The Perfect First Question. by T H Ray

Hi James,

You do not accept spheres and such?

My, my. What a world?

Spherically yours,

Joy

PS: Here is how a flat 3-sphere may look like from inside:

Hi Joy,

"PS: Here is how a flat 3-sphere may look like from inside: ..(then there is an image of maybe a ripe tomato)...

I am going to need Tom's help on this one! :)

Tom, Do we live inside three tomatoes or am I missing the point? :)

Thanks.

James

I am dreaming in live there ???

I have already seen a lot of things, but there frankly it is bizare.

In all the case,1 you are there to help me

2 you are there to steal me

In all the cases I come at New York.

ps the picture is false ...the universal entanglement and its rotations imply more than this picture.

Spherically yours indeed.

Tom,

Thank you for your comments. This stuff is extremely fun and interesting! But it also makes me feel so "deprived" and "underprivileged," and even "deficient" for lack of better terms. Whereas you and other are "living large," as it were, in your fancy 9-dimensional or even 11-dimensional universes, I'm stuck here in my lowly, humble, evolving 3-dimensional universe, believing that space-time is a myth perpetuated by a long-standing, faulty notion regarding the fundamental purpose and role of clocks.

These discussions often remind me of the adage that "using words to describe ideas is like using lumber to build a tree." It seems we're all just doing our best with the lumber we find available to us.

Cheers,

jcns

I was being flip, but to be serious I should have said 10 dimensional tomato, where every point is a 3-sphere.

(Yes, jcns, it's fun! Ray Munroe must be proud of us now.)

Best,

Tom

James,

I've got it now. I remember that I wanted to explain Scott Aaronson's argument in simpler and more accessible arithmetic, and then realized that the explanation grows ever more sophisticated and that I couldn't make it simpler.

So let me try again.

Remember, I claim that the answer to the first question *has* to be "yes," no matter what the question is. Here expressed in arithmetic, is why:

1 - 1/2 1/4 - 1/2 1/4 - 1/2 = 0

The important thing is that no value in the sum of these terms exceeds unity. Consistent with Scott's upper bound of probability .75 for a 2-player cooperative game, the first iteration (where the zeroth iteration is 1 - 1/2) is 1/2 1/4 = 3/4. When continued through the second and third iterations, we find 3/4 - 1/2 = 1/4 and 1/4 1/4 = 1/2. To make this easier to read:

(eqn 1) 1 - 1/2 1/4 - 1/2 1/4 - 1/2 = 0

= .5, .75, .25, .5

0 1 2 3 4 iterations

If we were to sum and average all the values of the results of these iterations -- which is what quantum mechanics does by averaging values of a run of experimental results -- we would get 1/2. This is the upper bound of a coin toss probability for sufficient length of n independent Bernoulli trials. When we revese signs for the above, we get:

(eqn 2) 1 1/2 - 1/4 1/2 - 1/4 1/2 = 2

Which is the CHSH upper bound for Bell-EPR type experiments.

What's the problem? The former case is algebraically closed; zero indicates that the computation halts. The Bell-CHSH case does not halt; it will increase monotonically to infinity. This is interpreted to mean that every experimental event not measured has a vanishing but non-zero probability of happening. The non-probabilistic result (the algebraic equation 1 summing to zero) tells us that no event is probabilistic; perfectly random tosses of a fair coin are precisely determined.

The way that quantum mechanics reconciles its probabilism (implying quantum entanglement and nonlocality), with actual physical reality, is by quantum unitarity -- the average of the set of iteration results in eqn 2 (1.5, 1.25, 1.75, 1.5) is unity, or probability 1.0 that the upper bound of any quantum pair correlation experiment obeys the upper bound of CHSH.

Now this is the simple arithmetic that Scott Aaronson, Richard Gill and many others believe without question is at the foundation of a probabilistic physical reality. Look, though, when expressed as the answers to yes-no questions (pairs of binary values):

(eqn 1) 1 - 1/2 (Yes) 1/4 (No) - 1/2 (Yes) 1/4 (No) - 1/2 (Yes) = 0

(eqn 2) 1 1/2 (No) - 1/4 (Yes) 1/2 (No) - 1/4 (Yes) 1/2 (No) = 2

If we allow the first iteration to answer "No" such that all subsequent iterative values exceed unity, we have loaded the dice in favor of an infinite dimensionless range of values that we ASSUME constitutes the sum of perfect information that we can treat by probability theory. This is reconciled to actual physical experiments (in which probability plays no actual physical role) by normalizing to quantum unitarity for any experimental result.

