Registered: May 2009
??? Lightbulb, lightbulb, lightbulb ... NKS & M-theorists still unreconciled
Does Wolfram’s NKS Chapter 9 hold the key to revamping M-theory for empirical prediction just as renormalization holds the key to using QED for empirical prediction?
Consider a passage from http://en.wikipedia.org/wiki/Renormalization :
Since the quantity infinity – infinity is ill-defined, in order to make this notion of canceling divergences precise, the divergences first have to be tamed mathematically using the limit, in a process known as regularization.
An essentially arbitrary modification to the loop integrands, or ''regulator'', can make them drop off faster at high energies and momenta, in such a manner that the integrals converge. A regulator has a characteristic energy scale known as the cutoff; taking this cutoff to infinity (or, equivalently, the corresponding length/time scale to zero) recovers the original integrals.
With the regulator in place, and a finite value for the cutoff, divergent terms in the integrals then turn into finite but cutoff-dependent terms. After canceling out these terms with the contributions from cutoff-dependent counterterms, the cutoff is taken to infinity and finite physical results recovered. If physics on scales we can measure is independent of what happens at the very shortest distance and time scales, then it should be possible to get cutoff-independent results for calculations.
Many different types of regulator are used in quantum field theory calculations, each with its advantages and disadvantages.
In the preceding passage, should we ask a question about physics “at the very shortest distance and time scales” and follow the M-theoretic geniuses to the Nambu quantum field theory at the Planck scale? But what about physics at the very longest distance and time scales? What do M-theorists now think about Wolfram’s cosmological principle:
THE MAXIMUM PHYSICAL WAVELENGTH IS THE PLANCK LENGTH TIMES THE FREDKIN-WOLFRAM CONSTANT?
In Einstein’s cosmological model with a nonzero cosmological constant, the universe expandes forever and keeps getting colder and colder, never quite reaching absolute zero on the Kelvin scale. First, is the cosmological constant nonzero because of alternate universes? Second, does the universe really keep getting colder and colder forever or does it hit the maximum wavelength barrier and undergo instantaneous quantum collapse?
If you have a string theory with a built-in higher limit to frequency, then you can avoid the dubious shenanigans of renormalization. But if you have a string theory with infinitely many degrees of freedom for string vibrations, then how can you choose a model among the infinite freedom explosion of models? Do you want a built-in lower limit to frequency?
DO YOU REALLY WANT A UNIVERSE REPRESENTED BY AN INFINITE OPERATOR WITH INFINITELY MANY EIGENVALUES INSTEAD OF A FINITE MATRIX WITH FINITELY MANY EIGENVALUES? Don’t you want a universe with both a minimum and a maximum in possible wavelengths? If M-theorists adopt Wolfram’s cosmological principle and EMBED A LATTICE GAUGE THEORY INTO THEIR BELOVED 11-DIMENSIONAL SUPERSYMMETRY MODEL, then what? WILL M-THEORISTS SUDDENLY FIND THAT THEY CAN MAKE MARVELLOUS EMPIRICAL PREDICTIONS THAT ARE 100% CORRECT?
If a Wolframian mobile automaton gradually builds time, space, and energy from informational substrate below the Planck scale, then can M-theorists understand the Nambu transfer machine that makes possible the model of finite, digital physical reality? Does the multiverse consist of a Wolframiam mobile automaton, or Fredkinian alternate-universe engine? Does the Fredkin-Wolfram information process for the multiverse consist of 3 main components:
(1) a Fredkin delivery machine that builds Nambu digital data for input to the Nambu transfer machine;
(2) an 11-dimensional supersymmetric model that smooths out the Nambu transfer machine and describes its structure;
(3) the process in which the Nambu transfer machine uses Nambu digital data to create the digitized physical reality found in general relativity theory and quantum field theory?
Last edited by David Brown on 04-30-2010 at 07:23 PM
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