated tautology, but few people tend to be happy with that - perhaps that's the issue.

The multiworlds idea appears to be a failed attempt to understand quantum theory due to the false assumption that quantum theory is fundamental, so I wouldn't bother with it all.

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  • Post #433

Hi John,

" 'physically, there is no measure zero, no absolute nonlocal origin where motion ceases.'"

I still don't see how to explain centrifugal force otherwise."

Easy. Centrifugal action is a fictitious force, not a true physically real force.

"If something is spinning in a complete void, does it mean it cannot be spinning if there is no outside reference, therefore no centifugal force is being exerted, yet if one pinpoint of light were to appear and quantify this spin, then would the centrifugal effect suddenly come into play?"

It is impossible that something is spinning in a complete void. Spinning relative to what? A void that contains a pinpoint of light -- for whatever you mean by that -- is not a void. A quantum of light is massless, so no force is involved in what you describe.

"It seems to me centrifugal force is due to spin relative to inertia. What is inertia, other than the spatial measure zero?"

We don't know what inertia is. It has nothing to do with centrifugal force, however -- the motion of points from the center of a centrifugally rotating object is rectilinear, i.e., uniform.

"'The void is a singularity.'"

Not only is a singularity not zero, being one/single, but it is dynamic."

If it is, you can describe the sound of one hand clapping. Can you?

. . .

"I know physics is about what is, yet what is not is also important, but overlooked."

What is not may be important to someone, but it isn't physics.

Tom

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  • Post #434

Hey Michael,

"The multiworlds idea appears to be a failed attempt to understand quantum theory due to the false assumption that quantum theory is fundamental, so I wouldn't bother with it all."

Multiworlds is, OTOH, a successful attempt to explain apparent collapse of the wavefunction when no such collapse is observed in the absence of boundary conditions. So I think it's a good way of saying that quantum theory fails to be fundamental.

Tom

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  • Post #435

Michael,

That is very much a problem, as formulation is a sequential operation, ie, based on the past to future effect as are other forms of cause and effect logic and narrative. The issue though, is not so much what levels of complexity are emergent from these thought processes, but what is physically foundational to them.

To me it would be a bit like the church arguing that it is immaterial whether or not the earth is the center of the universe, because it is our point of reference to the universe.

Michael,

In that case a fibration worth thinking about is this one:

S4 ---> S15 ---> S11,

with S11 locally giving S1 x S10 ---> S1 x S3 x your S7,

where "hidden" S4 and non-hidden S3 may be uncompactified to give my S7.

Joy

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  • Post #438

Joy,

I have never seen a simpler nor more mathematically intuitive way to describe the topological character of your framework than your phrase, "a 4 sphere's worth of 3 spheres." It unites all the elements in a -- pun intended -- compact way. You've used the phrase for a long time, and I struggle to understand why what seems beautifully complete to me has not gotten wider recognition.

Tom

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  • Post #439

Michael,

You did ask what time is and I offered an explanation which puts it in a category similar to temperature. Yes, it does cause other conceptual problems, but while they may be very inconvenient, that doesn't refute the point.

We still see the sun moving across the sky from east to west and while the idea created serious issues for the established views of the time, that didn't disprove the observation that it 'sactually the earth rotating west to east.

    Thanks, Tom. But I cannot take credit for the phrase. You have to be as smart and as English-speaking as Sir Roger Penrose to come up with such a compact phrase. I learned it from him.

    Joy

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    • Post #441

    Gravity is the fundamental requirement of physics, physical experience, life, vision, being, experience, and thought/physical description. In the absence of gravity, we are literally out of touch with reality.