Joy Christian's inspired realization was that ORIENTATION of the topological initial condition determines the experimental outcome which must be ALGEBRAICALLY CLOSED as eqn 1 shows, and which thereby obviates quantum entanglement, nonlocality and probabilistic measure. This initial condition -- if one follows Joy's objective mathematical argument without imposing one's personal beliefs on it -- clearly produces E(a,b) = - a.b. Very straightforward.

I've been playing with the consequences of algebraic closure for topology, for quite a while. I decided to attach a draft of one such effort; section 4.25 relates to the present argument.

Tom

Posting the link

http://home.comcast.net/~thomasray1209/SophieGermainprimes8411.pdf

Hi again jcs,

You wrote, "Whereas you and other are 'living large,' as it were, in your fancy 9-dimensional or even 11-dimensional universes, I'm stuck here in my lowly, humble, evolving 3-dimensional universe, believing that space-time is a myth perpetuated by a long-standing, faulty notion regarding the fundamental purpose and role of clocks."

Hmmm. I suppose Minkowski space could be described, in that context, as a myth. If one were disabused of the notion, though, that clocks have some fundamental purpose and role -- then the space-time model is the only one that makes sense in a relativistic universe. This is because we only infer facts of our physical existence by making measurements -- rods for length, clocks for time -- and if these were absolute, we would live in a dualistic universe; as it is, Minkowski discovered, we can only preserve physical reality for either of these notions by a continuum of the two. The fundamental role in physics is for spacetime.

Don't fear that any of us are living apart from you in a higher dimensional universe -- after all, we communicate within the same spacetime, and that's the only way, after all, in which we even know that either of us is "real" to the other. Extra dimensions are said by most string theorists to be hiding in our common space of measurement as curled up, compactified. I much prefer the explanation that Joy has offered: extra dimensions as an artifact of topological structure, not hidden at all. Living in 8-dimension space is not different, to our measurement and perceptions, than living in 4-dimension space.

"These discussions often remind me of the adage that 'using words to describe ideas is like using lumber to build a tree.' It seems we're all just doing our best with the lumber we find available to us."

Whether we used words or not, we'd still be compelled to use some formalized language. Even if we all had little computers with broadcasting stations in our heads to communicate with one another, the language would still have to have a common structure for encoding and decoding information.

All best,

Tom

Tom,

"I much prefer the explanation that Joy has offered: extra dimensions as an artifact of topological structure, not hidden at all. Living in 8-dimension space is not different, to our measurement and perceptions, than living in 4-dimension space."

Are you equating 'not hidden at all' with 'not different, to our measurement and preceptions'?

James

No, James, I don't think that is what Tom has in mind.

If I may pre-empt Tom's reply, the issue here, technically speaking, is between the "compactified" dimensions that string (et al.) theories require to bring us back to the "regular" 3+1 spacetime, versus what I am saying---which is that these dimensions are not compactrified at all. The strong quantum correlations we observe are in fact the *evidence* of these dimensions. They are all there in their naked glory, unashamed to not have been artificially compactified. And yet our measurement schema take place in the 3+1 dimensions.

But to understand the latter one must dig deep into the technical details of my (or rather Nature's) construction, well beyond the standard EPR correlation.

Joy

Joy,

"They are all there in their naked glory, unashamed to not have been artificially compactified. And yet our measurement schema take place in the 3+1 dimensions."

Thank you. I understand this. My non-expert opinion about compactification of dimensions is another hidding place allowing the theorist to offer an answer that is a guess and proceed forward with theory. I believe that I have seen this practice occur repeatedly during the development of theoretical physics. I do not presume that you, or anyone else, agree with this.

I do presume that you are equating "They are all there..." with "...not having been aritificially compactified." If this is correct, I wonder if the word 'artificially' were removed would you support the remaining statement. Obviously my question has to do with whether you say that dimensional compactification is inherently artificial or do you allow that it could be real but just not in this case?

James

Dear Joy,

Sorry 'equating was a poor choice of word'. I meant 'the opposite of'.

James

J.C.N Smith, James,

In Roger Penrose's lecture on "Twistors and quantum non locality" also available via FQXi resources, he gives an illustrated explanation of how the quaternion structure has to be projected onto the flat space-time representation. They are different representations of the same phenomenon. One of the representations seems more intuitively correct because it matches our own experience though it is not necessarily the most helpful way to think of what is occurring.