Essay Abstract
This short letter claims that the whole of physics comprises the predication of trivial exercises. The premise is metasymmetry, a self-consistent and unassuming notion which yields only trivial zero-sum statements. Therefore a theory of everything (TOE) also defines a theory of nothing (TON).
Author Bio
Ryan Westafer is.
You say, "must see processes cascade as series of opposites (or duals)" Create a multidimensional opposites space. Choose a variable, normalize it on a scale of 1 through zero to -1 inclusive. Love thy neighbor, kill thy neighbor. Each normalized line is assigned its own dimension and is appended orthogonal to all prior lines. The zero centers of all lines coincide as a common origin. N variables then create a filled N-dimensional unit hypersphere, a closed N-hyperball, with each line being one of its diameters. A hypercube with edge length 2 and volume 2^N circumscribes about any unit N-hypersphere. The ratio of the N-hyperball's volume to its circumscribed hypercube monotonically decreases as the dimension N, the number of independent variables, increases. Before you accumulate a useful number of opposites your overall collection implodes.
Failure is not a bad thing. Failure tells you to do something else while you can still crawl out of the hole.
Uncle Al,
I'm familiar with the limiting result for the N-ball, but I'm not sure what you're implying. I wouldn't think of an asymptotic approach to zero as implosion. Can you clarify your reasoning and its relation to the quoted statement about causal cascades?
26 parameters jury-rig the Standard Model, http://math.ucr.edu/home/baez/constants.html
"Processes cascade as series of opposites" obtains a 26-ball volume of considered combinations versus a circumscribed 26-cube space, (V_n) = (C_n)R^n/2^n, (C_n) = [(pi)^(n/2)]/[(n/2)!] (for n= even); [(pi)^13]/[(13)!], (V_26) =4.663x10^(-4) with R = 1. [4.663x10^(-4)]/2^26 = 6.95x10^(-12). Sampling seven trillionths of a total space as self-imposed limit could miss the answer.
No theory with c=c, G=G, h=0 has testable predictions. Compare Euclid's triangles to any triangle on a two-sphere (great circle geodesics as sides). Defective founding postulate! Physics demands parity symmetry: the universe and its mirror image are identical; then it waffles. Noether's theorems exclude parity. Quantum field theories with hermitian hamiltonians are invariant under the Poincaré group containing spatial reflections. Parity is a spatial reflection but parity is not a QFT symmetry. Covariance with respect to reflection in space and time is not required by the Poincaré group of Special Relativity or the Einstein group of General Relativity.
Vacuum isotropy has only been tested with massless photons. Nobody knows if the vacuum is isotropic to opposite parity atomic mass distributions. If not, the whole of physics is reduced to a (very good ) heuristic. Religion need only inculcate its defective methods. Somebody should look (my essay, fourth from the bottom), testing a loudly defective founding postulate.
Ryan
I know you are right because you know you are wrong.
PS Take no notice of Uncle Al whenever he uses numbers; he is only a chemist. Ask him what happens to the volume of a cube as a proportion of the circumscribing sphere ? Don't do it publicly. He is the last person we would want to upset, in case he gets angry with us.
Dear Ryan,
I think your premise does not hold. The universe cannot be based on symmetry, otherwise physical manifestations would not exist. Also it cannot sum to zero, it can only sum to an infinite number times unity if you know what I mean.
There is another way to describe the universe assuming is consists of smaller elements (quoted from KVK Nehru):
In a closed group of operators, like [1 i j k], the result of the combination of any number of the basal elements is also a member of the same group. The result of any such combination can be known only if all the possible binary combinations of the elements are first defined in terms of the basal elements i, j and k themselves (besides, of course, the identity operator, 1). Let there be n basal elements (excluding the unit operator 1) in a group. Then the number of unique binary combinations of these elements, in which no element occurs twice, is n(n-1)/2. We can readily see that a group becomes self-sufficient (finite) only if the number of binary combinations of the basal elements is equal to the number of those basal elements themselves, that is
n(n-1)/2 = n.
The only definite solution for n is 3. (Zero and infinity are other solutions.) Therefore if we regard space (&time) as a group of orthogonal rotations, its dimensionality has to be three in order to make it self-sufficient dimensionally. Otherwise the number of dimensions either has to shrink to zero, or proliferate to infinity.
Good luck with the contest!
Steven Oostdijk
